programme undedf by - dsin.ku.dk · tance since phase synchronization is regarded as essential for...
TRANSCRIPT
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 CopenhagenThe Faculty of ScienceThe Faculty of Health and Medical Sciences
http://dsin.ku.dk/calendar/workshop_sep14/
i
Venue Information and Maps
Venue:
University of CopenhagenThe Niels Bohr Institute, Auditorium ANiels Bohr Institutet Blegdamsvej 17, 2100 Copenhagen Ø
Welcome Reception and Poster Session
The Welcoming reception on Monday at 17.30 and the co�ee breaks will take place in the LilleFrokoststue (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 CopenhagenCanteen of Niels Bohr Institute Blegdamsvej 172100 Copenhagen Ø
Conference Dinner
Tuesday, September 2, 19:00Restaurant Søren KSøren Kierkegaards Plads 1, 1221 København K � map location
Internet
The entire Niels Bohr Institute is covered by the Eduroam wireless network.The eduroam wirelessnetwork 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 �ndguidance 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 Blegdamsvej17. 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 andfurther 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.
NBI CanteenCoffee
Poster session
Auditorium A
Blegdamsvej 17
The Niels Bohr Institute
Hotel Nora
Researcher Hotel
CabInnScandinavia
Nørreport St. Metro/Train to/from Kastrup airport
NBI Canteen,Coffee break, Poster session
Auditorium A
Blegdamsvej 17
Niels Bohr Institute
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. Nørreporttrain 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 theconference and in the city center. A detailed list and map can be found here. A good locationis 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: 130DKK.
• Zafran Restaurant: Persian food; main courses: 90-120 DKK; you can bring your ownbottle of wine.
• LéLé Street Kitchen: Vietnamese food; 50-100 DKK.
• Det Lille Apotek: Oldest restaurant in Copenhagen, Danish food. Main courses: 70-150DKK (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 inStefansgade.
• 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 Co�ee 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 di�usions observedwith 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 e�ective phase connectivity of oscillator networksfrom observations
15:50-16:30 Co�ee 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 Co�ee 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-inducedsignal propagation
15:10-15:50 Arkady Pikovsky: Collective dynamics of oscillator populations: nonlinear coupling andmultifrequency ensembles
15:50-16:30 Co�ee 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 Co�ee Break
11:00-11:40 Johnny Ottesen: Ultradian and circadian oscillations in the neuroendocrine HPA-axis andits 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 oscillatorsduring embryo developmentAulehla, Alexander (speaker)EMBL Heidelberg, Germany, [email protected]
In our group, we are focusing on the temporal aspect of embryonic development and thuson the role of embryonic oscillators. In mouse embryos, several signaling pathways oscillate intheir activity (period 2hours) during mesoderm patterning and these oscillations are linked to theformation of pre-vertebrae, or somites. Most strikingly, oscillations occur phase-shifted betweenneighbouring 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�cationsof oscillatory activities, revealing the potential of genetic oscillators to self-organize and generatecoherent spatio-temporal wave patterns from a randomized starting condition. I will present recent�ndings addressing underlying working principles.
Indistinguishable oscillators and chimerasAshwin, Peter (speaker)University of Exeter, UK, [email protected], 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 systemsthat can/cannot have chimera states in their dynamics using this de�nition. These include chimerastates for systems of at least four oscillators with two coupling strengths and Hansel-Mato-Meuniertype coupling. We also explore the relationship between this and a modular network structure.
Phase synchronization and cointegration: bridgingtwo theoriesDahlhaus, Rainer (speaker)Heidelberg University, Germany, [email protected] 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 foroscillators has been a major research topic in physics with many applications in di�erent areasof 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 di�erent brainregions. 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 closeconnection between both subjects. As a consequence several techniques on statistical inference forcointegrated systems can immediately be applied for statistical inference on phase synchronizationbased on empirical data. This includes tests for phase synchronization, tests for unidirectionalcoupling and the identi�cation of the equilibrium from data including phase shifts. We give anexample 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 systemDitlevsen, Peter (speaker)University of Copenhagen, Denmark, [email protected]
The dynamics of the climate system is governed by a complex network of interactions betweenthe atmosphere, the oceans, the land and ice-masses and the biosphere. In the latest geologicalepoch 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. Priorto that the glacial cycles lasted around 40.000 years. No change in the astronomical forcing hashappened, but the non-linear response to the forcing suddenly changed 1 million years ago. I willdiscuss possible dynamical mechanisms which could explain this behavior of the climate.
