Abstract Booklet

Editors: Thomas Dittrich and José Daniel Muñoz Universidad Nacional de Colombia XIV LAWNP Latin American Workshop on Nonlinear Phenomena Abstract Booklet

Editorship: John Naranjo • Carolina Rey Gallego Design LAWNP 2015 logo: Joachim Dittrich, Quickborn, Germany

ISBN: 978-958-58889-8-2 Made the legal deposit

All rights reversed. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording or any information storage or retrieval system, wthout prior permission in writing from the publisher. List of participants Posters 75 Contributed talks After-dinner talks Minisymposia 25 Invited talks Welcome address Contents: Urban dynamics Molecular dynamics El Niño Tropical ecosystems 113 49 53 33 42 37 27 13 5 3

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena had justobtainedherdiploma inarchitecturefromthe TechnicalUniversity ofStuttgart, herfamily onym, wasbornin1915 to a wealthy familyinHamburg,my (TD) home city. When in1939she bled overtheworkof a Venezuelanartist: Gertrud Goldschmidt,orGegobyherbriefpseud science andculturein Venezuela:for asuitablevisualmotif ourpublicity,Looking we stum- going tocelebratethisachievementwithus. ¡Bienvenido Mario,estaestucasa,estotaller! ofcomplexityscienceinVenezuelario Cosenzaasthedean and is found hiswaytoCartagena in the and Caribbean Prof. Ma- the adversities, all that despite we areveryglad Andes. Indeed, Venezuela,the entireregion,Colombia, as representing countries inthe and allneighbouring us consider should we beneficiaries, as that think We proposal. their withdraw to them forced Venezuela,in situation critical for theincreasingly it notbeen prevailed—had the end in which country,neighbouring our in of pertinentresearch tion have that theywould doubt is little there tradi- long the Given subcontinent. the of half northern the in LAWNP a have to first the being ly.in Venezuela Someyearsago,wewerestillinafriendlycompetition withourcolleagues for scientific event inthecountry.international major a realizing by supported being deserves Colombia that America facilitated our work within the country, it elsewhere inLatin also helpedconvincing colleagues spread optimismthat it will reachasuccessfulendinshorttime. This circumstance not only is stillincourse,therewide inHavana the peacedialogue growth, andwhile of sustainable Violence,ashes. substantially, ornottodrugs, reduced related to astate returned theeconomy from the 2000, thecountryroselikePhoenix Fromtheseverecrisisaround ment inColombia. of UNAMinCuernavaca,whoisaccompanyingusthisweek.¡GraciasGustavo! Prof. GustavoMartínez-Mekler directions: us in themostpromising pushing simultaneously and behind thescenes, person whoseactivitywasabsolutelydecisive,both backing us,ofteninvisibly Instead of presenting alonglistof supporters, I pars prototo, would liketo acknowledge, justone in Colombia. dynamics andcomplexsystemscommunities growth andmaturingofthenonlinear of LAWNP,the presence not enjoy did hitherto tinent which of the process recognized who and in thesubcon regions towards open series should thatthisworkshop our perception shared who spiracy ofvariousfortunatecircumstances: and numerousenthusiastsinthiscountrysincemanyyears.It came trueonlythankstothecon- in morethanonerespect:With this day, a dreamcomestruethat has beendreamtbyourselves lap ofhonourafteralong,longrace.Inourcase,hereandnow,this istrue 2015 inColombia, a Latin opening For theorganizers, WorkshopAmerican the is like Phenomena on Nonlinear Welcome to LAWNP 2015inColombia Quite unexpectedly, we weregladto encounter yet another, complementary, way to revere Weus indirect helped also in theregion that lessfortunatedevelopments cannotdenyeither and economicdevelop political from thegeneral At the sametime,wefeltasteadytailwind We are grateful for the persistent support byourcolleagues,withinLatin America andbeyond, 5 - - - - -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 6 decided to emigrate to the Americas to escape the holocaust. Venezuela was not Gertrud’s first choice, but once arrived to Caracas, she took the chance to readjust her professional orientation and became a free artist. After some experimenting with different contemporary currents, against the end of the 1960s she found her personal subject: networks, ordered ones, random ones, rendered in two dimensions as drawings and watercolours or in three dimensions, from table-top wire constructions to big sculptures made of aluminium rods for public spaces and buildings. With this work, she anticipated a development which decades later is dominating in particular the mathematics and physics of complex phenomena—at a time when Albert-László Barabási was barely born!

In this workshop, even if it was by no means intended, networks are ubiquitous, from quantum graphs through genetic networks and urban traffic through social networks on global scales. In 25 of the about 135 abstracts we received, the concept appears explicitly, in many others it is implicit. We therefore found it appropriate to choose an image of one of Gego’s “reticuláreas” as eye-catcher for poster and website, and we are glad that in this way, we can express our appre- ciation for Venezuelan culture and can contribute from the distance to keep the memory alive of a lost daughter of the city of Hamburg and a remarkable Venezuelan-German Jewish biography.

LAWNPs should end up with well-balanced accounts, financially, but also academically. From the moment on that we were invited to realize the workshop, we felt determined not to just add the (n+1)th event to the series, but to reciprocate for this privilege by contributing some novel elements to the workshop, thus leaving a specific Colombian fingerprint on it.

The benefits this event offers to the country and the region are obvious. Colombian researchers enjoy a unique opportunity to get into immediate contact with the internationally most advanced work in the field. Inversely, they can show their own achievements to the most distinguished audience. Indeed, as you will perceive in the course of this workshop, complexity science in Colombia has reached international standards with respect to methods, subjects, and presentation. At the same time—this is our personal impression—the country still has a long way to go concerning academic “soft skills”, such as an intuition and rigorous criteria for genuine quality, as opposed to mere quantity, the ability to tell short-lived fashions from lasting developments, a critical distance towards the work of others as well as one’s own, and in general the unshakable conviction that basic research is the key for progress, not only in technology. We hope that by bringing LAWNP to Colombia, we can contribute our part to this learning process, above all by providing examples of good practice in these points.

However, we think that the relevance and potential of complexity science should also become visible in a more tangible manner, by showing in specific contexts how it can help solving problems that afflict this region, a direct practical value of basic research. Looking around, we found that minisymposia, short workshops-within-the-workshop focused on a more confined subject, are the appropriate format. In addition, they introduce a structure into LAWNPs that allows high- lighting recent developments and emerging fields. Each minisymposium will be introduced and chaired by a renowned expert in the field and optionally concluded by a round-table discussion.

For the present event, we chose four areas: view of a number of about sixty indigenous idioms spoken within Colombia, many of them on the view ofanumberabout sixtyindigenousidiomsspokenwithinColombia, manyofthemonthe symposium, Complexity in linguistics—the dynamics of language learning, use, and evolution. In main workshop,ofcoursereducingscopeand durationaccordingly. this endeavour. Inanovernightemergencyaction,werescuedtheplan byreintegratingitintothe molecular dynamics.However, despiteallourefforts, wecouldnotraisesufficientfundstofinance which linksquantumand nonlinearity ina unique manner, offering ahostofapplications:complex complex quantumdynamics,wehaddecided todedicateanentiresatelliteworkshopasubject role within LAWNP. In orderto compensate for this tendency and to reservespacefor research in decreasing a played research 0” > “ħ years, recent in that regret some with observe could tems, Colleagues interestedinnonlineardynamics on microscopicscales,inparticularquantumsys- Complex classicalandquantummoleculardynamics is aparadigmoftheoreticalphysicsappliedtosocialsystems. Wolfganglike of pioneers work Weidlich development of urban physics the social the 1980s, in our control.Sincetheseminal to escape appear to theextreme,theynevertheless creations life. Human and economic roleinthesocial play anincreasingandoftendominating glomerates just as intherestofLatin to therainforest,alsoinColombia, As antipole con- America, bigurban Urban dynamics:modelling,simulation,andcontrol of megacities this country, wefind being analyzedintermsofconceptsnonlineardynamics,suchasintermittency. to invites Niño El of evolution time complex the particularities, its all By evident. are coast, Pacific climatic phenomenon.Itseffects, oftencatastrophic, onlifeandeconomy, in particularalongthe Asked about El Niño, every Colombian farmer or fisherman will tell about his experiences with this Oscillation The ElNiño/LaNiñaphenomenon:analyzing,forecasting, andconfronting theSouthern There isanintenseinterplaybetweentherainforestand namics isanindispensabletool. In order to analyze their behaviour andto strategies fordy- develop their protection,nonlinear factors. to anthropogenic owing known; atthesametime,thesetreasuresareinseriousdanger Amazon rainforest andtropicalshelfregions. the Their importancefortheclimateonglobalscalesiswell all above ecosystems, various its of biodiversity the is riches Colombia’s of One Resilience andsensitivityof terrestrial andmarinetropical ecosystems In order to save this subject, we had to sacrifice another, originally intended for the fourth mini - fourth the for another, intended sacrifice originally to had we subject, this save to order In On the opposite end on the range, as concerns human involvement, but at least as decisive for Terrestrialsubsystems. ecosystems,theatmosphere,andoceansarestronglycoupled 7

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 8 way of extinction, this is another issue of great regional relevance. We were positively surprised that despite the cancellation, we received a sufficient number of submitted talks and posters to assem- ble a kind of undeclared fifth minisymposium on complexity in linguistics.

With minisymposia, we are adopting a model that has proven fruitful since quite some time, for example in the Dynamics Days Europe. Another “novelty” we are going to implement revives in fact an old academic tradition: after-dinner talks. Our intention is decidedly not to contrast scientific rigour during daytime with entertaining retrospects at night; rather, we would like to open the already broad scope of nonlinear dynamics towards the arts and humanities, to show that even there, our concepts and ideas can trigger important insights. This requires leaving technicalities behind, a useful exercise for ourselves, and an invitation for the general public to enjoy some of the best we have to offer. We are grateful to two of our guests, Profs. Uzy Smilansky and Theo Geisel, that they are willing to share their respective passions with us, archaeology and music, and to show how apparently dry theory can be made to bear on subjects once considered strongholds of intuitive reasoning. Apart from these academic aspects, it will be a pleasure to give our guests a feeling, during this workshop, of the beauties Colombia offers to all our senses, its sounds, images, smells, and tastes.

Opening the thematic scope of LAWNP, we also made an attempt to widen its basin of attraction in the geographical sense. We are glad to welcome guests from the Middle East, from India—and from Australia, in times when the Pacific region gains attention and interest in Latin America. Like- wise, we are glad to have Prof. Selyshchev from Pretoria University with us: Intensifying contacts with the incipient complexity science in the neighbouring continent towards the East, Africa, remains a challenge for the future.

Dishing up this menu which hopefully contains something tasty for everyone, we should not deny that it rests and depends on a solid financial basis. In a country still fighting with precarious conditions in large parts of its territory, and in times of adverse global economic tendencies, it comes close to a miracle that we could realize LAWNP almost the way we had conceived it. This is a good opportunity to thank all the institutions that supported us with generous funding. In particular, our alma mater, Universidad Nacional de Colombia, as principal host and sponsor of this event, more than complied with its role. We would like to thank personally our Rector, Prof. Ignacio Mantilla, for his unconditional help. We appreciate the support by the Vicerectorate for Research, the Research and Public Outreach Management (DIEB), the Faculty of Science, and the Physics Department of our campus in Bogotá, as well as advice and help by the administrative staff who accompanied us to complete all procedures.

Moreover, we would like to express our gratitude for material help and immaterial support, extended to us by the Colombian Academy of Science ACCEFYN, Universidad de los Andes through its Faculty of Science, Universities de Antioquia and de Cartagena, ICTP, and the Banco de la República de Colombia through its Fund for the Promotion of Research and Technology.

Let’s make of this LAWNP a science feast, a nonlinearity biennial—in short, an intellectual ad- venture!

José Daniel Muñoz Thomas Dittrich Benvenuti! Bienvenue! সুস্বাগতম Serdecznie witamy! സ്വാഗതം Willkommen! д обро́пжа́лвать! םיכורב םיאבה! Welcome! सुस्वागतम ¡Bienvenidos! Bemvindos! 9

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena Snapshots of the production process of our LAWNP 2015 paper bags at Carteles Relámpago, a traditional printers’ shop in downtown Bogotá. the owner, Mr. Luis Sierra, is composing the text by hand from wooden letters, chosen from his rich collection of old-style fonts.

Invited talks Within each subsection, contributions are ordered alphabetically according to the surname of the presenting author.

Presenting authors appear in upright font, all other authors (if any) in italics. der much nutrientsinorder tobeablereproducequickly. between beingresistantenoughasto survive in the presenceof antibiotic and not losingtoo by increased mutationrates. Rather,cannot beexplained it emerges from a delicatebalance sistance. In contrast with our modelpredictsthat the standardassumption, adaptive resistance of adaptivere- the emergence network (EPRN)modeltoidentifythemain mechanisms behind regulatory pump efflux an use we Here unclear.reversibility, remain its cause processes what resistance, and adaptive govern and variability inheritance by which the precisemechanisms terns that are, in particular, associated with the production of porins and efflux pumps. However, of gene expressionpat - andheterogeneity inheritance adaptive resistancerequiresepigenetic that shows work Recent from themedia. is removed the antibiotic when phenotype non-resistant of antibiotics. It is characterizedbyarapidemergenceofresistanceandfast to the reversibility increases to gradual are subjected of bacteria populations when emerges resistance Adaptive Instituto deCienciasFísicas,UniversidadNacional Autónoma deMéxico,Cuernavaca,Mexico Aldana Maximino A stochastic formulation Epigenetic inheritanceof antibiotic resistance inbacteria: species. This modeofspeciation,termedallopatry, wasuntilrecently that leadtheirreproductiveisolationand,therefore,tonew eventually acquiringincompatibilities barrier,lation isseparatedintotwogroupsbyageographic the groupsevolveindependently, and theultimatedriverofbiodiversity.is acentralprocessinbiology Speciation Whenapopu 4 3 2 1 de Aguiar M. Marcus A. Simulating thegenetics andgeography inprocesses of speciation I willdiscusssomerecenttheoreticalresultsonthepopulationgeneticsofassortativemating. to ringspecies.Finally in aprocesssimilartopatternformationand showanapplication scenario in this can happen distributed. Iwillshowhowspeciation that arespatially acts onpopulations by distance,that on geographicisolation.InthistalkI will discussaprocessbasedonisolation sibility. Inthepast20years,however,do notrely which othermechanismshavebeenproposed Departamento de Física, Universidade Federal de Pernambuco, Recife,PE,Brazil Departamento deFísica,UniversidadeFederalPernambuco, Universidade FederaldaIntegraçãoLatino Americana, FozdoIguaçu,PR,Brazil USA New EnglandComplexSystemsInstitute,Cambridge,MA, Instituto deFísica‘GlebWataghin’, deCampinas,SP, UniversidadeEstadual Brazil 1 , EduardodoCarmo 1 , Ayana B.Martins 3 , PauloR.A.Campos 1 , Yaneer Bar-Yam 4

thought tobetheonlypos- 2 , DavidM.Schnei 15 - -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 16

Time delays and nonlinear phenomena on networks

Fatihcan Atay

Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

The behavior of coupled dynamical systems under information transmission delays will be discussed. Using prototype limit-cycle and phase oscillators, a variety of dynamical phenomena will be studied, ranging from fixed point behavior to multi-stability and synchrony, eventually leading to chimera states, where synchronous and incoherent behavior coexist in the same system at different spatial locations. The emphasis will be, on the one hand, the novel dynamics induced by the delays, and on the other hand, the relation of the dynamics to the connection topology of the underlying network.

A simple model for the location of Saturn’s F ring

Luis Benet

Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca, Mexico

In this talk I will discuss a simple model to understand the location of Saturn’s F ring and address some of its structural properties. The model is a planar restricted five-body problem defined by the gravitational field produced by Saturn, including its second zonal harmonic $J_2$, the shepherd moons Prometheus and Pandora, Titan, and a ring particle, and considers an ensemble of non-interacting ring particles. We compute precise long-time numerical integrations for ring particles initially located in the region between the orbits of Prometheus and Pandora, and address whether the test particles escape or remain trapped in this region. We obtain a wide region of initial conditions of the test particles that remain confined. We define a stability indicator based on a frequency-like analysis. Using this indicator in the set of trapped initial conditions, we select the subset of the most stable test particles, and obtain a narrow slightly eccentric ring with sharp edges. Comparison of our results with the nominal location of the F ring shows a remarkable agreement including its width.

Structure and dynamics of multilayer networks

Ginestra Bianconi

School of Mathematics, Queen Mary University of London, London, UK

Many complex systems as different as the brain or complex infrastructures, cannot be fully understood if we don’t consider their multilayer network structure. Vidal Marcel Clerc media Optical vortex induction vialight-matter interaction inliquidcrystal the classicalUniversemaybeencodableinatwo-dimensionalmapping. of function outofamechanisticsubstrate,orwhy emergence and (6)issuesofrepresentation, inability of a system to settle to (4) regular behavior; undecidability, in the Turing sense;(5)the (2) the interaction of multiple scales—andwhytwoareenough;(3) dynamical frustration—the algorithmic complexity,intractability (encompassing depth andrelatedconcepts); computational difficulty in achieving a unified definition or measure of complexity. These are: (1) computational In thistalkIwillreviewseveralaspectsofcomplexsystems,andhowtheyareattheheart ofthe Department ofPhysicsand Astronomy, UniversityofHawaiiatHilo,USA Philippe Binder representation A survey of complexity: computability, frustration and induced by umbilics, that is, defects arising inhomeotropically alignednematiccells,whichact the mainmechanisms ofinliquidcrystals, in particular,vortex generation on vortexgeneration crystal media.Wein liquid oflight-matterinteraction are basedontheexploitation focus here on ferent methodstogenerate opticalvorticeshavebeendevisedup to now. Among them,several devices. Dif- imaging systems, optical processing,communications,enhanced and bio-inspired of fields various in applications their of because attention of lot a attracting are vortices Optical 2 1 of differentto thepercolation phase transitionscorresponding layersofthenetworknetworks. not onebutmany to thiscandisplay and inaddition or continuous, tems canbediscontinuous works, i.e., network of networks. We will multilayer networksby statistical-mechanicsapproaches. of structure correlated the modeling on results recent discuss will we Here them. on defined es types ofstructuralcorrelationsthathavebeenshownto strongly affect the dynamicalprocess- Institut NonlinéairedeNice,UniversitéNice-Sophia Antipolis, Nice,France UniversidaddeChile,Santiago,Chile Departamento deFísica,FacultadCienciasFísicas yMatemáticas, Moreover we will present Moreover wewillpresent resultsrelatedtotherobustnessof a specialtypeof multilayer net- A multilayernetworkisasystemofdifferentby different interacting networkscharacterized 1 1 , RaulBarboza 1 , UmbertoBortolozzo show in particular 2 , StefaniaResidori that the percolation 2 in thesesys- , Stefania 17

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 18 as topological matter templates able to realize the conversion from spin to orbital angular momentum of an incoming Gaussian beam. Optical vortex induction in a photosensitive light valve is presented as a self-stabilizing mechanism leading to reconfigurable and programable vortex arrays. On each lattice site every matter vortex acts as a photonic spin-to-orbital momentum coupler, converting input arrays of circularly polarized beams into output arrays of vortex beams with topological charges consistent with the matter lattice symmetry.

Emergence of communities in coevolutionary networks

Mario Cosenza

Centro de Física Fundamental, Universidad de Los Andes, Mérida, Venezuela

Many social, biological, and technological systems possess a characteristic network structure consisting of communities or modules, which are groups of nodes distinguished by having a high density of links between nodes of the same group and a low density of links between nodes of different groups. We investigate the formation of communities through a recently proposed mechanism of adaptive rewiring in coevolutionary networks. We characterize the topological structures arising in a coevolutionary network subject to two coupled processes: an adaptive rewiring process and a node dynamics given by a simple voter-like rule. For some values of the parameters describing the adaptive rewiring process, a community structure emerges on a connected network. A community structure arises due to the adaptive rewiring process, even in the absence of node dynamics. The emergence of communities is associated to a decrease in the number of links that connect nodes in different states. The lifetime of the community structure state scales exponentially with the system size. Additionally, a small noise in the node dynamics can sustain a diversity of states and a community structure in time in a finite size system. Thus, large system size and/or local noise can explain the persistence of communities and diversity observed in many systems. An analytical approach to adaptive rewiring process in coevolutionary networks is also presented.

Random focusing from nanostructures to tsunamis: Where do the strongest wave heights occur?

H. Degueldre, R. Fleischmann, J. Metzger, T. Geisel

Max Planck Institute for Dynamics and Self-Organization, Göttingen, and Department of Physics, Georg August University Göttingen, Germany

Wave flows propagating through weakly scattering random media exhibit random focusing and branching of the flow as universal phenomena. Examples are found on many scales from electron flow in semiconductor nanostructures [1-3] to tsunamis traveling through the oceans. Even [4] Jesús Gómez-Gardeñes Urban mobility, socialstatus,andcontagion processes [3] [2] [1] special conditions the transition can also become of first order. I will illustrate the mechanisms the illustrate will order. I first of become also can transition the conditions special fi- a of appearance cluster.spanning nite under transition, phase a continuous exhibits percolation normally While sudden the to traced be often can society and Nature in changes Abrupt Institute forBuildingMaterials,ETHZürich,Switzerland, andDepartamentodeFísica,UFCFortaleza,CE,Brazil Hans Herrmann Discontinuous percolation croscopic contagionprocessesandthe(macroscopic)developmentofepidemics. its effectsand analyze status ofindividuals, the socioeconomic ingredient, social novel overmi- such asmobilitypatterns,thataffecta we willincorporate In addition, theonsetofepidemics. social ingredients, tractable, modelsthatincorporate yet computationallyandmathematically models andnetworkscienceopensthedoorto nation of realistic, and epidemic metapopulation real mobilitypatternsobservedinurbanareas.Weincorporating diseases showthatthecombi- of analysis of complex problemsinrealsettings.Herewefocusontheanalysisofspreading physics toolstothe many statisticalandnonlinear The adventofnetworksciencehasprovided 3 2 1 accurate tsunamiforecasts. of thebathymetry.tical properties of for thefeasibility Ourresultshaveimportantconsequences statis- the of function a as occur fluctuations wave strongest the typical which at distance propagation the determine We floor. ocean the of fluctuations height complex for account to etries branching [4]; we model them by linearized shallow water wave equations with random bathym- distributions. Herewestudyhowtsunamiwavesareaffectedwave intensityandheavy-tailed by for very weak disorder in the medium, branching can lead to extremely strong fluctuations in the Institute for Biocomputation and Physics of Complex Systems, UniversidaddeZaragoza,Spain Institute forBiocomputationandPhysicsofComplexSystems, Bogotá,Colombia Departamento deFísica,UniversidadNacionalColombia, Universidad deZaragoza,Spain BiocomputationandPhysicsofComplexSystems, Department ofCondensedMatterPhysicsandInstitutefor Henri Degueldre, JakobJ.Metzger,Henri Degueldre, RagnarFleischmann, Theo Geisel,tobepublished. Jakob J.Metzger, RagnarFleischmann, Theo Geisel,Phys.Rev. Lett. Phys. Rev. B D. Maryenko,F. Ospald,K.v. Klitzing, J.H.Smet, Metzger, R.Fleischmann, T. Geisel,andV. Umansky, Jakob Metzger, RagnarFleischmann, Theo Geisel,Phys.Rev. Lett. 85, 195329(2012). 1 , LauraLotero 2 , SandroMeloni 105, 020601(2010). 111 , 013901(2013). 3 , RafaelHurtado 2 19

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 20 behind the sudden appearance of a macroscopic percolating cluster. Very instructive is the history of the product rule also called “explosive percolation”. The scaling of bridge bonds allows to exactly solve the spanning cluster model having a first order transition atp c = 1. Suppressing the largest cluster by forcing a Gaussian size distribution renders an abrupt transition at pc < 1. An interesting relation to the watersheds of random landscapes and SLE can then be established. Finally one can find exactly the transition from a second to a first order phase percolation transition by establishing a relation to the q-state Potts model using Gliozzi’s algorithm. This model appears as a limiting case in the pollution of dielectric plates by metallic dust.

Quantal and classical shortcuts to adiabaticity

Ayoti Patra, Christopher Jarzynski

Department of Chemistry and Biochemistry, University of Maryland, College Park, MD, USA

Adiabatic invariants play an important role in classical mechanics, quantum mechanics and thermodynamics. In a variety of settings, there are benefits to driving a system slowly (adiabatically) from a given initial state to a desired final state. Within the field of quantum control, the term “shortcuts to adiabaticity” refers to strategies for gaining the benefits of quantum adiabatic evolution without paying the price of slow driving. In other words, these are strategies for preserving the adiabatic invariant during rapid (non-adiabatic) processes. This topic has emerged as an active field of study in recent years. I will discuss a number of quantal and classical shortcuts and I will illustrate them using model systems. The derivations of these shortcuts are often surprisingly simple, involving basic analyses of the Schrödinger equation or Hamiltonian dynamics. I will end with a brief summary of open questions.

