Timme, Marc

[["dc.bibliographiccitation.artnumber","UNSP e1004002"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","PLoS Computational Biology"],["dc.bibliographiccitation.volume","11"],["dc.contributor.author","Arnoldt, Hinrich"],["dc.contributor.author","Chang, Shuwen"],["dc.contributor.author","Jahnke, Sven"],["dc.contributor.author","Urmersbach, Birk"],["dc.contributor.author","Taschenberger, Holger"],["dc.contributor.author","Timme, Marc"],["dc.date.accessioned","2018-11-07T10:01:14Z"],["dc.date.available","2018-11-07T10:01:14Z"],["dc.date.issued","2015"],["dc.description.abstract","Fundamental response properties of neurons centrally underly the computational capabilities of both individual nerve cells and neural networks. Most studies on neuronal input-output relations have focused on continuous-time inputs such as constant or noisy sinusoidal currents. Yet, most neurons communicate via exchanging action potentials (spikes) at discrete times. Here, we systematically analyze the stationary spiking response to regular spiking inputs and reveal that it is generically non-monotonic. Our theoretical analysis shows that the underlying mechanism relies solely on a combination of the discrete nature of the communication by spikes, the capability of locking output to input spikes and limited resources required for spike processing. Numerical simulations of mathematically idealized and biophysically detailed models, as well as neurophysiological experiments confirm and illustrate our theoretical predictions."],["dc.description.sponsorship","BMBF Germany [01GQ1005B]; Max Planck Society"],["dc.identifier.doi","10.1371/journal.pcbi.1004002"],["dc.identifier.isi","000352081000008"],["dc.identifier.pmid","25646860"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/13555"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/37971"],["dc.notes.intern","Merged from goescholar"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Public Library Science"],["dc.relation.issn","1553-7358"],["dc.relation.issn","1553-734X"],["dc.relation.orgunit","Fakultät für Physik"],["dc.rights","CC BY 4.0"],["dc.rights.uri","https://creativecommons.org/licenses/by/4.0"],["dc.subject.mesh","Action Potentials"],["dc.subject.mesh","Animals"],["dc.subject.mesh","Cells, Cultured"],["dc.subject.mesh","Computer Simulation"],["dc.subject.mesh","Models, Neurological"],["dc.subject.mesh","Neurons"],["dc.subject.mesh","Patch-Clamp Techniques"],["dc.subject.mesh","Rats"],["dc.subject.mesh","Rats, Wistar"],["dc.subject.mesh","Trapezoid Body"],["dc.title","When Less Is More: Non-monotonic Spike Sequence Processing in Neurons"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","175002"],["dc.bibliographiccitation.issue","17"],["dc.bibliographiccitation.journal","Journal of Physics A Mathematical and Theoretical"],["dc.bibliographiccitation.volume","43"],["dc.contributor.author","van Bussel, Frank"],["dc.contributor.author","Ehrlich, Christoph"],["dc.contributor.author","Fliegner, Denny"],["dc.contributor.author","Stolzenberg, Sebastian"],["dc.contributor.author","Timme, Marc"],["dc.date.accessioned","2018-11-07T08:43:56Z"],["dc.date.available","2018-11-07T08:43:56Z"],["dc.date.issued","2010"],["dc.description.abstract","Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics."],["dc.identifier.doi","10.1088/1751-8113/43/17/175002"],["dc.identifier.isi","000276674400004"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/20092"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Iop Publishing Ltd"],["dc.relation.issn","1751-8113"],["dc.title","Chromatic polynomials of random graphs"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","015108"],["dc.bibliographiccitation.firstpage","1"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Chaos: An Interdisciplinary Journal of Nonlinear Science"],["dc.bibliographiccitation.lastpage","16"],["dc.bibliographiccitation.volume","16"],["dc.contributor.author","Timme, Marc"],["dc.contributor.author","Geisel, Theo"],["dc.contributor.author","Wolf, Fred"],["dc.date.accessioned","2017-09-07T11:46:16Z"],["dc.date.available","2017-09-07T11:46:16Z"],["dc.date.issued","2006"],["dc.description.abstract","We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is determined by multiple operators, for which standard analysis is not suitable. We describe a general nonstandard solution to the multioperator problem. Subsequently, we derive a class of neuronal rise functions for which all stability operators become degenerate and standard eigenvalue analysis becomes a suitable tool. Interestingly, this class