Dynamics of bacterial stress responseGarcia-Ojalvo, Jordi (speaker)Universitat Pompeu Fabra, Spain, [email protected]
Cells respond to environmental conditions by activating regulatory programs that are frequentlydynamic. This is specially true for the case of stress responses, since stress conditions usually varyas time progresses, and the best way for cells to react to these dynamic conditions is by respondingdynamically. In this talk I will give an overview of recent work on the dynamics of stress responsesin the bacterium Bacillus subtilis, using a combination of experimental monitoring by time-lapsemicroscopy and mathematical modelling.
Cdk oscillations drive the mammalian cell cycleGoldbeter, 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 Librede 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 phasesG1, S (DNA replication), G2 and M (mitosis) of the mammalian cell cycle. To better understandthe dynamics of this key cellular system, a detailed computational model based on regulatoryinteractions between the Cdks and other proteins of the network was developed. The modelcontains four modules, each centered around one cyclin/Cdk complex: cyclin D/Cdk4-6 and cyclinE/Cdk2 promote progression in G1 and elicit the G1/S transition, respectively; cyclin A/Cdk2ensures progression in S and the transition S/G2, while the activity of cyclin B/Cdk1 brings aboutthe G2/M transition. This model shows that in the presence of supra-threshold amounts of growthfactor 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 thecell cycle [1, 2]. The results suggest that the switch from cellular quiescence to cell proliferationcorresponds to the passage through a bifurcation point associated with the transition from a stablesteady state to sustained oscillations in the Cdk network. Such transition is governed by a �nelytuned balance between factors that promote or hinder progression in the cell cycle. Among thefactors capable of altering this balance and the passage through the bifurcation point separating cellcycle 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 drivingthe mammalian cell cycle. Proc Natl Acad Sci USA 106, 21643-21648.[2] Gérard C, Goldbeter A (2012). From quiescence to proliferation : Cdk oscillations drive themammalian 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 coupledoscillatorsHerzel, Hanspeter (speaker)Humboldt-University Berlin, Germany, [email protected], Grigory Humboldt-University, BerlinAnanthasubramaniam, 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 ownproduction after a delay of about 6 hours leading to single cell rhythms. Synchronization of 20000neurons in the suprachiasmatic nucleus (SCN) orchestrates sleep-wake cycles, hormone oscillationsand 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 forcedby 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, 1200Brussels, Belgium
References
[1] Ananthasubramaniam, B. and Herzel, H. (2014) Positive feedback promotes oscillations innegative feedback loops, PLoS One 9:e104761.[2] Ananthasubramaniam, B., Herzog, E.D. and Herzel, H. (2014) Timing of neuropeptide couplingdetermines synchrony and entrainment in the mammalian circadian clock, PLoS ComputationalBiology 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 Interface10:0221.[5] Brown, S.A., Kunz, D., Dumas, A., Westermark, P.O., Vanselow, K., Tilmann-Wahnscha�e,A., Herzel, H., and Kramer, A. (2008) Molecular insights into human daily behavior, Proc NatlAcad Sci USA 105, 1602-1607.[6] Granada, A.E., Bordyugov, G., Kramer, A., and Herzel, H. (2011) Human chronotypes from atheoretical perspective, PLoS One 8:e59464.