Shaping a fly wing

Frank Jülicher

Max Planck Institute for the Physics of Complex Systems, Dresden, Germany

A fundamental question in biology is to understand the morphogenetic processes by which an organism of complex shape forms from a fertilized egg. This morphogenesis involves the dynamic remodeling of tissues consisting of many cells that grow and divide. The fly wing is an important model system for the study of multicellular dynamics during tissue morphogenesis. During pupal stages, the early fly wing undergoes a spectacular dynamic reorganization that involves cell flows, cell divisions and cell shape changes. This dynamic process generates the final shape of the wing. We characterize tissue remodeling by the contributions of specific cellular processes such as cell shape changes and cell neighbour exchanges to macroscopic shear duce pattern-forming instabilities that result in spatial self-organization of lifeforms andresourc- that result inspatialself-organization duce pattern-forminginstabilities in- also can changes environmental extended, spatially and nonlinear are inherently ecosystems Since dynamics. community and interactions interspecific through indirectly, or forms, life ual Environmental changes canaffect ecosystem functiondirectly, through the response of individ Campus, Israel Blaustein InstitutesforDesertResearchandPhysics Department,Ben-GurionUniversityoftheNegev, SdeBoqer Ehud Meron scales andorganization levels Ecosystem response to environmental changesacross multiple numerical simulations. lytically. by direct of themodelarecomparedfavorablywithresultsobtained The predictions ana- model this analyze and formation cluster the describe to theory field mean a develop We waves. as traveling and thatcanbeinterpreted is oneofclustersthatmoveataconstantspeed configuration spatiotemporal resultant the Instead, synchronization. global no is there result, a is chosensoasto The coupling disfavorthecrowdingof interacting unitsinthesamestate. As (referred toaslocalcoupling). interaction nor isitanearestneighbor coupling), ferred asglobal with whichit interacts. that is nonlocal, is, This couplingit is neitheranall-to-allinteraction(re- of thetransitionratesaunitonstates of theunits tween unitsoccurthroughadependence rate processes. by Markovian these statesaregoverned sitions between be- The interactions Wetran- an arrayofunitseachwhichcanbeinone ofthreestates. Unidirectional consider 3 2 1 Katja Lindenberg wave formation Arrays of stochastic oscillators: nonlocalcoupling,clustering, and tissue shape. final the determining in role key a play conditions boundary mechanical that show We wing. fly in the drive tissueremodelling active processes together withanisotropic tissue contraction local Our worksuggeststhat physics oftissueremodeling. theory thatcapturestheessential medium at different times. We discuss the dynamics and the mechanics of this tissue usinganactive João Pessoa,PB,Brazil Jolla,USA,andUniversidadeFederaldeParaíba, Biocircuits Institute,UniversityofCaliforniaSanDiego,La Facultad deIngenieríayCiencias delos Aplicadas, Universidad Andes, Santiago,Chile Department ofChemistryandBiochemistry, UniversityofCaliforniaSanDiego,LaJolla,USA 1 , DanielEscaf 2 , ItaloivoLimaDiasPinto 3 21 -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 22 es. This, in turn, can affect interspecific interactions and community structure, and make the response of ecosystems to environmental changes far more complex. In this talk I will introduce a platform of mathematical models for dryland ecosystems that captures several biomass-water feedbacks, discuss the conditions under which these feedbacks can induce pattern-forming instabilities, and delineate ways by which pattern formation can affect community dynamics and ecosystem function.

Thermodynamics of information

Juan Manuel Parrondo

Grupo Interdisciplinar de Sistemas Complejos, Universidad Complutense de Madrid, Madrid, Spain

Soon after the discovery of the second law of thermodynamics, Maxwell illustrated its probabilistic nature with a gedanken experiment, now known as Maxwell’s demon. He argued that if an intelligent being—a demon—had information about the velocities and positions of the particles in a gas, then that demon could transfer the fast, hot particles from a cold reservoir to a hot one, in apparent violation of the second law. Maxwell’s demon reveals a fundamental relationship between entropy and information. Information is a thermodynamic resource and consequently, information manipulation involves some thermodynamic cost. In this talk I will present some ideas about the physical nature of information and how can be incorporated into thermodynamics. The starting point is that information is stored in slow degrees of freedom that are out of equilibrium. Form this viewpoint, information thermodynamics is the study of a certain class of non-equilibrium states. Those states involve the coexistence of macro- or mesoscopic phases, such as in a memory that stores bits of information, and correlations, like those that come out when a “demon” measures on a system.

Random walks and random matrices

Christopher Joyner1, Uzy Smilansky2

1 Queen Mary College London, UK 2 Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel

Matrices with entries which are randomly chosen from 0 or 1 (Bernoulli matrices) appear in many applications—in particular in graph theory. Numerical simulations show that their spectral statistics, in the limit of large matrix dimension, converge to the canonical Wigner-Dyson statistics. To study this approach to universality, we reformulate Dyson’s Brownian motion theory for these discrete models: we consider random walks in the space of Bernoulli matrices, and follow the resulting stationary distributions of the corresponding spectral data. This way we demonstrate range semanticscales. long- of quantification the and words of ordering the in contained information the of universality results: the we focusontwoinformation-theoretical oflanguage, features oftheorganization the statisticalpropertiesof some well-known such structures. In thistalk,aftershortlyreviewing of thematiccontexts. the scale to disclose theory can beused tools ofinformation The powerful structuresat many levels,from the scaleof organizational sess complex grammatical patternsto to pos- languages human requires in theformofwordsequences information elaborate Coding Centro Atómico BarilocheandInstitutoBalseiro,CNEA,Bariloche, Argentina Damián H.Zanette Quantifying thestructure of language intuitive ratherthanformal. matrix dimensionsarelargebutfinite. to universality,not onlytheasymptoticconvergence the when butalsoestimatethedeviations No prior knowledge of Random Matrix No priorknowledge Theory willbeassumed,andtheexposition 23

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena

Minisymposia Resilience and sensitivity of terrestrial and marine tropical ecosystems (véase http://www.xivlawnp.org)

Tropical rain forests are a paradigm for the robustness of ecosystems, owing to their complex organization. They are considered hotbeds of speciation and biodiversity. Even so, and despite their crucial relevance for the biosphere, tropical ecosystems are increasingly threatened by human activity, in particular in the Amazon region and the Caribbean and Pacific continental shelves. Resilience, foodwebs, vegetation patterns, equilibrium vs. unbound growth, ..., are but a few of the keywords that suggest the relevance of complex systems research. basin, however Northwestern Amazonia is one of the wettest part of the basin and the atmo- Climate change has increased the prevalence of climate-driven fires over most of the Amazon 2 1 Armenteras Dolors relation to climate anddeforestation of satellite detected active fires inNorthwestern Amazonia in Subregional differences in temporal dynamics and spatialpatterns Invited talks between TNA SST and AM hydroclimatologyatseasonalandinterannualtimescales. coupling two-way feedbacksandadynamical of theexistencehighlynonlinear evidences cesses occurringoverthe Tropical North Atlantic (TNA). Here weprovidestatisticalandphysical effectsfocused onthepossible of pro- on oceanic-atmospheric hydroclimatology Amazonian nia affect climate andweatherpatternsat continental andglobalscales.But few studieshave the other hand, studies have shownthatdynamicsof modeling the hydroclimatological Amazo- arising from the tropical Pacific and Atlantic, as well as land-surface-atmosphere feedbacks. On lation (ENSO)isthemainmodulatorof owing to teleconnections Amazonian hydroclimatology Oscil- Niño/Southern El timescales, interannual rainforests. At tropical the by exerted moisture of thebioticpumpatmospheric mechanism and bytheroleofrecentlyproposed piration, via evapotrans of precipitation soil moistureandvegetation,therecycling between interactions and South feedbacks that Zones, bylandsurface-atmosphereinvolvethe Atlantic Convergence by sea surfacetemperatures(SST) over the tropical Atlantic, by the dynamics of the Intertropical influenced is of Amazonia variability hydroclimatic the timescales, seasonal system. At climate Earth’s of points tipping critical most the among considered is (AM) basin River Amazon The Colombia Escuela deGeocienciasyMedio Ambiente, FacultaddeMinas,UniversidadNacionalColombia,Medellín, Germán Poveda surface temperatures andAmazonian hydroclimatology Nonlinear two-way feedbacks between tropical NorthAtlantic sea Presentation CREAF andUniversitat Spain Autónoma deBarcelona, Bogotá,Colombia Departamento deBiología, UniversidadNacionaldeColombia, 1 , JuánSebastiánBarreto 1 , JavierRetana 2 27 -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 28 sphere-vegetation interactions in tropical rainforests in this region are further influenced by humans. Four countries share a big portion of this region with sections north and south of the Equator. We have used satellite data on active fire detections from the Moderate Resolution Imaging Spectroradiometer (MODIS) sensors and precipitation data from the Tropical Rainfall Measuring Mission (TRMM) to assess the hemispheric differences in response of fires to climate over a fifteen-year period. We have also analyzed the proximity to forest edges, roads and rivers. The patterns of fires and climate and their linkages show hemispheric differences in Northwestern Amazonia. In the northern hemisphere fires occur mostly in at the beginning of the year between January-March whilst in the south they occur mostly in the August-Octo- ber period. The highest number of recorded fires in Northwestern Amazonia occurred in 2007. We show that fire occurrence correlates well with proximity to forest (most within 2 km of the forest edge) and within 5 km of rivers indicating that most fires are anthropogenically driven deforestation fires.

Numerical coupling waves models for complex systems: Colombian Caribbean Sea

Andrés F. Osorio1, Daniel Peláez1, Victor Saavedra1, Rubén Montoya1,2, Gladys Bernal1

1 Grupo de Investigación en Oceanografía e Ingeniería Costeras, (OCEANICOS), Universidad Nacional de Co- lombia, Medellín, Colombia 2 Programa de Ingeniería Civil, Universidad de Medellín, Medellín, Colombia

In the last years, the wave models for generation and propagation of waves have been used for hindcast and forecast, in this way, some international oceanographic and meteorological agencies (like NOAA, ECMWF, among others) have implemented these models at global and regional scales. On local scales, however, it is necessary to develop methodologies for coupling wave models between global and local scales and to study local nonlinear processes. This study develops a strategy to couple the global model WaveWatch IIITM (in the Caribbean Sea) to the local one SWAN (in the Rosario Island, Cartagena). The results were validated with buoys from National Data Buoy Center (www.ndbc.noaa.gov) and local fieldwork carried out between 2013 and 2014. This strategy allows studying the mean and extreme conditions of waves in the Co- lombian Caribbean sea, where it is clear that both conditions were generated due to the nonlinear interaction between different factors (wind, wave dissipation, wave-wave interaction, among others). Finally the coupling system developed is implemented operationally and could be used in the future as a tool to study other complex interaction processes like sediment transport (ero- sion and sedimentation), biodiversity distribution, coastal flooding, waves and natural structure interaction, among others. of isolated termite individuals and individuals in groups under social interactions. We find a sharp social insectswidelydistributed inthe tropics. In this study we reportonthe movement patterns as beingsuperdiffusive.known for thisisnowoverwhelming. evidence Biological Termites are follow Lévyprobability distributionsinthe distances traveled. These movement patternsarealso physics. and both inbiology in fractalpatternsthat space explore seem tomoveand Animals The study of animal movement hasbecomea very important researchtopicinrecentyears, Autónoma deMéxico,MéxicoD.F., Mexico Complex SystemsDepartment,PhysicsInstituteand CenterforComplexitySciences,UniversidadNacional Octavio Miramontes Collective phasetransitioninthewalking behaviour of termites Edgardo Brigatti abundance timeseriesof asmallmammal insoutheastern Brazil Deciphering theeffects of delayed density-dependence in Contributed talks a consistencycheckbetweenmodeloutputsandindependentmeasurements. this analysisschemeisthat interpretable, allowing the model parameters aredirectlybiologically ty asacentraltemporalscaleforthedynamicsofthisspecies.Infact, of an importantadvantage series and, for the first time, clearly outlines the importance of the time of attaining sexual maturi- main driversofthedynamics. model that autoregressiveincorporatesthe and from these resultswebuildanad-hocminimalist son, wedetecttheprincipaltemporalstructuresonbasisofdifferentmeasures, correlation results. Forthisrea- clear is notthebestpracticeforobtaining of statisticalgenerality principles on based tools analysis of application the and interval time long sufficiently a represent to fail density-dependent factorsandtheirpossibledelayedeffects. by generated eventually processes regulation population and modeling the intentofdetecting Weaurita ) with size timeseriesofsmallmammal(Didelphis studythepopulation aNeotropical 2 1 Universidade FederalFluminense,NiteroiRJ,Brazil Universidade FederaldoRiodeJaneiro,JaneiroRJ,Brazil Surprisingly our model is capable of reproducing very wellthetimepatternsofempirical of reproducing our modeliscapable Surprisingly time series often obtained taxa,empirically and long-lived As iscommonforseriesofhigher 1 , M.V. Vieira 1 , M.Kajin 1 , M. A. deMenezes 2 , R.Cerqueira 1 29

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 30 transition from superdiffusion to subdiffusion as a function of space density and remark that the subdiffusive regime is possible only because individuals interact in a way that produces social crowding. Morever, this condition is bistable having clustered subdiffusive individuals coexisting with free-moving superdiffusive ones.

The coevolution of community ties and strategies of human space- time allocation

Harish Padmanabha1, Fabio Correa2, Drew Gerkey3, Sean Downey4

1 Centro de Investigaciones en el Desarrollo Humano (CIDHUM), Universidad del Norte, Barranquilla, Colombia, and National Socio-Environmental Synthesis Center (SESYNC), University of Maryland, College Park, MD, USA 2 Department of Anthropology, University of Maryland, College Park, MD, USA, and Grupo de Simulaciones en Sistemas Complejos, Universidad Nacional de Colombia, Bogotá, Colombia 3 Department of Anthropology, School of Language, Culture and Society, Oregon State University, Corvallis, OR, USA 4 Department of Anthropology, University of Maryland, College Park, MD, USA

Humans evolved in small-scale societies where the social ties between people residing in a community of homes gave rise to systems of cumulative knowledge and cooperative behavior that allowed adaptation to a broad suite of ecological challenges. In this paper we model the coevolution of community networks (social networks between individuals residing in the same place) and strategies of space-time allocation. We present an agent-based model of an age-structured human community of 150 people, where individuals make decisions on where and with whom to spend each 6hr time step and either fail or succeed in increasing their capacity to reduce future environmental uncertainty. Sufficiently frequent space-time coincidence between individuals allows formation of social learning links that reduce future probability of failure whenever contacts coincide in the same cell. Individuals modify their activity space in order to maximize the probability of success, taking into account the decisions of their social learning links. Model parameters determine environmental variation, travel velocity, geographic biases of individuals, capacity to form social links and capacity to learn from prior success and failure. We set initial conditions that pressure individuals towards carrying out activities in more distant areas and explore the adaptive feedbacks that arise between changes in activity space and community network density over 10 years. Simulations clearly demonstrate the reciprocal relationship between increased density of community networks and the human preference for spending time closer to home. Sensitivity highlights three factors that reduce reduced spatial clustering in activity patterns and the consequent demise community networks: the inability to build social ties with individuals in the general vicinity, the lack of perceived resources in the local environment and the inability or lack of agency to change space-time allocation based on prior failures and success. We discuss these results in the context of the radical changes in human space-time allocation amidst transformations in technology and subsistence modes over the past few centuries, with generally less and less time devoted to social interactions among neighbors. and inthecaseofColombiatofocusonhubs. the trade routesof them independently each speciesandsuperposingina considering multiplex, ing degreecentralitycriteria.Wetrade isby alternative tomodel illegal that avaluable conclude us- is network multiplex the attacking to alternative best the findings, our network. to According the of component largest the and hubs of enlargement the in resulting coefficients, clustering and the centralization in thedegree an increase plexesproduces results showthataggregating attack strategy.a random with are compared the results and feature (participation) tiplex Our and amul- and PageRank) networks (degree,betweenness centrality propertiesofmonoplex networks. of theprojected testing therobustness multiplex in the These strategiesarebased a multiplextothe10taxamostfrequentlytraded. Wesigning usefourstrategiestoattackthis it as- trade networksusingthespatialstructureofroutesandmodeling the dynamicsofillegal some featuresof Here weanalyze is unknown. and howtheycanbeweakened are connected works to move specimens inColombia,as was shownpreviously, however howthosenetworks regional, and international markets. This illegal trade functions through routes that configure net- local, to supply harvested of specimens quantities huge trade asitcompromises sult fromillegal species andmosttreatsre- reptiles arehighlyendangered useit.InColombia that traditionally the communities and to protectwildlife in order important trade isextremely and illegal poaching it ispresent. where in theregions dynamics and economic social fects ecological, The combat of af- and the world through activities criminal of themostimportant is one trade ofwildlife Illegal 3 2 1 Felber J. Arroyave B. robustness underattackby nodalremoval The multiplex network of illegal tradeof reptiles inColombia: Poster Instituto deEstudios Colombia,Bogotá,Colombia Ambientales, UniversidadNacionalde NacionaldeColombia,Bogotá,Colombia Departamento deFísica,FacultadCiencias,Universidad Instituto deEstudios Colombia,Bogotá,Colombia Ambientales, UniversidadNacionalde 1 , RafaelHurtadoH. 2 , OscarRomeroGoyeneche 3 31

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena The El Niño / La Niña phenomenon: analysing, forecasting, and confronting the Southern Oscillation (véase http://www.xivlawnp.org)

The Southern Oscillation, an atmospheric phenomenon on global scales, invites to be interpret- ed in terms of nonlinear dynamics: Is it chaos, or intermittent chaos, or ...? At the same time, it has drastic practical consequences in particular for the Pacific coast of Latin America, causing catastrophic droughts or inundations. Recently, El Niño is increasingly recognized as an active factor within global warming scenarios. Robyn M.Stuart several avenuesforfurther investigations. form, anddiscuss simpler in aneven can be presented features of this model that thedynamical show We gradient. temperature land-to-ocean the by hydrology, driven surface the and fluxes, and surface of clouds,radiative representations phenomenological and includes subcontinent Indian the over balance moisture and heat the captures model This 10.1029/2005GL022771). al circulationmodels.We study a simple boxmodelthat by was developedZickfeldet al. (doi: Niño andtheIndianoceandipole,arenotwell understoodeithertheoreticallyorthroughgener effectsaspects ofthedynamics,including Several subcontinent. the Indian ofeventssuchasEl that hasaprofoundimpactonlifein The Indiansummermonsoonisacomplex phenomenon 3 2 1 Raj Saha A simplifiedmodelformonsoondynamics Invited talks related spatio-temporalclusteringmethodology. patches. of attractiongarbage and eddies,domains Timea permitting,Iwillalsodescribe efficiently can models or observations coherent structuressuchasgyres identify andtrackimportantregionsintheocean,including on based techniques probabilistic how describe will I 6 5 4 3 2 1 Gary Froyland dynamics A briefintroduction to probabilistic methods foranalyzing ocean Presentation Imperial CollegeLondon,UK Københavns Universitet,Copenhagen,Denmark Spain Campus UniversitatdelesIllesBalears,PalmaMallorca, Technische UniversitätDresden,Germany Universität Paderborn,Germany University ofNewSouthWales, Sydney, Australia TIFR CentreforInterdisciplinarySciences,Hyderabad, India International Centrefor Theoretical Sciences– TIFR, Bangalore,India Bates College,Lewiston,ME,USA 1 , AmitApte 1 , ChristianHorenkamp 5 , ErikvanSebille 2 , RamaGovindarajan 6 2 , KathrinPadberg-Gehle 3 3 , Vincent Rossi 4 33 , -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 34

Nonlinear El Niño regimes

Ken Takahashi

Instituto Geofísico del Perú, Lima, Peru

El Niño and La Niña are anomalous warming and cooling events, respectively, in the equatorial Pacific ocean, with both positive and negative atmosphere-ocean feedbacks that lead totheir growth and demise, that can affect climate worldwide. Recent efforts on classifying and explaining different types of El Niño have focused on where along the equatorial line the largest sea surface temperature (SST) anomalies occur (i.e., East Pacific vs. Central Pacific). We show, through the joint analysis of long simulations with a global climate model and observations using the E and C indices for representing the SST anomalies, that two well-separated regimes exist for the warm El Niño events (Takahashi et al., 2011; Takahashi and Dewitte, 2015). One of these regimes includes all of the moderate-sized El Niño events, including both the central Pacific type and most of the eastern Pacific ones. The other regime contains only the extreme El Niño, like those of 1982-1983 and 1997-1998. We propose that the essential element for the existence of the two regimes is a threshold in the eastern Pacific SST that, if exceeded, activates a larger positive feedback associated with heavy precipitation in this otherwise dry region (Takahashi and Dewitte, 2015).

A low-dimensional model with this threshold nonlinearity, but no explicit geographical dependence, can reproduce the bursting behaviour associated with the extreme El Niño. In contrast to previous nonlinear el Niño models, aimed mainly at explaining its irregularity, this model is not chaotic or have self-sustained oscillations. It has one stable fixed point and requires stochastic forcing to maintain the variability. We find that the statistics of the extreme El Niño are sensitive to the amplitude of this forcing and to the value of the SST threshold. This model is dynamically similar to the FitzHugh-Nagumo model for neurons, with the extreme El Niño corresponding to neuron spikes. Despite the crudity of this model, we believe that it can provide useful insights into the nature of El Niño and its predictability, as well as to guide the improvement of compre- hensive climate models.

Coping with El Niño 2015-2016, progress and remaining challenges

Rodney Martínez (via videoconference)

Centro Internacional para la Investigación del Fenómeno de El Niño (CIIFEN), Guayaquil, Ecuador

After a failed development of El Niño during 2014 which was mainly due to the intermittent and erratic atmospheric response, it finally consolidated during the first quarter of 2015. Since May, the persistent SST anomalies over the tropical Pacific influenced in a consistent weakening in the zonal wind which leads on the establishment of a robust ocean-atmosphere coupling typical J. Martínez-Mardones Rotating convection inaviscoelasticmagnetic fluid Poster [2] [1] are emphasized. suspension magnetic for adiluted the rotationrateoninstabilitythresholds of and rheology the of effects The [2]. conditions boundary realistic of case the for thresholds Weconditions. boundary tem inthecaseofidealized the convective alsocalculatenumerically in termsoftheparameterssys- fortheconvectivethresholds expressions obtain explicit We[1]. model Oldroyd the by given are properties viscoelastic rotation. The under liquid carrier viscoelastic a in fluid magnetic a for convection on results numerical and theoretical report We 4 3 2 1 countries intheworld. This isonlythefirstpartofstory. and to impactmanyregions and isexpected in 2016 continue will which 2015 cope withElNiño to authorities. Ato aresharedasresultoftheexperience summaryofgoodandbadexperiences demonstrate the effectiveness of modest but consistent predictionsadequatelycommunicated pected responseof decision makers.In contrast, other practicalexperiencesevidencedin2015, tion strategy, mechanismsconspireto governance andcoordination misinform anddelaythe ex- could beoneofthefactors, however, other crucialelementssuchasanadequatecommunica the access,understandingandeffective useandapplicationofclimateinformation. and countriesdemonstratethebiggapsbetweenENSOscience,operationalservices such as agriculture, fisheries, water resources or health. Considerable differences between regions tions forearlypreparednessandadoptpreventionmeasuresinthedifferent sectorsoftheeconomy and ENSOpredictionshasnotbeenenough(atthetimetowritethisabstract)fosterconcreteac- ing robustinformationabouttheoceanandatmosphericconditions,acceptableseasonalforecast this information to national authorities, decision makers and different stakeholders. The fact of hav- patterns similartoElNiño1997-1998whichisknownasthestrongestoflastcentury. variables aregettingmagnitudesandspatial of El Niño.Sincethen,theoceanandatmosphere Departamento de Ciencias Físicas, Universidad de La Frontera, Departamento deCienciasFísicas,UniversidadLa Frontera, Temuco, Chile Instituto de Alta Investigación,Universidadde Tarapacá, Arica, Chile Departamento deFísicayMatemática deNavarra,Pamplona,España Aplicada, Universidad Instituto deFísica,PontificiaUniversidadCatólica Valparaíso, Valparaíso, Chile terials 364,98(2014). L. M.Pérez,D.Laroze,P. Díaz,J.Martínez-Mardones,H.L.Mancini, JournalofMagnetismandMagneticMa ofViscoelasticD. Joseph,FluidDynamics Liquids In the overallproblem,uncertaintyonpredictionof local impactsassociatedto El Niño, With a global consensus on El Niño establishment, a complex process started to communicate 1 , L.M.Pérez 2 , D.Laroze , Springer(New York, 1990). 3 , P. Díaz 4 , H. L.Mancini 2 35 - -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena Complex classical and quantum molecular dynamics (véase http://www.xivlawnp.org)

The workshop is dedicated to nonlinear dynamics and chaos in molecules, comprising: - Classical and quantum (ab-initio) molecular dynamics simulations, in particular of macromol- ecules, - Complex nonlinear dynamics in molecules, - Classicality generated by decoherence vs. semiclassical methods and approximations, - Functional roles of quantum coherence and complex classical dynamics in biomolecules. ulations, focused on its application to determine the molecular driving force defining the positions positions the defining force driving molecular the determine to application its on focused ulations, applications in biology and medicine. During this talk, I will present the state of the art of MD sim- different biomolecules,notonly underhealthybutalsodiseaseconditions, withpromising potential, Itsenormous complemented byexperimental studies,isallowingtounravelthemechanism offunctionmany experimentally. access impossible—to not difficult—if usually is that tion biomolecular systemsatatomisticresolution, to obtaindynamic,structural,andenergeticinforma- biomolecules. It offers the extraordinary possibility of monitoring the spatio-temporal evolution of namics (MD) simulations has nowadays become a robust technique to assess the dynamics of the transmission of information, energy transduction, or the transport of substances. Molecular dy- Biomolecules are molecular machines carrying out key biological processes for the cell, such as Heidelberg Institutefor Theoretical Studies(HITS)Heidelberg, Germany Aponte-Santamaría Camilo molecular dynamicssimulations Elucidating themechanismof function of biomoleculesthrough Invited talks molecular dynamicsmethods,ontheotherside. on the one side,andlarge-scalecourse-grained equations, Liouville quantum and Schrödinger the time-dependent methods forintegrating sical of the mechano-activation proteins. Thus, my review willtouchonfullyquantum and semiclas in like sufficient, is description classical-mechanical a and manifestations quantum all or most ily bequantum-mechanical. obliterates decoherence At theotherend,environmentally-induced transfer,excitation-energy fundamental, likeintheubiquitous and thetreatmentmustnecessar effectsdegree towhichquantum will bemanifested. is At oneendofthespectrum,coherence tures. A centralconceptinthedynamicsof molecules iscoherence,becauseitdeterminesthe fea- dynamical with complex phenomena these systemscanexhibit all membrane, sid, oracell complexity, be it molecule invacuum,aphotosyntheticmolecularcomplex,viruscap- a single of structural of thedegree Dynamics. Regardless Quantum Molecular and Classical Complex on in theMinisymposium speakers by theinvited aspects tobecovered tems, emphasizing I review onthe will presenta state course-grained of the art of the dynamics of molecular sys- Departamento deQuímica,UniversidaddelValle, Cali,Colombia Arce Julio molecule to theclassicalbiomolecularassembly Complex dynamicsinmolecularsystems: from thequantalisolated Presentation 37 - -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 38 of lipids around membrane proteins [1] and the mechano-activation of the proteins triggering primary hemostasis [2].

