Stefan Bornholdt

Self-organized criticality and adaptation in discrete dynamical networks (2008)

Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation...

From differential equations to Boolean networks: A Case Study in modeling regulatory networks (2008)

It has been proposed that adaptation in complex systems is optimized at the critical boundary between ordered and disordered dynamical regimes. Here, we review models of evolving dynamical networks...

Davidich, Maria, Bornholdt, Stefan

Methods of modeling cellular regulatory networks as diverse as differential equations and Boolean networks co-exist, however, without any closer correspondence to each other. With the example system...

Reliability of regulatory networks and its evolution (2008)

Braunewell, Stefan, Bornholdt, Stefan

The problem of reliability of the dynamics in biological regulatory networks is studied in the framework of a generalized Boolean network model with continuous timing and noise. Using well-known...

Reliability of genetic networks is evolvable (2007)

Braunewell, Stefan, Bornholdt, Stefan

Control of the living cell functions with remarkable reliability despite the stochastic nature of the underlying molecular networks -- a property presumably optimized by biological evolution. We here...

Boolean network model predicts cell cycle sequence of fission yeast (2007)

Davidich, Maria I., Bornholdt, Stefan

A Boolean network model of the cell-cycle regulatory network of fission yeast (Schizosaccharomyces Pombe) is constructed solely on the basis of the known biochemical interaction topology. Simulating...

Dynamic Effects Increasing Network Vulnerability to Cascading Failures (2007)

Simonsen, Ingve, Buzna, Lubos, Peters, Karsten, Bornholdt, Stefan, Helbing, Dirk

We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws to investigate the impact of transient dynamics caused by the rebalancing of...

Longevity of orders is related to the longevity of their constituent genera rather than genus richness (2006)

Bornholdt, Stefan, Sneppen, Kim, Westphal, Hildegard

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...

Partitioning and modularity of graphs with arbitrary degree distribution (2006)

When are networks truly modular? (2006)

We solve the graph bi-partitioning problem in dense graphs with arbitrary degree distribution using the replica method. We find the cut-size to scale universally with . In contrast, earlier results...

Superstability of the yeast cell cycle dynamics: Ensuring causality in the presence of biochemical stochasticity (2006)

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...

Braunewell, Stefan, Bornholdt, Stefan

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...

Statistical Mechanics of Community Detection (2006)

eBay users form stable groups of common interest (2005)

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...

Konstantin Klemm, Stefan Bornholdt, Konstantin Klemm, Stefan Bornholdt

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...

Reprints Notes: (2005)

doi:10.1073/pnas.0509132102 This information is current as of February 2007. High-resolution figures, a citation map, links to PubMed and Google Scholar, etc., can be found at:...

Stable and unstable attractors in Boolean networks (2005)

Topology of biological networks and reliability of information processing (2005)

Stable and unstable attractors in Boolean networks (2004)

Topology of biological networks and reliability of information processing (2004)

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...

Detecting fuzzy community structures in complex networks with a Potts model (2004)

Biological systems rely on robust internal information processing: Survival depends on highly reproducible dynamics of regulatory processes. Biological information processing elements, however, are...

Morphogenesis by coupled regulatory networks (2004)

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...

Self-organized pattern formation and noise-induced control from particle computation (2003)

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,...

Robust gene regulation: Deterministic dynamics from asynchronous networks with delay (2003)

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....

Dynamics of social networks (2003)

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...

Ebel, Holger, Davidsen, Joern, Bornholdt, Stefan

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...

Evolutionary games and the emergence of complex networks (2002)

Ebel, Holger, Bornholdt, Stefan

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...

Critical percolation in self-organized media: A case study on random directed networks (2002)

Viral evolution under the pressure of an adaptive immune system - optimal mutation rates for viral escape (2002)

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...

Kamp, Christel, Wilke, Claus O., Adami, Christoph, Bornholdt, Stefan

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...

Co-evolutionary games on networks (2002)

Ebel, Holger, Bornholdt, Stefan

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...

Dynamics of price and trading volume in a spin model of stock markets with heterogeneous agents (2002)

Kaizoji, Taisei, Bornholdt, Stefan, Fujiwara, Yoshi

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...

Scale-free topology of e-mail networks (2002)

Ebel, Holger, Mielsch, Lutz-Ingo, Bornholdt, Stefan

We study the topology of e-mail networks with e-mail addresses as nodes and e-mails as links using data from server log files. The resulting network exhibits a scale-free link distribution and...

From HIV infection to AIDS: A dynamically induced percolation transition? (2002)

Criticality in Random Threshold Networks: Annealed Approximation and Beyond (2002)

The origin of the unusual incubation period distribution in the development of AIDS is largely unresolved. A key factor in understanding the observed distribution of latency periods, as well as the...

Dynamics of social networks (2002)

Random Threshold Networks with sparse, asymmetric connections show complex dynamical behavior similar to Random Boolean Networks, with a transition from ordered to chaotic dynamics at a critical...