Networks of stochastic neuron-like systemsJanson, Natalia (speaker)Loughborough University, United Kingdom, [email protected], Scott Loughborough University, United KingdomPatidar, Sandhya Heriot-Watt University, United KingdomPototsky, Andrey Swinburne University of Technology, Australia
Keywords: stochastic; synchronisation; neuron; network
We consider networks of stochastic units mimicking excitable neurons of various sizes andcoupled in a variety of ways: from mean �eld coupling [1,2], through sparse couplings �xed intime, 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 atthe level of synchronisation in the network [3]. We observe some counter-intuitive behaviour insuch 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 casethe delayed feedback is applied to the network. The delayed feedback results suggest that evenweakly and globally applied delayed feedback may reduce excessive degrees of synchronisation tomore moderate levels; it is also possible to strengthen weak synchronisation. Cumulant analysisis used to reduce stochastic equations describing a network with constant non-mean-�eld couplingto 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 excitablenetworks, New Journal of Physics 11(21), 073001.[2] Janson, NB, Pototsky A and Patidar, S (2010) Delayed feedback control in stochastic excitablenetworks, From Physics to Control Through an Emergent View, Luigi Fortuna, Alexander Fradkov,Mattia Frasca Eds., pp. 51�56, World Scienti�c.[3] Dickson S (2014) Stochastic neural network dynamics: synchronisation and control, PhD thesis,Loughborough University.
Oscillators and Arnold tongues in cell dynamicsJensen, Mogens Høegh (speaker)Niels Bohr Institute, Copenhagen, Denmark, [email protected]
Oscillating genetic patterns have been observed in networks related to the transcription factorsNFkB, p53 and Hes1 [1]. We identify the central feed-back loops and found oscillations whentime 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-kBsystems in single cells we have observed that the two signals lock when the ration between the twofrequencies is close to basic rational numbers [2]. The resulting response of the cell can be mappedout as Arnold tongues. When the tongues start to overlap we observe a chaotic dynamics of theconcentration in NF-kB [2]. Oscillations in some genetic systems can be triggered by noise, i.e. alinearly stable system might oscillate due to a noise induced instability. By applying an externaloscillating signal to such systems we predict that it is possible to distinguish a noise induced linearsystem from a system which oscillates via a limit cycle. In the �rst case Arnold tongues will notappear, 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 Development20, 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 undernoise", Chaos, Chaos 23, 023125 (2013).
Structural self-assembly in locally adaptivenetworksKatifori, Eleni (speaker/presenter)Max-Planck Institute for Dynamics and Self-Organization, Germany, [email protected] Gräwer Max-Planck Institute for Dynamics and Self-Organization, GermanyCarl D. Modes The Rockefeller University, USAMarcelo 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 modelthese adapting network architectures using a generic dynamical system on weighted graphs drivenby �uctuating load, and �nd in simulation that these networks ultimately develop a hierarchicalorganization of the �nal weighted architecture accompanied by the formation of a system-spanningbackbone. 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) StructuralSelf-Assembly and Glassy Dynamics in Locally Adaptive Networks, arXiv:1405.7870 [nlin.AO]
Oscillations in multiple time scale dynamics:Autocatalysis, Koper, Olsen, and beyondKuehn, 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 classifyoscillatory patterns. After some basic introduction to geometric singular perturbation theory, threedi�erent models will be introduced to illustrate di�erent oscillatory patterns. For autocatalyticreactions, I will highlight the role of global and local singular mechanisms to generate relaxationoscillations [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 e�ect ofde-coupling the local and global dynamics will be stressed [3]. Then, I will show the potentialcomplexity 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 jointwork with Peter Szmolyan (Vienna). In the last part of my talk, I shall motivate why the techniquesI sketched for the three models, can also be applied to models of extremely high complexity suchas 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.Di�erential Equat., 252(9):4786�4841, 2012.[2] N. Berglund, B. Gentz, and C. Kuehn. From random Poincaré maps to stochastic mixed-mode-oscillation patterns. arXiv:1312.6353, pages 1�55, 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):1351�1366, 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):693�720, 2013.[7] C. Kuehn and P. Szmolyan. Multiscale geometry of the Olsen model and non-classical relaxationoscillations. arXiv:1403.5658, pages 1�46, 2014.
