PROGRAMME
Organized by the Dynamical Systems Interdisciplinary Network, University of Copenhagen
Funded by The UCPH Excellence Programme for Interdisciplinary Research and The Center for Models of Life, Niels Bohr Institute Last update: August 29, 2014 Contents
Venue Information and Maps ii
Programme v
Abstracts vii
List of Participants xviii
Organizing Committee Erik Andreas Martens Susanne Ditlevsen Rune Berg Olga Sosnovtseva Niels-Henrik Holstein-Rathlou
University of Copenhagen The Faculty of Science The Faculty of Health and Medical Sciences
http://dsin.ku.dk/calendar/workshop_sep14/
i Venue Information and Maps
Venue:
University of Copenhagen The Niels Bohr Institute, Auditorium A Niels Bohr Institutet Blegdamsvej 17, 2100 Copenhagen Ø
Welcome Reception and Poster Session
The Welcoming reception on Monday at 17.30 and the coee breaks will take place in the Lille Frokoststue (Small Lunch Room) near the NBI lunch room. Poster boards and pins are provided; poster sizes should be size A1 or A2 (but not A0) to save the limited space.
Lunch:
University of Copenhagen Canteen of Niels Bohr Institute Blegdamsvej 17 2100 Copenhagen Ø
Conference Dinner
Tuesday, September 2, 19:00 Restaurant Søren K Søren Kierkegaards Plads 1, 1221 København K map location
Internet
The entire Niels Bohr Institute is covered by the Eduroam wireless network.The eduroam wireless network can be accessed with your username and password from your home institution. Alterna- tively, you can connect to the network Conference using the password Bohr2013. You can nd guidance regarding network security and printers at the website www.nbi.dk/computation.
How to get to the Institute
All talks will take place in Auditorium A at the Niels Bohr Institute (NBI) on Blegdamsvej 17. All information you need for how to reach the Niels Bohr Institute from hotels/metro sta- tions/railway stations can be found here. There you will also nd a detailed map of the area and further relevant information, e.g. tickets for public transportation.
ii Maps of the Venue
A detailed map with all hotel, restaurant, bar and conference venue locations is available here.
The Niels Bohr Institute
NBI Canteen NBI Canteen,Coffee CoffPosteree break, session Poster session
Auditorium A
Auditorium A
Blegdamsvej 17 Blegdamsvej 17
Niels Bohr Institute
Hotel Nora
CabInn Nørreport St. Scandinavia Metro/Train to/from Kastrup airport
Researcher Hotel
Figure 1: Top Map: Auditorium A (lecture hall) and nearby lunch restaurant. Bottom Map: Auditorium A (lecture hall), Hotel Nora, CabInn Scandinavia and Researcher Hotel. Nørreport train and metro station. Where to eat and drink
There are plenty of choice on where to eat and drink in Copenhagen, both near the Venue of the conference and in the city center. A detailed list and map can be found here. A good location is Sankt Hans Torv (10 minutes walking from the venue of the conference) and nearby, where you nd several nice bars, cafe, restaurants and pubs. Other options (all listed here) are the following:
Where to eat Restaurant (Reservation is recommended)
• Halifax Burgers: one of the best burger place in Copenhagen. Burger + side dishes: 130 DKK.
• Zafran Restaurant: Persian food; main courses: 90-120 DKK; you can bring your own bottle of wine.
• LéLé Street Kitchen: Vietnamese food; 50-100 DKK. • Det Lille Apotek: Oldest restaurant in Copenhagen, Danish food. Main courses: 70-150 DKK (lunch), 170-240 DKK (dinner).
• Søren K Restaurarant: Danish food; main course: 175 DKK (lunch), 225 DKK (dinner)
Where to drink Café where you can also eat burgers/salads
• The Laudromat Cafe , Elmegade 15
• Cafe 22 , Sortedam Dossering 21 • Restaurant Barcelona , Fælledvej 21
If you are thirsty, then it is time for a beer at:
• Mikkeller: Microbrewery. Mikkeller bar in Viktoriagade 8 B-C. Mikkeller & friends in Stefansgade.
• Brew Pub: Microbrewery in the city center.