[1] C. Aponte-Santamaría, R. Briones, A. D. Schenk, T. Walz, B. L. de Groot, Proc. Nat. Acad. Sci. 109, 9887 (2012). [2] C. Aponte-Santamaría, V. Huck, S. Posch, A. K. Bronowska, S. Grässle, M. A. Brehm, T. Obser, R. Schnep- penheim, P. Hinterdorfer, S. W. Schneider, C. Baldauf, F. Gräter, Biophys. J. 108, 2312 (2015)

Semiclassical hybrid dynamics with molecular applications

Frank Großmann

Institut für Theoretische Physik, TU Dresden, Dresden, Germany

The semiclassical initial value formalism to solve the time-dependent Schrödinger equation will be reviewed. Special focus will be laid on the multi-trajectory Herman-Kluk method [1] and Hell- er’s thawed Gaussians [2]. The connection of the two methods by a Gaussian integration will be stressed. This connection lays the foundation for the semiclassical hybrid formalism that combines both approaches [3].

We then present results for the quenching of quantum interference in Iodine molecules in solution, described by a Caldeira-Leggett Hamiltonian [4], as well as the decoherence dynamics of Iodine in a Krypton matrix, with special emphasis on possible coherence flow into the bath [5]. Finally, we discuss the combination of the hybrid approach with time-averaging methods [6] to quickly calculate vibrational spectra.

[1] M. Herman, E. Kluk, Chem. Phys. 91, 27 (1984). [2] E. J. Heller, J. Chem. Phys. 62, 1544 (1975). [3] F. Grossmann, J. Chem. Phys. 125, 014111 (2006). [4] C.-M. Goletz, F. Grossmann, J. Chem. Phys. 130, 244107 (2009). [5] M. Buchholz et al., J. Phys. Chem. A 116, 11199 (2012). [6] A. L. Kaledin, W. H. Miller, J. Chem. Phys. 118, 7174 (2003).

Simulating coherent quantum processes in thermal and nonequilibrium environments

Craig C. Martens

Department of Chemistry, University of California, Irvine, CA, USA

In this talk, we describe recent work on investigating the role of the environment in influencing coherent quantum dynamics. We describe numerical methodology for simulating quantum co- [5] cell’s genome. Retroviruses like Rous Sarcoma Virus (RSV) infect cells during mitosis, when the viral DNAby theirabilitytoincorporate Retroviruses arepathogens characterized intoahost Beckman Institute,University ofIllinoisatUrbana-Champaign,Urbana,IL,USA Juan R.Perilla Chemical visualization of humanpathogens :theretroviral capsids [4] [3] [2] [1] ular processescouldbenchmarkacommonprinciplefornon-trivialquantumeffects inbiology. in biomolec sensing and transduction, transport, photo assisting motions molecular tum-scale synthesis. Our work suggests that a careful inspection of the dynamics and fluctuations of quan photo- of steps primary the of aspects quantum on [1-5] research our discuss will I talk, this In correlate totheeffective energymanagementbyphotosyntheticcomplexes. dynamical featurescanonlybepredictedwithinaframeworkandhow they quantum mechanical and conversionof excitation energy, in the picosecond time scale, it is not entirely clearwhich of sunlight. However,for optimalabsorption they areessential referring tothetransfer when that formthesecomplexes,and of thechromophores collective electronicquantumbehaviour are aclearmanifestationof biomolecules electronic excitationsof the collective light-gathering or excitons For instance, phenomena. mechanical rely onquantum process the photosynthetic steps of that theprimary known processes. Itiswell their life that sustain reactions the chemical Photosynthesis istheprocessbywhichplants,algaeandsomebacteriausesunlighttoinitiate Department ofPhysicsand Astronomy, UniversityCollegeLondon,UK Alexandra Olaya-Castro Quantum phenomenainlight-initiated reactions inbiology tems inthepresenceofanenvironmentthatisnotatthermalequilibrium. methods for studying quantumsys- then describenoveltheoreticalmodelsandcomputational and applythe in condensed phasesystems. approach to dephasing Wesimulating vibrational molecular dynamicssimulationandensembleaveraging, herent processesusingclassical-like A. Olaya-Castro,C.F. Lee,F.F. Olsen,N.F. Johnson,Phys.Rev. B F. Fassioli, A. Olaya-Castro,NewJ.of Phys. A. Olaya-Castro,F. Fassioli,ProcediaChemistry A. Kolli,E.J.O’Reilly, G.D. Scholes, A. Olaya-Castro,J.Chem.Phys.137,174109(2012). E. J.O’Reilly, 5,3012(2014). A. Olaya-Castro,NatureCommunications 12, 085006(2010). 3, 176(2011). 78, 085115 (2008). 39 - -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 40 chromatin is exposed to the cytoplasm. Conversely, the genus of lentiviruses, like the human immunodeficiency virus (HIV), have evolved to infect non-dividing cells. Despite infecting cells at different stages of their life cycles, RSV and HIV share a similar late stage replication cycle that is highly dependent on the group actin polyprotein precursor (Gag), which contains the matrix (MA), capsid (CA) and nucleocapsid (NC) proteins. Both HIV’s CA and Gag are considered unexploited targets for pharmaceutical intervention. In this talk, we describe the computational techniques that were used to build [1,3], simulate [2], analyze and visualize the structures of both Gag [1] and CA [3]. Our studies are able to incorporate large-scale molecular dynamics simulations, state-of-the-art polarizable force-fields, as well as experimental constraints obtained from magic angle spinning NMR and cryo-electron microscopy. Overall, our findings have deep implications for the replication cycle of the virus.

[1] B. C. Goh, J. R. Perilla, M. R. England, K. J. Heyrana, R. C. Craven, K. Schulten, Structure 23,1414 (2015). [2] J. R. Perilla, B. C. Goh, C. K. Cassidy, B. Liu, R. C Bernardi, T. Rudack, H. Yu, Z. Wu, K. Schulten, Current Opinion in Structural Biology 31, 64 (2015). [3] G. Zhao, J. R. Perilla, E. L. Yufenyuy, X. Meng, B. Chen, J. Ning, J. Ahn, A. M. Gronenborn, K. Schulten, C. Aiken, P. Zhang, Nature 497, 643 (2013).

Contributed talks

Unexpected coherence behavior in the light-harvesting antenna PC645 induced by natural thermal light

Juan D. Botero1, Paul Brumer2,3, Leonardo A. Pachón1

1Física Atómica y Molecular, Instituto de Física, Universidad de Antioquia, Medellín, Colombia 2Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Canada 3Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Canada

The nature of excited states produced by incoherent natural thermal light is analyzed in the context of the light-harvesting system. In the absence of proteomic environments or solvents, it is shown that natural thermal light generates extremely long-lasting coherent dynamics in photosynthetic light-harvesting systems provided by the super-Ohmic character of the radiation, the lack of pure dephasing dynamics and the small energy gap between donors and acceptors. Al- though this unexpected result has the potential of changing the entire direction of the discussion on the nature of excitonic states prepared by sunlight, when the environment is considered, the extremely long-lasting coherences induced by incoherent light are removed and stationary coherences are established in the photosynthetic light-harvesting system. Interestingly, it is further shown that some features of the energy pathways landscape depend on the nature of the light source that excited the photosynthetic complex. to theC-Smodeafterabout2psoflaser switch-on. bond with considerable probability, but find that the efficiency of this process is hampered by IVR mode. Weof theO-C bond excitation selective that enable this breaking at selectively succeed chirping and intensity laser the of ranges consider We field. laser negatively-chirped strong a with scheme implemented and aladder-climbing dipoleapproximation, modes, thesemiclassical to thebond mode of thebending to theweakcoupling due is appropriate which model, collinear (OCS) in itsgroundelectronicstate. Wea quantum simulationsemploying perform numerical sulfide carbonyl of dissociation and excitation mode-selective optical the attempt we prototype, schemes. control for optical a greatchallenge is already sought, which channel reaction As a final the on depending modes”), (“bond modes vibrational local specific of excitation selective the level. Suchcontrolrequires reaction atthemolecular the outcomeofachemical controlling (IVR) isthenaturalfoeofchemist´sdream redistribution vibrational-energy Intramolecular Departamento deQuímica,UniversidaddelValle, Cali,Colombia Juan BernardoPérez, mode-selective excitation of OCS Effects of theintramolecularvibrational energy redistribution inthe based ontheresultsforFrank’s model. models, generation solid theoreticalandfundamentalbaseto study morecomplexhomochirality proposed to explain the origin of homochirality. Also, the purpose of this research is to establish a models other of studies detailed more for point starting a is model Frank’s of SNAstudy the of kind ofmodels. As farasweknow, thiskindofstudyhasnotbeenmadepriortonow. The results stochiometric networkanalysis(SNA),apowerfultoolfortheofdynamicsthis this awesome historical event. The dynamical behavior of Frank’s model was investigated using explain to developed model autocatalytic first the perhaps model, Frank’s using homochirality A hugeamountofresearchhasbeendoneonthistopic. Inthiswork,westudytheoriginof inprebioticsubstanceswasa very importantconditionfor The homochirality the origin of life. Departamento deQuímica,UniversidadNacionalColombia,Bogotá,Colombia Rubén DaniloBourdonGarcía, the originof homochirality Stochiometric network analysis of Frank’s modelforthestudyof Julio César Arce César Julio Jesús Alberto ÁgredaBastidas 41

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena Urban dynamics: modeling, simulation, and control of megacities (véase http://www.xivlawnp.org)

Megacities are spearheading economic, social, and cultural development in particular in the Southern hemisphere. They challenge science and politics with often unprecedented phenomena that are difficult to analyze, let alone to control. Complex systems and dynamics matter on all levels and scales, traffic flow and networks, scaling and growth laws, urban tribes and spontaneous collective phenomena. er contextofoutputin social andbiologicalsystems. trade literature. international of thisframeworkisfurther discussedinthebroad The importance the in findings recent by inspired framework mathematical novel a using facts stylized these for size. Wevariance of the output givenpopulation larger theconditional giveatheoreticalbasis size, and(iii)the across cities,(ii)thelargeritsrelativerateof changewithrespecttopopulation es its output ways. in severalpredictable The morecomplextheactivity (i)thelesscommon activity chang of anurban that thecomplexity that suggests sources data from several evidence to howcomplextheseactivitiesare.Weentiation ofurbanactivitiesaccording presentempirical Werelationship. average asimplepower-law builduponthisbodyof work andproposeadiffer- size ison output ofagivenurbanactivityandpopulation between theaggregate relationship that the noted crime. Ithasbeen and contagion disease butalso opportunities, innovation, job servation that agglomerateeconomic activities, better cities areplacesthat disproportionately affectsmon tourbanenvironments output. We aggregate ob- start from thewidelyrecognized The presentstudyisaneffortcauses com- how thediversityofcomplementary tounderstand 2 1 Andres Gomez-Lievano The complexity of urbanactivities determines theirscaling Invited talks fit togetheracrosstheseveralpresentations. needs to be done.I will then introducesomeof and howthey the ideas of this minisymposium how manyof these propertiescanbepredictedandundestoodtopointoutwhatwork still gether classicalmodelsof urban agglomerationwith modern ideasof complex systems to show history.throughout and nations to- that brings framework theoretical an integrated present Iwill via theanalysisofnewdataandcomparativestudiesbetweenurbanareasacross discovered currently of citiesbeing properties quantitative many oftheemerging review In thistalkIwill Santa FeInstitute,Fe,NM,USA Bettencourt A. Luis Cities ascomplex systems Presentation Harvard T.H. ChanSchoolofPublicHealth,HarvardUniversity, Cambridge,MS,USA Center forInternationalDevelopment,HarvardUniversity, Cambridge,MS,USA 1 , OscarPatterson-Lomba 2 , RicardoHausmann 1 43 - -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 44

Spatial selection and the statistics of neighborhoods

José Lobo1, Luis A. Bettencourt2, Jose Hand2, Christa Brelsford2, Jonah Nono- maque2

1 Julie Ann Wrigley Global Institute of Sustainability, Arizona State University, Tempe, AZ, USA, 2 Santa Fe Institute, Santa Fe, NM, USA

Biological and social systems are often characterized by the emergence of general macroscopic patterns within a structure of local variations. Such variations—whether in an ecosystem or a city—express not only statistical accidents but also a rich history of innovation, selection and resulting local adaptations. For these reasons, it has remained a challenge to analyze the structure of complex systems and characterize how much information they contain at different scales of organization. Here we develop a unifying framework for studying the local heterogeneity of complex systems across scales. We show how methods from evolutionary biology and statistical learning theory can be used to quantify how much information is encoded at local levels and how complexity builds up from coarse-grained simple patterns to rich local structures. To illustrate our approach, we apply these ideas to the neighborhood structure of U.S. and Brazilian cities. We observe a strong pattern of local heterogeneity in household income across cities and neighborhoods within a simple and general statistical pattern at the metropolitan level. In this way, we identify variable strengths of local selection by income and quantify the complexity of explana- tion needed to account for different neighborhood structures observed across urban areas.

Contributed talks

Socioeconomic structure of urban mobility networks: case of Bogotá and Medellín

Laura Lotero1, Rafael Hurtado2, Patricia Jaramillo1, Alessio Cardillo3,5, Jesús Gó- mez-Gardeñes4,5

1 Departamento de Ciencias de la Computación y de la Decisión. Universidad Nacional de Colombia, Medellín, Colombia 2 Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia 3 Laboratoire de Biophysique Statistique, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzer- land 4 Departamento de Física de la Materia Condensada, Universidad de Zaragoza, Zaragoza, Spain 5 Instituto de Biocomputación y Física de Sistemas Complejos, Universidad de Zaragoza, Zaragoza, Spain

Socioeconomic stratification is a Colombian system that classifies housing into six strata according to its characteristics and the paying capacity of householders. It has been used as a proxy Frery is compatible with a correlated noise with f noise a correlated with is compatible to identifydifferentused were plane plexity-Entropy and behaviors. regimes velocity The global hicle speedis stored as a time series. The Bandt-Pompe methodologycombinedwiththe Com- taxicabsdataset city of≅ collected inBeijing,China,whereeachve- Borlänge; andiii)Beijing on HighwayI-880, near UnionCity, California; ii)BorlängeGPS data set collected inthe Swedish through theirvelocities. Century datasetcollected data setswereused:i)Mobile Three public This workproposestheuseofInformation of vehicles behavior Theory forthecharacterization 2 1 Andre L. Aquino Characterization of vehicle behavior withinformationtheory correlated velocities( systems. of thesemultiplex impact inthelayerorganization have anextraordinary istics ofthepopulation and the socioeconomic status of travelers. Our results showthat the socioeconomic character- interesting featuresof mobility: thetransportationmode,to tackle themultimodalnatureof trips, network propertiesevolveandemergeaswejoinlayers.Withthisapproach,combinetwo the how analyze and modes) of transportation a group representing layer (each by sixlayers a multiplex perspective.We study six (each for multiplexes a status) socioeconomic composed regation patternsinurbanmobilityofhighestandlowestincometravelers. structural differences if analyzed by socioeconomic strata of the population. We also unveilseg- cities. Westrata andbetween between comparisons networks have mobility foundthaturban and directednetworks.Weproperties oftheseinordertomake considerthemaintopological them intoweighted represent and cities inColombia, the twomostpopulated Medellín, and patterns oftravelersaccordingtotheirsocioeconomicstrata. of income In level of individuals. this work, we aimto explore andanalyzethe urban mobility traffic behaviors as, for instance, random velocities (k velocities random instance, for as, behaviors traffic AL, Brazil Instituto Tecnológico deBuenos Aires (ITBA), Buenos Aires, Argentina DepartamentodeFísica,UFAL, Maceió, LaCCAN/CPMAT, UniversidadeFederalde Alagoas (UFAL), Maceió, AL, Brazil Then, we present an adiabatic projection approach to analyze urban mobility networks under mobility urban to analyze approach Then, wepresentanadiabaticprojection Wesurveys ofBogotá data fromorigin-destination analyzeurbanmobilitybasedonempirical 1 , Osvaldo A. Rosso k 1

, Tamer S.G.Cavalcante ≅ 3) inthepresence offreetrafficflow. 2 – k ≥ 0. With this we identify we this With 0. ≥ spectrum withk power 1 Eliana S. Almeida , Eliana

≅ 0) whenthereiscongestion,and more 1 , AlejandroC. 45

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 46

Posters

Scaling-based metrics for predicting the evolution of urban indicators and quantifying the performance of cities

Luiz G. A. Alves1, Haroldo V. Ribeiro2, Renio S. Mendes1, Ervin K. Lenzi3

1 Departamento de Física, Universidade Estadual de Maringá, Maringá, PR, Brazil 2 Departamento de Física, Universidade Tecnológica Federal do Paraná, Apucarana, PR, Brazil 3 Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa, PR, Brazil

Currently more than half of world population lives in cities and this number is expected to increase for two-thirds by 2050. Fostered by the importance of a better understand of urban metrics for public policies and resource allocation, researchers have made an impressive progress on this topic over the last few years. In this context, one of the most striking and universal findings was the discovery of robust allometric scaling laws between several urban indicators and the population size. How- ever, several works and government agencies still ignore these nonlinearities, by employing per capita value of urban indicators in order to rank cities. This practice actually make the urban metrics biased towards small or large cities depending on whether we have super- or sublinear allometries. To overcome this bias, Bettencourt et al. [PLoS ONE 5: e13541 (2010)] proposed to evaluate the difference between the actual value of an urban indicator and the value expected by the allometry with the population size. Here we apply this scaling-based metric in the data from Brazilian cities in order to have a more appropriate/informative summary of the evolution of urban indicators. Our analysis reveals patterns that do not appear in the evolution of the per capita values of indicators. Moreover, we show that these scaling-based metrics are strongly correlated with their past values by a linear correspondence and that they also display cross-correlations among themselves. Sim- ple linear models account for 31% – 97% of the observed variance in data and correctly reproduce the average of the scaling metric when grouping the cities in above and below the allometric laws. We further employ these models to forecast future values of urban indicators and, by visualizing the predicted changes, we verify the emergence of spatial clusters characterized by regions of the Brazilian territory where we expect an increase or a decrease in the values of urban indicators. particles atareasonablecomputationalcost. to approach has make numericalsimulationsfor allowed long timesandfor systems of many using theJuliaandCUDA inparallel implemented simulations languages. programming This response. collective and spreading, bation numerical out through is carried analysis The model pertur- interactions, aframeworktostudycomplexnetwork-network provides hand, themodel extend it to other kinds of collective dynamics such as traffic and opinion dynamics. On the other moment themodelisfocusedondescriptionofanimalcollectivebehaviour, but weintendto system’sthe cohesion. maintaining for required are they Wethat interactions. the claim local At particles interactthroughaninteractionnetworkwhichinducesnon- geometric neighbourhood, Vicsekas intheclassic particles between withthedifference model, to thelocal thatinaddition interactions alignment on based is model The times. long at together remain particles system’s the of most as cohesion and parameter) order the of value high a in (reflected tem’scoherence the sys- of maintaining motion modelinopenspacewhichiscapable a collective we propose state breaksapartanddiffusesordered is relaxed,thecollective condition inspace.Inthiswork this when and conditions boundary periodic within defined are models motion collective Most Instituto deCienciasFísicas,UniversidadNacional Autónoma deMéxico,Cuernavaca,Mexico Aldana Martín Zumaya,Maximino and nonlocalinteractions How to keep theflock together: Acollective motion modelwithlocal 47

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena

After-dinner talks me inthisfascinatingendeavor. and join share myconviction ology canbehappyandfruitfultoallpartiesinvolved.Ihopeyou’ll archae and science computer of fields distant rather the between marriage the that convinced to mostofus“exact”scientists. incognita” I am archaeologists After some15yearsofworkwith “terra a - domain this in forays my during gathered I which experience and impressions the you In this and sharewith lecture I archaeology shall describesomeofmy work incomputational Department ofPhysicsComplexSystems,Weizmann InstituteofScience,Rehovot,Israel Uzy Smilansky Computational archaeology computer-performed musictosoundmorehuman. allows which algorithm” “humanizing a is findings these of application One brain. the in cessing in musicandits he willhighlighttheroleofcorrelations connection to information pro- long-range strations and musical examples ranging from J. S. Bach’s The Art of Fugue to stochastic music, laws underlying rhythmic fluctuations and their role in musical perception. With acoustic demon fromstatisticalphysicsandchaostheory,ner talk,usingtechniques discuss the Theo Geiselwill by humans.Inthisafter-din- of musicplayed characteristic beat patternareafundamental ideal Even thebest musicians donotplayrhythmswithperfectprecision.Slightdeviationsfrom an Göttingen, Germany Max PlanckInstituteforDynamicsandSelf-Organization,BernsteinCenterComputationalNeuroscience, Theo Geisel 51 - -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena

Contributed talks

so thatthegrowinginterfacecanbeplacedwithinKPZuniversalityclass[1,2]. when thethermodynamic limit(L The localization-delocalization transitionoftheinterfacebecomesa truewettingphasetransition act. So,samplesareassumed tohaveasizeL tween twowallsseparated byadistanceL be- confined magnets [1] Blume-Capel and Ising differentboth of in domains orientation, magnetic We present a numerical study of the localization-delocalization transition of theinterfacebetween ta, LaPlata, Argentina Instituto deFísicaLíquidosySistemasBiológicos, CCT–CONICET–LaPlata,UniversidadNacionaldeLaPla VicenteAlbano, Ezequiel transitions inconfinedferromagnets withimpurities. Multicritical wetting uponinterface localization-delocalization [2] [1] with the predictions of the Kardar-Parisi-Zhang (KPZ) [2] equation (β more, the set of evaluated exponents fulfills the Family-Vicsek [1] relationship and it is consistent results. Further- and the numerical the experimental there isanexcellentagreementbetween setup, yields imental of of simulations numerical discrete modelfor cell culturesin-vitro,aimedto describe the exper- exponent single curvewitha growth exponent β = 0.33(2). From the structure factor a global roughness ( of theinterface of thewidth that plots shows colonies cell = 0.22 ± 0.02 mm/min (v = 0.9 ± 0.05 mm/min). The dynamic scaling analysis [1] of both cultured that the front of Vero (HeLa)cellcoloniesmoves forward withanaverageconstantvelocityof show Experiments cells. HeLa Veroand studied: are lines cell Twodifferent [1]. theory scaling simulations. The interfacial propertiesofinterms of the coloniesarerationalized the dynamic computer and both Invitrocultures by performing is investigated colonies of cell The growth 2 1 VicenteAlbano Ezequiel behavior of cellcultures Experimental andcomputationalstudyof thegrowth andinterfacial al deLaPlata, Argentina Instituto deInvestigacionesFisicoquímicas Teóricas y Aplicadas, CCT-CONICET-La Plata,UniversidadNacion ta, LaPlata, Argentina Instituto deFísicaLíquidosySistemasBiológicos,CCT-CONICET-La Plata,UniversidadNacionaldeLaPla M. Kardar, G. Parisi,and Y.-C. Zhang,Phys.Rev. Lett. L. Barabasi,H.E.Stanley, FractalConceptsinSurfaceGrowth,CambridgeUniversityPress(Cambridge,1995). α = 0.50(5) isobtained,sothat the dynamicexponentisz= 1.5(2). Also, theanalysis β =0.32(2),α0.49(5),and 1 , NaraGuisoni Luciana MelinaLuque

→ ∞, M

→ , where short-range competitive surface magnetic fields fields magnetic surface competitive short-range where , ∞) is properly taken, as it follows from scaling theory [2]. x M 1 , BelénMoglia , 56, 889(1986). L beingthewidthandM = 1.49(2). Summing up, we conclude that up, weconclude z =1.49(2).Summing , MartaTrobo W ) versusthetime( ) 1 , AnaMaríaHuergo = 1/3, thelength,respectively. α =1/2, and t ) collapse in a in collapse ) z = 3/2), 2 55 - - v -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 56

By considering fixed (quenched) vacancies or non-magnetic impurities along the centre (i.e. for x = L/2) of an Ising sample, we found that the wetting transition can be of either first or second order, depending on the concentration of vacancies. While first-order transitions are precisely located by means of thermodynamic integration methods [3], second-order transitions are accurately determined by using a suitable scaling theory [2]. In this way, at the intersection between second- and first-order lines we found tricritical wetting points.