Twisted states in phase oscillator arraysLaing, Carlo (speaker)Massey University, New Zealand, [email protected] Omel'chenko Weierstrass Institute, GermanyMatthias Wolfrum Weierstrass Institute, Germany
Keywords: coupled oscillators; Kuramoto model; twisted states; Ott/Antonsen; Eckhausbifurcation
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 coherentstates that are uniformly �twisted� in space. To analyze these we take the continuum limit, performan 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 stabilitycan be calculated explicitly. We �nd that stable twisted states with di�erent wave numbers appearfor 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 inarrays of coupled phase oscillators, Chaos 24, 023102.
Ultradian and circadian oscillations in theneuroendocrine HPA-axis and its relation todepressionOttesen, Johnny T. (speaker)Roskilde University, Denmark, [email protected] timmermann H. Lundbeck A/S, DenmarkJohanne Gudmand-Hoeyer Roskilde University, Denmark
Keywords: HPA-axis; Depression; Non-Linear Mixed E�ects 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 showscircadian rhythm as well as a faster ultradian rhythm with a period of 1-2 hours [1,2]. Theseoscillations are generally disturbed during many illnesses and are believed to relate to a number ofpathological conditions. Recently we have shown that these oscillations correlate with three groupsof di�erent health conditions (two depressed states and one healthy control group) in a clinicalexperiment involving 29 subjects [3]. In addition, a novel model has been proposed, which �ts dataindividually using the Shu�ed Complex Evolution (SCE) method [4]. The model has also beenembedded in a Non-Linear Mixed E�ects (NLME) framework giving a population approach and re-sulting in a four parameter characterization of the aforementioned three groups [4]. This approachshows that di�erent health conditions are re�ected in a few parameters suggesting a method fornot only exact but also re�ned diagnoses based on the modeling of the complex oscillations of theHPA axis. The procedure may suggest di�erent treatment plans and target candidates in drugdevelopment.
References
[1] Vinther F, Andersen M and Ottesen JT. (2010) The Minimal Model of the Hypothalamic-Pituitary-Adrenal Axis, Journal of Mathematical Biology 29, 467�483. 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 endocrineHPA-axis and its relation to depression: Ultradian and circadian oscillations., Accepted by Math-ematical Biosciences. Elsevier.
Exact firing-rate description for networks ofspiking neuronsPazó, Diego (speaker)Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Spain,[email protected]ó, Ernest Universitat Pompeu Fabra, SpainRoxin, 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 tomodel 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 actualdynamics, suggesting the existence of other meaningful macroscopic quantities involved. Which arethese quantities, and how do they interact with the �ring rate to determine the network activityis unknown.
Here we present the �rst exact �ring-rate model corresponding to a heterogeneous population ofquadratic integrate-and-�re neurons. Our equations show that the mean-�eld dynamics is shapedby 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 networkmodel. 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 wheremacroscopic 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) fordiffusions observed with measurement error andlarge sample sizes: an application to protein foldingdataPicchini, Umberto (speaker)Centre for Mathematical Sciences, Lund University, Sweden, [email protected] Forman Dept. Biostatistics, University of Copenhagen, Denmark
Keywords: Likelihood-free inference; MCMC; protein folding; stochastic di�erential equation.
In recent years statistical inference has been provided with a range of breakthrough MonteCarlo methods to perform exact Bayesian inference for dynamical models. However it is oftennot 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 di�erential equation observedwith correlated measurement errors. Exact inference proved impossible for the size of our data: inorder to allow inference for model parameters within reasonable time constraints an ApproximateBayesian Computation Markov chain Monte Carlo (ABC-MCMC) algorithm is suggested. Thealgorithm uses simulations of subsamples as well as a so-called �early rejection� strategy to speedup computations in the ABC-MCMC sampler. A small sample simulation study is conducted tocompare our strategy with exact Bayesian inference, the latter resulting two orders of magnitudeslower 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 thedetails of our contribution.
References
Picchini, U. and Forman, J. (2014) Accelerating inference for di�usions observed with measurementerror and large sample sizes using Approximate Bayesian Computation, arXiv:1310.0973.