• Ølbaren: Plenty of beers from all over the world. Programme
Monday, September 1
08:30-09:00 Registration 09:00-09:10 Welcome and practical informations
09:10-09:50 Albert Goldbeter: CDK oscillations drive the mammalian cell cycle
09:50-10:30 Alexander Aulehla: Self-organization of cellular genetic oscillators during embryo devel- opment
10:30-11:00 Coee Break
11:00-11:40 Ala Trusina: Dynamic complexity of NF-kB regulatory network
11:40-12:20 Hanspeter Herzel: The circadian clock a system of coupled oscillators
12:20-13:00 Umberto Picchini : Approximate Bayesian Computation (ABC) for diusions observed with measurement error and large sample sizes: an application to protein folding data
13:00-14:30 Lunch at the NBI Cafe
14:30-15:10 Peter Ashwin: Indistinguishable oscillators and chimeras
15:10-15:50 Michael Rosenblum: Reconstructing eective phase connectivity of oscillator networks from observations
15:50-16:30 Coee Break
16:30-17:30 Plenary Discussion
17:30-19:00 Welcome reception + Poster session
v Tuesday, September 2
09:00-09:10 Announcements
09:10-09:50 Mogens H. Jensen: : Oscillators and Arnold tongues in cell dynamics
09:50-10:30 Rainer Dahlhaus: Phase synchronization and co-integration: bridging two theories
10:30-11:00 Coee Break
11:00-11:40 Christian Kuehn : Oscillations in multiple time scale dynamics: Autocatalysis, Koper, Olsen, and beyond
11:40-12:20 Diego Pazo: Exact ring-rate description for networks of spiking neurons
12:20-13:00 Carlo Laing: Twisted states in phase oscillator arrays
13:00-14:30 Lunch at the NBI Cafe
14:30-15:10 Marc Timme: Information routing in complex networks: remote control and hub-induced signal propagation
15:10-15:50 Arkady Pikovsky: Collective dynamics of oscillator populations: nonlinear coupling and multifrequency ensembles
15:50-16:30 Coee Break
16:30-17:30 Plenary Discussion
19:00-open! Conference Dinner at Restaurant Søren K
Wednesday, September 3
09:00-09:40 Jordi Garcia-Ojalvo: Dynamics of bacterial stress response
09:40-10:20 Eleni Katifori: Structural self-assembly in locally Adaptive Networks
10:20-11:00 Natalya Janson: Networks of stochastic neuron-like systems
10:30-11:00 Coee Break
11:00-11:40 Johnny Ottesen: Ultradian and circadian oscillations in the neuroendocrine HPA-axis and its relation to depression
11:40-12:20 Michael Zaks: Dynamics in regular networks: hierarchy of couplings
12:20-13:00 Peter Ditlevsen: The glacial cycles, a puzzle of the Climate System
13:00-14:30 Lunch at the NBI Cafe Abstracts
Self-organization of cellular genetic oscillators during embryo development Aulehla, Alexander (speaker) EMBL Heidelberg, Germany, [email protected]
In our group, we are focusing on the temporal aspect of embryonic development and thus on the role of embryonic oscillators. In mouse embryos, several signaling pathways oscillate in their activity (period 2hours) during mesoderm patterning and these oscillations are linked to the formation of pre-vertebrae, or somites. Most strikingly, oscillations occur phase-shifted between neighbouring cells, producing spatio-temporal wave patterns that traverse the embryo. In this talk, I will discuss a novel in vitro assay for segmentation and real-time quanti cations of oscillatory activities, revealing the potential of genetic oscillators to self-organize and generate coherent spatio-temporal wave patterns from a randomized starting condition. I will present recent ndings addressing underlying working principles.
Indistinguishable oscillators and chimeras Ashwin, Peter (speaker) University of Exeter, UK, [email protected] Burylko, Oleksandr National Academy of Sciences, Kiev, Ukraine
Keywords: Coupled oscillator; Symmetry; Chimera state.
This talk will look at an approach to understanding some emergent dynamics in coupled oscil- lator systems composed of identical and indistinguishable oscillators in terms of modules. In par- ticular we propose a checkable de nition for a chimera state and give some basic results on systems that can/cannot have chimera states in their dynamics using this de nition. These include chimera states for systems of at least four oscillators with two coupling strengths and Hansel-Mato-Meunier type coupling. We also explore the relationship between this and a modular network structure.
Phase synchronization and cointegration: bridging two theories Dahlhaus, Rainer (speaker) Heidelberg University, Germany, [email protected] Jan C. Neddermeyer DZ Bank, Frankfurt, Germany
Keywords: phase synchronization, cointegration, state space model, statistical tests
vii The theory of cointegration has been the leading theory in econometrics with powerful appli- cations to macroeconomics during the last decades. On the other hand phase synchronization for oscillators has been a major research topic in physics with many applications in dierent areas of science. In particular in neuroscience the understanding of phase synchronization is of impor- tance since phase synchronization is regarded as essential for functional coupling of dierent brain regions. In an abstract sense both theories describe the dynamic uctuation around some equilib- rium. In this talk we point out that, after some mathematical transformation, there exists a close connection between both subjects. As a consequence several techniques on statistical inference for cointegrated systems can immediately be applied for statistical inference on phase synchronization based on empirical data. This includes tests for phase synchronization, tests for unidirectional coupling and the identi cation of the equilibrium from data including phase shifts. We give an example where a chaotic Rössler-Lorenz system is identi ed with the methods from cointegration. Cointegration may also be used to investigate phase synchronization in complex networks. References
Dahlhaus, R. and Neddermeyer, J.C. (2012). On the relationship between the theory of cointegra- tion and the theory of phase synchronization. arXiv:1201.0651
The glacial cycles, a puzzle of the climate system Ditlevsen, Peter (speaker) University of Copenhagen, Denmark, [email protected]
The dynamics of the climate system is governed by a complex network of interactions between the atmosphere, the oceans, the land and ice-masses and the biosphere. In the latest geological epoch the climate has changed regularly between iceages and warm periods like our present climate. The periodicity of the glacial cycles has been around 100.000 years for the last million years. Prior to that the glacial cycles lasted around 40.000 years. No change in the astronomical forcing has happened, but the non-linear response to the forcing suddenly changed 1 million years ago. I will discuss possible dynamical mechanisms which could explain this behavior of the climate.