On the other hand, we also considered both standard and modified Blume-Capel [1] models in order to gain insight on the role of mobile impurities. Here, tricritical wetting is also found but for a tiny concentration of impurities.

Our study concludes that a proper density of both quenched and mobile nonmagnetic impurities can effectively cause the pinning-depinning transition of magnetic interfaces. Both cases are fully discussed and the relevance of the results for the design of nano-magnetic storage devices is stressed.

[1] M. Blume, Phys. Rev. B 141, 517 (1966); H. W. Capel, Physica 32, 966 (1966). [2] Ezequiel V. Albano, Kurt Binder, Phys. Rev. Lett. 109, 036101 (2012). [3] Marta L. Trobo, Ezequiel V. Albano, Kurt Binder, Phys. Rev. E 90, 022406 (2014).

Emergence of small-world anatomical networks in self-organizing neuronal cultures

Juan A. Almendral1, Daniel de Santos Sierra2, Irene Sendiña Nadal1, Inmaculada Leyva1, Stefano Boccaletti3

1Universidad Rey Juan Carlos, Madrid, Spain 2Biological Networks, Center for Biomedical Technology, Madrid, Spain 3Embassy of Italy in Tel Aviv

We present an experimental research with in vitro primary cultures of dissociated invertebrate neurons from locust ganglia. Our main objective is to characterize, from the Complex Networks viewpoint, the morphological evolution of these living neurons, as they self-organize from collec- tions of separated cells into elaborated, clustered, networks [1].

By means of dedicated software, we identify the locations of neurons and neurites at all the different stages of the culture development. In this manner, we can extract an adjacency matrix from each image of the culture, which allows us to perform a systematic statistical analysis of different topological measures. Remarkably, our methodology grants us the possibility of quantifying and tracking the progression of the main network’s characteristics at any moment during the self-organization process of the culture [2]. spread ofvector-bornediseases. yond thelimitsofclassicalmodelscontrol. differences,the spatial therobustnessofcontrolstrategiesthatconsider us toexamine be- The available data on the flow of people and the incidence of the disease in different areas allow there). todistantareas(bycausingtheinfectionofvectorsplaced spread ing theepidemic (dynamics within nodes) whereas the flows of people between nodes are responsible of promot- ing areas of the city. In this way, infections have a “well-mixed” character inside each of the areas correspond the between people of flow the describe them between connections the and areas between humansandvectorswithinthem.Inourcase,thenodesofnetworkdenote urban contact the and areas different between flows individual the of structure the incorporate to as mosquitoes. However,so modeling to combinenetworktheoryandmetapopulation it ispossible and people between the contactpatterns of capturing theimpossibility to overcome has proach or Malaria,theuseofnetworkap- transmission ofvector-bornediseases,suchasDengue In thecaseof outbreaks. of epidemic characterization and the prediction a greatsuccessin During the last decade the use of the network approach in the field of epidemiology has achieved 2 1 Arias-Castro Heliana Vector-borne diseasesinmetapopulations [2] [1] experimental observations. of set overall the reproduces qualitatively that model growth simplified a into them embed and transformations, morphological culture’s the ruling processes physical main the identify we ly, Final- emerge. properties mesoscale graph’s and relevant micro several which in configuration, network to asmall-world state corresponding Our resultspointtotheexistenceofaparticular plejos, UniversidaddeZaragoza,Spain de BiocomputaciónyFísicadeSistemasCom Departamento deFísicalaMateriaCondensadaandInstituto Departamento deMatemáticas,UniversidaddelValle, Colombia Cali, caletti, submittedtoCytometry A (2014). D. Santos-Sierra,I.Sendiña-Nadal,Leyva,J. A. Almendral, A. Ayali, S. Anava, C.Sanchez-Avila, S.Boc- ONE 9e85828(2014). D. Santos-Sierra,I.Sendiña-Nadal,Leyva,J. A. Almendral, S. Anava, A. Ayali, D.Papo,S.Boccaletti,PLoS Following the former approach here we show the influence of human transportation in the in transportation human of influence the show we here approach former the Following 1 , JesúsGómez-Gardeñes 2 , HéctorMartínez-Romero 1 57 - -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 58

Dynamically emergent explosive synchronization

Vanesa Avalos-Gaytán1, Juan A. Almendral2, Stefano Boccaletti3

1 Universidad Autónoma Coahuila, Saltillo, Coahuila, Mexico 2 Universidad Rey Juan Carlos, Madrid, Spain 3 Italian Embassy in Israel

One of the most significant challenges of present-day research is bringing to light the processes underlying the spontaneous organization of networked dynamical units. Discontinuous transitions to synchronized states of networked phase oscillators were initially reported in a Kuramoto model for a particular frequency distribution and network topology [1]. The same finding was also described for both periodic [2] and chaotic [3] phase oscillators in the yet particular condition of a heterogeneous degree distribution with positive correlations between the node degree and the corresponding oscillator’s natural frequency. Later on, a more general framework was proposed [4] where this explosive synchronization is obtained in weighted networks, if the weights are adequately selected. More recently, it has been shown that explosive synchronization can be obtained for any given frequency distribution, provided the connection network is constructed following a rule of frequency disassortativity [5,6].

These studies so far have concentrated on proposing topologies for which the transition is explosive, given a specific frequency distribution on the dynamical units, or vice versa, proposing a frequency distribution on the oscillators, given a specific connectivity structure. However, no models have yet succeeded in generating dynamically the conditions for a transition to be explosive. We show here that these conditions may spontaneously emerge in an adaptive network of interacting oscillators, as the result of a delicate interplay between synchronization processes and coevolution of the connectivity structure. When the connectivity dynamics is such that links coupling the nodes with non-synchronous (synchronous) dynamics are promoted (weakened), we prove that an initially unstructured clique configuration evolves in time toward an emerging structured network whose transition is explosive. We also study the parameter space of this model to demarcate the region in which this happens.

[1] D. Pazó, Phys. Rev. E 72, 046211 (2005). [2] J. Gómez-Gardeñes, S. Gómez, A. Arenas, Y. Moreno, Phys. Rev. Lett. 106, 128701 (2011). [3] I. Leyva, R. Sevilla-Escoboza, J.M. Buldú, I. Sendiña-Nadal, J. Gómez-Gardeñes, A. Arenas, Y. Moreno, S. Gómez, R. Jaimes-Reátegui, S. Boccaletti, Phys. Rev. Lett. 108, 168702 (2012). [4] X. Zhang, X. Hu, J. Kurths, Z. Liu, Phys. Rev. E 88, 0108012(R) (2013). [5] I. Leyva, A. Navas, I. Sendiña-Nadal, J. A. Almendral, J.M. Buldú, M. Zanin, D. Papo, S. Boccaletti, Nature Sci. Rep. 3, 1281 (2013). [6] I. Leyva, I. Sendiña-Nadal, J. A. Almendral, A. Navas, S. Olmi, S. Boccaletti, Phys. Rev. E 88, 042808 (2013). abilistic urnandgeneticsmodelsarepresented forillustratingthisexceptionalcase. studied throughthreeexamples.Oneofthe examples presentsanunexpectedoutcome.Prob- of trials) distributions andtheirrelatedentropiesare of of binomial symmetric generalizations interpretation. and preservestheprobabilistic Asymptotic behavior(withrespectto the number the symmetrywin-loss. that preserves numbers functions on generating is based This approach Weof positive with asequence associated distribution ofthebinomial presentageneralization 3 2 1 Herve Bergeron correlated systems Symmetrically deformedbinomialdistributions:examples of strong aspects ofcomplexprocesses. ance that can not be modeledby traditional methods,usefulfor modeling andstudy important iments to find the best model of an observable represented by a time series of complex appear solutions that may bechaotic. exper- This toolallowstoeasilyandaccuratelyperformnumerical with order up tosecond in termsofpolynomials or nonlinear is linear if themodel determine to correspondingthe system time in threedimensions series. The values of these parameters determine the numerical values of the parameters that define the unique and optimal dynamical series. The toolisself-consistentusingstatisticalandinformationoptimizationprocessesto constructed fromthetime models tionarity ofthetimeseriesandtheirimpactsonnonlinear the effectsto estimateandcontrol vary theparametersofreconstruction, and non-sta- ofnoise theorem. systems fromtimeseries,usingthereconstruction dynamical sional to The toolallows models intermsofthree-dimen tool thatbuildsnonlinear This paperpresentsacomputational CICBA, Universidad Antonio Nariño,Bogotá,Colombia J. L.Cruz, models basedontimeseries Computational tool fortheautomatic construction of nonlinear drigues Université ParisDiderot,Paris,France Brazil Centro BrasileirodePesquisasFisicas,RioJaneiro,RJ, Université ParisSud,Orsay, France 2 R. M.Gutiérrez 1 , EvaldoM.F. Curado 2 , JeanPierreGazeau 3 , LigiaM.C.S.Ro- 59 - -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 60

Synthetic genetic networks, quorum sensing, and multistability

Syamal K. Dana1, Edward H. Hellen2, Evgenii Volkov3, Jürgen Kurths4, Sudesh- na Sinha5

1 CSIR – Indian Institute of Chemical Biology, Kolkata, India 2 University of North Carolina, Greensboro, NC, USA 3 Lebedev Physical Institute, Moscow, Russia 4 Potsdam Institute of Climate Impact Research, Potsdam, Germany, Indian Institute of Science Education and Research, Mohali, India

The synthetic genetic oscillator (SGN) consists of three single genes connected in a cyclic order inhibiting each other, which mimics the circadian clock. A collection of such SGN units shows interesting dynamical features under a special type coupling called as quorum sensing. The quorum sensing coupling is well known in bacterial colony that demonstrates a coherent dynamics. Our model of synthetically designed genetic oscillators with a quorum sensing coupling reproduces such collective behaviours, most importantly multistability.

In this report, I will describe the dynamics of SGN and their collective behaviours as mul- tistable systems, such as homogeneous steady states, inhomogeneous steady states and inhomogeneous limit cycles which are coexisting. We implemented the SGN by their electronic circuit analog and explored some behaviours of practical importance.

[1] E. H. Hellen, S. K. Dana, B. Zhurov, E. Volkov, PLoS ONE 8, e62997 (2013). [2] E. H. Hellen, S. K. Dana, J. Kurths, E. Kehler, S. Sinha, PLoS ONE 8, e76032 (2013). [3] E. H. Hellen, E. Volkov, J. Kurths, S. K. Dana, PLoS ONE 6, e23286 (2011).

Flow in microchannels with structured cross section

Ivonne Domínguez Román, Rafael Ángel Barrio Paredes

Instituto de Física, Universidad Nacional Autónoma de México, México D.F., Mexico

When a liquid invades a small channel with cross sectional area of the order of microns or nano- meters, surface effects become most relevant and the flow is dominated by surface tension and the wetting properties of the solid liquid interface. In channels with constant area, the penetration distance is known to increase as the square root of time (Washburn Law). It is also known that in channels with cross section increasing linearly with distance, the exponent becomes 1/3, instead of 1/2. We demonstrate, theoretically and numerically, that in channels whose area varies periodically, the long-time behaviour of the penetration distance obeys a power law with different exponent. In the case when the shape variations consists of a series of wedges, the flow attains regime where the exponent is one, that is, flow without friction. This regime could be tuned for [2] [1] why thisequivalencedoes notpersistforfrequencysynchronization. between oscillatorsandburstingneurons we willpointouthowcanbuildanequivalence nization, theyhaveacompletelydifferentIn thiswork forfrequencysynchronization. behavior phase synchro- concerning and Kuramotooscillatorsareequivalent that whileburstingneurons alent to the observed phase synchronizationamongKuramotooscillators.We have observed exhibit phasesynchronization. is equiv The observedtransitiontowardsphase synchronization among themisincreasedthey neurons arecoupledandthecoupling neurons. Whenbursting we usetheRulkovmodeltodescribebursting quiescent periodoftimeoccurs.Forouranalysis by a when atrainofspikesfollowed potential in themembrane ing characterizedbychanges features. Oneofthesefeaturesisburst- nonlinear to exhibit known is well dynamic The neuronal Universidade FederaldoParaná,Curitiba,PR,Brazil Fabiano A. S.Ferrari, they are not When burstingneurons are well describedby oscillators andwhen ics areconsidered. associated to particles withoverdampeddynam- ordered phasesof models whereself-propelled typically features fluctuations, number giant and order, long-range coexistence, phase motion, thermal equilibrium, with no net flux of particles, to far-from-equilibrium ones exhibiting collective Moreover,namics canbeguaranteed. the system crosses overfrom a stationary phasescloseto dy- particle underdamped as long as place, take to transition flocking the for feature necessary force thatdoesnotaffectvelocity-alignment is nota their speed,weshowthatself-propulsion a local through only themselves that interactamong particles, a systemofBrownian By studying 2 1 Victor Dossetti particles Emergence of collective motion inamodelof interacting Brownian drophobic surface.Otherextensionsofthisideasarepresented. long times. This resultcouldbeextendedto hy- the caseof a channelwithperiodichydrophilic- Instituto deFísica,UniversidadNacional MéxicoD.F.,Autónoma deMéxico, Mexico CIDS –InstitutodeCiencias,BeneméritaUniversidad Autónoma dePuebla,Mexico F. A. S.Ferrari, R.L.Viana, S.R.Lopes, R.Stoop,NeuralNetworks66,107(2015). F. A. S.Ferrari, F. Gomez, T. Lorimer, R.L.Viana, R.Stoop,N.J.Phys. 1 , FranciscoJ.Sevilla Ricardo L.Viana 2 17, 055024(2015). 61 -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 62

Phase-shielding soliton in degenerate optical parametric oscillators

Mónica García Ñustes1, Marcel G. Clerc2, Saliya Coulibaly3, Yair Zárate4

1 Instituto de Física, Pontificia Universidad Católica de Valparaíso, Avenida Brasil, Valparaíso, Chile 2 Departamento de Física, FCFM, Universidad de Chile, Santiago, Chile 3 PhLAM, CNRS UMR 8523, Université des Sciences et Technologies de Lille, Villeneuve d’Ascq, France 4 Nonlinear Physics Center, RSPE, Australian National University, Canberra, Australia

Localized structures in optics have attracted attention for their potential applications in telecom- munications and information storage. In this talk, localized structures with non-uniform phase structure in the degenerate optical parametrical oscillator will be shown. Dissipative solitons with non-uniform phase structure in parametrically driven systems have already been reported. Such structure surrounds the soliton, shielding it. Notwithstanding, the effects of higher order terms can modify dramatically the final con figuration of the phase. In particular, we will show that the nonlinear saturation present in this physical system is responsible for a relaxation dynamics and the appearance of a unique symmetry in the phase configuration.

Random walk model of a subdiffusion-reaction process

Tadeusz Kosztolowicz1, Katarzyna D. Lewandowska2

1 Institute of Physics, Jan Kochanowski University, Kielce, Poland 2 Department of Radiological Informatics and Statistics, Medical University of Gdansk, Gdansk, Poland

We present a Cattaneo-type nonlinear subdiffusion-reaction equation that describes persistent subdiffusive random walks in a system with chemical reactions [1]. We base the method considered in this contribution on a random walk model in a system with both discrete time and discrete space variables. Then the system with discrete variables is transformed into a system with both continuous variables [2,3]. The considered model, which assumes a correlation between successive steps of particles, provides hyperbolic normal diffusion or fractional subdiffusion equations. Persistent random walk is a process with memory as well as subdiffusion. The subdiffusive memory effect is long and vanishes in the case of normal diffusion. The persistent random walk memory effect, which arises from the correlation of the successive random walker’s steps, is relatively short. The considerations presented in this contribution show that this effect changes the effective subdiffusion coefficient and provides new terms in the subdiffusion-reaction equation, which can change the dynamic of the process.

[1] T. Kosztolowicz, Phys. Rev. E 90, 042151 (2014). [2] T. Kosztolowicz, K. D. Lewandowska, Phys. Rev. E 90, 032136 (2014). [3] T. Kosztolowicz, Phys. Rev. E 91, 022102 (2015). phenomena isresponsible forthedistinctwavefunctiondynamics in linearandsquarelattices. of the transition. We unveil that instability andself-trapping the interplay betweenmodulational in thevicinity the exponential increaseofperturbations well asthecharacteristic timegoverning in bothlattices,as instability strengths formodulational compute thecriticalnonlinear analytically patterns. Wecomplex breathing dynamics develops forwhichthewavefunction linear chains regime in distributions.Ontheotherhand,thereisanintermediate with stationaryprobability solutions localized of asymptotically and theregime the regimeofstableuniformwavefunctions 1/L inlinearchains.Insquarelattices,thereis a directtransitionbetween as decays it lattices, square in finite remains occurs instability modulational which above coupling nonlinear critical the while that, show We lattices. square and chains linear finite in equation Schrödinger linear Weby thediscretenon- governed of uniform wavepackets instability investigatethemodulational 3 2 1 Rodrigo P. A. Lima nonlinear discrete lattices Interplay between modulationalinstabilityandself-trapping in they interact. and thusdifferson theotherhand,isheight-independent, fromthatoftheparticleswithwhich temperature, kinetic disks’ the height; with vary to found indeed is particles the of temperature the kinetic ensemble, force. Inthemicrocanonical to aconstantexternal particles aresubjected simple mechanicalmodel:a Lorentz Gas where particles andspinningdisksinteract and the different,are generally at thesameheight. even a by studying in detail These factsareshown is influenced by the field while the other is not, we find that the two species’ kinetic temperatures creases with a gradient of order 1/N. Even more,if we haveamixtureof two species,onewhich particles affected by the field is not constant with height, but that rather, generally speaking, it de- tem is small. Weensemble thekinetictemperatureof showherethatthe in themicrocanonical sys- the when even height, of independent is temperature kinetic the ii) and profile density the for formula barometric a obeys i) system the ensemble canonical the in known, well is field. As We the consider statistical mechanicsof a small gaseoussystem subject to a constantexternal Instituto deCienciasFísicas,UniversidadNacional Autónoma deMéxico,MéxicoD.F., Mexico François Leyvraz,HernánLarralde systems inanexternal field Temperature gradientsinequilibrium:smallmicrocanonical Instituto deFísica,UniversidadeFederal Alagoas, Maceió, AL, Brazil Instituto FederaldeEducação,Ciênciae Tecnologia de Alagoas, Satuba AL, Brazil de GISC andGFTC,InstitutodeFísica,UniversidadeFederal Alagoas, Maceió, AL, Brazil 1 , Valdemir L.ChavesFilho , AlbertoSalazar 2 , MarceloL.Lyra 3 63

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 64

Counter-ion condensation around a charged disk: beyond the mean-field regime

Juan Pablo Mallarino1, Gabriel Téllez2

1 Facultad de Ciencias - Laboratorio Computacional HPC, Universidad de los Andes, Bogotá, Colombia 2 Departamento de Física, Universidad de los Andes, Bogotá, Colombia

We present an analysis of the condensation phenomenon of counter-ions around a charged disk. The model under consideration is a two-dimensional (2D) system formed by an impenetrable disk of charge Q1 surrounded by ions of charge q dispersed freely in a larger disk with external charged boundary Q2, at thermal equilibrium at a temperature T. In mean field, it is known that a disk with a dimensionless charge (qQ1/(2kT) ) inferior to unity is unable to bind counter-ions. When the charge is above unity, it attracts an ion cloud in such a way that it neutralizes partially the disk so that the effective dimensionless charge of the disk and the cloud is unity. We explore the faith of this counter-ion condensation beyond the mean field regime for large values of the Coulomb coupling. In particular, for some special values of the coupling, exact analytical results can be obtained for the system, which give an interesting insight on the condensation phenomenon.

Connector links support functional centrality distribution in brain hemispheres

J. H. Martínez1, J. M. Buldú2, D. Papo3, J. M. Pastor4, M. Chávez5, F. de Vico Fallani6

1 Modeling and Simulation Laboratory, Universidad del Rosario de Colombia, Bogotá, Colombia, Complex Sys- tems Group, Technical University of Madrid, Madrid, Spain 2 Complex Systems Group, Universidad Rey Juan Carlos, Madrid, Spain, Center for Biomedical Technology, Ma- drid, Spain 3 Center for Biomedical Technology, Madrid, Spain 4 Complex Systems Group, Technical University of Madrid, Madrid, Spain 5 CNRS, UMR 7225, Hôpital Pitié-Salpêtrière, Paris, France 6 INRIA and Institut du Cerveau et de la Moelle Epinière, Paris, France

In the last decade, complex networks theory has led to a paradigm shift in the neuroscience as a powerful tool to characterize brain organization underlying cognitive processes and diseases [1]. The fact that brain networks are spatially embedded and each brain node has a precise spatial position results in useful information that it is not always accessible in other kinds of real networks. In particular, the human brain consists of two large modules (i.e. the hemispheres), which usually exhibit different but complementary functions. To better understand the role of the functional interaction between the brain hemispheres, we adopted a network approach aimed to evaluate if and to what extent they engage a competitive behavior in terms of centrality distribu- reassuring. differentialconstructive to alternative network issimilar Also, thereduced equation with networkreduction basedonattractor landscape argumentsandcorrelationcalculations is criticality aswellnon-chaoticity, we reduce the networkandidentifymodules. The comparison coexist. Furthermore,based on operates atacriticalregime, whererobustnessandevolvability dynamics network the that show we Here [3,4]. chemotaxis and action drug membrane, gellum fla- the of electrophysiology the of understanding better a to leading experimentally confirmed subsequently were from themodel predictions [2]. Several modify spermnavigation oscillations tions in the flagella of sea urchin sperms, triggered by chemicals surrounding the oocyte. These G. Martínez-Mekler Is fertilization critical? [2] J. Aguirre, D.PapoandJ.M.Buldú,NaturePhysics [1] F. DeVico Fallani,J.Richiardi,M.Chávez,S. Achard, Trans. R.Soc.B troduced a logical regulatory network for the signaling pathway of [Ca of pathway signaling the for network regulatory logical a troduced in- we [1] work previous In systems. living of processes fundamental the of one is Fertilization 4 3 2 1 eased brainnetworks. mechanisms inhealthyanddis- spheres that can beusedto better understandorganizational These resultsopenthewaytoof a newcharacterizationtheinteractionsbetweentwohemi- asymmetry,are characterizedbydynamical hemispheres andbydifferentpatterns. connection links. Ourresultsshowthat, even atrest, of theinter-hemispheric to thedistribution according parameter acompetition through quantified The extent to its which eachhemispheremaximized centrality duringthe rewiring processwas ulate theircentralitythrougha rewiring mechanisminthe connection betweenhemispheres. Wetheir distribution. analyzed and hemispheres) (between both networkstomod- thenallowed frequency bands. We differentiated betweenintra-links(insideeachhemisphere)andinter-links in therightone)theta(4-7Hz),alpha(8-13beta(14-29Hz)andgamma(30-40 to construct and 24 the functionallinksbetween48corticalregions(24inleft hemisphere (EEG). was recordedbymeansof electroencephalography The imaginarycoherencewasused matrix [2], which is known as the eigenvector centrality. Resting connection brain the activity of of eigenvalue 54 largest healthy the adults to associated eigenvector the of means by quantified centrality oftheirnodes.Centrality maximize vie to which right (R)hemispheres, i.e., theleft(L)and of twosub-networks, system composed a as brain the Specifically, studied solution. trade-off we a to or,close conversely,tion are they jandro Aguado jandro Instituto deBiotecnología,UniversidadNacional Autónoma deMéxico,Cuernavaca,Mexico Instituto deCienciasFísicas,UniversidadNacional Autónoma deMéxico,Cuernavaca,Mexico Instituto NacionaldeMedicinaGenómica co, Cuernavaca,Mexico UniversidadNacional Instituto deCienciasFísicas,CentrolaComplejidad, Autónoma deMéxi 3 , AlbertoDarszon 1 , JesúsEspinal-Enríquez 4 Dfeet eiig taeis ol b defined be could strategies rewiring Different Ω. , i.e., the importance of thenetworknodes,was C, i.e.,theimportance 9, 230(2013). 2 Daniel A. Priego-Espinosa A. , Daniel 369, 20130521(2014). 2+ ] concentration oscilla concentration ] 3 , Ale- 65 - -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 66 model we have developed. Our findings are relevant to the discussion of the role of criticality in essential biological processes and may be of significance to evolution.