Collective dynamics of oscillator populations:nonlinear coupling and multifrequency ensemblesPikovsky, Arkady (speaker)Potsdam University, Germany, and Nizhny Novgorod University, Russia,[email protected], Michael Potsdam University, GermanyKomarov, 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 interms of closed equations for the collective modes. This description is applied to two setups. Inthe �rst one, nonlinear coupling of identical oscillators leads to their desynchronization. In thesecond case, we consider mutual interaction of several populations having signi�cantly di�erentnatural frequencies. Here both mutual synchronization and desynchronization can occur, togetherwith 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) E�ects of non-resonant interaction in ensembles of phaseoscillators, Phys. Rev. E, v. 84, 016210.[3] Pikovsky, A. and Rosenblum, M. (2011)Dynamics of heterogeneous oscillator ensembles in termsof 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 ofoscillator networks from observationsRosenblum, Michael (speaker)University of Potsdam, Germany, [email protected], Björn University of Kiel, GermanyPikovsky, 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 invariantreconstruction of phase dynamics from observations; invariance here means independence of therecovered model on the observables used for the analysis. We start with the simplest case of twointeracting oscillators and present an application of the approach to cardio-respiratory interactionin humans. We demonstrate the invariance property of our technique by showing that the couplingfunctions reconstructed using respiratory �ow and either electrocardiogram or arterial pulse arevery close [1].
Next, we present an approach for recovery of the directional connectivity of a small oscillatornetwork by means of the phase dynamics reconstruction from multivariate time series data. Themain idea is to use a triplet analysis instead of the traditional pairwise one. Our technique reveals ane�ective phase connectivity which is generally not equivalent to a structural one. We demonstratethat by comparing the coupling functions from all possible triplets of oscillators, we are able toachieve in the reconstruction a good separation between existing and non-existing connections, andthus reliably reproduce the network structure [2].
References
[1] Kralemann, B, et al., (2013) In vivo cardiac phase response curve elucidates human respiratoryheart rate variability , Nat. Comm. 4, 2418.[2] Kralemann, B, Pikovsky, A., Rosenblum, M., (2014) Reconstructing e�ective phase connectivityof oscillator networks from observations, New J. Phys., in press.
Dynamic complexity of NF-kB regulatory networkTrusina, Ala (speaker)Niels Bohr Institute, Denmark, [email protected], 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-regulateproduction of its own triggering signal�namely, in�ammatory cytokines such as TNF, IL-1, andIL-6. In this paper we investigate a previously presented model of the NF-κB, which includes bothspatial e�ects and the positive feedback from cytokines. The model exhibits the properties of anexcitable medium and has the ability to propagate waves of high cytokine concentration. Thesewaves represent an optimal way of sending an in�ammatory signal through the tissue as they createa chemotactic signal able to recruit neutrophils to the site of infection. The simple model displaysthree qualitatively di�erent states; low stimuli leads to no or very little response. Intermediatestimuli leads to reoccurring waves of high cytokine concentration. Finally, high stimuli leads to asustained high cytokine concentration, a scenario which is toxic for the tissue cells and correspondsto chronic in�ammation. Due to the few variables of the simple model, we are able to perform aphase-space analysis leading to a detailed understanding of the functional form of the model andits limitations. The spatial e�ects of the model contribute to the robustness of the cytokine waveformation 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 heartor gene regulatory networks in cells. Such collective dynamics of biological networks cruciallyunderlies 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 notwell understood.
Here we present two advances: First we develop a theory to predict patterns of informationrouting in oscillator networks of arbitrarily complex connectivity as a function of an underlyingcollective dynamical state. We uncover how local modications in individual oscillator properties,the connectivity structure or external inputs provide mechanisms to �exibly change informationrouting through the entire network, even remotely. Second, we identify a new role of hubs incomplex networks: in neural circuits hubs may co-activate with oscillatory dynamics thereby jointlyenabling propagation of signals through such networks.
These results o�er novel directions of future research on information routing and propagationacross complex oscillatory systems.
References
[1] Jahnke, S., Timme, M. and Memmesheimer, R.-M. (2012) Guiding synchrony through randomnetworks, 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 incomplex 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 ofcouplingsZaks, Michael (speaker)I will report on unusual dynamics observed in ensembles of locally coupled active rotators onregular lattices with repulsive (frustrating) interaction. The ensembles split into clusters whichperform periodic oscillations; the number of attracting periodic solutions is in�nite, and at �xedparameter 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 isexplained by the fact that from the point of view of cluster evolution, local coupling turns intothe global (mean �eld) one. In this context, I will discuss bifurcational mechanisms as well as theinterplay of symmetry and stability for di�erent cluster patterns.