Dynamics of bacterial stress response Garcia-Ojalvo, Jordi (speaker) Universitat Pompeu Fabra, Spain, [email protected]
Cells respond to environmental conditions by activating regulatory programs that are frequently dynamic. This is specially true for the case of stress responses, since stress conditions usually vary as time progresses, and the best way for cells to react to these dynamic conditions is by responding dynamically. In this talk I will give an overview of recent work on the dynamics of stress responses in the bacterium Bacillus subtilis, using a combination of experimental monitoring by time-lapse microscopy and mathematical modelling.
Cdk oscillations drive the mammalian cell cycle Goldbeter, Albert (speaker) Unité de Chronobiologie théorique, Faculté des Sciences, Université Libre de Bruxelles (ULB), Campus Plaine, CP 231, B-1050 Brussels, Belgium, [email protected] Claude Gérard Unité de Chronobiologie théorique, Faculté des Sciences, Université Libre de Bruxelles (ULB), Campus Plaine, CP 231, B-1050 Brussels, Belgium 1
Keywords: cell cycles; growth factors
A network of cyclin-dependent kinases (Cdks) drives progression through the successive phases G1, S (DNA replication), G2 and M (mitosis) of the mammalian cell cycle. To better understand the dynamics of this key cellular system, a detailed computational model based on regulatory interactions between the Cdks and other proteins of the network was developed. The model contains four modules, each centered around one cyclin/Cdk complex: cyclin D/Cdk4-6 and cyclin E/Cdk2 promote progression in G1 and elicit the G1/S transition, respectively; cyclin A/Cdk2 ensures progression in S and the transition S/G2, while the activity of cyclin B/Cdk1 brings about the G2/M transition. This model shows that in the presence of supra-threshold amounts of growth factor the Cdk network is capable of sustained oscillations, which correspond to the repetitive, sequential activation of the various cyclin/Cdk complexes that control the successive phases of the cell cycle [1, 2]. The results suggest that the switch from cellular quiescence to cell proliferation corresponds to the passage through a bifurcation point associated with the transition from a stable steady state to sustained oscillations in the Cdk network. Such transition is governed by a nely tuned balance between factors that promote or hinder progression in the cell cycle. Among the factors capable of altering this balance and the passage through the bifurcation point separating cell cycle arrest from cell proliferation are growth factors, oncogenes, Cdk inhibitors, tumor suppressors, the extracellular matrix, and cell contact inhibition [1-3]. References
[1] Gérard C, Goldbeter A (2009). Temporal self-organization of the cyclin/Cdk network driving the mammalian cell cycle. Proc Natl Acad Sci USA 106, 21643-21648. [2] Gérard C, Goldbeter A (2012). From quiescence to proliferation : Cdk oscillations drive the mammalian cell cycle. Front. Physiol. 3:413, doi: 10.3389/fphys.2012.00413. [3] Gérard C, Goldbeter A (2014). The balance between cell cycle arrest and cell prolifera- tion: control by the extracellular matrix and by contact inhibition. Interface Focus 4: 20130075. (http://dx.doi.org/10.1098/rsfs.2013.0075)
The circadian clock a system of coupled oscillators Herzel, Hanspeter (speaker) Humboldt-University Berlin, Germany, [email protected] Bordyugov, Grigory Humboldt-University, Berlin Ananthasubramaniam, Bharath Humboldt-University, Berlin
Keywords: circadian clock; synchronization; entrainment; chronotypes
The mammalian circadian clock is generated by negative feedbacks in gene-regulatory networks. Clock genes such as period and rev-erb are transcribed during the day and inhibit their own production after a delay of about 6 hours leading to single cell rhythms. Synchronization of 20000 neurons in the suprachiasmatic nucleus (SCN) orchestrates sleep-wake cycles, hormone oscillations and multiple physiological rhythms. We discuss synergies of feedback loops to generate oscillations [1], the role of neuropeptide phases for synchronization [2], nonlinear phenomena in rodents forced by extreme zeitgeber periods [3,4], and the variability of human chronotypes [5,6].
1Present address: de Duve Institute, Université catholique de Louvain (UCL), Avenue Hippocrate 75, 1200 Brussels, Belgium References [1] Ananthasubramaniam, B. and Herzel, H. (2014) Positive feedback promotes oscillations in negative feedback loops, PLoS One 9:e104761. [2] Ananthasubramaniam, B., Herzog, E.D. and Herzel, H. (2014) Timing of neuropeptide coupling determines synchrony and entrainment in the mammalian circadian clock, PLoS Computational Biology 10:e1003565. [3] Granada, A.E., Cambras, T., Diez-Noguera, A., and Herzel, H. (2011) Circadian desynchro- nization, J R Soc Interface Focus 1, 153-166. [4] Erzberger, A., Hampp, G., Granada, A.E., Albrecht, U., and Herzel, H. (2013) Genetic redun- dancy strengthens the circadian clock leading to a narrow entrainment range, J R Soc Interface 10:0221. [5] Brown, S.A., Kunz, D., Dumas, A., Westermark, P.O., Vanselow, K., Tilmann-Wahnschae, A., Herzel, H., and Kramer, A. (2008) Molecular insights into human daily behavior, Proc Natl Acad Sci USA 105, 1602-1607. [6] Granada, A.E., Bordyugov, G., Kramer, A., and Herzel, H. (2011) Human chronotypes from a theoretical perspective, PLoS One 8:e59464.