[1] J. Espinal, M. Aldana, A. Guerrero, C. D. Wood, A. Darszon, G. Martínez-Mekler, PloS ONE 6, e22619 (2011). [2] A. Guerrero., T. Nishigaki, J. Carneiro, Tatsu Yoshiro, C. D. Wood, A. Darszon, Dev. Biol. 344, 52 (2010). [3] A. Guerrero, J. Espinal, C. D. Wood, J. M. Rendon, J. Carneiro, G. Martínez-Mekler, A. Darszon, J. Cell Sci- ence 126, 1477 (2013). [4] J. Espinal, A. Darszon, C. D. Wood, A. Guerrero, G. Martínez-Mekler, PLoS ONE 9, e104451 (2014).

Simulation of the electrical properties of the neuron models, Morris- Lecar, Hodgkin-Huxley, and Hindmarsh-Rose, through the study of synchronization with the RCLSJ circuit

Fernando Naranjo Mayorga1, Oscar Fabián Téquita Vargas2, José Antonio Diáz Merchán1

1 Universidad Pedagógica y Tecnológica de Colombia, Tunja, Colombia 2 Universidad de Boyacá, Tunja, Colombia

We present the complete and generalized synchronization of the action potential time series of some neuron models with RCL-shunted Josephson junction (RCLSJ circuit). In addition to synchronization, the main characteristics of the neuron are reproduced, such as; the action potential, refractory period, and firing threshold. The synchronization is developed using the adaptive control scheme via Lyapunov functions, which allows to calculate a controlling function for every model to synchronize and enables the RCLSJ circuit to reproduce the electric characteristics of the neuron. The results of synchronization allow us to show some of the dynamic properties of each neuron model and provide information to build neural networks with Josephson junction circuits.

Handwritten signature verification using time causal information theory quantifiers

Raydonal Ospina1, Alejandro C. Frery2, Osvaldo A. Rosso3

1 Departamento de Estatística, Universidade Federal de Pernambuco, Recife, PE, and Instituto de Computação, Universidade Federal de Alagoas, Maceió, AL, Brazil 2 Instituto de Computação, Universidade Federal de Alagoas, Maceió, AL, Brazil 3 Instituto Tecnológico de Buenos Aires, Buenos Aires, Argentina and Departamento de Física, UFAL, Maceió, AL, Brazil

Handwritten signature verification is a behavioral biometric modality that relies on a rapid personal gesture. Each hand-drawn signature has a level of complexity which depends on the the deterministiclimit. case, whichconvergesto the invariantmeasure of the mapin process intheone-dimensional attractors. Wedistribution of the probability thepropertiesof the quasi-stationary alsoexplore the effectsto examine order in and twodimensions, one on differentnoise ofintrinsic typesof functions. autocorrelation spectrum and as wellitspower is testedin scheme The proposed or point fixed a around fluctuations of distribution the obtain to the (d by 0and bounded to theregion to mapswhosestatespacecorresponds d >1,thisprocedurecanbegeneralized of thestatespace.Indimension stem fromthediscreteness and in origin are intrinsic tuations way,this In processes. tinuous-time fluc- the where map, a of version stochastic a construct we equation, whichareroutinelyemployedforcon- and theLangevin the Fokker-Planckequation for equation the of man-Kolmogorov discrete-timeMarkovprocess,wederivethe analogues from theChap distribution; of abinomial by means model a Markovchain by constructing begin limit givenbyamapoftheunitinterval.Wekovian anddiscreteintime,withadeterministic We present atheoryto study stochasticprocesses with a bounded state space whichareMar- 3 2 1 César Parra-Rojas Mesoscopic description of stochastic processes indiscrete time be veryattractiveintermsofcomputationalrequirements. errors, andisshownto base. Ourresultsarecompetitiveintermsofacceptanceandrejection system, whose performanceisassessedoverthewellknownMCTY 100 signaturedata parametric descriptor. These measures are used as the input features of a signature verification statistical complexityandFisherinformationmeasure),onthe Bandt-Pompe non- generalized coordinates (x,y process: signing the during points sampled of sequence a namely signatures, line” of the signing process. Such dynamical information is captured by a digitizer and generates “on- outcome the just not information, dynamic signature’s the of introduction the allows verification is theonethathaswidestsocialacceptanceforidentityauthentication.Onlinesignature author. Among allthebiometrictraits that thesignature can becategorizedaspurebehavioral, Università degli Studi di Firenze and INFN, Florence, Italy Università degliStudidiFirenzeandINFN,Florence,Italy Imperial CollegeLondon,UK The UniversityofManchester, Manchester, UK x and y at time t. We computeinformation-theoreticmeasures(Shannonentropy, 1 , JosephD.Challenger – 1)-simplex. Using a linear noise approximation approach allows us allows approach approximation a linearnoise Using 1)-simplex. – 2 , DuccioFanelli -cycle of the deterministic map, of thedeterministic n-cycle 3 , AlanJ.McKane )( t ), the ), 1 67 -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 68

Rheology of active granular matter

Anton Peshkov1,2, Bruno Andreotti2, Philippe Claudin2, Eric Clement2

1Departamento de Física, Universidad de Chile, Santiago, Chile 2Laboratoire de Physique et Mécanique des Milieux Hétérogènes, ESPCI, Paris, France

Numerous experimental studies of collectively moving bacteria suspensions have shown a drastic viscosity reduction with an increasing level of activity. Here we investigate the rheology of a simple system of active granular particles, by means of numerical simulations. In our model, spherical particles are submitted to a constant active force in the direction of their orientation. They are immersed in a viscous fluid from which they feel a drag force. The whole system grain plus fluid is subjected to a constant shear stress and normal pressure. We study the frictional law of the system as a function of dimensionless viscous number J and active number A.

Different regimes of viscosity reduction are observed as a function of A; a constant viscosity for low values of A, a linear decrease of viscosity for intermediate values of A and a stagnation at high values of activity. A drastic reduction of viscosity (down to zero) is observed when in comparison to the case of a passive granular suspension. Some possible explanations for the different observed regimes are presented.

Rank diversity of languages: Generic behavior in computational linguistics

Carlos Pineda, Germinal Cocho, Carlos Gershenson, S. Sánchez, Jorge Flores

Instituto de Física, Universidad Nacional Autónoma de México, México D.F., Mexico

Statistical studies of languages have focused on the rank-frequency distribution of words. In- stead, we introduce here a measure of how word ranks change in time and call this distribution rank diversity. We calculate this diversity for books published in six European languages since 1800, and find that it follows a universal log-normal distribution. Based on the mean and standard deviations associated with the log-normal distribution, we define three different word regimes of languages: “heads” consist of words which almost do not change their rank in time, “bodies” are words of general use, while “tails” are comprised by context-specific words and vary their rank considerably in time. The heads and bodies reflect the size of language cores iden- tified by linguists for basic communication. We propose a Gaussian random walk model which reproduces the rank variation of words in time and thus the diversity. Rank diversity of words can be understood as the result of random variations in rank, where the size of the variation depends on the rank itself. We find that the core size is similar for all languages studied. distributed in equally spaced (by ∆v (by spaced equally in distributed rections. For particles with initial positions uniformly distributed inS transition occurs. no phase potential, of temperature;(ii)forarepulsive value for agiven phase a homogeneous clustered phaseto an attractivepotential,aphasetransitionoccurs fromaninhomogeneous, known as Mean Field(HMF) the Hamiltonian model. This model hastwo behaviours, viz. (i) for Wecommonly to theHamiltonian according studythedynamicsofanN-particlesystemevolving 3 2 1 Bruno Vieira Ribeiro Field model Brownian corrections to particlemotion intheHamiltonian Mean function oftheenergyfluxesandfluctuationrelationsinsystemsthiskind. deviation of thelarge the shape analyze also we hand, in concept With thatreconciling noise. of the by then-thordercumulant that isrepresented scale the typicalenergy characterizes which cal propertiesof non-standard reservoirs,weintroducethe concept of temperature of can emerge. of thermodynamics with theanalyti Aiming to reconcilethesuchnaturalprinciples nature ofashotnoisereservoirinthelimelight.Inthat case, speciousviolationsoftheprinciples singular the puts nonlinearities of introduction the temperature, canonical a defining of means cases by linear systemsintostandard reservoir to mapathermal a goodextent,itispossible the system-reservoirinteraction.If, for mimicking to terms intoconsideration shot-noise sonian Gaussian. As amatter of fact, most of those systems are verywelldescribedbytakingPois- but anything to be ought equations in thedynamical nature ofthenoise the stochastic which of as thehydrolysis such reactions chemical by exergonic motors powered molecular ATP—for there is an importantset go from of diffusiveproblems—which motioninlittledensemediato noises, by Gaussian are described description the contextofaLangevin that within reservoirs to thermal is related statistical mechanics in nonequilibrium stake ofproblems a huge Although 2 1 Sílvio M.DuarteQueirós What isatemperature of n-thorder? Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, RJ,Brazil Pontifical CatholicUniversityofRiodeJaneiro, Brazil Centro BrasileirodePesquisasFísicas,RioJaneiro,RJ, International Center for Condensed Matter Physics, Universidade deBrasília,DF,International CenterforCondensedMatterPhysics,Universidade Brazil Marseille, France Equipe turbulenceplasma,case321,PIIM,UMR7345 CNRS, Aix-Marseille université,campusSaint-Jérôme, Instituto FederaldeEducação,Ciênciae Tecnologia Câmpus Valparaíso, deGoiás, GO,Brazil In the second case, particle motion may be approximated by ballistic motion withsmallcor- by ballistic In thesecondcase,particle motionmaybeapproximated 1 , Yves Elskens 1 , Welles A. M.Morgado 0 ) beamscontainingone particleeach,i.e., 2 Marco Antonio Amato , MarcoAntonio 2 2π , while initialvelocitiesare 3 v j 0 ~ (j/N – 1/2) – (j/N ~ n-th order 69 -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 70

∆v0 for the initial velocity of the j-th particle, it is shown that corrections to the ballistic velocities are in the form of independent Brownian noises. Moreover, we also estimate a time validity for this approximation. Molecular dynamics simulations of the HMF model with the proposed “particles in monokinetic beams” initial conditions are presented to confirm our preliminary theoretical results.

For the attractive case, we model the system, in presence of the ordered phase, as composed of two sets of particles: Np passing particles move according to a ballistic motion corrected by the presence of Nc cluster particles, that lay inside the cat’s eye and are assumed to have fixed positions. Thus, we focus on the dynamics of the passing particles with the same strategy as above. The presence of cluster particles, however, no longer allows us to admit small corrections to ballistic motion. Preliminary numerical simulations for this case show that these corrections diverge from a Brownian noise in very short times.

We are still carrying out the calculations for the attractive case. As a first-order correction to the velocities, we expect to obtain Brownian noise and non-negligible corrections for higher orders.

Effects of translational coupling on dissipative localized states

Francisco del Campo1, Florence Haudin2, René G. Rojas3, Umberto Bortolozzo2, Marcel G. Clerc1, Stefania Residori2

1 Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile 2 Institut Nonlinéaire de Nice, Université de Nice-Sophia Antipolis, Nice, France 3 Instituto de Física, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile

Nonequilibrium localized states under the influence of translational coupling are studied experimentally and theoretically. We show that localized structures are deformed and advected in the direction of the coupling, thus undergoing different instabilities. Experimentally, localized structures are obtained in a light valve with optical feedback. By introducing a tilt of one mirror in the feedback loop, localized structures acquire a translational coupling. To understand the phenomenon in a universal framework we consider a prototypical model of localized states with translational coupling in one and two spatial dimensions. The model allows us to analytically characterize the propagation speed and the deformation exhibited by the localized state profiles as well as to figure out different mechanisms of destabilization of these dissipative structures. The results are in good qualitative agreement with the experimental and numerical observations. below acriticalReynoldsnumberandorbits around thepredictedfixedpoint. unstable becomes point fixed the that show also we But experiment. and theory between cord the possibility of a range of fixed points. Our results support the latter with good quantitative ac- suggest spheres sized finite with calculations whereas flow the of centreline the on point fixed horizontal drum filled with viscous fluid. Stokesian dynamics calculations indicate a single stable Weinto themotionof light spheresinarotating investigations presenttheresultsof experimental The UniversityofManchester, Manchester, UK Tania Sauma, The dynamicsof alightparticleinStokes flow data manipulation. with consistent be could that crisis, financial last the of time the around especially detected, is of thetimeseries. stochastic dynamics in theintrinsic changes in theLibor behavior Anomalous in timeseries.Wechaotic regimes ent stochasticand to assess windows temporal usesliding plane. causality the complexity-entropy literature: to classifydifferis able This representation - financial the in tool statistical pioneering a using out carried is analysis The 2014. to 1999 riod This paperanalyzesseveralinterestratestimeseriesfromtheUnitedKingdomduringpe- 3 2 1 Rosso A. Osvaldo approach The (in)visiblehandintheLibormarket: aninformationtheory Martínez tina Instituto deInvestigacionesEconómicasySocialesdelSur, UniversidadNacionaldelSur, BahíaBlanca, Argen- Department ofBusiness,UniversitatRoviraiVirgili, Spain Reus, Brazil Instituto Tecnológico deBuenos Aires (ITBA),Buenos Aires, Argentina, Departamento deFísica,UFAL, Maceió, 3 Thomas Mullin 1 , AurelioFernandezBariviera 2 , M.BelénGuercio 3 , LisanaB. 71

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 72

Bacterial motion in confined geometries

Rodrigo Soto

Physics Department. Universidad de Chile, Santiago, Chile

Bacteria are microorganisms that swim at low Reynolds numbers by the propulsion of rotary flagella. Their motion, described by the Stokes equation for viscous fluids, is well understood in unconfined conditions. Bacteria, likeE. coli can be modeled as force dipoles pushing the fluid on the head and tail. However, it is known that bacteria are hydrodynamically attracted to surfaces making the study under these conditions relevant. In this talk I will present a simple physical model for swimmers. It models E. coli as two spheres joined by a rod. The finite size of the swim- mer accounts for features found experimentally, namely the tendency to approach the surface at a finite speed and the ulterior swim in circles. When an external flow is imposed, the coupling with surface gets relevant because regions of high shears develop. The shear profile generates rotation on the swimmers that compete or enhance the attraction to surfaces. It is found that the combined result is an enhanced probability to be attracted to surfaces swimming upstream. However, increasing the flow even further swimmers detach in a process that corresponds to a saddle point bifurcation. Finally, on the long term, under external flows in a Couette flow, swimmers present a longitudinal diffusion similar to Taylor dispersion, but where the microscopic diffusion is replaced by jump processes between Jeffery orbits. Different regimes are obtained depending if the free flow or the Jeffery orbits dominate.

A Brownian dynamics model relating the self-assembly of stiff π-stacking polymers to the rheology of a complex fluid

G. Villalobos1, W. J. Briels2

1 Facultad de Ciencias Naturales e Ingeniería, Universidad de Bogotá Jorge Tadeo Lozano, Bogotá, Colombia 2 Computational Biophysics, University of Twente, Enschede, The Netherlands

We have developed a brownian dynamics model aimed to study the self-assembly process of long slender laths who interact mostly in the direction perpendicular to their areas, and named it the Brownian Orientational Lath moDel (BOLd). It is characterized by a potential energy that depends both on the angle between orientation vectors, along the long axis of the laths, as well as on the vectors normal to the plane of the laths, and which has only one energetic parameter. The emergent self-assembly process generates long ordered aggregates of laths, called whis- kers in the literature. Our calculations show the path for stress auto-correlation development and reveal its relationship with the whisker formation. An application of this model is the study of the aggregation of P3HT molecules due to the aromatic interaction, a process that is of fundamental importance in the production of organic solar cells. [2] [1] n the at that find we [2], function Wigner the of propagator the of terms in space, phase in mation approxi with asemiclassical the initialstate.exactnumericalquantumcalculations Comparing a nonlinearmediumandissimilartothesquareofharmonicoscillatorHamiltonian. Kerr Hamiltonian describes the self-interaction of the quantum electromagnetic quantum field in We dynamicsgeneratedbytheKerrmodel. analysis ofthequantum presentaphase-space The Departamento deFísica,UniversidadNacionalColombia,Bogotá,Colombia Yonatan Zuleta,ThomasDittrich Phase-space analysis of revivals intheKerr model pairs oftheclassicalKerrHamiltonian. trajectory of thecontributing of theinitialdeltafunctionintermstopology replicas multiple these to explain how a hypothesis present we account, into trajectories of classical tor frompairs tions alongtheclassicaltrajectory. Taking the construction of the semiclassical Wignerpropaga -th quantum revival, the propagator in phase space collapses to agroupof2n in phasespacecollapses quantumrevival,thepropagator -th T. Dittrich,E. A. Gómez,L. A. Pachón,J.Chem.Phys.132,214102(2010) G. J.Milburn,Phys.Rev. A 33 , 674(1986). The most striking feature of the quantumdynamicsof this modelaretheperiodicrevivalsof –1 deltafunc- –1 73 - -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena

Posters

Alejandro Aguado Alejandro entropy Study of heartrate –bloodpressure relations interms of transfer multipolar response. external field, which would be expected if there is liquid water under Europa’s ice surface, has a of atime-variable layer inthepresence ocean shows thatonespherical studies (A.Peña,2013) recent but dipolar, is field induced the that suggests 2000), from M. Kivelson (Kivelson et al. model The field. magnetic time-variable a by produced field induced an to corresponds which a magnetic field that does not appear to have an internal origin. Nevertheless, it has a signature liquid waterunderthismoon’s icesurface. of possibility the exploring for relevant is study This fields. current plasma neighboring its and Europa’sfield between magnetic coupling induced magnetic of study a present we work, this In Departamento deGeociencias,Universidadlos Andes, Bogotá,Colombia Jeffersson Agudelo, surrounding plasmacurrents field Study of magnetic couplingbetween Europa’s inducedfield and [1] face (lying upward) isinprogress. clinostatism in participants for work this of extension The . [1] work previous in ed that BPeffector istheregulatoryvariable,whileHRsubordinate as wassuggest- variable from BPis higher transfer entropy sense. toHRthanintheopposite an indication This provides group [1], of healthy young participants in orthostatism (active standing) conditions. We find that BPbetween research by our undertaken studies in clinical determined time series, HR and determined terms oftransferentropy in this relation into look we Here research. medical intense (BP) andheartrate(HR)ismatterof pressure blood between of therelation The understanding 4 3 2 1 tavo Martínez-Mekler Instituto deCienciasFísicas,UniversidadNacional Autónoma deMéxico,Cuernavaca,Mexico Facultad deCiencias,UniversidadNacional México,MéxicoD.F.,Autónoma de Mexico D.F.,Instituto NacionaldeCardiologíaIgnacioChávez,México Mexico Universidad Mexico Autónoma delEstadodeMorelos,Cuernavaca, P. Martínez-García,C.Lerma,O.Infante, Mex. Arch. Cardiol. The magnetometer measurements recovered from the Galileo mission orbiting Europa show Europa orbiting mission from theGalileo The magnetometermeasurementsrecovered 1 , ClaudiaLerma Natalia Gómez 4 2 , HortensiaGonzález 82, (2012). 3 , OscarInfante 2 ,

Gus- 77

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 78

In agreement with these findings, we explore coupling the magnetic field from plasma currents neighboring Europa to the previous model using the program Magnetic Inner Core (MagIC). We vary the adimensional numbers magnetic Prandtl Pm and Ekman Ek, to obtain the coupled behavior of both these magnetic fields and finally contrast the results obtained with the Galileo data.

Soliton-like structures in models of nerve signals

Maximo Aguero1, Ma. De Loudes Najera Lopez2

1 Facultad de Ciencias, Universidad Autónoma del Estado de México, México D.F., Mexico 2 Plantel Nezahualcoyotl, Universidad Autónoma del Estado de México, México D.F., Mexico

After some reduction procedure made on the nonlinear evolution equation for nerve pulses, based on thermodynamic principles of zero transfer of energy to the media, new classical and non-classical traveling solutions have been obtained. We have studied this model for particular values in the parameter space and obtained both pedestal solitons on the condensate and bubble like solutions as typical non-topological representative solutions. The analysis of the properties of the solutions provides us with available permitted velocities and the prediction of the constant density value of the background at long distances far from the excited zone in the nerve. For trivial boundary condition the non-classical structures named compactons were obtained. These solutions, due to their robust configuration, could be considered in some sense a more realistic type of nonlinear information carriers. The last solutions do not have tails and as adiabatic waves could propagate along the nerve with constant velocity that could be equal, smaller or higher than the sound velocity.

A dynamical analysis of allele frequencies in populations evolving under assortative mating and mutations

David Marcelo Schneider1, Eduardo do Carmo2, Marcus A. M. de Aguiar1

1 Instituto de Física ‘Gleb Wataghin’, Universidade Estadual de Campinas, Campinas, SP, Brazil 2 Universidade Federal da Integração Latino Americana, Foz do Iguaçu, PR, Brazil

We study the evolution of allele frequencies for infinitely large populations subjected to mutations and assortative mating. Haploid individuals are described by two biallelic genes, and assortativity is introduced by preventing mating between individuals whose alleles differ at both loci. In the absence of mutations, evolution leads to the disappearance of one of the alleles. However, a particular combination of the allele frequencies at the two loci is maintained constant. We show that this combination remains constant even when mutations are present, revealing the robustness of the epistatic correlation introduced by the non-random mating mechanism. We obtain of elements chosen at random at every at random chosen acts on afractionpofelements driving an external interaction, global field acts with a probability (1 – (1 probability a with acts field a probability acts with driving anexternal interactions, global neous is externalandinternal.Inhomoge interactions, whoseorigin global neous orheterogeneous homoge systems possessing are studied in amodelofdynamical phenomena Synchronization 2 1 Orlando Álvarez-Llamoza Inner synchronization of chaos insystems withdualinteractions troscopy, andnonlinearoptics. for processes interaction training studentsinatomphysics,coherentlight-atominteraction,highresolutionatomic spec- rubidium-atom-field for components opto-electronic with equipped filled withrubidiumatomsatroomtemperature. source arealsopresentedthroughdirectandsaturatedabsorptionspectroscopyina vapor cell emission of operation andnarrow-bandthe nm pump wavelength. Singlemodecontinuum-wave diode lasertunedto atoms at795 the D1lineof and current-controlled rubidium ture-stabilized coherent violetlight. The pumplaserbeamisalow-cost,low-power, free running,tempera- a fewtenthmilliwattsof power of the pumpbeamweobtainaround18microwattof power of 54.5 around crystal the of temperature conversion efficiency maximum a For presented. and °C crystaland ofthe are also beam of thepump power the square versus conversion power harmonic the second thetemperature of afunction as conversion efficiency doubling frequency poled potassiumtitanylphosphate(PPKTP) crystal. 397.5 nmwavelengthinaperiodically The In this work wepresenta simple experimentof a single-pass secondharmonicgenerationat Departamento deFísica,FacultadCienciasFísicasyMatemáticas,UniversidadConcepción,Chile González José Vargas Roco with low-power diodelasertunedto theD1lineof rubidiumatoms Violet lightgenerationat397.5 nmwavelength inaPPKTPcrystal dynamics onthebasisofabifurcationanalysis. of the a description of themutationrateandprovide for arbitraryvalues solutions the equilibrium Universidad PolitécnicadeSinaloa,Mazatlán,Mexico Universidad CatólicadeCuenca,Ecuador The present work can be used as a complementary undergraduate laboratory for those undergraduate The present work canbeusedasacomplementary , José Aguirre Gómez , SebastiánLavínVarela 1 , EulaliaVintimilla

), on all elements ofthesystem.Incareheterogeneous p), onallelements , JavierLeónSuazo 1 , MichaelCabrera in time, and an endogenous time, and p in 1 , JavierGutiérrez , EberOrozco 2 79 - -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 80 time, and an internal field acts on the another fraction (1 – p). Our results show that the presence of the autonomous global field in this systems induces synchronization among the elements in the system but not with the driving, which can not be called generalized synchronization because no functional relation exists between one element of the system and the driving. We call this inner synchronization. In addition to this, generalized and complete synchronization can also be observed in these systems. The synchronization behavior in the system with homogeneous global interactions can be inferred by considering the dynamics of a three-dimensional map. The synchronized states for these systems are characterized in their common parameter space.

