arXiv subjects

Stefan Bornholdt

Publications and source records attributed to Stefan Bornholdt.

At least 19 recordsLinked to original sources

arXiv2025

Circulation of Elites in an Adaptive Network Model

Societies experience politically stable and unstable phases along history, whereas political power is usually passed to new elite groups by these changes. Structural dynamics of the elites in a society have been proposed to be one of the core drivers shaping long term behavior. As current models and data are rather macroscopic, the emergence of macroscopic behavior from microscopic dynamics is largely unclear. Here, we introduce an adaptive network model of directed links representing political power and competing political ideas, based on local dynamical rules, only. The model is based on two socially motivated behaviors: the cumulative advantage effect of political power and intra-elite conflict. We observe punctuated equilibria as an emergent behavior and find a phase transition towards a disordered phase. We define an advance warning measure for elite collapse and find that the states of only a few largest nodes are suitable as a proxy with predictive information.

physics.soc-ph↗

arXiv2025

Self-organized Collapse of Societies

Why are human societies unstable? Theories based on the observation of recurring patterns in historical data indicate that economic inequality, as well as social factors are key drivers. So far, models of this phenomenon are more macroscopic in nature. However, basic mechanisms at work could be accessible to minimal mathematical models. Here we combine a simple mechanism for economic growth with a mechanism for the spreading of social dissatisfaction. Broad wealth distributions generated by the economic mechanism eventually trigger social unrest and the destruction of wealth, leading to an emerging pattern of boom and bust. We find that the model time scales compare well with empirical data. The model emphasizes the role of broad (power law) wealth distributions for dynamical social phenomena.

physics.soc-ph↗

arXiv2022

A toy model for brain criticality: self-organized excitation/inhibition ratio and the role of network clustering

The critical brain hypothesis receives increasing support from recent experimental results. It postulates that the brain is at a critical point between an ordered and a chaotic regime, sometimes referred to as the "edge of chaos." Another central observation of neuroscience is the principle of excitation-inhibition balance: Certain brain networks exhibit a remarkably constant ratio between excitation and inhibition. When this balance is perturbed, the network shifts away from the critical point, as may for example happen during epileptic seizures. However, it is as of yet unclear what mechanisms balance the neural dynamics towards this excitation-inhibition ratio that ensures critical brain dynamics. Here we introduce a simple yet biologically plausible toy model of a self-organized critical neural network with a self-organizing excitation to inhibition ratio. The model only requires a neuron to have local information of its own recent activity and changes connections between neurons accordingly. We find that the network evolves to a state characterized by avalanche distributions following universal scaling laws typical of criticality, and to a specific excitation to inhibition ratio. The model connects the two questions of brain criticality and of a specific excitation/inhibition balance observed in the brain to a common origin or mechanism. From the perspective of the statistical mechanics of such networks, the model uses the excitation/inhibition ratio as control parameter of a phase transition, which enables criticality at arbitrary high connectivities. We find that network clustering plays a crucial role for this phase transition to occur.

cond-mat.dis-nn↗

arXiv2021

A q-spin Potts model of markets: Gain-loss asymmetry in stock indices as an emergent phenomenon

Spin models of markets inspired by physics models of magnetism, as the Ising model, allow for the study of the collective dynamics of interacting agents in a market. The number of possible states has been mostly limited to two (buy or sell) or three options. However, herding effects of competing stocks and the collective dynamics of a whole market may escape our reach in the simplest models. Here I study a q-spin Potts model version of a simple Ising market model to represent the dynamics of a stock market index in a spin model. As a result, a self-organized gain-loss asymmetry in the time series of an index variable composed of stocks in this market is observed.

