76 DS05 Abstracts
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Data Assimilation and Parameter Estimation for a Multiscale Stochastic System with Α-Stable Lévy Noise
Data assimilation and parameter estimation for a multiscale stochastic system with α-stable L´evy noise Yanjie Zhang1, Zhuan Cheng2, Xinyong Zhang3, Xiaoli Chen1, Jinqiao Duan2 and Xiaofan Li2 1Center for Mathematical Sciences & School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China 2Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA 3Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] and [email protected] . ∗This work was partly supported by the NSF grant 1620449, and NSFC grants 11531006, 11371367, and 11271290. Abstract. This work is about low dimensional reduction for a slow-fast data assimilation system with non-Gaussian α stable L´evy noise via stochastic averaging. − When the observations are only available for slow components, we show that the averaged, low dimensional filter approximates the original filter, by examining the corresponding Zakai stochastic partial differential equations. Furthermore, we demonstrate that the low dimensional slow system approximates the slow dynamics of the original system, by examining parameter estimation and most probable paths. Keywords: Multiscale systems, non-Gaussian L´evy noise, averaging principle, Zakai equation, parameter estimation, most probable paths arXiv:1801.02846v1 [math.DS] 9 Jan 2018 1. Introduction Data assimilation is a procedure to extract system state information with the help of observations [18]. The state evolution and the observations are usually under random fluctuations. The general idea is to gain the best estimate for the true system state, in terms of the probability distribution for the system state, given only some noisy observations of the system. -
Communications with Chaotic Optoelectronic Systems Cryptography and Multiplexing
COMMUNICATIONS WITH CHAOTIC OPTOELECTRONIC SYSTEMS CRYPTOGRAPHY AND MULTIPLEXING A Thesis Presented to The Academic Faculty by Damien Rontani In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Electrical and Computer Engineering Georgia Institute of Technology December 2011 Copyright c 2011 by Damien Rontani COMMUNICATIONS WITH CHAOTIC OPTOELECTRONIC SYSTEMS CRYPTOGRAPHY AND MULTIPLEXING Approved by: Professor Steven W. McLaughlin, Professor Erik Verriest Committee Chair School of Electrical and Computer School of Electrical and Computer Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Professor David S. Citrin, Advisor Adjunct Professor Alexandre Locquet School of Electrical and Computer School of Electrical and Computer Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Professor Marc Sciamanna, Co-advisor Professor Kurt Wiesenfeld Department of Optical School of Physics Communications Georgia Institute of Technology Ecole Sup´erieure d'Electricit´e Professor William T. Rhodes Date Approved: 30 August 2011 School of Electrical and Computer Engineering Georgia Institute of Technology To those who have made me who I am today, iii ACKNOWLEDGEMENTS The present PhD research has been prepared in the framework of collaboration between the Georgia Institute of Technology (Georgia Tech, USA) and the Ecole Sup´erieured'Electricit´e(Sup´elec,France), at the UMI 2958 a joint Laboratory be- tween Georgia Tech and the Centre National de la Recherche Scientifique (CNRS, France). I would like to acknowledge the Fondation Sup´elec,the Conseil R´egionalde Lorraine, Georgia Tech, and the National Science Foundation (NSF) for their financial and technical support. I would like to sincerely thank my \research family" starting with my two advisors who made this joint-PhD project possible; Prof. -
Recurrence Plots for the Analysis of Complex Systems Norbert Marwan∗, M