Networks of stochastic neuron-like systems Janson, Natalia (speaker) Loughborough University, United Kingdom, [email protected] Dickson, Scott Loughborough University, United Kingdom Patidar, Sandhya Heriot-Watt University, United Kingdom Pototsky, Andrey Swinburne University of Technology, Australia Keywords: stochastic; synchronisation; neuron; network We consider networks of stochastic units mimicking excitable neurons of various sizes and coupled in a variety of ways: from mean eld coupling [1,2], through sparse couplings xed in time, to sparse connections varying in time randomly and slowly to imitate learning in the brain, with couplings between each pair of units being bi- or uni-directional. In all cases we look at the level of synchronisation in the network [3]. We observe some counter-intuitive behaviour in such networks, such as a larger coupling strength needed to induce synchronisation with higher, rather than lower, connectivity. We also examine how synchronisation is being altered in case the delayed feedback is applied to the network. The delayed feedback results suggest that even weakly and globally applied delayed feedback may reduce excessive degrees of synchronisation to more moderate levels; it is also possible to strengthen weak synchronisation. Cumulant analysis is used to reduce stochastic equations describing a network with constant non-mean- eld coupling to deterministic ones in the attempt to explain the results of numerical simulations. References [1] Patidar, S, Pototsky, A and Janson, NB (2009) Controlling noise-induced behavior of excitable networks, New Journal of Physics 11(21), 073001. [2] Janson, NB, Pototsky A and Patidar, S (2010) Delayed feedback control in stochastic excitable networks, From Physics to Control Through an Emergent View, Luigi Fortuna, Alexander Fradkov, Mattia Frasca Eds., pp. 5156, World Scienti c. [3] Dickson S (2014) Stochastic neural network dynamics: synchronisation and control, PhD thesis, Loughborough University. Oscillators and Arnold tongues in cell dynamics Jensen, Mogens Høegh (speaker) Niels Bohr Institute, Copenhagen, Denmark, [email protected]
Oscillating genetic patterns have been observed in networks related to the transcription factors NFkB, p53 and Hes1 [1]. We identify the central feed-back loops and found oscillations when time delays due to saturated degradation are present. By applying an external periodic signal, it is sometimes possible to lock the internal oscillation to the external signal. For the NF-kB systems in single cells we have observed that the two signals lock when the ration between the two frequencies is close to basic rational numbers [2]. The resulting response of the cell can be mapped out as Arnold tongues. When the tongues start to overlap we observe a chaotic dynamics of the concentration in NF-kB [2]. Oscillations in some genetic systems can be triggered by noise, i.e. a linearly stable system might oscillate due to a noise induced instability. By applying an external oscillating signal to such systems we predict that it is possible to distinguish a noise induced linear system from a system which oscillates via a limit cycle. In the rst case Arnold tongues will not appear, while in the second subharmonic mode-locking and Arnold tongues are likely [3]. References
[1] B. Mengel, A. Hunziker, L. Pedersen, A. Trusina, M.H. Jensen and S. Krishna, "Modeling oscil- latory control in NF-kB, p53 and Wnt signaling", Current Opinion in Genetics and Development 20, 656-664 (2010). [2] M.H. Jensen and S. Krishna, "Inducing phase-locking and chaos in cellular oscillators by mod- ulating the driving stimuli", FEBS Letters 586, 1664-1668 (2012). [3] N. Mitarai, U. Alon and M.H. Jensen, "Entrainment of linear and non-linear systems under noise", Chaos, Chaos 23, 023125 (2013).
Structural self-assembly in locally adaptive networks Katifori, Eleni (speaker/presenter) Max-Planck Institute for Dynamics and Self-Organization, Germany, [email protected] Johannes Gräwer Max-Planck Institute for Dynamics and Self-Organization, Germany Carl D. Modes The Rockefeller University, USA Marcelo O. Magnasco The Rockefeller University, USA
Keywords: adaptive Networks; Physarum
Transport networks play a key role across four realms of eukaryotic life: slime molds, fungi, plants, and animals. In addition to the developmental algorithms that build them, many also em- ploy adaptive strategies to respond to stimuli, damage, and other environmental changes. We model these adapting network architectures using a generic dynamical system on weighted graphs driven by uctuating load, and nd in simulation that these networks ultimately develop a hierarchical organization of the nal weighted architecture accompanied by the formation of a system-spanning backbone. In addition, we nd that the long term equilibration dynamics exhibit behavior char- acterized by long periods of slow changes punctuated by bursts of reorganization events [1]. References
[1] Johannes Gräwer, Carl D. Modes, Marcelo O. Magnasco, and Eleni Katifori (2014) Structural Self-Assembly and Glassy Dynamics in Locally Adaptive Networks, arXiv:1405.7870 [nlin.AO] Oscillations in multiple time scale dynamics: Autocatalysis, Koper, Olsen, and beyond Kuehn, Christian (speaker) Vienna University of Technology, Austria, [email protected]
Keywords: MMOs; Unbounded Manifolds; GSPT; Patterns.