Patterns in movie ratings

Marlon Ramos, Angelo Calvao, Celia Anteneodo

Departamento de Física, PUC-Rio, Rio de Janeiro, RJ, Brazil

Nowadays, users and consumers can review and rate products through online services, which provide huge databases that can be used to explore people’s preferences and unveil behavioral patterns. In this work, we aim to explore patterns in movie rating behavior. As a source of information on the distribution of people’s preferences, we consider IMDb (Internet Movie Database), a highly visited site worldwide. The number of votes (where a vote consists of assigning a star rating) rather than, for example, the total number of movie admissions, is a suitable way to measure the popularity of a given movie. We find that the distribution of votes presents scale-free behavior over several orders of magnitude, with exponent very close to –3/2 and exponential cutoff. It is remarkable that this pattern emerges independently of movie attributes such as average rating, age and genre, with the exception of a few genres and of high-budget films. These results point to a very general underlying mechanism for the propagation of adoptions across potential audiences that is independent of the intrinsic features of a movie and that can be understood through a simple spreading model of avalanche dynamics.

Scaling laws of suicide rates around the world: a gender approach

Fernando J. Antonio1, Andreia S. Itami2, Renio S. Mendes2

1 Departamento Acadêmico de Ciências da Natureza, Universidade Tecnológica Federal do Paraná, Cornélio Procópio, PR, Brazil 2 Departamento de Física, Universidade Estadual de Maringá, Maringá, PR, Brazil

Suicide is ranked among the top causes of death for individuals of all ages worldwide by World Health Organization. In this work, we analyze how the suicide epidemics is spread over the data, itwaspossibletoassessthemethodat different stages. networks thatdiffersof simulated fromrandomnetworkstructure).Bystudying the behavior features ofregular (therearedistributional associated withtheeigenvalues statistics distribution of verification 3) eigenvalues, of spacing the finding 2) matrix, adjacency the from obtained ues gene coexpressionnetworks. of theeigenval The methodconsistsofthreesteps:1)unfolding on randommatrix theory in orderto suggest ajustmentsandimprovementsto the construction of based method detection threshold efficiency the evaluate to is study this of aim The networks. inthisworktoaddresstheproblem oftheconstructiongenecoexpression was implemented Matrix other areas(Sarika,Random Networks, 2007). Analysis ofComplex This methodology to applied gradually systems, andhasbeen in chaoticquantum particles between interaction of patterns of definition in 1967) Physics, in Matrices Random (Wigner, physics of field the in proposed first was which (RMT), theory matrix random by given approach the located is one, real and network random between on acomparison based of methodologies, the lastgroup based ontheseparationofnetworkintwoparts, one randompartandothersystematic. In others some and similarity, of measures on significance statistical of tests with related others odologies, some linked to arbitrary criteria that depend on specific knowledge of the researcher, meth- choice, therehavebeenseveral thenetwork.Forthreshold within as realinteractions tween unitsthroughsimilaritymatricesandthethresholdat which suchsimilaritiescanbecome differentunder other each be- with teract associations of definition the both on based is criteria, The constructionof networks, which represent dynamicalsystems constituted byunitsthat in- Departamento deEstadística,UniversidadNacionalColombia,Bogotá,Colombia Laura NoheliaBaracaldo, theory Setting of similaritymatricesthreshold basedonrandommatrix connected tothepopulationsizeofcountrieslocally, butthisbehaviorisbrokenglobally. are rates suicide that find we relation. last, scaling At a to leading results, the affect distribution how weevaluated Next suicide ratesamongmencorrelatewithwomenandhowthegeographical by gender. rates suicide the influence constraints geographical how the suicideratesamongmenandwomen. This approachwastweakedbyinvestigating globe at the level of countries. The first approach was to identify numerical results distinguishing Liliana LópezKlein 81 -

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Discreteness effects in the FKPP equation

Karin Alfaro Bittner1, Marcel G. Clerc2, Mónica García-Ñustes1, René G. Rojas1

1 Instituto de Física, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile 2 Universidad de Colo Colo, Santiago, Chile

In nature we can find many phenomena in which the principal mechanism of propagation are wave fronts, such as chemical signals, mechanical deformations, among others. We focus on the analysis of a special kind of wave front, which connects a stable and unstable state, the Fisher-Kolmogorov-Petrovskii-Piskunov reaction diffusion equation (FKPP equation), and the effects of the discretization in systems governed by this equation. We have found that both velocity behavior and the front shape are heavily dependent on the discretization of these systems.

Experimental determination of high-order bending elastic constants of lipid bilayers

Mauricio D. Carbajal-Tinoco, Liliana G. Toscano-Flores, Damián Jacinto-Méndez

Physics Department, Cinvestav-IPN, México D.F., Mexico

A method describing the formation of small lipid vesicles is presented here. Our method combines a general expression for the elastic free energy of the bilayer that depends on three bending elastic constants, together with a thermodynamic description of the molecular aggregation. Such bending elastic constants are obtained from an analysis of the size distribution of liposomes, which is determined from small-angle X-ray scattering experiments of vesicular suspensions made of different phophatidylcholine lipids.

Monte Carlo study of a single grain of the distribution of contact forces on a mono-dispersed granular material

Manuel Cárdenas-Barrantes, Jose Daniel Muñoz, William Oquendo

Simulación de Sistemas Físicos, Universidad Nacional de Colombia, Bogotá, Colombia

We develop a Monte Carlo method to sample the force network ensemble on a single grain which is part of a static granular system, and use this method to investigate the ensemble and the possibility to extrapolate these results to the whole system, as we actually found. We show that this ensemble of a single grain follows an equipartition theorem < p > = k’ \alpha–1, with < p found forthevolumeVofatessellationcellinEdwards’ volumeensemble. interactions. in allcases,thesamedistribution Also thepressureshowsak-gammadistribution or frictional gas) forsystemswitheitherfrictionless to theoneforanideal parallel dom (closely atom interacting with the field of thermal radiation in a cavity, described by the density operator. We ists chaosinthelatter case. Forthispurpose,weconsiderthenonlinear dynamicsofatwo-level ex- really there whether quantify we work this In states. thermal for dynamics” “chaotic and states several regimes:Rabi oscillations forinitialFockstates,collapsesand revivalsforinitialcoherent view, itsimportanceliesinthefact thatitisanalyticallysolvable.Itsdynamicalbehaviorpresents from atomic ions in radiofrequency traps to superconducting qubits. From the theoretical point of matter. Itsexperimental applicabilityhasbeendemonstratedinalargenumberofphysicalsystems, The Jaynes-Cummingsmodelistheparadigm offullyquantuminteractionbetweenradiationand Grupo deFísica Atómica yMolecular, Universidadde Antioquia, Medellín,Colombia Julieth Viviana CastañoPuerta, Chaos inthenonlinearJaynes-Cummings dynamics and quantitatively.are established,bothqualitatively are numericallysimulated,andconclusions realizations Several is proposed. technology of information inthearea of aProjectManagement risks, and possible interactions and decision making. Finally, as an example, a specific modeling unforeseeable and team, foreseeable the operational team and of themanagement dynamics mentation, obtaining a significant increase of success. In particular, it distinguishes between the are included. These hybridcomplextoolswillallowanapproachtothereality ofprojectimple complex networks,gametheory,dynamics, neuralnetworks,etc. adaptive theories, nonlinear... science, canbeapplied.In knownascomplexity these sciences, niques whicharenowadays finally,and, developed tech- and thought be can management project how shows modeling, ity successful projects.In that spirit, thispaper,and well-planned well-managed based oncomplex of failures. of the number to increase shiftisrequired or paradigm concept Therefore, anew are still valid and provide a good tool for monitoring. However, the figures show an alarming 70% linear techniques and execution.Itthattheso-called is considered century intermsofplanning Today,of thelast to theparadigm usesthesamemethodsascorrespond management project Universidad NacionaldeColombia,Manizales Luz StellaCardonaMesa, Project management through complex networks >, the average pressure on the grain, \alpha Gerard Olivar TostGerard Boris A. RodríguezRey –1 theangoricityandk’ the number of degrees of free- 83 - -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 84 assume that the atom is initially in the excited state and in resonance with the field. Under these conditions, a time series is obtained with high temporal resolution corresponding to the atomic inversion, since an observable of this type contains information about the dynamics of the system.

Under the paradigm of deterministic chaos we performed a time series analysis in phase space to determine the nonlinear dynamics of the system. According to the Takens theorem, we reconstruct the phase space using the well-known delay coordinates method. Converting scalar inputs of the time series to vectors in phase space, we obtain the system’s attractor, and more importantly some quantities that allow us to quantify the chaos in terms of the correlation dimension and Lyapunov exponents. Our main result is that the quantum dynamics in not chaotic but quasi-periodic.

Nonlinear skin effect simulation using a lattice-Boltzmann model for electrodynamics

César Castellanos, José Daniel Muñoz

Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia

Hereby we show the nonlinear skin effect in a material using the three-dimensional lattice-Boltz- mann method (LBM) developed by Mendoza and Muñoz (Phys. Rev. E 82, 056708 (2010)). We demonstrate that LBM for electrodynamics can be used to simulate the time evolution of an electromagnetic wave penetrating into a conducting medium. We investigate the case for plane and cylindrical electromagnetic waves. The skin effect predicts that the amplitude of the wave decrease exponentially as it penetrates the material. We compare the results with the theoretical solutions given by (Mayergoyz) scientific reports and the data obtained by Mendoza and Muñoz in their publications about the three-dimensional lattice Boltzmann model for electrodynamics.

Chimera-like states in an ensemble of oscillators under attractive and repulsive global coupling

Syamal Kumar Dana1, Arindam Mishra2, Chittaranjan Hens3, Prodyot Kumar Roy4, Mridul Bose2

1 CSIR-Indian Institute of Chemical Biology, Kolkata, India 2 Jadavpur University, Kolkata, India 3 Bar Ilan University, Ramat Gan, Israel 4 Presidency University, Kolkata, India

Chimera-like states are reported in an ensemble of oscillators under both attractive and repulsive mean-field type global coupling. Two types of chimera-like states emerge in a network of ic field confined to a compact region in space leads to irregular scattering andtriggersspinflips toirregular in spaceleads ic fieldconfinedtoa compact region scattering inthe regime of fast and strongdriving. A spin-orbit couplingthrougha kicked magnet- Wedriven studydirectedtransport of charge andintrinsicangularmomentum byperiodically 2 1 Thomas Dittrich Classical andquantumchaotic angular-momentum pumps Duffing, RösslerandLorenz. expected value. systems: The resultshavebeentestedwithfourwellknowndynamicalUeda, criteria that could helptodeterminecorrectlytheseparameterssothat the LLEisclose to the works, weherepresentthree previous Unlike trajectories. distance between time andtheinitial We estimationoftheLLEisbased on thesettingofrenormalization showthattheincorrect Lyapunovequations ofthesystem. exponentiscomputedfromthesolution of thevariational ettin nearby orbits.Inthispaper,by Ben- method introduced two-particle weshowthattheso-called ponent (LLE). of rate ofdivergence This quantityprovidesameasure ofthemeanexponential A general indicatorofthe presence of chaos inadynamicalsystem is thelargestLyapunov ex- dad delosLlanos,Villavicencio, Colombia Facultad deCienciasHumanasylaEducación,ProgramaLicenciaturaenMatemáticasFísica,Universi Fredy L.Dubeibe Lyapunov exponent Optimal conditionsforthenumericalcalculationof thelargest a networkofchaoticRösslersystemsandalsoobservechaos-chaostypechimera-likestates. to coupling the apply we Furthermore, states. chimera-like chaos-chaos find we where system, Duffing - Pol der van forced a system, bistable second a present we scheme, coupling global population. the whole between Tostates underthis of thechimera-like the generality investigate in time migrating shows subcluster the coherent state where a metastable a parameterregion, Most interestingly,components. to thetwocoupling strengths related coupling in weobserve, systems, states we locatetheregionsof For theLienard in aphasediagramoftwo chimera-like close tothesteadystate. oscillations shows smallirregular the coherentsubpopulation while state is inperiodic subpopulation type, thenon-coherent are inchaoticstatesand,another bistable Lienardsystems: in onetype,subpopulations both thecoherentandnon-coherent sidad delosLlanos,Villavicencio, Colombia deLicenciaturaenMatemáticasyFísica,Univer Facultad deCienciasHumanasylaEducación,Programa BogotáD.C.,Colombia Departamento deFísica,UniversidadNacionalColombia, et al. could leadtospuriousestimationsoftheLLE. As acomparatormethod,themaximum 1 , FredyL.Dubeibe 2 85 - -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 86 in a spatially asymmetric manner which allows to generate polarized currents. The dynamical mechanisms responsible for the spin separation carry over to the quantum level and give rise to spin pumping. Our theory [1,2], based on the Floquet formalism, is confirmed by numerical solutions of the time-dependent inhomogeneous Schrödinger equation with a continuous source term.

[1] T. Dittrich, F. L. Dubeibe, Rev. Col . Fís. 41, 428 (2009). [2] T. Dittrich, F. L. Dubeibe, Phys. Rev. Lett. 114, 094101 (2015).

Chimera states in a system with local coupling

Marcel Clerc1, Saliya Coulibaly2, Michel Ferré3, Mónica García-Ñustes3, René Rojas3

1 Universidad de Chile, Santiago, Chile 2 Laboratoire de Physique des Lasers, Atomes et Molécules, Université Lille 1, Villeneuve d’Ascq, France 3 Instituto de Física, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile

The chimera state, discovered by Kuramoto and his colleagues, is characterized by a coexistence of a coherent state and an incoherent one in the same system of oscillators. It is believed that these are only possible in systems with nonlocal and global coupling. In this work we show that it is possible to find such states in systems with local coupling where the discreteness effect prevents the invasion of the incoherent state into the coherent one. Allowing concurrently the existence of a family of chimera states, which are organized by a snaking bifurcation diagram.

Lattice-Boltzmann model for Rayleigh-Bénard convection

Juliana García-Sarmiento, Juan Carlos Gutiérrez-Vanegas

Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia

We developed a coupled lattice-Boltzmann model which simulates the behaviour of 2D Rayleigh- Bénard convection using two configurations: D2Q9 was used to simulate the fluid field and D2Q5 to solve the thermal advection-diffusion equation as well as to simulate the temperature field. Both distribution functions are described by a LBGK dynamic. They are coupled through the buoyancy term for the first component and the equilibrium distribution for the second. Isothermal no-slip boundary conditions were imposed on the horizontal walls and periodic BC on the vertical walls. We also simulated a Poiseuille flow and natural convection, in the last case similar boundary conditions were used. We study the stability of this model by modifying the Rayleigh number according to literature and theoretical predictions. ro Neto Iram MarceloGleria differential equations Modeling immuneresponse to aviralinfection withdelayed of atwo values of the parameters, the same system is capable of chaotic motion,henceis a generic case ilar modelssuchas, e.g., potential withfriction, and alsoshowasthat a washboard for extreme capements servestoachieveandoptimizethisbehaviour, so markedlydifferent fromthatofsim- es- traditional of construction specific the Wehow force. analyze input the of range wide a over constant clock andshowthat the periodoftickingisapproximately mode ofamechanical input energyisabsorbedbyfrictionintheclockwork. not dependonthe on timethroughthe but angle tension of parametrically the mainspring. The in the anchor periodic by apotential coupled wheel, that oftheanchor and with hairspring) wheel (or balance clocks. elements of the modelaretwodegreesof The principal freedom, that of the pendulum torque, withastablefrequencyoverwiderangeofsystemparameters. mechanism that generates a inversely periodic force as output from a constant input force or put, ratchet transport and synchronization. We here consider a “pacemaker system”, a nonlinear dependonaperiodicforcingascrucialin- In nonlinear dynamics,twoimportantphenomena 2 1 David GarzónCasas systems Pacemakers: escapementsof mechanicalclocks asnonlinear fected and infected cells, free virus and Lymphocytes [1], low-dimensional models that consider of unin for the dynamics modeling a reliable in order toprovide is required set ofvariables large Weinfection. to a viral due immune response for thedelayed some models analyze a Although 3 2 1 Fachbereich Informatik und Informationswissenschaft, Universität Konstanz,Germany Fachbereich InformatikundInformationswissenschaft,Universität Bogotá,Colombia Departamento deFísica,UniversidadNacionalColombia, Department of Economics, FEAC, Universidade Federal de Department ofEconomics,FEAC,UniversidadeFederal de Alagoas, Maceió, AL, Brazil Department ofPhysics,UniversidadeFederalde Campus Alagoas, Arapiraca, Brazil Instituto deFísica,UniversidadeFederal Alagoas, Maceió, AL, Brazil Numerical simulations of this dissipative two degrees of freedom system reproduce the ticking system reproduce of freedom two degrees of thisdissipative simulations Numerical Wemechanical of traditional the escapement numerically and and studyanalytically model -dimensional nonlinearsystem. 3 , DemitryMessiasSantos wheel angle. As energy input,weassumea torque onthe anchor wheelthat does 1 , AskeryCanabarro 1 , ThomasDittrich 1 1 , JuanCarlosQuintana 2 , MarceloLeiteLyra 1 , AdhemarRancia 2 87 - -

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a nonlinear response can describe general trends associated with the virus load reduction and the correlations between virus load and the immune response. Here we investigate some models for the cellular immune response to a virus infection with a characteristic response time [2-4]. We show how non-instantaneous response induce sustainable oscillations of the relevant population densities in which the virus load can reach a minimum value which is orders of magnitude smaller than those obtained from an instantaneous response. We also show that, in some of the models, the asymptotic solution display a sequence of bifurcations with increasing response times which can evolve towards a chaotic behavior, a feature often observed in real time series data of the immune state [5].

[1] M. A. Nowak, R. M. May, Virus Dynamics: mathematical principles of immunology and virology, Oxford Univer- sity Press (New York, 2000). [2] A. A. Canabarro, Iram Gleria, M. Lyra, Physica A 342, 234 (2004). [3] E. de Souza, M. Lyra, Iram Gleria, Chaos, Solitons and Fractals 42, 2494 (2009). [4] Iram Gleria, Askery Canabarro, Adhemar Ranciaro Neto, Brazilian J. Phys., to be published. [5] H. Mayer, K. S. Zaenker, U. an der Heiden, Chaos 5, 155 (1995).

Construction of Type-II Backlund transformation for the mKdV hierarchy

J. F. Gomes, A. L. Retore, A. H. Zimerman

Instituto de Física Teórica IFT-Unesp, São Paulo, SP, Brazil

From an algebraic construction of the mKdV hierarchy we observe thatthe space component of the Lax operator plays the role of an universal algebraic object. This fact induces the universality of a gauge transformation that relates two field configurations of a given member of the hierarchy. Such gauge transformation generates the Backlund transformation (BT). We propose a systematic construction of Backlund transformation for the entire mKdV hierarchy form the known Type-II BT of the sinh-Gordon theory. We explicitly construct the BT of the first few integrable models associated to positive and negative grade-time evolutions. Solutions of these transformations for several cases describing the transition from vacuum-vacuum and the vacuum-to-one-soliton solutions which determines the value for the auxiliary field and the Backlund parameter respectively, independently of the model. The same follows for the scattering of two one-soliton solutions. [1] which aresuccessfullycomparedwiththeirexperimental counterparts. CD spectra, todeterminetheircorresponding together withthestructureofsimulatedpeptides molar absorptivity.from theexperimental peptides) are thenused polarizabilities The complex of case the in (residues, monomers individual of polarizability the determine we stage, first In theory of optical activity, developed by DeVoe [1], in order to predict CD spectra of polypeptides. Wemodel ofcirculardichroism(CD)thatisbasedontheclassical presentacoarse-grained 2 1 Giovana Granados-Ramírez Circular dichroism spectra prediction of homopolymerpeptides noise canexplainthepersistenceofcommunitiesanddiversityinmanyrealsystems. local and/or size system large Thus, system. size finite a in time in structure community a and nentially withthesizeofsystem. connect twonodesindifferent states. The lifetimeofthecommunitystructurestatescalesexpo- that the system, i.e.,links in links of active the number in to adecrease is associated munities community structureemergesonaconnectednetwork. We show that the emergence of com- node dynamicsgivenbyasimplevoterlikerule. a and process rewiring to anadaptive subject network in acoevolutionary structures arising networks.Wein coevolutionary rewiring of adaptive mechanism the topological characterize Wethrough arecentlyproposed of communities investigatetheemergenceandpersistence 3 2 1 J. C.Gonzalez-Avella networks Emergence andpersistence of communitiesincoevolutionary Departamento de Cálculo, Escuela Básica de Ingeniería, UniversidaddeLos Departamento deCálculo,EscuelaBásicaIngeniería, Andes, Mérida,Venezuela Centro deFísicaFundamental,UniversidadLos Andes, Mérida,Venezuela Departamento deFísica,PUC-Rio,RioJaneiro,RJ,Brazil Physics Department,Cinvestav-IPN,MéxicoD.F., Mexico Bogotá, Colombia –LIBBIQ,UniversidadNacionaldeColombia, Chemistry Department,BasicBiochemistryResearchLaboratory Howard DeVoe, J.Chem.Phys. 43,3199(1965). Additionally, we find that small noise in the node dynamics can sustain a diversity of states of diversity a sustain can dynamics node the in noise small that find Additionally,we a process, rewiring adaptive the describing parameters the of values some for that, find We 1 , M.G.Cosenza 1 , MauricioCarbajal-Tinoco 2 , K.Tucci 2 , J.L.Herrera 2 3 89

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 90

G-concurrence and three-tangle in mixed states

Claudia Grisales, Carlos Viviescas

Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia

We develop a fast algorithm to evaluate the G-Concurrence in the three-tangle of mixed states of bipartite systems and systems of three qbits respectively. Both entanglement measures are defined as the convex-roof extension of the measure for pure states and as such they pose an optimization problem in an analytical landscape in a high-dimensional parameter space. Our algorithm is based on a hybrid algorithm proposed earlier [1] for entanglement of formation which combines steepest-decent and conjugate-gradient algorithms, yet its performance is improved by the use of the SL-invariance of the entanglement measures considered. Our results provide a standard to compare with analytical works advanced in this area.

[1] S. Ryu, W. Cai, A. Caro, Phys. Rev. A 77, 052312 (2008).

Critical phenomena in granular media

Marcelo Guzmán, Rodrigo Soto

Departamento de Física, FCFM, Universidad de Chile, Santiago, Chile

Experimental studies have analyzed the non-equilibrium solid-liquid-like transition that takes place in vibrated granular matter. The transition is characterized by the bond-orientational order parameter ξ, which measures the degree of local crystallization with square symmetry. It was found that depending on the height of the container, the transition can be of first or second order. Furthermore, near the critical point, independent critical exponents associated to the correlation length and static susceptibility were measured. Numerical simulations allow us to vary contin- uously the control parameters, which in the experimental counterpart were highly restricted. A trajectory that joins the first and second order cases was determined in the parameter space, finding a tricritical point. Moreover, the microscopic parameters in the simulation (coefficients of friction and restitution) are different from the experiments, allowing the verification of the universality of critical exponents for this system. do exhibitpersistentbehaviorontheabsolute valuesandanti-persistentbehaviorforthesigns. differences their but persistence, exhibit not does fitness performance the that verify we terns, times after practicing becomesmallerobeyinga linear rule.In addition to these universal pat- distribution whosewidth diminishes withpractice. We found that the differences of the reaction their differenceswhile skewed distribution, positively symmetrically asaLaplace aredistributed the reaction times. Aside from the fitness improvement, we identify that the reaction times have a with ascalefactoractingover can beassociated a broaderscenario,weshowthatthelearning trials. We investigate the learning interms of average valuesandtheirrespectivevariability. In directly obtainedasthe interevent timeinthesubsequenttrialscomparingtwodifferent blocksof composed ofalargenumbertrialswithoutbreaks.Wefactor evaluate thelearning numerically In this study, we analyzethe reaction times obtained from participants ina psychomotor activity Universidade EstadualdeMaringá,PR,Brazil S. Itami, universality andpersistence Very prolonged practice inblocks of trials:Scalingof fitness, calculated. Toof DDE,theLyapunov characterizethecomplexbehavior exponentandreturnmapswere a specialsetofparameters,thedynamicswillbechaoticevenforrelativelysmalltimedelay. Furthermore, for are increases. some ofitsparameters when behavior chaotic an increasingly Chaotic Maps.Wea particularexampleofLissajous willshowthatthissetofDDEcanexhibit of delaydifferentialby chaotic system,inspired Lissajous time-delay (DDE), called equations of chaoticdynamicsbyaset transmission lines.Inthepresentwork,westudygeneration in of losses control and communications in secure role has amain of complexity Generation 3 2 1 M. Garcia-Ñustes and delay differential equations Connections between exactly solvable chaotic functional equations Departamento deFísica,Universidad Tarapacá, Arica, Chile Centro deFísica,InstitutoVenezolano Científicas,Caracas, deInvestigaciones Venezuela Instituto deFísica,PontificiaUniversidadCatólica Valparaíso, Valparaíso, Chile F.J. Antonio 1 J. A. González , J.A. , R.S.Mendes 2 , FernandoM.Humire 1,3 91

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 92

The energetics of self-oscillators

Alejandro Jenkins

Escuela de Física, Universidad de Costa Rica, Ciudad Universitaria Rodrigo Facio Brenes, Costa Rica

A self-oscillator generates and maintains a periodic motion at the expense of an energy source without a corresponding periodicity. Small perturbations about equilibrium are negatively damped, leading to instability of the linear equations of motion. Non-linearity accounts for the steady-state oscillation and for the ability of coupled self-oscillators to exhibit spontaneous synchronization (“entrainment”) and chaos. The theory of self-oscillators has achieved its greatest sophistication in control theory and in the theory of ordinary differential equations. I shall explain how an understanding better suited to the needs of engineers and physicists can be founded on considerations of energy, efficiency, and irreversibility. After reviewing how forced and parametric resonances are described by energy flow into a driven oscillator, I shall explain how a simple example of self-oscillation (the swaying of the London Millennium Footbridge in 2000) results from positive feedback between the oscillation and an external energy source (the motion of pedestrians on the bridge). I shall explain how the nonlinearity of self-oscillators connects to entrainment and to the thermodynamic irreversibility of motors, before commenting on how this approach throws new light on concrete problems, like electromagnetic super-radiance, the maintenance of the Chandler wobble in geophysics, and the efficiency limits of solar cells. This talk will be based on the review article A. Jenkins, Phys. Rep. 525, 167 (2013).