physics.soc-ph↗

arXiv2021

Universal computation using localized limit-cycle attractors in neural networks

Neural networks are dynamical systems that compute with their dynamics. One example is the Hopfield model, forming an associative memory which stores patterns as global attractors of the network dynamics. From studies of dynamical networks it is well known that localized attractors also exist. Yet, they have not been used in computing paradigms. Here we show that interacting localized attractors in threshold networks can result in universal computation. We develop a rewiring algorithm that builds universal Boolean gates in a biologically inspired two-dimensional threshold network with randomly placed and connected nodes using collision-based computing. We aim at demonstrating the computational capabilities and the ability to control local limit cycle attractors in such networks by creating simple Boolean gates by means of these local activations. The gates use glider guns, i.e., localized activity that periodically generates "gliders" of activity that propagate through space. Several such gliders are made to collide, and the result of their interaction is used as the output of a Boolean gate. We show that these gates can be used to build a universal computer.

cs.ET↗

arXiv2020

Self-organized criticality in neural networks from activity-based rewiring

Neural systems process information in a dynamical regime between silence and chaotic dynamics. This has lead to the criticality hypothesis which suggests that neural systems reach such a state by self-organizing towards the critical point of a dynamical phase transition. Here, we study a minimal neural network model that exhibits self-organized criticality in the presence of stochastic noise using a rewiring rule which only utilizes local information. For network evolution, incoming links are added to a node or deleted, depending on the node's average activity. Based on this rewiring-rule only, the network evolves towards a critcal state, showing typical power-law distributed avalanche statistics. The observed exponents are in accord with criticality as predicted by dynamical scaling theory, as well as with the observed exponents of neural avalanches. The critical state of the model is reached autonomously without need for parameter tuning, is independent of initial conditions, is robust under stochastic noise, and independent of details of the implementation as different variants of the model indicate. We argue that this supports the hypothesis that real neural systems may utilize similar mechanisms to self-organize towards criticality especially during early developmental stages.

cond-mat.dis-nn↗

arXiv2020

Epidemics with asymptomatic transmission: Sub-critical phase from recursive contact tracing

The challenges presented by the COVID-19 epidemic have created a renewed interest in the development of new methods to combat infectious diseases. A prominent property of the SARS-CoV-2 transmission is the significant fraction of asymptomatic transmission. This may influence the effectiveness of the standard contact tracing procedure for quarantining potentially infected individuals. However, the effects of asymptomatic transmission on the epidemic threshold of epidemic spreading on networks are largely unknown. Here we study the critical percolation transition in a simple epidemic network model in the presence of a recursive contact tracing algorithm for instant quarantining. We find that, above a certain fraction of asymptomatic transmission, standard contact tracing loses its ability to suppress spreading below the epidemic threshold. However, we also find that recursive contact tracing opens a possibility to contain epidemics with a large fraction of asymptomatic or presymptomatic transmission. In particular, we calculate the required fraction of network nodes participating in the contact tracing for networks with arbitrary degree distributions and for varying recursion depths and discuss the influence of recursion depth and asymptomatic rate on the epidemic percolation phase transition. We test and illustrate our theoretical results using numerical simulations on infection trees and networks. We anticipate recursive contact tracing to provide a basis for digital, app-based contact tracing tools that extend the efficiency of contact tracing to diseases with a large fraction of asymptomatic transmission.

physics.soc-ph↗

arXiv2019

Repulsion in controversial debate drives public opinion into fifty-fifty stalemate

Opinion formation is a process with strong implications for public policy. In controversial debates with large consequences, the public opinion is often trapped in a fifty-fifty stalemate, jeopardizing broadly accepted political decisions. Emergent effects from millions of private discussions make it hard to understand or influence this kind of opinion dynamics. Here we demonstrate that repulsion from opinions favors fifty-fifty stalemates. We study a voter model where agents can have two opinions or an undecided state in-between. In pairwise discussions, undecided agents can be convinced or repelled from the opinion expressed by another agent. If repulsion happens in at least one of four cases, as in controversial debates, the frequencies of both opinions equalize. Further we include transitions of decided agents to the undecided state. If that happens often, the share of undecided agents becomes large, as can be measured with the share of undecided answers in polls.