List of Participants
Ashwin, Peter University of Exeter, UK [email protected], Alexander EMBL Heidelberg, DE [email protected], Alexander Loughborough University, UK [email protected], Rune University of Copenhagen, DK [email protected], Harrie University of Copenhagen, DK [email protected], J. Christian Technical University of Denmark, DK [email protected] Jacobsen, Jens C. University of Copenhagen, DK [email protected], Alexey Moscow State University, RU [email protected], Daniele University of Copenhagen, DK [email protected], Lars University of South Carolina / DTU [email protected], Rainer University of Heidelberg, DE [email protected]
heidelberg.deDitlevsen, Susanne University of Copenhagen, DK [email protected], Peter University of Copenhagen, DK [email protected], Elisenda University of Copenhagen, DK [email protected], Henning EMBL, DE [email protected], Jordi Universitat Pompeu Fabra, ESP [email protected], Albert Université Libre de Bruxelles, B [email protected], Anne University of Copenhagen, DK [email protected]ÿe Ruse, Mareile University of Lund, SE [email protected], Hanspeter Inst. Theoretical Biology Berlin, DE [email protected], Niels-Henrik University of Copenhagen, DK [email protected], Oliver DRCMR, DE [email protected], Henrik University of Copenhagen, DK [email protected], Natalia Loughborough University, UK [email protected], Mogens Høgh University of Copenhagen, DK [email protected], Eleni MPI Dynamics & Self-Organization [email protected], Maxim University of Potsdam, DE [email protected], Christian Vienna University of Technology, AU [email protected], Carlo Massey University, NZ [email protected], Kang University of Copenhagen, DK [email protected], Mirko MPI Dynamics & Self-Organization [email protected] de Freitas, Michael University of Copenhagen, DK [email protected], Arianna Niels Bohr Institute, DK [email protected], Erik Andreas University of Copenhagen, DK [email protected], Troels University of Copenhagen, DK [email protected]önke, Gregor MDC Berlin, DE [email protected], Tobias DRCMR, DE [email protected], Anastasiia University of Copenhagen, DK [email protected], Alexander Valentin University of Copenhagen, DK [email protected], Mor Hebrew University, Jerusalem [email protected]
xviii
Ottesen, Johnny Roskilde University, DK [email protected]ó, Diego CSIC-University of Cantabria, ESP [email protected], Matthew University of Copenhagen, DK [email protected], Arkady University of Potsdam, DE [email protected], Umberto University of Lund, SE [email protected], Dmitry University of Copenhagen, DK [email protected], Stefan University of Heidelberg, DE [email protected], Per University of Copenhagen, DK [email protected], Michael University of Potsdam, DE [email protected]áez, Meritxell University of Copenhagen, DK [email protected], Thomas Technical University of Denmark, DK [email protected]øgaard Juul, Jonassl CMol, NBI, DK [email protected]ørensen, Michael University of Copenhagen, DK [email protected]ørensen, Helle University of Copenhagen, DK [email protected]ørensen, Preben Graae University of Copenhagen, DK [email protected], Olga University of Copenhagen, DK [email protected], Katharina EMBL Heidelberg, Germany [email protected], Amanuel University of Copenhagen, DK [email protected], Marc MPI Dynamics & Self-Organization, DE [email protected], Ala University of Copenhagen, DK [email protected], Charisios EMBL Heidelberg, DE [email protected], Britta, University of Heidelberg, DE [email protected], Vladimir University of Potsdam, DE [email protected], Mikkeller University of Copenhagen, DK [email protected], Ann-Katrine, University of Copenhagen, DK [email protected], Carsten University of Copenhagen, DK [email protected], Azamat University of Potsdam, DE [email protected], Michael Humboldt University Berlin, DE [email protected]Østergaard, Jacob Nordea, DK [email protected]