Non-Markovian work fluctuation theorem in a magnetic field

J. I. Jiménez-Aquino

Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, México D.F., Mexico

The validity of the transient work fluctuation theorem for a Brownian harmonic oscillator embedded in non-Markovian heat bath and under the action of crossed electric and magnetic fields is investigated. The theorem is verified to be valid within the context of the generalized Langevin equation with arbitrary memory kernel and arbitrary dragging in the potential minimum. The fluctuation-dissipation relation of second kind is assumed to be valid and shows that the non-Markovian stochastic dynamics associated with the particle in the absence of the an external electric field is stationary, as precisely demanded by such a relation. The Jarzynski equality in this problem is also analyzed. Pulgar Susana Márquez Physical modelforthecollective migrationinzebrafish gastrulation tions ofthesephenomenatodisk-shapedJosephsonjunctionsarediscussed. a returneffectsymmetry oftheforces,producing applica structures. Possible bubble-like and solitons arecreateddueto the spatial travelling where theshapemodesareunstable,ring-like forces.Intheregionofparameterspace localized of afamilyparametrized the application We study sine-Gordon modeldueto the activationof internal shapemodes inatwo-dimensional Instituto deFísica,PontificiaUniversidadCatólica Valparaíso, Valparaíso, Chile Juan F. Marín, dimensional sine-Gordon solitons Return effect andactivation of internal shapemodes intwo- experimental observations isobtained. results showthatthere existsetsofparametersforwhichgood agreementwiththe simulation and clustering. migration that compare thecollective quality indices by using experiments The the to fit are depths well Lennard-Jones the model, the Towalk. complete random experience well. Finally,ing anhysteresisloopinthepotential and thecells thedynamics isoverdamped effects.volume the excluded and us- is modeled experiments in that isobserved The adhesion spherical particlesthat potentials, whichaccountfor interact their attraction via Lennard-Jones anaccuratemodel fortheDFCscollectivemigration.It model cellsas of thisworkistodevelop in theclusteratendofprocess. at least75%ofthetotalcellsareinvolved The objective that on theexperiments, based we require, where a group, in of cells is thecongregation tering manner.migration istheprocessinwhichagroupofcellsmovecoordinate Collective Clus- lost intheprocess. linkbetweenDFCsandEVLs,whichisgradually be relatedtothephysical Twomay which clustering, and migration are thecollective features ofthisperiod interesting the down. are going Layer cells(EVL),which surface oftheyolkcellattachedtosomeEnveloping over move (DFC) Cells Forerunner Dorsal where Zebrafish, the on focus we particular In growth. animal of differentin thedevelopment period This processispartofgastrulation animals. In thisworkwepresentasimplemodelforthecollectivemigrationofcellsinearlyphases of 3 2 1 cine, UniversityofChile,Santiago,Chile Neuroscience Institute(BNI),ICBM,FacultyofMedi- Laboratory ofExperimentalOntogeny(LEO),Biomedical of Medicine,UniversityChile,Santiago,Chile Laboratory forScientificImage NeuroscienceInstitute(BNI),ICBM,Faculty Analysis(SCIAN-Lab),Biomedical Chile Departamento deFisica,FCFM,UniversidadChile,Santiago, 3 Monica A. Garcia-Ñustes A. Monica 1 , RodrigoSoto 1 , S.Härtel 2 , F. Santibañez 2 , M.L.Concha 3 , E. 93 -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 94

The emergent role of the interplay between spikes dynamical properties and structural neural networks

J. H. Martínez1,3, D. de Santos2, D. Papo2, J. M. Pastor3, E. Jover4, I. Sendiña-Nadal5

1 Modeling and Simulation Laboratory, Universidad del Rosario de Colombia, Bogotá, Colombia 2 Biological Networks, Center for Biomedical Technology, Madrid, Spain 3 Complex Systems Group, Technical University of Madrid, Madrid, Spain 4 Neuroengineering research group, Universitas Miguel Hernández. Valencia, Spain 5 Complex Systems Group, Universidad Rey Juan Carlos, Madrid, Spain, Biological Networks, Center for Bio- medical Technology, Madrid, Spain

The hippocampus is a well-known structure of the mammals limbic system, which is associated to physiological responses from afferent emotional stimuli as well as memory and space orientation. Several studies have shown similar emergent properties in experiments with in vitro and in vivo cultures. Based on that, we have investigated the dynamical and topological properties of functional complex networks of several hippocampus cultures, aiming to identify the interplay between them. To do that, Six Multi Electrode Array experiments were designed in order to record the spikes dynamics from spontaneous activated neurons. Specifically, we study how neural networks evolve and mature (from day 7 to day 26). From the dynamical point of view, we obtain the ordinal patterns of Inter Spike Intervals (ISIs) of the cultures. With this data, we compute their respective normalized permutation Shannon entropy, the disequilibrium and its statistical complexity. In addition, the Kuramoto order parameter was computed to capture the emergence of the synchronous behaviour of the cultures. The Pearson correlation parameter between neuron phases along culture maturation is used to determine the weight of the functional connections between neurons, altogether leading to a complex functional network whose topology evolves in time. Thus, complex network parameters such as strength, weighted clustering, local efficiency, global efficiency, averaged shortest path, and eigenvector centrality were computed to topolog- ically characterize the evolution of the cultures. Our results revealed two different stages in the evolution of the hippocampus cultures: a growing stage and a mature demeanour. Also, due to their inherent spontaneous generation of spikes, the growing scenario depicts a high phase synchronization which evolves to an asynchronous regime. On the other hand, the network metrics show differences correlated with the culture growth. Interestingly, we found correlations between two specific topological and dynamical metrics: the higher (lower) the clustering, the lower (higher) the entropy of the whole culture. Renio S.Mendes Nonlinear Kramersequationandmotion of Hydra cells clustering coefficient. sidering its of topological properties:degreedistribution,time dependence the connectivity, and the BAbetween parisons con- model present our and model, homophilic the scale-free model, com- and work, this in introduced correlation fitness a particular in correlation, of differentkinds about discussion a detailed support attachmentprocess.Ourresults on preferential homophily of the tunes theimportance which parameter a control with model the scale-freehomophilic (BA) model and It neighbors.jointlygeneralizestheBarabási–Albert the numberofattaching parameters: homophily,essential namely,ones, and of sitestolinkwithsimilar thetendency We propose asimplenetwork growth processwherethe preferential attachmentcontainstwo 2 1 Mendes A. Gabriel Generalized scale-free homophilicnetwork experimental results. and superdiffusion.components with these agreement is inquantitative The presentanalysis aggregates, for which previous measurements have verified q-Gaussian distributions for velocity gated. cellular is discussed,namelythemotionofHydracells intwo-dimensional An application with and itsconnection for thisequation The H-theoremisanalyzed Tsallis entropy isinvesti- Kramers equation. with thoseknownforthestandardlinear is studiedandcompared behavior asymptotic and thecorresponding Kramers equation,anansatzisconsidered such anonlinear solutions arefoundfor analytical time-dependent sive statisticalmechanics.Sincenogeneral ated nonlinearFokker-Planckequations,areinvestigatedwithinthe context of Tsallis nonexten Kramers equation,aswellitsassoci- solutionsofanonlinear Stationary andtime-dependent 4 3 2 1 Fernando D.Nobre Universidade EstadualdeMaringá,PR,Brazil Brazil Universidade FederaldoRioGrandeNorte,Natal,RN, Universidade FederaldoMaranhão,SãoLuís,MA,Brazil Universidade Estadual de Ponta Grossa, Ponta Grossa, PR, Brazil Universidade EstadualdePontaGrossa,PR, Brazil Centro BrasileirodePesquisasFísicas,RioJaneiro,RJ, Universidade FederaldoMaranhão,SãoLuís,MA,Brazil 1 , Gabriel A. Mendes 1 , A.M.DosSantos 3 2 2 , MaurícioS.Ribeiro , M.L.De Almeida 2 , L.R.DaSilva 3 , ErvinK.Lenzi 2 4 , 95 -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 96

The onset of traffic flow phases

A. R. Méndez1, R. M. Velasco2,

1 Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana--Cuajimalpa, Méxi- co D.F., Mexico 2 Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, México D.F., Mexico

We present numerical results obtained from a macroscopic traffic model with the aim to understand the over-acceleration and adaptation effects in a two vehicle-class mixture of aggressive drivers. The first-order model for two vehicle classes is presented and numerically tested by solving with different parameters and under several initial conditions. Numerical results show the onset of Kerner three-phases and suggest that besides the drivers’ aggressivity, the most relevant aspect in the adaptation process is that |ρ2 – ρ1| > 0, the leading role is played by the most numerous vehicle class.

Teaching chaos control by means of jerk circuits

José Mendoza, Luis Araque-Lameda,

Escuela de Ciencias, Universidad de Oriente, Cumaná, Venezuela

Presently, scientists in various areas are interested in studying the control of chaos and ap- plying it in diverse problems, such as the control of chemical oscillations, the optimization of laser power, the control of perturbed heart rhythms in animals, and, particularly interesting, the electronic encryption of messages for secure communication. This interest leads to performing experiments designed to verify certain mathematical results of the theory of chaos. It has been found that certain electronic circuits, comprising one or two nonlinear elements, can be used to verify various theoretical predictions. For example, the Duffing oscillator and the Chua diode have been suggested for the experimental study of chaotic behaviour. However, the use of such circuits often proves difficult, owing to the large number of elements required for their assembly. In particular, they include inductances which, by their inherent impedance, may limit the applica- bility and the performance of the circuits.

Therefore, the present work proposes a novel method to study chaotic behaviour by means of a family of nonlinear electronic circuits that contain capacitors, resistances, diodes, and operational amplifiers. It has already been shown that these circuits can be described by third-order ordinary differential equations. For example, Lorenz found a system of differential equations with only three variables and and two quadratic nonlinearities that generate chaos. Later, Sprott proposed various simple equations which exhibit chaos with only a single quadratic or cubic nonlinearity, the latter known as jerk equation. It determines the time derivative of the acceleration of an object, described by a set of three simultaneous ordinary differential equations of first amendments arebeingincorporatedintothemodelattimeofwriting. systems, termstobeaddedintheequations. the latterrequirescoupling uncoupled These by meansofasettwo-dimensional nanowires: Whiletheformer canbemodeled phosphide with indium conducted with resultsfromexperiments good agreement cles, anditisinpartially position, whichhasdirectrelationwiththenon-conservativenatureofopticalforce. trapping the equilibrium the persistentbiastocyclicmotionaround cies; alsoastocharacterize frequen its critical and density spectral the power distribution, in termsoftheprobability sponse duction isrenderedinorderto simplify thisstudyandprovideafulldescriptionof the system re- Gaussian optical beams. ratio nanowiresaxiallytrappedinlinearlypolarized, A parameter re- Aaspect of high to studythedynamics is proposed stochastic model two-dimensional, simple 2 1 Ignacio OrtegaPiwonka trapped by focusedGaussianbeams Use of astochastic modelto studythecyclic motion innanowires teaching thecontrolofchaos. of tools foranoveltechnique In this work,weproposejerkcircuitsaseducational acceleration. order. the velocity,are theposition, in thissystemofequations variables The dependent the and School ofPhysics,UniversityNewSouthWales, Sydney, Australia Wales,School ofMathematicsandStatistics,UniversityNewSouth Sydney, Australia This model is in good agreement with simulations of nanowires modeled asarraysofparti- of nanowires This modelisingoodagreementwithsimulations 1 , BruceHenry 1 Christopher Angstmann , Christopher 1 , PeterReece 2 97 -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 98

Synchronization of FitzHugh-Nagumo neurons in a ring

G. De Polsi, C. Cabeza

Instituto de Física, Universidad de la República, Montevideo, Uruguay

Although a huge stake of problems in nonequilibrium statistical mechanics is related to thermal reservoirs that within the context of a Langevin description are described by Gaussian noises, there is an important set of problems—which go from diffusive motion in little dense media to molecular motors powered by exergonic chemical reactions such as the hydrolysis of ATP—for which the stochastic nature of the noise in the dynamical equations ought to be anything but Gaussian. As a matter of fact, most of these systems are very well described by taking Pois- sonian shot-noise terms into consideration for mimicking the system-reservoir interaction. If, to a good extent, it is possible to map athermal linear systems into standard reservoir cases by means of defining a canonical temperature, the introduction of nonlinearities puts the singular nature of a shot noise reservoir in the limelight. In that case, specious violations of the principles of thermodynamics can emerge. Aiming to reconcile the such natural principles with the analytical properties of non-standard reservoirs, we introduce the concept of temperature of n-th order which characterizes the typical energy scale that is represented by the n-th order cumulant of the noise. With that reconciling concept in hand, we also analyze the shape of the large deviation function of the energy fluxes and fluctuation relations in systems of this kind.

Faraday waves with inhonmogeneous localized injection in a quasi- one-dimensional system

Héctor Ignacio Ramos Urra1, Mónica García Ñustes1, Leonardo Gordillo2, Saliya Coulibaly3

1 Instituto de Física, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile 2 Universidad de Chile 3 Laboratoire de Physique des Lasers, Atomes et Molécules, Université Lille 1, Villeneuve d’Ascq, France

Faraday waves are nonlinear wave patterns forming on the surface of a vertically vibrated liquid. These stationary waves oscillate at half the excitation frequency, with low amplitude. We study these wave on the surface of a Newtonian liquid in a quasi-one-dimensional container, subject to a spacially localized parametric vibration. Measurements are performed on a cell with elastic bottom, which is deformed in various points in a synchronized manner by means of mechanical pistons. The pistons, in turn, are actuated by a servo motor that allows to control the frequency as well as the amplitude of the vibration. Haroldo Valentin Ribeiro Giuliano Agostinho Ridolfi Long-range correlations in written texts atsentence level the firststeptodevelopanonlinemonitoringsystembasedonthisinformationtheoryfunction. state twobegins. when to classifythestatusofarotarymachine,leading All thesefactsallow stable value a maximum reaches period startsand the transition when its value increases ibility a stablevalue whenstatetwostarts, when thetransitionstartsandachievesirrevers - function decays of thepersistence thevalue starts andneverreachastablevalue, transition one to state two starts. and symmetry The autocorrelation functions breaktheirvalueswhenthe their transitions. from state the transition when abruptly their values change All thefourfunctions permutation entropy. Wefunctions tobothstates as well the fourautocorrelation-like applied by thesignal. generated bolic alphabet functions arepartitionsofthe These autocorrelation symmetry,persistence, study autocorrelation, on thesym- based of asignal irreversibility and to http://arxiv.org/pdf/1411.3904.pdf allowing in Bandt by defined are entropy permutation the of functions basedon the both states acceleration were recorded.Severalautocorrelation-like from i.e., statetwo,andsignals i.e., stateone,andafteramisalignment, run balanced, machine at Instituto was conducted experiment Tecnológicode Buenos where arotating Aires (Argentina) through linearmethodsmaynotbeeffective atalltodetect dynamic changesonthesignal. An study ofthevibrations vibrations and,therefore,thetraditional es ofnonstationaryandnonlinear the bench or broken fastenersmay occur duringthelifetimeof the machine. These areallsourc- parts, fracturesin between mobile status.Friction,strikes,clearance uate themachineworking in ordertoeval- from rotarymachineshaveoftenbeenmeasuredandthenanalyzed generated Normally,directly. thestatusofrotarymachinescannotbeevaluated Instead,vibrationsignals Instituto Tecnológico deBuenos Aires (ITBA),Buenos Aires, Argentina, andCONICET (Argentina) Francisco Redelico, entropy-autocorrelation functions Characterizing theoperatingstate of rotary machinesusing ysis, more than thirty languages were considered. Our results are robust, holding for several Our resultsarerobust,holding were considered. ysis, morethanthirty languages correlations whilesignseriesareanticorrelated. In magnitude seriesexhibit long-range this anal and series sentence-length that find We series. sign a and series magnitude a subsequences, consecutive increments of sentence lengths.We decompose theincrement sequencesintotwo We statisticalproperties ofwrittentextsand focusing sentence lengthsequences investigate 2 1 Universidade Tecnológica Brazil Federaldo Paraná,Curitiba,PR, Universidade EstadualdeMaringá,PR,Brazil Marcelo Risk 2 1 , RêniodosSantosMendes , OsvaldoRosso 1 , SérgiodePicoliJúnior 99 1 , -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 100 text samples. Our findings may contribute to a better understanding of the complex mechanisms underlying human language.

Semiclassical approximation to the propagator of the Wigner function for confined spaces: quantum carpets in phase space?

Thomas Dittrich, Óscar Rodríguez

Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia

The Wigner function, as a one-to-one representation of the quantum mechanical density operator in phase space, allows for semiclassical approximations that are superior in various respects to those based, e.g., on a configuration-space representation. Recently, a semiclassical propagator of the Wigner function has been developed which replaces “the” classical trajectory by pairs of neighbouring orbits [1]. It is, however, valid only for potentials with a smooth anharmonicity.

We here resume this development to derive a semiclassical Wigner propagator for potentials in confined spaces, that is, restricted by infinitely high potential walls on one or two sides. This requires to rethink and to evaluate from scratch the parameters, in particular the actions, related to the trajectory pairs involved, taking as much advantage as possible of their relatively elementary geometry. We hope to reproduce on these semiclassical grounds the phenomenon of “quantum carpets” in potential boxes [2], and applications to, e.g., the Casimir effect [3].

[1] T. Dittrich, E. A. Gómez, L. A. Pachón, J. Chem. Phys. 132, 214102 (2010). [2] A. E. Kaplan, I. Marzoli, W. E. Lamb, Jr., W. P. Schleich, Phys. Rev. A 61, 032101 (2000). [3] G.-L. Ingold and A. Lambrecht, Am. J. Phys. 83, 156 (2015)

A simple model for superdiffusive transport in naturally fractured porous media

Julio César Rubén Romo-Cruz, Damián Hernández-Herrán, Luis Oliva- res-Quiroz, Fernando Ramírez-Alatriste

Colegio de Ciencia y Tecnología, Universidad Autónoma de la Ciudad de México, México D.F., Mexico

In the study of problems like anomalous diffusion in disordered media, we study a set of random walkers that move in a fractured medium composed of a set of parallel layers discretely distributed, where each fracture has a non-zero random velocity. The nature of the model describes a flux that present a diffusive and advective transport motion, therefore we observe a superdiffusive behavior in the mean square displacement (MSD) for the random walkers. This topic has been treated by Nicolás Rubido Transmission of energyincomplex networks Shannon Entropy. space trajectory, using a time causal space:StatisticalComplexityvs. Fisher Informationvs. the phase- neurons that were previouslydescribedbyIzhikevichconsidering neurophysiological information theoreticalapproachto accurately distinguishthemost fundamental properties of Weof theionicchannel. variable voltage versustheactivation membrane diagram presentan through thephase it canbeusuallydescribed over thebiophysicsanddynamicsbehind activity. spiking to resting more- generation; of spike for asthesource can beaccounted mechanisms ionic Many possible from bifurcation a near are they when spike a fire to tend Neurons 2 1 Fernando Montani dynamics An informationtheoretical approach to characterize theneural topological representation of representation how the topological units inthe complex system are interconnected,i.e., the system. of acomplex the behaviour the structureand between lationship The structureisa Are- the implicit predict and istounderstand Sciences in Complexity motivation fundamental 3 2 1 verify thatinthiscasetheMSDfromwalkersgoesliket form, aidedbynumeric simulations wecomparetheanalyticalsolutionwithnumericaldata. We (inert particles carried by diffusive-advective flow). We show a solution for the MSD in this discrete medium byusing(forexample)conventionalmethodsliketheinjectionandrecollectionoftracers the of characteristics the of prediction good a make to difficult is it where processes, extraction oil model hasimportantapplicationsinresearchastothecontaminantpropagationaquifersand Resources Research,Vol. 16.No.5,1980),wherethecontinuous casewasstudied. This typeof Matheron andMarsily(Istransportinporousmediaalwaysdiffusive? A counterexample,Water Baptista vection anddiffusion couplinginthistypeofmediumisalsoasuper-diffusive dynamics. Instituto deFísica,UniversidadeFederal Alagoas, Maceió, AL, Brazil Argentina Instituto deFísicaLíquidosySistemasBiológicos(IFLYSIB), UniversidadNacionaldeLaPlata, University of Aberdeen, King’s SystemsandMathematicalBiology, College,Institute forComplex Aberdeen, UK de Ciencias, Montevideo,Uruguay Universidad delaRepública,InstitutoFísicaFacultad King’s College, InstituteforComplexSystemsandMathematicalBiology, Aberdeen, UK de Ciencias, Uruguay,Universidad delaRepública,InstitutoFísicaFacultad and Universityof Aberdeen, 3 1 , E.Catsigeras 1 , RománBaravalle 2 , C.Cabeza 2 , LisandroMontangie 2 , A.C.Mart a , wherea í 2 , C.Grebogi = 3/2, showing that the ad- the that showing 3/2, = 2 , Osvaldo A. Rosso 3 , M.S. 101 2

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 102 system’s connectivity skeleton. It constitutes the backbone of the system’s interactions and it is formally described by the theory of graphs. Behaviour is a functional observable of the collective dynamics that the units in the network have. It shows how the dynamical properties of the complex system evolve and can be measured by a variety of different methodologies. The importance of understanding this relationship is because, in nature and society, both quantities are usually not simultaneously known. For example, in the brain, the behaviour can be measured (e.g., EEG and fMRI) but the exact structure is unknown. On the other hand, the structure of the modern power-grids are known, but the behaviour sometimes is unpredictable (e.g., black-outs and power drops). In this work I am going to focus on the derivation of explicit relationships between the structure and the dynamics of supply-demand networks, in particular, in the results we find for a phase-oscillator model of the power-grid transmission of energy known as the swing equations. Despite our particular choice, the results are unrestricted to power-grids and can be extended to other complex systems of interacting oscillators.

Persistent photoconductivity in SrTiO3 single-crystalline fibers

Jorge-Enrique Rueda-P.1, J. E. F. S. Rodrigues2, Antonio Carlos Hernandes2

1 Departamento de Física, Universidad de Pamplona, Pamplona, Colombia 2 Instituto de Física de São Carlos, Universidade de São Paulo, SP, Brazil

A metastable increase of the dark conductivity caused by short illumination, known as persistent photoconductivity (PPC), has been observed in a variety of semiconductor materials. PPC has mainly been observed in III-V or II-V semiconductors and in crystalline organic semiconductors. Room temperature PPC has been observed in semiconductors such as GaN and GaInNAs, between other materials as polymorph of \alpha-sexithiophene. Recently, room temperature PPC has been observed in Verneuil-grown SrTiO3 bulk single crystal. We have found persistent photoconductivity in a SrTiO3 single-crystal fiber. The fiber was obtained using the Laser-Heat Ped- estal Growth technique, and after the fiber had been annealed at high temperature with SrCO3 powder in order to produce vacancy defects. When exposed to laser light of 450 nm wavelength at room temperature, the effect was observed for 24 hours after the light had been turned off.