In this talk, I will give an overview of multiple time scale dynamics approaches to classify oscillatory patterns. After some basic introduction to geometric singular perturbation theory, three dierent models will be introduced to illustrate dierent oscillatory patterns. For autocatalytic reactions, I will highlight the role of global and local singular mechanisms to generate relaxation oscillations [5]. In the context of the Koper model, I am going to introduce mixed-mode oscillations (MMOs), which are patterns of alternating small- and large-amplitude oscillations. The eect of de-coupling the local and global dynamics will be stressed [3]. Then, I will show the potential complexity encountered in a more realistic model for the peroxidase-oxidase reaction by Olsen, including a new mechanism fast-slow mechnism for chaos [7]; the work on the Olsen model is joint work with Peter Szmolyan (Vienna). In the last part of my talk, I shall motivate why the techniques I sketched for the three models, can also be applied to models of extremely high complexity such as fast-slow dynamics in adaptive networks [4], generalized models [6] and stochastic systems [1,2]. References
[1] N. Berglund, B. Gentz, and C. Kuehn. Hunting French ducks in a noisy environment. J. Dierential Equat., 252(9):47864841, 2012. [2] N. Berglund, B. Gentz, and C. Kuehn. From random Poincaré maps to stochastic mixed-mode- oscillation patterns. arXiv:1312.6353, pages 155, 2013. [3] C. Kuehn. On decomposing mixed-mode oscillations and their return maps. Chaos, 21(3):033107, 2011. [4] C. Kuehn. Time-scale and noise optimality in self-organized critical adaptive networks. Phys. Rev. E, 85(2):026103, 2012. [5] C. Kuehn. Loss of normal hyperbolicity of unbounded critical manifolds. Nonlinearity, 27(6):13511366, 2014. see also arXiv:1204.0947. [6] C. Kuehn and T. Gross. Nonlocal generalized models of predator-prey systems. Discr. Cont. Dyn. Syst. B, 18(3):693720, 2013. [7] C. Kuehn and P. Szmolyan. Multiscale geometry of the Olsen model and non-classical relaxation oscillations. arXiv:1403.5658, pages 146, 2014.
Twisted states in phase oscillator arrays Laing, Carlo (speaker) Massey University, New Zealand, [email protected] Oleh Omel'chenko Weierstrass Institute, Germany Matthias Wolfrum Weierstrass Institute, Germany
Keywords: coupled oscillators; Kuramoto model; twisted states; Ott/Antonsen; Eckhaus bifurcation
We consider a one-dimensional array of phase oscillators with non-local coupling and a Loren- ztian distribution of natural frequencies. The primary objects of interest are partially coherent states that are uniformly twisted in space. To analyze these we take the continuum limit, perform an Ott/Antonsen reduction, integrate over the natural frequencies and study the resulting spatio- temporal system on an unbounded domain. We show that these twisted states and their stability can be calculated explicitly. We nd that stable twisted states with dierent wave numbers appear for increasing coupling strength in the well-known Eckhaus scenario. References
[1] Omel'chenko, O., Wolfrum, M., and Laing, C. R. (2014) Partially coherent twisted states in arrays of coupled phase oscillators, Chaos 24, 023102.
Ultradian and circadian oscillations in the neuroendocrine HPA-axis and its relation to depression Ottesen, Johnny T. (speaker) Roskilde University, Denmark, [email protected] Stine timmermann H. Lundbeck A/S, Denmark Johanne Gudmand-Hoeyer Roskilde University, Denmark
Keywords: HPA-axis; Depression; Non-Linear Mixed Eects Model; Parameter Estimation.
The hypothalamus-pituitary-adrenal (HPA) axis is a complex neuroendocrine system control- ling the stress hormone cortisol in human. Serum concentration of the involved hormones shows circadian rhythm as well as a faster ultradian rhythm with a period of 1-2 hours [1,2]. These oscillations are generally disturbed during many illnesses and are believed to relate to a number of pathological conditions. Recently we have shown that these oscillations correlate with three groups of dierent health conditions (two depressed states and one healthy control group) in a clinical experiment involving 29 subjects [3]. In addition, a novel model has been proposed, which ts data individually using the Shu ed Complex Evolution (SCE) method [4]. The model has also been embedded in a Non-Linear Mixed Eects (NLME) framework giving a population approach and re- sulting in a four parameter characterization of the aforementioned three groups [4]. This approach shows that dierent health conditions are re ected in a few parameters suggesting a method for not only exact but also re ned diagnoses based on the modeling of the complex oscillations of the HPA axis. The procedure may suggest dierent treatment plans and target candidates in drug development. References
[1] Vinther F, Andersen M and Ottesen JT. (2010) The Minimal Model of the Hypothalamic- Pituitary-Adrenal Axis, Journal of Mathematical Biology 29, 467483. Springer-Verlag. [2] Andersen, M, Vinther F and Ottesen JT. (2013) Mathematical modelling of the hypothalamic- pituitary-adrenal gland (HPA) axis: Including hippocampal mechanisms., Mathematical Bio- sciences 246(1), 122-138. Elsevier. [3] Ottesen, JT. (2013) Etiology and diagnosis of major depression a novel quantitative approach., Open Journal of Endocrine and Metabolic Diseases 3, 120-127. Scienti c Research. [4] Gudmand-Hoeyer, J, Timmermann ST and Ottesen JT. (2014) Patient-speci c of the endocrine HPA-axis and its relation to depression: Ultradian and circadian oscillations., Accepted by Math- ematical Biosciences. Elsevier.
