arXiv subjects

Stefan Bornholdt

Publications and source records attributed to Stefan Bornholdt.

At least 55 records · Page 3Linked to original sources

arXiv2006

Longevity of orders is related to the longevity of their constituent genera rather than genus richness

Longevity of a taxonomic group is an important issue in understanding the dynamics of evolution. In this respect a key observation is that genera, families or orders can each be assigned a characteristic average lifetime [Van Valen, L., (1973) Evolutionary Theory 1, 1-30]. Using the fossil marine animal genera database [Sepkoski, J.J.Jr. (2002) A Compendium of Fossil Marine Animal Genera, Bull. Am. Paleontol. 363, 563 pp.] we here examine key determinants for robustness of a higher taxonomic group in terms of the characteristics of its constituents. We find insignificant correlation between the size of an order and its stability against extinction, whereas we observe amazingly large correlation between the lifetime of an order and the lifetime of its constituent genera.

q-bio.PE↗

arXiv2006

eBay users form stable groups of common interest

Market segmentation of an online auction site is studied by analyzing the users' bidding behavior. The distribution of user activity is investigated and a network of bidders connected by common interest in individual articles is constructed. The network's cluster structure corresponds to the main user groups according to common interest, exhibiting hierarchy and overlap. Key feature of the analysis is its independence of any similarity measure between the articles offered on eBay, as such a measure would only introduce bias in the analysis. Results are compared to null models based on random networks and clusters are validated and interpreted using the taxonomic classifications of eBay categories. We find clear-cut and coherent interest profiles for the bidders in each cluster. The interest profiles of bidder groups are compared to the classification of articles actually bought by these users during the time span 6-9 months after the initial grouping. The interest profiles discovered remain stable, indicating typical interest profiles in society. Our results show how network theory can be applied successfully to problems of market segmentation and sociological milieu studies with sparse, high dimensional data.

physics.soc-ph↗

arXiv2006

When are networks truly modular?

Study of the cluster- or community structure of complex networks makes an important contribution to the understanding of networks at a functional level. Despite the many efforts, no definition of community has been agreed on and important aspects such as the statistical significance and theoretical limits of community detection are not well understood. We show how the problem of community detection can be mapped onto finding the ground state of an infinite range spin glass. The ground state energy then corresponds directly to the quality of the partition. The network modularity Q previously defined by Girvan and Newman [Phys. Rev. E, 69, 026113 (2004)] turns out to be a special case of this spin glass energy. Through this spin glass analogy, we are able to give expectation values for the modularity of random graphs that can be used in the assessment of the statistical significance of real network clusterings. Further, it allows for assessing the theoretical limits of community detection.

cond-mat.dis-nn↗

arXiv2006

Superstability of the yeast cell cycle dynamics: Ensuring causality in the presence of biochemical stochasticity

Gene regulatory dynamics is governed by molecular processes and therefore exhibits an inherent stochasticity. However, for the survival of an organism it is a strict necessity that this intrinsic noise does not prevent robust functioning of the system. It is still an open question how dynamical stability is achieved in biological systems despite the omnipresent fluctuations. In this paper we investigate the cell-cycle of the budding yeast Saccharomyces cerevisiae as an example of a well-studied organism. We study a genetic network model of eleven genes that coordinate the cell-cycle dynamics using a modeling framework which generalizes the concept of discrete threshold dynamics. By allowing for fluctuations in the transcription/translation times, we introduce noise in the model, accounting for the effects of biochemical stochasticity. We study the dynamical attractor of the cell cycle and find a remarkable robustness against fluctuations of this kind. We identify mechanisms that ensure reliability in spite of fluctuations: 'Catcher' states and persistence of activity levels contribute significantly to the stability of the yeast cell cycle despite the inherent stochasticity.

q-bio.MN↗

arXiv2006

Statistical Mechanics of Community Detection

Starting from a general \textit{ansatz}, we show how community detection can be interpreted as finding the ground state of an infinite range spin glass. Our approach applies to weighted and directed networks alike. It contains the \textit{at hoc} introduced quality function from \cite{ReichardtPRL} and the modularity $Q$ as defined by Newman and Girvan \cite{Girvan03} as special cases. The community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices. We elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study. Further we show, how hierarchies and overlap in the community structure can be detected. Computationally effective local update rules for optimization procedures to find the ground state are given. We show how the \textit{ansatz} may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension. Finally, we give expectation values for the modularity of random graphs, which can be used in the assessment of statistical significance of community structure.