Physics Reports 438 (2007) 237–329 www.elsevier.com/locate/physrep Recurrence plots for the analysis of complex systems Norbert Marwan∗, M. Carmen Romano, Marco Thiel, Jürgen Kurths Nonlinear Dynamics Group, Institute of Physics, University of Potsdam, Potsdam 14415, Germany Accepted 3 November 2006 Available online 12 January 2007 editor: I. Procaccia Abstract Recurrence is a fundamental property of dynamical systems, which can be exploited to characterise the system’s behaviour in phase space. A powerful tool for their visualisation and analysis called recurrence plot was introduced in the late 1980’s. This report is a comprehensive overview covering recurrence based methods and their applications with an emphasis on recent developments. After a brief outline of the theory of recurrences, the basic idea of the recurrence plot with its variations is presented. This includes the quantification of recurrence plots, like the recurrence quantification analysis, which is highly effective to detect, e. g., transitions in the dynamics of systems from time series. A main point is how to link recurrences to dynamical invariants and unstable periodic orbits. This and further evidence suggest that recurrences contain all relevant information about a system’s behaviour. As the respective phase spaces of two systems change due to coupling, recurrence plots allow studying and quantifying their interaction. This fact also provides us with a sensitive tool for the study of synchronisation of complex systems. In the last part of the report several applications of recurrence plots in economy, physiology, neuroscience, earth sciences, astrophysics and engineering are shown. The aim of this work is to provide the readers with the know how for the application of recurrence plot based methods in their own field of research. -
Limit Theorems for Non-Stationary and Random
LIMIT THEOREMS FOR NON-STATIONARY AND RANDOM DYNAMICAL SYSTEMS by Yaofeng Su A dissertation submitted to the Department of Mathematics, College of Natural Sciences and Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics Chair of Committee: Andrew T¨or¨ok Committee Member: Vaughn Climenhaga Committee Member: Gemunu Gunaratne Committee Member: Matthew Nicol University of Houston May 2020 Copyright 2020, Yaofeng Su ACKNOWLEDGMENTS This dissertation would not have been possible without the guidance and the help of several in- dividuals who in one way or another contributed and extended their valuable assistance in the preparation and completion of this study. First, my utmost gratitude to my advisor Dr. Andrew T¨or¨okfor the support and help he provided me throughout my graduate education; my commit- tee members, Dr. Vaughn Climenhaga, Dr. Gemunu Gunaratne, and Dr. Matthew Nicol for their participation and their thoughtful comments; all professors in the dynamical system research group of University of Houston, Dr. Vaughn Climenhaga, Dr. Alan Haynes, Dr. Matthew Nicol, Dr. William Ott, and Dr. Andrew T¨or¨okfor organizing the wonderful \Houston Summer School on Dynamical Systems", where I learned a lot about dynamical systems, ergodic theory, number theory, and quantum mechanics. iii ABSTRACT We study the limit behavior of the non-stationary/random chaotic dynamical systems and prove a strong statistical limit theorem: (vector-valued) almost sure invariance principle for the non- stationary dynamical systems and quenched (vector-valued) almost sure invariance principle for the random dynamical systems. It is a matching of the trajectories of the dynamical system with a Brownian motion in such a way that the error is negligible in comparison with the Birkhoff sum. -
A Translation Of
2011 A Translation of NJV 72^ dsgecr 1 2011 NJV 72^ dsgecr 2 2011 American Mathematical Society Providence, Rhode Island USA ISSN 0077-1554 TRANSACTIONS OF THE MOSCOW MATHEMATICAL SOCIETY Translation edited by Frances H. Goldman with the assistance of AMS staff A translation of TRUDY MOSKOVSKOGO MATEMATIQESKOGO OBWESTVA Editorial Board A. G. Sergeev (Editor in Chief) V. M. Buchstaber E.` B. Vinberg Yu. S. Ilyashenko A. A. Shkalikov A. V. Domrin (Corresponding Secretary) Advisory Board R. A. Minlos S. P. Novikov N. Kh. Rozov Library of Congress Card Number 65-4713 SUBSCRIPTION INFORMATION. Transactions of the Moscow Mathematical Society for 2011 will consist of one issue. Beginning in 2004, Transactions of the Moscow Mathematical Society is accessible from www.ams.org/journals/. The subscription prices for 2011 are US$532.00 list; US$425.00 institutional member. Upon request, subscribers to paper delivery of this journal are also entitled to receive electronic delivery. For paper delivery, subscribers outside the United States and India must pay a postage surcharge of US$6.00; subscribers in India must pay a postage surcharge of US$13.00. Expedited delivery to destinations in North America US$8.00; elsewhere US$17.00. Subscription renewals are subject to late fees. See www.ams.org/journal-faq for more journal subscription information. BACK NUMBER INFORMATION. For back issues see www.ams.org/bookstore. Subscriptions and orders should be addressed to American Mathematical Society, P.O. Box 845904, Boston, MA 02284-5904, USA. All orders must be accompanied by payment. Other cor- respondence should be addressed to 201 Charles St., Providence, RI 02904-2294, USA. -