Nonlinear transport in pump-ratchet hybrids

Nicolás Medina Sánchez, Thomas Dittrich

Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia

Directed transport by means of nonlinear dynamics has been studied in two alternative frame- works, in periodically driven sawtooth potentials (“ratchets”) and in the context of driven chaotic scattering (“pumps”). We here consider hybrids between these two types, spatially periodic po- hydrodynamic coupling. hydrodynamic Aof the incompressibility method, basedonthelocal directcalculation ered. We calculate a first-order correction for the correlation function for a planar membrane with The phenomenon of thermal fluctuations in planar membranes and spherical vesicles is consid Departamento deFísica,Universidadlos Andes, Bogotá,Colombia Jorge LuisSánchezRuiz, spherical vesicle withlocalsurfacetension. planar membraneandfluctuation-dissipation relation foraquasi- Perturbative correction forthecorrelation function foraquasi- memoryisnotperfectbutdecaysslowlyintime. space useisachievedwhentheforager’s model therefore combines random search with resource exploitation and shows that an efficient resources. Our its visitstotheavailable to synchronize and to changes to adapt some conditions in able is walker the lifetime, finite a have inhomogeneities the i.e., unpredictable, partially and dynamical is environment the If sites). (food inhomogeneities fixed around localization sharp a rule. erential of ahomerange,orveryslowdiffusion,predicts theemergence This model with with memory,pref- to a simple visited sitesaccording a walkertendstorevisitpreviously where model walk a random by considering movement of animal a description In thisworkwepropose Instituto deFísica,UniversidadNacional Autónoma deMéxico,MéxicoD.F., Mexico Denis PierreBoyer Random walks withmemoryandanimalforaging evidence fordirectedcurrentsontheclassicallevel. condition thattransitionsareallowedonlybetweentheBlochbandsofasymptoticregions. energy conservationmoduloexchangeof of an integernumberphotonsof the driving,and ic asymptotic regions. Scatteringis therefore restricted both by Floquet theory, which implies driven scatterers, combined withBlochtheoryto periodically be appliedto the spatiallyperiod currents. scattering, asanexacttheoryfor in theframeworkofFloquet They canbequantized a collimatedlaserbeam. by irradiated surfaces semiconductor or metal by e.g., inspired, are “Punchets” time. in periodic tentials which,however,in space)driving, are subjecttoalocal (restrictedtoacompactregion Wenumerical transport inpunchetsandpreliminary of directed analysis presentageneral Classically,rise todirected scattering, thusgiving thesesystemsexhibitasymmetricirregular , Edgar Anuar SánchezHernández Gabriel Téllez Acosta Téllez Gabriel 103 - -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 104 membrane, it is proposed to derive results previously reported in the literature for the correlation function on a quasi-spherical vesicle with local incompressibility.

Zero density of open paths in the Lorentz mirror model for arbitrary mirror probability

Atahualpa S. Kraemer1, David P. Sanders2

1 Institute for Theoretical Physics II, Heinrich-Heine-Universität, Düsseldorf, Germany 2 Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, México D.F., Mexico

We study the Lorentz mirror model of deterministic dynamics in a random environment: a point particle moves in an array of randomly-oriented mirrors on a square lattice. Using a mixture of numerical simulations and analytical estimates, we show [1] that the density of open paths in any finite box tends to zero as the box size tends to infinity, for any mirror probability.

[1] Atahualpa S. Kraemer, David P. Sanders, J. Stat. Phys. 156, 908 (2014).

Non-Gaussian center-of-pressure velocity distribution during quiet stance

E. S. D. Santos, S. Picoli, P. P. Deprá, R. S. Mendes

Universidade Estadual de Maringá, Maringá, PR, Brazil

In the present study, we investigate patterns in the postural sway that characterize the static balance in human beings. To measure the postural sway, sixteen healthy young subjects performed quiet stance tasks providing the center-of-pressure (COP) trajectories. From these trajectories, we obtained the COP velocities. We verified that the velocity distributions exhibit non-normal behavior and can be approximated by generalized Gaussians with fat tails. We also discuss possible implications of modeling COP velocity by using generalized Fokker-Planck equations related to Tsallis statistics and Richardson anomalous diffusion. tics areobtained.Bifurcation pointsarefound. through are represented The results weobtained dynamical systemiscarried out. Different kindsof microstructure evolutionandtheircharacteris different components ofmicrostructureandtemperature. Aanalysis ofthisnonlinear qualitative oped viatheformalism ofPoincaré.Wedifferential asystem ofnonlinear consider equationsfor which aresurveyedinthispresentation. temperature solids’ the of self-oscillations and conductivity, of self-oscillations decomposition, Well-knownate conditions. alloy voids, periodic ofradiation-induced examplesaresuperlattices rise todifferentEach ofthesescenariosdevelopsunder appropri ofself-organization. scenarios differentfeedbacks, whichgive with nonlinear timeandspacescales.Many ofthemarelinked very at operating mechanisms various of combination the in all, of effectsfirst radiation is, of ity multiscale processes. and inherently structure andpropertiesthroughhierarchical The peculiar scale, whichevolveoverlongerscalesto shortest timeandlength produce changesinmicro- or functionstakesplaceinsolidunderirradiation. structures ofspatial,temporal,spatiotemporal librium. It is wellknownthattheself-organization equi from thermal systems faraway nonlinear of open, isanexample under irradiation Material Department ofPhysics,UniversityPretoria,South Africa Pavlo Selyshchev Self-organization insolidsunderirradiation with amaximumclosetozeroandanother0.1. Lyapunovtakes placethesecond where theerosion distribution exhibits abimodal exponent Weof thecoupling. in theintensity with theincrease progresses that intheregion observed also from theoutside,andthaterosion to beeroded existed begins structures thatpreviously fraction. its positive We observethat,whentheslavesystemiscoupledtomaster, periodic theshrimp-shaped and exponents Lyapunov finite-time of distribution the space, parameter in diagrams exponents Lyapunov employ we so do to order In configuration. master-slave a in In thisworkweinvestigatetheparameterspaceofasystemconsistingtwooscillatorscoupled 2 1 Vagner dosSantos of couplednonlinearsystems Analysis of periodicstructures anderosion intheparameter space Departamento de Matemática, Universidade Estadual de PontaGrossa,Brazil Departamento deMatemática,UniversidadeEstadual Programa dePós-GraduaçãoemCiências/Física,UniversidadeEstadualPontaGrossa,Brazil Tois devel evolution damage to radiation approach a theoretical these phenomena describe and interstitialatoms) atthe point defects(vacancies produces mobile Foremost, radiation 1 , JoséDaniloSzezechJr. 2 , AntonioMarcosBatista 2 105 - - - - -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 106 a set of phase portraits. It is shown that the degradation of irradiated material can be limited by choosing an appropriate kind of evolution of materials using irradiation energy.

Finite-size effects on computer calculations of supercooled liquids

Natália C. de Sena1, Marco A. Amato2, Tarcísio M. da Rocha Filho2, Ademir E. Santana3

1 Instituto Federal de Brasília and Instituto de Física, Universidade de Brasília, Brasília, DF, Brazil 2 Centro Internacional de Física da Matéria Condensada and Instituto de Física, Universidade de Brasília, Brasília, DF, Brazil 3 Centro Internacional de Física da Matéria Condensada and Instituto de Física, Universidade de Brasília, Brasília, DF, Brazil

Some materials remain in the liquid phase even at temperatures lower then their melting point, in an out-of-equilibrium state known as supercooled liquid. At even lower temperatures, these materials stop flowing, passing through the glass transition, solidifying to an amorphous glassy phase. A large number of computer simulations of these systems have been done, and the influence of the system size in the outcome is a problem that remains open.

In this work, we develop a numerical study concerning the effects of changing the system size for two different potentials in two and three dimensions: the Kob-Andersen model (Kob and An- dersen, 1995) for a binary mixture and a power law repulsive interaction used by Karmakar and Procaccia (2012). We use a fourth-order symplectic integrator (Yoshida, 1990), implemented in CUDA language to allow for a wider range of system sizes.

Along these lines, size effects may be discussed and their effects properly accounted for. In the theoretical context we attempt to study the problem using methods of quantum field theory.

Measurement of optical nonlinearities with an electrically focus- tunable lens

Juan Serna1, Hamad Abdullatif2, Edgar Rueda1, Hernando Garcia2

1 Universidad de Antioquia, Medellín, Colombia 2 Southern Illinois University, Edwardsville, IL, USA

We have measured the two-photon absorption coefficients and nonlinear refractive index by using a recently proposed single beam setup based on the well-known Z-scan technique. This new f-scan technique uses an electrically focus-tunable lens (EFTL) instead of a mechanical translation stage, simplifying the experimental setup and reducing dramatically the cost of equip- is smaller than the entropy of a long random composition [1]. Tse, Liu and Small found that suc- ress of a melody the entropy growswitheachnew musical noteuntilit takes a limiting valuethat for constructing algorithmsto compose music.Gündüz andGündüzfoundthat during the prog- manner cognitiveelements involvedinconveyingemotionsaswell as standing inaquantitative properties of complex systems as macroscopic quantitiesrelevantfor can beinterpreted under canbeusedtoexplorepropertiesofmusicalpieces. as statisticalmechanics, These statistical for Recent worksshowthat studying complexsystems, concepts andanalyticaltoolsdeveloped Departamento deFísica,UniversidadNacionalColombia, Bogotá,Colombia Jorge EduardoUsecheRamírez, Link weight distributioninnetworks of musicalmelodiclines last quantitygivesameasureofthedepartureprobabilitydistributionfromGaussian. at for all times. the mean-squaredisplacementandkurtosisgiveexacttimedependence The Wediscussed. persistence that ourprescription simulations Brownian dynamics showthrough ment and for the kurtosis of the probability distributionfunctionarepresentedandthe effects of displace for themean-square in alltimeregimes.Explicitexpressions active particles butionof Péclet number,distri- of thepositions evolution the out-of-equilibrium us toanalyze thisallows tive swimmers. of the for arbitraryvalues analytically are solved equations The Smoluchowski model ofac- to aLangevin-like that corresponds time regimesfromtheFokker-Planckequation and to active fluctuations on the rotational one. Smoluchowski equations are derived in different that swim with constant speed and are subject to passive fluctuations on the translational motion Weparticles, of activeBrownian for thepositiondistribution analysis presentacoarse-grained 2 1 Francisco J.Sevilla Smoluchowski diffusionequationsforactive Brownian particles presented. also is EFTL characterization correct of lack to due coefficients the of determination inaccurate values reportedintheliterature.Examplesof to thewell-established and compared measured results forCdSare of thetechniqueisshown.Experimental implementation The experimental parameters. fitting the as index refractive nonlinear the and coefficient absorption two-photon the use to only setup withregard of theoptical the characterization theory and underlying of the sensitivity.the experimental ment whilemaintaining the development Inthisworkweemphasize Departamento deFísica,Universidad MéxicoD.F.,Autónoma Metropolitana, Mexico Instituto deFísica,UniversidadNacional MéxicoD.F.,Autónoma deMéxico, Mexico 1 , MarioSandoval Rafael GermánHurtadoHeredia 2 , AlejandroVásquezOrzola 1 107 - -

XIVP LAWNP - Latin American Workshop on Nonlinear Phenomena 108 cessive notes in musical pieces can be represented as complex networks that exhibit power-law distributions for some connectivity properties like node degree [2]; in their work nodes represent musical notes and links between nodes represent successive notes. We assign to each link a value of a psychoacoustically relevant quantity related with consonance: the difference between the squares of the fundamental frequencies of successive notes, in such a way that the magnitude of this quantity distinguishes any pair of pitches (except for the unisons with a degenerated value 0) and the sign gives information about the direction of the corresponding link (positive for ascending musical intervals and negative for descending ones). We use the standard Twelve equal-tempered scale with A = 440 Hz. The link weight is the frequency of occurrence of the respective transition. We find that the probability distribution for the link weight can be represented as an Asymmetric Laplace Distributions and we use an extremum principle of entropy to reproduce the main characteristics of the corresponding probability distributions.

[1] G. Gündüz, U. Gündüz, Physica A 357, 565 (2005). [2] X. Liu, M. Small, C. Tse, Physica A 389, 126 (2010).

Quantum entanglement in random states of indistinguishable particles

Natalia Herrera Valencia, Sergio Solórzano, Carlos Viviescas

Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia

In contrast to the well-developed and established theory of entanglement for distinguishable particles, and despite the numerous attempts and significant effort invested in it, an entanglement theory for states of indistinguishable particles still remains in a precarious state. The main hurdles faced by the theory derive from the subtleties of the quantum correlations inherent to the statistical properties of states of indistinguishable particles.

In an attempt to illustrate basic differences between the nature of entanglement in systems of distinguishable and indistinguishable particles, we propose a possible measure for the entanglement of bipartite systems of indistinguishable particles which emerges as a natural extension of an existing monotone for N x N systems of distinguishable particles. This measure allows the characterization of the entanglement distribution on particular ensembles of random states of high-dimensional bipartite systems of bosons and fermions. detectors ofsmallperturbations. as better significantly perform out-in, the of values lower and in-out the of value higher of cients curve analysis. of the network (less than5%of under asmallrandomperturbation nodes) isassessedbyROC ing with fixed coupling strenght under background noise. The effects of rewiring for the sensitivity interact- neurons binary stochastic of networks simulate we profiles, assortativity attainable the with realizations graphs underlying the Finally, over coefficients. pearson of values decreased or increased with profiles assortativity different achieve to order in rewiring preserving degree models. use asnull that we correlations degree given in-out exhibiting them by Then, weevolve and distributions fromGaussiandegree we generaterandomgraphswithsparseconnectivity which constitutesanintrinsicsurvivalmechanismforthecultures. ronal cultures have shownthe presence of assortativity giving shapeto a connectivity backbone Moreover,conditions. normal under activity neu- stochastic clustered stable on findings recents maintaining while todetectverysmallstimuli their ability networks, namely erties ofrealneural be optimalintermsofenhancementnetworksensitivityandstability. in and out degrees at single-node level, but also the capability for certain assortativity profiles to the fourdifferentbetween the between correlations node there existalready when assortativities explored. In this work, we address numericallya few questions suchas the interdependencies as spreading or percolation, however for directed networks the subject has not been sufficiently such properties such asthespectralradiusordynamical network measuresorrelatedquantities other with assortativities related have works Several profile. assortativity the as known out-out) a fewauthors, therebye givingrisetoaset in-in, in-out,out-inand of four assortativities(labeled by networks directed to extended naturally was idea the 2010 in Later fields. several in applied network theoryand successfully usedincomplex in 2002,hasbeen by Newman work measure net- a as proposed assortativity,coefficient, degree degree The correlation Pearson called also Grupo deBiofísica,InstitutoFísica,Universidad Antioquia, Medellín,Colombia caurte Avella Juan CarlosVásquezBetancur, Marco Antonio GiraldoCadavid random neuralnetworks: astudycase Optimal sensitivityisachieved by directed assortativityprofiles in Preliminary results show that networks with assortativity profiles containing correlation coeffi- Therefore, to explore the impact of directed assortativityonthe sensitivity of neural networks prop- important unraveled have [4] rodents in cortex barrel in experiments important Indeed, , Cesar Alfredo UribeLeon , GermanRi- 109

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Study of the Atwood number effect on hydrodynamic instabilities with a multi-phase lattice-Boltzmann model

Ali Mauricio Velasco Sabogal, José Daniel Muñoz Castaño

Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia

Rayleigh–Taylor and Kelvin–Helmholtz hydrodynamic instabilities are frequent in many natural and industrial processes, but its dependence on the relative relative density difference between the fluids (known as the Atwood number A) has not been deeply studied. This work uses a lattice Boltzmann model on multiphase fluids at a liquid-vapour interface, instead of multicomponent systems like the oil–water one to simulate these instabilities. The model, proposed by He, Chen and Zhang (1999) was modified to increase the precision by computing the pressure gradients with a higher order, as proposed by McCracken and Abraham (2005). The resulting model correctly simulates both instabilities by using almost the same parameter set and allow us to study the relation between the growing rate of the Rayleigh–Taylor instability and the Atwood number, finding a good agreement with theoretical expectations for high Atwood numbers, but including also deviations observed in recent experiments at low density differences. The results show that the implemented model is a useful tool for the study of hydrodynamic instabilities, drawing a sharp interface and exhibiting numerical stability for moderately high Reynolds numbers.

Reaction time distributions in chemical kinetics: oscillations and other strange behaviors

Ramon Xulvi-Brunet, Marco Bayas

Escuela Politécnica Nacional, Quito, Ecuador

Chemical reactions proceed through intermediate species which tend to have a finite “characteristic lifetime”. After this lifetime, the intermediates either become the final products of the reaction or disassociate themselves back into the initial reactants. Depending on the probability distribution which the intermediate compounds decay with, the kinetics of a chemical reaction may be one or another. We explore the effects of several of such time distributions on the kinetics of a few chemical reactions, and conclude that, depending on the distribution, the kinetics of a reaction can present unexpected oscillations and other strange behaviors. and suggeststhatgradualregimeshiftsmayoccurinotherpattern-formingecosystems, too. processes, birth ordeath of fairy-circle cascades shifts asunidirectional regime of gradual sibility stable states. multiple processes astransitionsbetween The studyfurtherdemonstratesthefea- death birth and fairy-circle interprets interactions, and by water-vegetation driven phenomenon as aself-organization of fairycircles for theview support new Our studyprovides cipitation. and aretodateleftunexplained. reported, been have gaps these of “death” and Moreover,“birth” patterns. of periodic dynamics tured by circular gapsof sandy baresoil,thefairy circles, that on landscapescalesform nearly and undisturbed. geneous grass, punc- This ecosystemconsistsofauniformmatrixperennial is fairlyhomo- ecosystem, which fairy-circle is theNamibian for suchaninvestigation candidate result ingradualratherthancatastrophicregimeshifts. systems can self-organize in a multitude of spatial patterns. In fluctuating environments, this can have beensuggested,stemmingfromthespatialnatureofsystem. Spatially extended eco- across theecosystem.However,uniformly stable statesoccurring responses morecomplex alternative two between transitions abrupt as conceived are shifts” regime “catastrophic These or disturbancescaninducelargeresponses. changes tipping points,wheresmallenvironmental mental aspectofecology.of ecosystemsnear to thebehavior Muchattentionhasbeendevoted is afunda- disturbances andanthropogenic The responseofecosystemstoclimatevariability 2 1 Yuval Zelnik Gradual regime shiftsinfairycircles

Department ofPhysics,Ben-GurionUniversity, Beer Sheva,Israel Department of Environmental Physics, BIDR, Ben-Gurion University,Department ofEnvironmentalPhysics,BIDR,Ben-Gurion BeerSheva,Israel Using our model we can explain the dynamics of the system as a result of variability in pre- the dynamicsofsystemasaresultvariability Using ourmodelwecanexplain This predictionof pattern formationtheoryhasneverbeentestedinarealecosystem.One 1 , GolanBel 1 , EhudMeron 1,2 111

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List of participants

Bourdon García Botero Binder Bianconi Benet Bettencourt Beims Barrios Pulido Barbosa Baracaldo Avalos-Gaytán Arroyave-Bermúdez Armenteras Arias Castro Arce Apte Atay Aponte Santamaría Antonio Anteneodo Alves de Andrade Alvarez-Llamoza Almendral Allende Alfaro Bittner Aldana Albano Aguirre Gómez de Aguiar Agüero Agudelo Aguado Last Name Rubén Danilo Juan David Philippe Ginestra Luis Luis Marcus Werner Olga Lucía Fernando Laura Nohelia Vanesa Félber Dolors Juddy Heliana Julio Cesar Amit Fatihcan Camilo Fernando J. Celia Luiz Gustavo Orlando A. Juan Carolina Karin Maximino Ezequiel Vicente Jose Gabriel M. Marcus A. Maximo Jeffersson Alejandro First Name Colombia Colombia USA UK Mexico USA Brazil Colombia Brazil Colombia Mexico Colombia Colombia Colombia Colombia India Germany Germany Brazil Brazil Brazil Ecuador Spain Uruguay Chile Mexico Argentina Chile Brazil Mexico Colombia Mexico Nationality 44, 45,47 15, 48,66 Pages 37, 41 37, 38 80, 91 56, 58 55, 56 65, 79 15, 78 65, 77 41 40 17 16 16 81 58 31 27 57 33 16 80 47 80 82 78 77 - - - - 115

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Brigatti Edgardo Brazil 29 Cabrera Capera Emilse Colombia 79 Carbajal-Tinoco Mauricio D. Mexico 82, 89 Cárdenas-Barrantes Manuel Colombia 82 Cardona Meza Luz Stella Colombia 83 Castaño Puerta Julieth Viviana Colombia 83 Castellanos César Colombia 84 Clerc Marcel Chile 17, 62, 70, 82, 86 Coelho de Sena Natália Brazil 106 Cosenza Mario Venezuela 7, 18, 89 Coy Mondragón Tathiana Colombia - Cruz José Colombia 59 Cuellar Milena USA - Curado Evaldo M.F. Brazil 59 Dana Syamal Kumar India 60, 84 73, 85, 86, 87, 100, Dittrich Thomas Colombia 102 Domínguez Román Ivonne Mexico 60 Dossetti Victor Mexico 61 Dubeibe Fredy Colombia 85, 86 Ferrari Fabiano Brazil 61 Ferré Michel Chile 86 Froyland Gary Australia 33 García Anamaría Colombia - García Sarmiento Juliana Colombia 86 García-Ñustes Mónica Chile 62, 82, 86, 93, 98 Garzón Casas David Colombia 87 Geisel Theo Germany 10, 18, 19, 51 Giraldo Marco Colombia 109 Gleria Iram Brazil 87, 88 Gomes Jose Francisco Brazil 88 Gómez-Gardeñes Jesús Spain 19, 45, 57 Gomez-Lievano Andrés USA 44 Gonzalez-Avella Juan Carlos Brazil 89 Mendes Mellado Humire Medina Sánchez Martínez-Mekler Martínez-Mardones Martínez Quimbayo Martínez Martínez Martens Márquez Marín Luque Lotero Lobo Lindenberg Lima Leyvraz Waltz Kumar Dana Kosztolowicz Jülicher Jotty Jiménez-Aquino Jenkins Jarzynski Itami daSilva Herrera Valencia Herrmann Guzmán Gutiérrez Vanegas Gutiérrez Mesa Großmann Grisales Granados-Ramírez Gabriel Fernando Nicolás Gustavo Javier Jennyffer Stefania Rodney Johann H. Craig Susana Juan F. Bartolo Laura José Katja Rodrigo François Syamal Tadeusz Frank Karick José Inés Alejandro Christopher Andréia Natalia Hans J. Marcelo Juan Carlos Sandra Frank Claudia Carmen Giovana Brazil Chile Colombia Mexico Chile Colombia Ecuador Colombia USA Chile Chile Spain Colombia USA USA Brazil Mexico India Poland Germany Colombia Mexico Costa Rica USA Brazil Colombia Switzerland Chile Colombia Colombia Germany Colombia Colombia 5, 65,66,77 64, 94 19, 45 84, 60 102 108 117 95 91 35 34 39 93 93 45 21 63 63 62 20 92 92 20 80 90 86 38 90 89 - - - - 117

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Méndez R. Alma R. Mexico 96 Mendoza José Venezuela 96 Meron Ehud Israel 21, 111 Miramontes Octavio Mexico 29 Montealegre Cárdenas Mauro Colombia - Muñoz José Daniel Colombia 8, 82, 84, 110 Naranjo Fernando Colombia 66 Olaya Castro Alexandra UK 39 Olivar Tost Gerard Colombia 83 Ortega Piwonka Ignacio Australia 97 Osorio Andrés F. Colombia 28 Ospina Raydonal Brazil 66 Oviedo Mauricio Colombia - Pachón Leonardo Augusto Colombia 40, 73, 100 Padmanabha Harish Colombia 30 Parra Rojas César UK 67 Parrondo Juan M. R. Spain 22 Pérez Sánchez Juan Bernardo Colombia 41 Perilla Juan Roberto USA 40 Peshkov Anton Chile 68 Pineda Carlos Mexico 68 De Polsi Gonzalo Uruguay 98 Poveda Germán Colombia 27 Queirós Sílvio M. Duarte Brazil 69 Ramírez Sara Colombia - Ramos Urra Héctor Ignacio Chile 98 Francisco Redelico Argentina 99 Ricaurte Avella Germán Colombia 109 Ridolfi Giuliano Brazil 99 Rodríguez Villalba Oscar Eduardo Colombia - Rojas René Chile 70 Romo Cruz Julio César Rubén Mexico 100 Rosso Osvaldo Anibal Brazil 46 Rubido Nicolás Uruguay 101 Zumaya Zuleta Ochoa Zelnik Zanette Xulvi-Brunet Viviescas Viviescas Villalobos Vieira Ribeiro Velasco Sabogal Vásquez Betancur Useche Torres Zalabata Toledo Tequita Vargas Téllez Takahashi Soto Smilansky Silva Sevilla Serna de Sena Selyshchev Sauma Pérez dos Santos dos SantosMendes Santos Santander Rodríguez Sanders Sánchez Ruiz Sánchez Hernández Rueda-Parada Rueda Martín Yonatan Yuval Damián Ramon Fernando Carlos Gabriel Bruno Ali Mauricio Juan Carlos Jorge Teirungumu Benjamín Oscar Fabián Gabriel Ken Rodrigo Uzy Nelson Francisco J. Juan Natália C. Pavlo Tania Vagner Renio Edenize Luis David P. Jorge Luis Anuar Edgar Jorge-Enrique Edgar Mexico Colombia Israel Argentina Ecuador Colombia Colombia Colombia Brazil Colombia Colombia Colombia Colombia Chile Colombia Colombia Peru Chile Israel Colombia Mexico Colombia Brazil South Africa UK Brazil Brazil Brazil Colombia Mexico Colombia Mexico Colombia Colombia 47, 80,91,95,99,104 72, 90,93 8, 22,51 90, 108 64, 103 61, 107 109 107 106 106 105 104 104 104 103 103 102 106 110 110 111 48 73 23 72 69 66 34 71 - - - - - 119

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