Holger Ebel, Jörn Davidsen, Stefan Bornholdt

Complex networks such 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...

Stability of money: Phase transitions in an Ising economy (2001)

Bornholdt, Stefan, Wagner, Friedrich

The stability of money value is an important requisite for a functioning economy, yet it critically depends on the actions of participants in the market themselves. Here we model the value of money...

Self-organized critical neural networks (2001)

Bornholdt, Stefan, Roehl, Torsten

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...

Co-Evolution of quasispecies: B-cell mutation rates maximize viral error catastrophes (2001)

Emergence of a small world from local interactions: Modeling acquaintance networks (2001)

Co-evolution of two coupled quasispecies is studied, motivated by the competition between viral evolution and adapting immune response. In this co-adaptive model, besides the classical error...

Davidsen, Joern, Ebel, Holger, Bornholdt, Stefan

How does one make acquaintances? A simple observation from everyday experience is that often one of our acquaintances introduces us to one of his acquaintances. Such a simple triangle interaction may...

Expectation bubbles in a spin model of markets: Intermittency from frustration across scales (2001)

Bornholdt, Stefan

A simple spin model is studied, motivated by the dynamics of traders in a market where expectation bubbles and crashes occur. The dynamics is governed by interactions which are frustrated across...

Expectation Bubbles in a Spin Model of Markets: Intermittency from Frustration Across Scales (2001)

Stefan Bornholdt, S. Bornholdt

A simple spin model is studied, motivated by the dynamics of traders in a market, where expectation bubbles and crashes occur. The dynamics is governed by interactions, which are frustrated across...

World-Wide Web scaling exponent from Simon's 1955 model (2000)

Bornholdt, Stefan, Ebel, Holger

Recently, statistical properties of the World-Wide Web have attracted considerable attention when self-similar regimes have been observed in the scaling of its link structure. Here we recall a...

Robustness as an Evolutionary Principle (2000)

Bornholdt, Stefan, Sneppen, Kim

We suggest to simulate evolution of complex organisms constrained by the sole requirement of robustness in their expression patterns. This scenario is illustrated by evolving discrete logical...

Topological Evolution of Dynamical Networks: Global Criticality from Local Dynamics (2000)

Bornholdt, Stefan, Rohlf, Thimo

We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average...

Robustness as an evolutionary principle (2000)

Stefan Bornholdt

We suggest simulating evolution of complex organisms using a model constrained solely by the requirement of robustness in its expression patterns. This scenario is illustrated by evolving discrete...

Beyond Hebb: Exclusive-OR and Biological Learning (1999)

Klemm, Konstantin, Bornholdt, Stefan, Schuster, Heinz Georg

A learning algorithm for multilayer neural networks based on biologically plausible mechanisms is studied. Motivated by findings in experimental neurobiology, we consider synaptic averaging in the...

Genetic algorithm dynamics on a rugged landscape (1999)

Bornholdt, Stefan

The genetic algorithm is an optimization procedure motivated by biological evolution and is successfully applied to optimization problems in different areas. A statistical mechanics model for its...

Annealing schedule from population dynamics (1999)

Bornholdt, Stefan

We introduce a dynamical annealing schedule for population-based optimization algorithms with mutation. On the basis of a statistical mechanics formulation of the population dynamics, the mutation...

Neutral Mutations and Punctuated Equilibrium in Evolving Genetic Networks (1997)

Bornholdt, Stefan, Sneppen, Kim

Boolean networks may be viewed as idealizations of biological genetic networks, where each node is represented by an on-off switch which is a function of the binary output from some other nodes. We...

The statistical mechanics approach to genetic algorithms : annealing schedules from population dynamics / (1997)

Bornholdt, Stefan.

Kiel, University, Habil.-Schr., 1997 (Nicht für den Austausch).

Hierarchical Crossover and Probability Landscapes of Genetic Operators (1995)

Bornholdt, Stefan, Schuster, Heinz Georg

The time evolution of a simple model for crossover is discussed. A variant of this model with an improved exploration behavior in phase space is derived as a subset of standard one- and multi-point...

Hierarchical Crossover and Probability Landscapes of Genetic Operators (1995)

Stefan Bornholdt, Heinz Georg Schuster

The time evolution of a simple model for crossover is discussed. A variant of this model with an improved exploration behavior in phase space is derived as a subset of standard one- and multi-point...

Topology of biological networks and reliability of information processing

Topology of biological networks and reliability of information processing

Survival of living cells and organisms is largely based on highly reliable function of their regulatory networks. However, the elements of biological networks, e.g., regulatory genes in genetic...

From HIV infection to AIDS: a dynamically induced percolation transition?

Survival of living cells and organisms is largely based on highly reliable function of their regulatory networks. However, the elements of biological networks, e.g., regulatory genes in genetic...