Math.DS] 5 Aug 2014 Etns E PK O Opeesv Uvyo H Ujc.I Subject
SYNCHRONIZATION PROPERTIES OF RANDOM PIECEWISE ISOMETRIES VICTOR KLEPTSYN AND ANTON GORODETSKI Abstract. We study the synchronization properties of the random double rotations on tori. We give a criterion that show when synchronization is present in the case of random double rotations on the circle and prove that it is always absent in dimensions two and higher. 1. Introduction The observation of a synchronization effect goes back at least to 17th century, when Huygens [Hu] discovered the synchronization of two linked pendulums. Since then, synchronization phenomena have been observed in numerous systems and settings, see [PRK] for a comprehensive survey of the subject. In the theory of dynamical systems, synchronization usually refers to random dynamical system trajectories of different initial points converging to each other under the applica- tion of a sequence of random transformations. A first such result is the famous Furstenberg’s Theorem [Fur1], stating that under some very mild assumptions, the angle (mod π) between the images of any two vectors under a long product of random matrices (exponentially) tends to zero. Projectivizing the dynamics, it is easy to see that this theorem in fact states that random trajectories of the quotient system on the projective space (exponentially) approach each other. For random dynamical systems on the circle, several results are known. Surely, in random projective dynamics there is a synchronization due to the simplest pos- sible case of Furstenberg’s Theorem. In 1984, this result was generalized to the setting of homeomorphisms (with some very mild and natural assumptions of min- imality of the action and the presence of a North-South map) in the work of a physicist V. -
A Model of Gene Expression Based on Random Dynamical Systems Reveals Modularity Properties of Gene Regulatory Networks†
A Model of Gene Expression Based on Random Dynamical Systems Reveals Modularity Properties of Gene Regulatory Networks† Fernando Antoneli1,4,*, Renata C. Ferreira3, Marcelo R. S. Briones2,4 1 Departmento de Informática em Saúde, Escola Paulista de Medicina (EPM), Universidade Federal de São Paulo (UNIFESP), SP, Brasil 2 Departmento de Microbiologia, Imunologia e Parasitologia, Escola Paulista de Medicina (EPM), Universidade Federal de São Paulo (UNIFESP), SP, Brasil 3 College of Medicine, Pennsylvania State University (Hershey), PA, USA 4 Laboratório de Genômica Evolutiva e Biocomplexidade, EPM, UNIFESP, Ed. Pesquisas II, Rua Pedro de Toledo 669, CEP 04039-032, São Paulo, Brasil Abstract. Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node is modeled by a RDS. The main virtues of this approach are the following: (i) it provides a natural way to obtain arbitrarily large networks by coupling together simple basic pieces, thus revealing the modularity of regulatory networks; (ii) the assumptions about the stochastic processes used in the modeling are fairly general, in the sense that the only requirement is stationarity; (iii) there is a well developed mathematical theory, which is a blend of smooth dynamical systems theory, ergodic theory and stochastic analysis that allows one to extract relevant dynamical and statistical information without solving -
Arxiv:1708.06571V1 [Nlin.AO] 22 Aug 2017 the Generating Unit, Which Is the Pressure Reservoir Be- Coupling: Neath the Pipe at a Basically Constant Rate