Exact firing-rate description for networks of spiking neurons Pazó, Diego (speaker) Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Spain, [email protected] Montbrió, Ernest Universitat Pompeu Fabra, Spain Roxin, Alex Centre de Recerca Matemàtica, Spain Keywords: Firing-rate model; Quadratic integrate-and- re neuron. The spiking activity generated by large neuronal networks is the principal mode of communi- cation and information processing in the brain. Collective neuronal responses are typically charac- terized by a macroscopic quantity that measures the rate at which action potentials are emitted: the ring rate. In turn, ring-rate equations have become one of the most common tools used to model large populations of neurons in terms of their aggregate spiking activity. Unfortunately, and despite their popularity among researchers, ring-rate models do not con- stitute exact derivations from the original spiking neuron networks, and fail to replicate the actual dynamics, suggesting the existence of other meaningful macroscopic quantities involved. Which are these quantities, and how do they interact with the ring rate to determine the network activity is unknown. Here we present the rst exact ring-rate model corresponding to a heterogeneous population of quadratic integrate-and- re neurons. Our equations show that the mean- eld dynamics is shaped by the nonlinear interplay of the ring rate and the population-averaged mean membrane potential. Our approach provides an exact description of all dynamical regimes in the original network model. It also permits the exact description of (i) a population under temporal forcing, or (ii) two interacting populations of excitatory and inhibitory neurons, to cite two examples where macroscopic chaos is found and exactly quanti ed by our reduced equations. References [1] Montbrió, E., Pazó D. and Roxin, A. (unpublished).
Approximate Bayesian Computation (ABC) for diffusions observed with measurement error and large sample sizes: an application to protein folding data Picchini, Umberto (speaker) Centre for Mathematical Sciences, Lund University, Sweden, [email protected] Julie Forman Dept. Biostatistics, University of Copenhagen, Denmark Keywords: Likelihood-free inference; MCMC; protein folding; stochastic dierential equation. In recent years statistical inference has been provided with a range of breakthrough Monte Carlo methods to perform exact Bayesian inference for dynamical models. However it is often not feasible to apply exact methodologies in the context of large datasets and complex models. This talk consider modelling of protein folding data via a stochastic dierential equation observed with correlated measurement errors. Exact inference proved impossible for the size of our data: in order to allow inference for model parameters within reasonable time constraints an Approximate Bayesian Computation Markov chain Monte Carlo (ABC-MCMC) algorithm is suggested. The algorithm uses simulations of subsamples as well as a so-called early rejection strategy to speed up computations in the ABC-MCMC sampler. A small sample simulation study is conducted to compare our strategy with exact Bayesian inference, the latter resulting two orders of magnitude slower in computer time than ABC-MCMC. Finally our algorithm is applied to a large size protein data. We will try to introduce the generality of ABC methodology before going into the details of our contribution. References Picchini, U. and Forman, J. (2014) Accelerating inference for diusions observed with measurement error and large sample sizes using Approximate Bayesian Computation, arXiv:1310.0973. Collective dynamics of oscillator populations: nonlinear coupling and multifrequency ensembles Pikovsky, Arkady (speaker) Potsdam University, Germany, and Nizhny Novgorod University, Russia, [email protected] Rosenblum, Michael Potsdam University, Germany Komarov, Maxim Potsdam University, Germany, and Nizhny Novgorod University, Russia
Keywords: synchronization; Collective dynamics
We discuss possibility of description of the collective dynamics of populations of oscillators in terms of closed equations for the collective modes. This description is applied to two setups. In the rst one, nonlinear coupling of identical oscillators leads to their desynchronization. In the second case, we consider mutual interaction of several populations having signi cantly dierent natural frequencies. Here both mutual synchronization and desynchronization can occur, together with complex states like heteroclinic cycle and chaos. References
[1] Komarov, M. and Pikovsky, A. (2013) Dynamics of Multifrequency Oscillator Communities, Phys. Rev. Lett. 110, 134101. [2] Komarov, M. and Pikovsky, A. (2011) Eects of non-resonant interaction in ensembles of phase oscillators, Phys. Rev. E, v. 84, 016210. [3] Pikovsky, A. and Rosenblum, M. (2011)Dynamics of heterogeneous oscillator ensembles in terms of collective variables , Physica D, v. 240, 872-881. [4] Pikovsky, A. and Rosenblum, M. (2009)Self-organized partially synchronous dynamics in pop- ulations of nonlinearly coupled oscillators, Physica D, v. 238, n. 1, pp. 27-37.