is found to consist of networks of leaky integrate-and-fire neurons. For random networks of inhibitory integrate-and-fire neurons, we then develop an analytical approach, based on the theory of random matrices, to precisely determine the eigenvalue distributions of the stability operators. This yields the asymptotic relaxation time for perturbations to the synchronous state which provides the characteristic time scale on which neurons can coordinate their activity in such networks. For networks with finite in-degree, i.e., finite number of presynaptic inputs per neuron, we find a speed limit to coordinating spiking activity. Even with arbitrarily strong interaction strengths neurons cannot synchronize faster than at a certain maximal speed determined by the typical in-degree.The individual units of many physical systems, from the planets of our solar system to the atoms in a solid, typically interact continuously in time and without significant delay. Thus at every instant of time such a unit is influenced by the current state of its interaction partners. Moreover, particles of many-body systems are often considered to have very simple lattice topology (as in a crystal) or no prescribed topology at all (as in an ideal gas). Many important biological systems are drastically different: their units are interacting by sending and receiving pulses at discrete instances of time. Furthermore, biological systems often exhibit significant delays in the couplings and very complicated topologies of their interaction networks. Examples of such systems include neurons, which interact by stereotyped electrical pulses called action potentials or spikes; crickets, which chirp to communicate acoustically; populations of fireflies that interact by short light pulses. The combination of pulse-coupling, delays, and complicated network topology formally makes the dynamical system to be investigated a high dimensional, heterogeneous nonlinear hybrid system with delays. Here we present an exact analysis of aspects of the dynamics of such networks in the case of simple one-dimensional nonlinear interacting units. These systems are simple models for the collective dynamics of recurrent networks of spiking neurons. After briefly presenting stability results for the synchronous state, we show how to use the theory of random matrices to analytically predict the eigenvalue distribution of stability matrices and thus derive the speed of synchronization in terms of dynamical and network parameters. We find that networks of neural oscillators typically exhibit speed limits and cannot synchronize faster than a certain bound defined by the network topology."],["dc.identifier.doi","10.1063/1.2150775"],["dc.identifier.gro","3151890"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/8722"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","1054-1500"],["dc.title","Speed of synchronization in complex networks of neural oscillators: Analytic results based on Random Matrix Theory"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","138701"],["dc.bibliographiccitation.issue","13"],["dc.bibliographiccitation.journal","Physical Review Letters"],["dc.bibliographiccitation.volume","116"],["dc.contributor.author","Witthaut, Dirk"],["dc.contributor.author","Rohden, Martin"],["dc.contributor.author","Zhang, Xiaozhu"],["dc.contributor.author","Hallerberg, Sarah"],["dc.contributor.author","Timme, Marc"],["dc.date.accessioned","2020-12-10T18:25:40Z"],["dc.date.available","2020-12-10T18:25:40Z"],["dc.date.issued","2016"],["dc.description.abstract","Link failures repeatedly induce large-scale outages in power grids and other supply networks. Yet, it is still not well understood which links are particularly prone to inducing such outages. Here we analyze how the nature and location of each link impact the network's capability to maintain a stable supply. We propose two criteria to identify critical links on the basis of the topology and the load distribution of the network prior to link failure. They are determined via a link's redundant capacity and a renormalized linear response theory we derive. These criteria outperform the critical link prediction based on local measures such as loads. The results not only further our understanding of the physics of supply networks in general. As both criteria are available before any outage from the state of normal operation, they may also help real-time monitoring of grid operation, employing countermeasures and support network planning and