cond-mat.dis-nn↗

arXiv2005

Stable and unstable attractors in Boolean networks

Boolean networks at the critical point have been a matter of debate for many years as, e.g., scaling of number of attractor with system size. Recently it was found that this number scales superpolynomially with system size, contrary to a common earlier expectation of sublinear scaling. We here point to the fact that these results are obtained using deterministic parallel update, where a large fraction of attractors in fact are an artifact of the updating scheme. This limits the significance of these results for biological systems where noise is omnipresent. We here take a fresh look at attractors in Boolean networks with the original motivation of simplified models for biological systems in mind. We test stability of attractors w.r.t. infinitesimal deviations from synchronous update and find that most attractors found under parallel update are artifacts arising from the synchronous clocking mode. The remaining fraction of attractors are stable against fluctuating response delays. For this subset of stable attractors we observe sublinear scaling of the number of attractors with system size.

cond-mat.dis-nn↗

arXiv2004

Topology of biological networks and reliability of information processing

Biological systems rely on robust internal information processing: Survival depends on highly reproducible dynamics of regulatory processes. Biological information processing elements, however, are intrinsically noisy (genetic switches, neurons, etc.). Such noise poses severe stability problems to system behavior as it tends to desynchronize system dynamics (e.g. via fluctuating response or transmission time of the elements). Synchronicity in parallel information processing is not readily sustained in the absence of a central clock. Here we analyze the influence of topology on synchronicity in networks of autonomous noisy elements. In numerical and analytical studies we find a clear distinction between non-reliable and reliable dynamical attractors, depending on the topology of the circuit. In the reliable cases, synchronicity is sustained, while in the unreliable scenario, fluctuating responses of single elements can gradually desynchronize the system, leading to non-reproducible behavior. We find that the fraction of reliable dynamical attractors strongly correlates with the underlying circuitry. Our model suggests that the observed motif structure of biological signaling networks is shaped by the biological requirement for reproducibility of attractors.

q-bio.MN↗

arXiv2004

Detecting fuzzy community structures in complex networks with a Potts model

A fast community detection algorithm based on a q-state Potts model is presented. Communities in networks (groups of densely interconnected nodes that are only loosely connected to the rest of the network) are found to coincide with the domains of equal spin value in the minima of a modified Potts spin glass Hamiltonian. Comparing global and local minima of the Hamiltonian allows for the detection of overlapping (``fuzzy'') communities and quantifying the association of nodes to multiple communities as well as the robustness of a community. No prior knowledge of the number of communities has to be assumed.

cond-mat.stat-mech↗

arXiv2004

Morphogenesis by coupled regulatory networks

Based on a recently proposed non-equilibrium mechanism for spatial pattern formation [cond-mat/0312366] we study how morphogenesis can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing multicellular organism. As an example we study the developmental problem of domain formation and proportion regulation in the presence of noise and cell flow. We find that networks that solve this task exhibit a hierarchical structure of information processing and are of similar complexity as developmental circuits of living cells. A further focus of this paper is a detailed study of noise-induced dynamics, which is a major ingredient of the control dynamics in the developmental network model. A master equation for domain boundary readjustments is formulated and solved for the continuum limit. Evidence for a first order phase transition in equilibrium domain size at vanishing noise is given by finite size scaling. A second order phase transition at increased cell flow is studied in a mean field approximation. Finally, we discuss potential applications.

q-bio.MN↗

arXiv2003

Self-organized pattern formation and noise-induced control from particle computation

We propose a new non-equilibrium model for spatial pattern formation on the basis of local information transfer. Unlike standard models of pattern formation it is not based on the Turing instability. Information is transmitted through the system via particle-like excitations whose collective dynamics result in pattern formation and control. Here, a simple problem of domain formation is addressed by this model in an implementation as stochastic cellular automata. One observes stable pattern formation, even in the presence of noise and cell flow. Noise stabilizes the system through the production of quasi-particles that control the position of the domain boundary. Self-organized boundaries become sharp for large system with fluctuations vanishing with a power of the system size. Pattern proportions are scale-independent with system size. Pattern formation is stable over large parameter ranges with two phase transitions occurring at vanishing noise and increased cell flow.

cond-mat.stat-mech↗

arXiv2003

Robust gene regulation: Deterministic dynamics from asynchronous networks with delay

We compare asynchronous vs. synchronous update of discrete dynamical networks and find that a simple time delay in the nodes may induce a reproducible deterministic dynamics even in the case of asynchronous update in random order. In particular we observe that the dynamics under synchronous parallel update can be reproduced accurately under random asynchronous serial update for a large class of networks. This mechanism points at a possible general principle of how computation in gene regulation networks can be kept in a quasi-deterministic ``clockwork mode'' in spite of the absence of a central clock. A delay similar to the one occurring in gene regulation causes synchronization in the model. Stability under asynchronous dynamics disfavors topologies containing loops, comparing well with the observed strong suppression of loops in biological regulatory networks.