Reconstructing effective phase connectivity of oscillator networks from observations Rosenblum, Michael (speaker) University of Potsdam, Germany, [email protected] Kralemann, Björn University of Kiel, Germany Pikovsky, Arkady University of Potsdam, Germany
Keywords: oscillatory networks; Connectivity; Phase dynamics; Data analysis.
We discuss the problem of network inference from data and present an approach for invariant reconstruction of phase dynamics from observations; invariance here means independence of the recovered model on the observables used for the analysis. We start with the simplest case of two interacting oscillators and present an application of the approach to cardio-respiratory interaction in humans. We demonstrate the invariance property of our technique by showing that the coupling functions reconstructed using respiratory ow and either electrocardiogram or arterial pulse are very close [1]. Next, we present an approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The main idea is to use a triplet analysis instead of the traditional pairwise one. Our technique reveals an eective phase connectivity which is generally not equivalent to a structural one. We demonstrate that by comparing the coupling functions from all possible triplets of oscillators, we are able to achieve in the reconstruction a good separation between existing and non-existing connections, and thus reliably reproduce the network structure [2]. References
[1] Kralemann, B, et al., (2013) In vivo cardiac phase response curve elucidates human respiratory heart rate variability, Nat. Comm. 4, 2418. [2] Kralemann, B, Pikovsky, A., Rosenblum, M., (2014) Reconstructing eective phase connectivity of oscillator networks from observations, New J. Phys., in press.
Dynamic complexity of NF-kB regulatory network Trusina, Ala (speaker) Niels Bohr Institute, Denmark, [email protected] Yde, P. Jensen, Mogens H. Niels Bohr Institute, Denmark, [email protected]
The regulatory system of the transcription factor NF-κB plays a great role in many cell func- tions, including in ammatory response. Interestingly, the NF-κB system is known to up-regulate production of its own triggering signalnamely, in ammatory cytokines such as TNF, IL-1, and IL-6. In this paper we investigate a previously presented model of the NF-κB, which includes both spatial eects and the positive feedback from cytokines. The model exhibits the properties of an excitable medium and has the ability to propagate waves of high cytokine concentration. These waves represent an optimal way of sending an in ammatory signal through the tissue as they create a chemotactic signal able to recruit neutrophils to the site of infection. The simple model displays three qualitatively dierent states; low stimuli leads to no or very little response. Intermediate stimuli leads to reoccurring waves of high cytokine concentration. Finally, high stimuli leads to a sustained high cytokine concentration, a scenario which is toxic for the tissue cells and corresponds to chronic in ammation. Due to the few variables of the simple model, we are able to perform a phase-space analysis leading to a detailed understanding of the functional form of the model and its limitations. The spatial eects of the model contribute to the robustness of the cytokine wave formation and propagation.
Information routing in complex networks: remote control and hub-induced signal propagation Marc Timme1,2 (speaker) http://www.maxplanck.me, [email protected] Christoph Kirst1,2,3, Sven Jahnke1,2, Demian Battaglia4, Raoul-Martin Memmesheimer5 1Network Dynamics, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany, 2Bernstein Center for Computational Neuroscience, Göttingen, Germany, 3Center for Theoretical Studies, The Rockefeller University, New York, U.S.A., 4Institute of Systems Neuroscience, Aix-Marseille University, Marseille, France, 5Department for Neuroinformatics, Radboud University Nijmegen, Netherlands.
Keywords: information routing, signal propagation, network inverse problems
Oscillatory activity prevails across systems, from neural circuits in the brain, to the heart or gene regulatory networks in cells. Such collective dynamics of biological networks crucially underlies speci c system functions and requires exible information routing and propagation. Yet, how information may be specically communicated and dynamically routed in such systems is not well understood. Here we present two advances: First we develop a theory to predict patterns of information routing in oscillator networks of arbitrarily complex connectivity as a function of an underlying collective dynamical state. We uncover how local modications in individual oscillator properties, the connectivity structure or external inputs provide mechanisms to exibly change information routing through the entire network, even remotely. Second, we identify a new role of hubs in complex networks: in neural circuits hubs may co-activate with oscillatory dynamics thereby jointly enabling propagation of signals through such networks. These results oer novel directions of future research on information routing and propagation across complex oscillatory systems. References
[1] Jahnke, S., Timme, M. and Memmesheimer, R.-M. (2012) Guiding synchrony through random networks, Phys. Rev. X. 2, 041016. http://dx.doi.org/10.1103/PhysRevX.2.041016 [2] Jahnke, S., Memmesheimer, R.-M. and Timme, M. (2014) Hub-activated signal transmission in complex networks, Phys. Rev. E. 89, 030701(R). http://dx.doi.org/10.1103/PhysRevE.89.030701 [3] Kirst, C., et al. Dynamics of Information Routing in Complex Oscillatory Networks , in prep. (2014).