design."],["dc.identifier.doi","10.1103/PhysRevLett.116.138701"],["dc.identifier.eissn","1079-7114"],["dc.identifier.isi","000373099500017"],["dc.identifier.issn","0031-9007"],["dc.identifier.pmid","27082006"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/75784"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-354"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Amer Physical Soc"],["dc.relation.issn","1079-7114"],["dc.relation.issn","0031-9007"],["dc.title","Critical Links and Nonlocal Rerouting in Complex Supply Networks"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","821"],["dc.contributor.author","Timme, Marc"],["dc.contributor.author","Geisel, Theo"],["dc.contributor.author","Wolf, F."],["dc.date.accessioned","2017-11-21T15:34:02Z"],["dc.date.available","2017-11-21T15:34:02Z"],["dc.date.issued","2001"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/10167"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.relation.eventend","2001-11-15"],["dc.relation.eventlocation","San Diego"],["dc.relation.eventstart","2001-11-10"],["dc.relation.ispartof","Society for Neuroscience Abstracts"],["dc.title","Synchronization and Desynchronization in Neural Networks with General Connectivity"],["dc.type","conference_abstract"],["dc.type.internalPublication","unknown"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","224101"],["dc.bibliographiccitation.issue","22"],["dc.bibliographiccitation.journal","Physical Review Letters"],["dc.bibliographiccitation.volume","98"],["dc.contributor.author","Timme, Marc"],["dc.date.accessioned","2012-09-26T10:02:46Z"],["dc.date.accessioned","2021-10-27T13:22:29Z"],["dc.date.available","2012-09-26T10:02:46Z"],["dc.date.available","2021-10-27T13:22:29Z"],["dc.date.issued","2007-05-30"],["dc.description.abstract","We present a method to infer the complete connectivity of a network from its stable response dynamics. As a paradigmatic example, we consider networks of coupled phase oscillators and explicitly study their long-term stationary response to temporally constant driving. For a given driving condition, measuring the phase differences and the collective frequency reveals information about how the units are interconnected. Sufficiently many repetitions for different driving conditions yield the entire network connectivity (the absence or presence of each connection) from measuring the response dynamics only. For sparsely connected networks, we obtain good predictions of the actual connectivity even for formally underdetermined problems."],["dc.format.extent","4"],["dc.identifier.doi","10.1103/PhysRevLett.98.224101"],["dc.identifier.fs","53065"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/7965"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/92099"],["dc.language.iso","en"],["dc.notes.intern","Migrated from goescholar"],["dc.relation.issn","1079-7114"],["dc.relation.orgunit","Bernstein Center for Computational Neuroscience Göttingen"],["dc.rights","CC BY 3.0"],["dc.rights.uri","https://creativecommons.org/licenses/by/3.0"],["dc.title","Revealing Network Connectivity from Response Dynamics"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","188101"],["dc.bibliographiccitation.issue","18"],["dc.bibliographiccitation.journal","Physical Review Letters"],["dc.bibliographiccitation.volume","97"],["dc.contributor.author","Memmesheimer, Raoul-Martin"],["dc.contributor.author","Timme, Marc"],["dc.date.accessioned","2018-11-07T08:58:56Z"],["dc.date.available","2018-11-07T08:58:56Z"],["dc.date.issued","2006"],["dc.description.abstract","Precise timing of spikes and temporal locking are key elements of neural computation. Here we demonstrate how even strongly heterogeneous, deterministic neural networks with delayed interactions and complex topology can exhibit periodic patterns of spikes that are precisely timed. We develop an analytical method to find the set of all networks exhibiting a predefined pattern dynamics. Such patterns may be arbitrarily long and of complicated temporal structure. We point out that the same pattern can exist in very different networks and have different stability properties."],["dc.identifier.doi","10.1103/PhysRevLett.97.188101"],["dc.identifier.isi","000241757600063"],["dc.identifier.pmid","17155580"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/23768"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","American Physical Soc"],["dc.relation.issn","0031-9007"],["dc.title","Designing the dynamics of spiking neural networks"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","e0229230"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","PLoS