q-bio.MN↗

arXiv2003

Self-organized critical neural networks

A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics which is estimated from an observable at the single synapse level. This principle is studied in a two-dimensional neural network with randomly wired asymmetric weights. In this class of networks, network connectivity is closely related to a phase transition between ordered and disordered dynamics. A slow topology change is imposed on the network through a local rewiring rule motivated by activity-dependent synaptic development: Neighbor neurons whose activity is correlated, on average develop a new connection while uncorrelated neighbors tend to disconnect. As a result, robust self-organization of the network towards the order disorder transition occurs. Convergence is independent of initial conditions, robust against thermal noise, and does not require fine tuning of parameters.

cond-mat.stat-mech↗

arXiv2003

Dynamics of social networks

Complex networks as the World Wide Web, the web of human sexual contacts or criminal networks often do not have an engineered architecture but instead are self-organized by the actions of a large number of individuals. From these local interactions non-trivial global phenomena can emerge as small-world properties or scale-free degree distributions. A simple model for the evolution of acquaintance networks highlights the essential dynamical ingredients necessary to obtain such complex network structures. The model generates highly clustered networks with small average path lengths and scale-free as well as exponential degree distributions. It compares well with experimental data of social networks, as for example coauthorship networks in high energy physics.

cond-mat.dis-nn↗

arXiv2002

Evolutionary games and the emergence of complex networks

The emergence of complex networks from evolutionary games is studied occurring when agents are allowed to switch interaction partners. For this purpose a coevolutionary iterated Prisoner's Dilemma game is defined on a random network with agents as nodes and games along the links. The agents change their neighborhoods to improve their payoff. The system relaxes to stationary states corresponding to cooperative Nash equilibria with the additional property that no agent can improve its payoff by changing its neighborhood. Small perturbations of the system lead to avalanches of strategy readjustments reestablishing equilibrium. As a result of the dynamics, the network of interactions develops non-trivial topological properties as a broad degree distribution suggesting scale-free behavior, small-world characteristics, and assortative mixing.

cond-mat.dis-nn↗

arXiv2002

Critical percolation in self-organized media: A case study on random directed networks

A minimal model for self-organized critical percolation on directed graphs with activating and de-activating links is studied. Unlike classical self-organized criticality, the variables that determine criticality are separated from the dynamical variables of the system and evolve on a slower timescale, resulting in robust criticality. While activity of nodes percolates across the network, the network self-organizes through local adjustment of links according to the criterion that a link's adjacent nodes' average activities become similar. As a result, the network self-organizes to the percolation transition with activity avalanches propagating marginally across the graph. No fine-tuning of parameters is needed.

cond-mat.stat-mech↗

arXiv2002

Viral evolution under the pressure of an adaptive immune system - optimal mutation rates for viral escape

Based on a recent model of evolving viruses competing with an adapting immune system [1], we study the conditions under which a viral quasispecies can maximize its growth rate. The range of mutation rates that allows viruses to thrive is limited from above due to genomic information deterioration, and from below by insufficient sequence diversity, which leads to a quick eradication of the virus by the immune system. The mutation rate that optimally balances these two requirements depends to first order on the ratio of the inverse of the virus' growth rate and the time the immune system needs to develop a specific answer to an antigen. We find that a virus is most viable if it generates exactly one mutation within the time it takes for the immune system to adapt to a new viral epitope. Experimental viral mutation rates, in particular for HIV (human immunodeficiency virus), seem to suggest that many viruses have achieved their optimal mutation rate. [1] C.Kamp and S. Bornholdt, Phys. Rev. Lett., 88, 068104 (2002)

cond-mat.stat-mech↗

arXiv2002

Co-evolutionary games on networks

We study agents on a network playing an iterated Prisoner's dilemma against their neighbors. The resulting spatially extended co-evolutionary game exhibits stationary states which are Nash equilibria. After perturbation of these equilibria, avalanches of mutations reestablish a stationary state. Scale-free avalanche distributions are observed that are in accordance with calculations from the Nash equilibria and a confined branching process. The transition from subcritical to critical avalanche dynamics can be traced to a change in the degeneracy of the cooperative macrostate and is observed for many variants of this game.

cond-mat.dis-nn↗

arXiv2002

Dynamics of price and trading volume in a spin model of stock markets with heterogeneous agents

The dynamics of a stock market with heterogeneous agents is discussed in the framework of a recently proposed spin model for the emergence of bubbles and crashes. We relate the log returns of stock prices to magnetization in the model and find that it is closely related to trading volume as observed in real markets. The cumulative distribution of log returns exhibits scaling with exponents steeper than 2 and scaling is observed in the distribution of transition times between bull and bear markets.

cond-mat.stat-mech↗