Dynamics in regular networks: hierarchy of couplings Zaks, Michael (speaker) I will report on unusual dynamics observed in ensembles of locally coupled active rotators on regular lattices with repulsive (frustrating) interaction. The ensembles split into clusters which perform periodic oscillations; the number of attracting periodic solutions is in nite, and at xed parameter values the system possesses in the phase space a continuous family of periodic orbits, with explicit integrals of motion. The reason for this unexpected richness of dynamics is explained by the fact that from the point of view of cluster evolution, local coupling turns into the global (mean eld) one. In this context, I will discuss bifurcational mechanisms as well as the interplay of symmetry and stability for dierent cluster patterns. List of Participants
Ashwin, Peter University of Exeter, UK [email protected] Aulehla, Alexander EMBL Heidelberg, DE [email protected] Balanov, Alexander Loughborough University, UK [email protected] Berg, Rune University of Copenhagen, DK [email protected] Boonen, Harrie University of Copenhagen, DK [email protected] Brasen, J. Christian Technical University of Denmark, DK [email protected] Brings Jacobsen, Jens C. University of Copenhagen, DK [email protected] Brazhe, Alexey Moscow State University, RU [email protected] Cappelletti, Daniele University of Copenhagen, DK [email protected] Cleemann, Lars University of South Carolina / DTU [email protected] Dahlhaus, Rainer University of Heidelberg, DE [email protected] heidelberg.de Ditlevsen, Susanne University of Copenhagen, DK [email protected] Ditlevsen, Peter University of Copenhagen, DK [email protected] Feliu, Elisenda University of Copenhagen, DK [email protected] Falk, Henning EMBL, DE [email protected] Garcia-Ojalvo, Jordi Universitat Pompeu Fabra, ESP [email protected] Goldbeter, Albert Université Libre de Bruxelles, B [email protected] Grapin-Botton, Anne University of Copenhagen, DK [email protected] Groÿe Ruse, Mareile University of Lund, SE [email protected] Herzel, Hanspeter Inst. Theoretical Biology Berlin, DE [email protected] Holstein-Rathlou, Niels-Henrik University of Copenhagen, DK [email protected] Hulme, Oliver DRCMR, DE [email protected] Jahnsen, Henrik University of Copenhagen, DK [email protected] Janson, Natalia Loughborough University, UK [email protected] Jensen, Mogens Høgh University of Copenhagen, DK [email protected] Katifori, Eleni MPI Dynamics & Self-Organization [email protected] Komarov, Maxim University of Potsdam, DE [email protected] Kuehn, Christian Vienna University of Technology, AU [email protected] Laing, Carlo Massey University, NZ [email protected] Li, Kang University of Copenhagen, DK [email protected] Lukovic, Mirko MPI Dynamics & Self-Organization [email protected] Marcondes de Freitas, Michael University of Copenhagen, DK [email protected] Marchionne, Arianna Niels Bohr Institute, DK [email protected] Martens, Erik Andreas University of Copenhagen, DK [email protected] Mikkelsen, Troels University of Copenhagen, DK [email protected] Mönke, Gregor MDC Berlin, DE [email protected] Morville, Tobias DRCMR, DE [email protected] Neganova, Anastasiia University of Copenhagen, DK [email protected] Nielsen, Alexander Valentin University of Copenhagen, DK [email protected] Nitzan, Mor Hebrew University, Jerusalem [email protected]
xviii Ottesen, Johnny Roskilde University, DK [email protected] Pazó, Diego CSIC-University of Cantabria, ESP [email protected] Phelps, Matthew University of Copenhagen, DK [email protected] Pikovsky, Arkady University of Potsdam, DE [email protected] Picchini, Umberto University of Lund, SE [email protected] Postnov, Dmitry University of Copenhagen, DK [email protected] Richter, Stefan University of Heidelberg, DE [email protected] Roland, Per University of Copenhagen, DK [email protected] Rosenblum, Michael University of Potsdam, DE [email protected] Sáez, Meritxell University of Copenhagen, DK [email protected] Sams, Thomas Technical University of Denmark, DK [email protected] Søgaard Juul, Jonassl CMol, NBI, DK [email protected] Sørensen, Michael University of Copenhagen, DK [email protected] Sørensen, Helle University of Copenhagen, DK [email protected] Sørensen, Preben Graae University of Copenhagen, DK [email protected] Sosnovtseva, Olga University of Copenhagen, DK [email protected] Sonnen, Katharina EMBL Heidelberg, Germany [email protected] Teklu, Amanuel University of Copenhagen, DK [email protected] Timme, Marc MPI Dynamics & Self-Organization, DE [email protected] Trusina, Ala University of Copenhagen, DK [email protected] Tsiairis, Charisios EMBL Heidelberg, DE [email protected] Velten, Britta, University of Heidelberg, DE [email protected] Vlasov, Vladimir University of Potsdam, DE [email protected] Vestergaard, Mikkeller University of Copenhagen, DK [email protected] West, Ann-Katrine, University of Copenhagen, DK [email protected] Wiuf, Carsten University of Copenhagen, DK [email protected] Yeldesbay, Azamat University of Potsdam, DE [email protected] Zaks, Michael Humboldt University Berlin, DE [email protected] Østergaard, Jacob Nordea, DK [email protected]