One"],["dc.bibliographiccitation.volume","15"],["dc.contributor.author","Molkenthin, Nora"],["dc.contributor.author","Mühle, Steffen"],["dc.contributor.author","Mey, Antonia S. J. S."],["dc.contributor.author","Timme, Marc"],["dc.contributor.editor","Levy, Yaakov Koby"],["dc.date.accessioned","2021-04-14T08:27:01Z"],["dc.date.available","2021-04-14T08:27:01Z"],["dc.date.issued","2020"],["dc.identifier.doi","10.1371/journal.pone.0229230"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/82144"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-399"],["dc.relation.eissn","1932-6203"],["dc.title","Self-organized emergence of folded protein-like network structures from geometric constraints"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Scientific Reports"],["dc.bibliographiccitation.volume","11"],["dc.contributor.author","Schröder, Malte"],["dc.contributor.author","Bossert, Andreas"],["dc.contributor.author","Kersting, Moritz"],["dc.contributor.author","Aeffner, Sebastian"],["dc.contributor.author","Coetzee, Justin"],["dc.contributor.author","Timme, Marc"],["dc.contributor.author","Schlüter, Jan"],["dc.date.accessioned","2021-06-01T09:41:43Z"],["dc.date.available","2021-06-01T09:41:43Z"],["dc.date.issued","2021"],["dc.description.abstract","Abstract The future dynamics of the Corona Virus Disease 2019 (COVID-19) outbreak in African countries is largely unclear. Simultaneously, required strengths of intervention measures are strongly debated because containing COVID-19 in favor of the weak health care system largely conflicts with socio-economic hardships. Here we analyze the impact of interventions on outbreak dynamics for South Africa, exhibiting the largest case numbers across sub-saharan Africa, before and after their national lockdown. Past data indicate strongly reduced but still supracritical growth after lockdown. Moreover, large-scale agent-based simulations given different future scenarios for the Nelson Mandela Bay Municipality with 1.14 million inhabitants, based on detailed activity and mobility survey data of about 10% of the population, similarly suggest that current containment may be insufficient to not overload local intensive care capacity. Yet, enduring, slightly stronger or more specific interventions, combined with sufficient compliance, may constitute a viable option for interventions for South Africa."],["dc.identifier.doi","10.1038/s41598-021-84487-0"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/85013"],["dc.language.iso","en"],["dc.notes.intern","DOI-Import GROB-425"],["dc.relation.eissn","2045-2322"],["dc.title","COVID-19 in South Africa: outbreak despite interventions"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","265"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","Nature Physics"],["dc.bibliographiccitation.lastpage","270"],["dc.bibliographiccitation.volume","7"],["dc.contributor.author","Nagler, Jan"],["dc.contributor.author","Levina, Anna"],["dc.contributor.author","Timme, Marc"],["dc.date.accessioned","2018-11-07T08:58:46Z"],["dc.date.available","2018-11-07T08:58:46Z"],["dc.date.issued","2011"],["dc.description.abstract","How a complex network is connected crucially impacts its dynamics and function. Percolation, the transition to extensive connectedness on gradual addition of links, was long believed to be continuous, but recent numerical evidence of 'explosive percolation' suggests that it might also be discontinuous if links compete for addition. Here we analyse the microscopic mechanisms underlying discontinuous percolation processes and reveal a strong impact of single-link additions. We show that in generic competitive percolation processes, including those showing explosive percolation, single links do not induce a discontinuous gap in the largest cluster size in the thermodynamic limit. Nevertheless, our results highlight that for large finite systems single links may still induce substantial gaps, because gap sizes scale weakly algebraically with system size. Several essentially macroscopic clusters coexist immediately before the transition, announcing discontinuous percolation. These results explain how single links may drastically change macroscopic connectivity in networks where links add competitively."],["dc.identifier.doi","10.1038/NPHYS1860"],["dc.identifier.isi","000287844300028"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/23723"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Nature Publishing Group"],["dc.relation.issn","1745-2473"],["dc.title","Impact of single links in competitive percolation"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]