SAW16, dated September 28, 2018 Synchronization of organ pipes 1, 2 1 Jakub Sawicki, ∗ Markus Abel, and Eckehard Schöll 1Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany 2Department of Physics and Astronomy, Potsdam University, Karl-Liebknecht-Straße 24, 14476 Potsdam Germany We investigate synchronization of coupled organ pipes. Synchronization and reflection in the organ lead to undesired weakening of the sound in special cases. Recent experiments have shown that sound interaction is highly complex and nonlinear, however, we show that two delay-coupled Van-der-Pol oscillators appear to be a good model for the occurring dynamical phenomena. Here the coupling is realized as distance-dependent, or time-delayed, equivalently. Analytically, we investigate the synchronization frequency and bifurcation scenarios which occur at the boundaries of the Arnold tongues. We successfully compare our results to experimental data. PACS numbers: 05.45.Xt, 05.45.-a Introduction - The physics of organ pipes is an in- we investigate the bifurcation scenarios in the context of terdisciplinary topic where many fields of science meet. two delay-coupled Van-der-Pol oscillators as a represen- It is highly interesting as it includes elements of non- tation of the system of two coupled organ pipes, such linear dynamical system theory [4, 6, 11], aeroacoustic as in the experimental setup of Bergweiler et al. [5]. modeling [13] and synchronization theory [17]. The fo- In extension of previous work, we study the dependence cus of these different research areas is the “queen of in- of Arnold tongues under variation of the time delay τ struments” which captivates through the grandeur of her and the coupling strength κ, to explore how undesired sight and majesty of her sound. -
The Mathematics of Critical Shifts in Ecological Networks with Alternative Stable State Theory, a Potential Framework for Early Warning Indicators
The Mathematics of Critical Shifts in Ecological Networks with Alternative Stable State Theory, A Potential Framework for Early Warning Indicators by Michael Kupperman A THESIS submitted to Oregon State University Honors College in partial fulfillment of the requirements for the degree of Honors Bachelors of Science in Mathematics (Honors Scholar) Honors Bachelors of Science in Biochemistry & Molecular Biology (Honors Scholar) Presented June 14, 2019 Commencement June 2020 AN ABSTRACT OF THE THESIS OF Michael Kupperman for the degree of Honors Bachelors of Science in Mathematics and Honors Bachelors of Science in Biochemistry & Molecular Biology presented on June 14, 2019. Title: The Mathematics of Critical Shifts in Ecological Networks with Alternative Stable State Theory, A Potential Framework for Early Warning Indicators Abstract approved: David Koslicki A long running problem in mathematical biology is the prediction of extinction events, a specialized case of the larger global stability problem found in differential equations and dynamical systems theory. A central technical question is how to introduce the randomness observed in real ecological systems not accounted for in deterministic models. This work introduces the SP-system as a new mathematical object in which ecological parameters are treated as sequences of random variables that attain values over intervals of random lengths of time. The SP-system characterization of ecological networks leads to two differ- ent novel approaches for the simulation and extinction prediction. The first approach uses a construct new to modeling literature to describe the probability of a parameter transition event into an extinction event. The second approach utilizes Markov chains for both sim- ulation and extinction prediction. -
Transformacje Pilki Noznej
„Kultura Współczesna” 1(94)/2017 doi.org/10.26112/kw.2017.94.07 Konrad Niciński Transformacje piłki nożnej 1989–1993 Niedziela cudów jako studium przypadku Konrad Niciński eśli próbować pisać kulturową historię polskiej pił- doktor nauk humanistycz- Jki nożnej, to z pewnością uwagę przyciągać będzie nych, historyk kultury; absol- okres 1989–1993. Nie dlatego oczywiście, że obfitował went historii sztuki i polonistyki na Uniwersy- w sukcesy sportowe. Wręcz przeciwnie, jest to jeden tecie Warszawskim, gdzie z okresów dla krajowej piłki najczarniejszych. Nie tyl- obronił pracę doktorską w ko ze względu na niski poziom piłkarski. Nie tylko też Instytucie Literatury Polskiej; – choć ta przyczyna jest bardzo ważna – ze względu pracownik Zakładu Bałtysty- na wyjątkowy nawet na tle lat poprzednich i następ- ki UW; współpracuje z Pracownią Studiów Miej- nych poziom upadku moralnego całego środowiska. skich IKP UW, Pracownią Także dlatego, że osiągnięcia były odwrotnie propor- Literatury Modernizmu cjonalne do oczekiwań. Europy Środkowej i Wschod- O ile o kolejnych latach polskiej piłki często moż- niej przy ILP UW, Zespołem na powiedzieć za Andrzejem Stasiukiem „Nie mia- Badań Obszarów Trzecich Literatury przy IBL PAN; łem szczególnych oczekiwań, to i się zanadto nie zainteresowania badawcze: rozczarowałem” do szkicu (z konieczności) na temat literatura i kultura polska początków transmisji rozgrywek amerykańskiej ligi w latach 1905–1930, szcze- koszykarskiej”1, o tyle polskiej piłce okresu przełomu gólnie ówczesne projekty towarzyszyły poważne oczekiwania, przynajmniej antropologiczne i korespon- dencja sztuk; od 2013 jeśli idzie o występy międzynarodowe; i nie były one kierownik organizacyjny nieuzasadnione. Czy wypadki związane z korupcją, Olimpiady Literatury i Języka pijaństwem i ogólnym tumiwisizmem w polskiej lidze Polskiego; publikował m.in. -
Professor Richard Courant (1888 – 1972)
Professor Richard Courant (1888 – 1972) From Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Richard_Courant Field: Mathematics Institutions: University of Göttingen University of Münster University of Cambridge New York University Alma mater: University of Göttingen Doctoral advisor: David Hilbert Doctoral students: William Feller Martin Kruskal Joseph Keller Kurt Friedrichs Hans Lewy Franz Rellich Known for: Courant number Courant minimax principle Courant–Friedrichs–Lewy condition Biography: Courant was born in Lublinitz in the German Empire's Prussian Province of Silesia. During his youth, his parents had to move quite often, to Glatz, Breslau, and in 1905 to Berlin. He stayed in Breslau and entered the university there. As he found the courses not demanding enough, he continued his studies in Zürich and Göttingen. Courant eventually became David Hilbert's assistant in Göttingen and obtained his doctorate there in 1910. He had to fight in World War I, but he was wounded and dismissed from the military service shortly after enlisting. After the war, in 1919, he married Nerina (Nina) Runge, a daughter of the Göttingen professor for Applied Mathematics, Carl Runge. Richard continued his research in Göttingen, with a two-year period as professor in Münster. There he founded the Mathematical Institute, which he headed as director from 1928 until 1933. Courant left Germany in 1933, earlier than many of his colleagues. While he was classified as a Jew by the Nazis, his having served as a front-line soldier exempted him from losing his position for this particular reason at the time; however, his public membership in the social-democratic left was a reason for dismissal to which no such exemption applied.[1] After one year in Cambridge, Courant went to New York City where he became a professor at New York University in 1936. -
Homogenization 2001, Proceedings of the First HMS2000 International School and Conference on Ho- Mogenization
in \Homogenization 2001, Proceedings of the First HMS2000 International School and Conference on Ho- mogenization. Naples, Complesso Monte S. Angelo, June 18-22 and 23-27, 2001, Ed. L. Carbone and R. De Arcangelis, 191{211, Gakkotosho, Tokyo, 2003". On Homogenization and Γ-convergence Luc TARTAR1 In memory of Ennio DE GIORGI When in the Fall of 1976 I had chosen \Homog´en´eisationdans les ´equationsaux d´eriv´eespartielles" (Homogenization in partial differential equations) for the title of my Peccot lectures, which I gave in the beginning of 1977 at Coll`egede France in Paris, I did not know of the term Γ-convergence, which I first heard almost a year after, in a talk that Ennio DE GIORGI gave in the seminar that Jacques-Louis LIONS was organizing at Coll`egede France on Friday afternoons. I had not found the definition of Γ-convergence really new, as it was quite similar to questions that were already discussed in control theory under the name of relaxation (which was a more general question than what most people mean by that term now), and it was the convergence in the sense of Umberto MOSCO [Mos] but without the restriction to convex functionals, and it was the natural nonlinear analog of a result concerning G-convergence that Ennio DE GIORGI had obtained with Sergio SPAGNOLO [DG&Spa]; however, Ennio DE GIORGI's talk contained a quite interesting example, for which he referred to Luciano MODICA (and Stefano MORTOLA) [Mod&Mor], where functionals involving surface integrals appeared as Γ-limits of functionals involving volume integrals, and I thought that it was the interesting part of the concept, so I had found it similar to previous questions but I had felt that the point of view was slightly different.