physics.soc-ph↗

arXiv2019

Critical excitation-inhibition balance in dense neural networks

The "edge of chaos" phase transition in artificial neural networks is of renewed interest in light of recent evidence for criticality in brain dynamics. Statistical mechanics traditionally studied this transition with connectivity $k$ as the control parameter and an exactly balanced excitation-inhibition ratio. While critical connectivity has been found to be low in these model systems, typically around $k=2$, which is unrealistic for natural systems, a recent study utilizing the excitation-inhibition ratio as the control parameter found a new, nearly degree independent, critical point when connectivity is large. However, the new phase transition is accompanied by an unnaturally high level of activity in the network. Here we study random neural networks with the additional properties of (i) a high clustering coefficient and (ii) neurons that are solely either excitatory or inhibitory, a prominent property of natural neurons. As a result, we observe an additional critical point for networks with large connectivity, regardless of degree distribution, which exhibits low activity levels that compare well with neuronal brain networks.

cond-mat.dis-nn↗

arXiv2019

Discrimination emerging through spontaneous symmetry breaking in a spatial prisoner's dilemma model with multiple labels

Social discrimination seems to be a persistent phenomenon in many cultures. It is important to understand the mechanisms that lead people to judge others by the group to which they belong, rather than individual qualities. It was recently shown that evolutionary (imitation) dynamics can lead to a hierarchical discrimination between agents marked with observable, but otherwise meaningless, labels. These findings suggest that it can give useful insight, to describe the phenomenon of social discrimination in terms of spontaneous symmetry breaking. The investigations so far have, however, only considered binary labels. In this contribution we extend the investigations to models with up to seven different labels. We find the features known from the binary label model remain remarkably robust when the number of labels is increased. We also discover a new feature, namely that it is more likely for neighbours to have strategies which are similar, in the sense that they agree on how to act towards a subset of the labels.

nlin.AO↗

arXiv2019

Imitating the winner leads to discrimination in spatial prisoner's dilemma model

The occurrence of discrimination is an important problem in the social and economical sciences. Much of the discrimination observed in empirical studies can be explained by the theory of in-group favoritism, which states that people tend to act more positively towards peers whose appearances are more similar to their own. Some studies, however, find hierarchical structures in inter-group relations, where members of low-status groups also favor the high-status group members. These observations cannot be understood in the light of in-group favoritism. Here we present an agent based model in which evolutionary dynamics can result in a hierarchical discrimination between two groups characterized by a meaningless, but observable binary label. We find that discriminating strategies end up dominating the system when the selection pressure is high, i.e. when agents have a much higher probability of imitating their neighbor with the highest payoff. These findings suggest that the puzzling persistence of hierarchical discrimination may result from the evolutionary dynamics of the social system itself, namely the social imitation dynamics. It also predicts that discrimination will occur more often in highly competitive societies.

physics.soc-ph↗

arXiv2019

Ensembles, Dynamics, and Cell Types: Revisiting the Statistical Mechanics Perspective on Cellular Regulation

Genetic regulatory networks control ontogeny. For fifty years Boolean networks have served as models of such systems, ranging from ensembles of random Boolean networks as models for generic properties of gene regulation to working dynamical models of a growing number of sub-networks of real cells. At the same time, their statistical mechanics has been thoroughly studied. Here we recapitulate their original motivation in the context of current theoretical and empirical research. We discuss ensembles of random Boolean networks whose dynamical attractors model cell types. A sub-ensemble is the critical ensemble. There is now strong evidence that genetic regulatory networks are dynamically critical, and that evolution is exploring the critical sub-ensemble. The generic properties of this sub-ensemble predict essential features of cell differentiation. In particular, the number of attractors in such networks scales as the DNA content raised to the 0.63 power. Data on the number of cell types as a function of the DNA content per cell shows a scaling relationship of 0.88. Thus, the theory correctly predicts a power law relationship between the number of cell types and the DNA contents per cell, and a comparable slope. We discuss these new scaling values and show prospects for new research lines for Boolean networks as a base model for systems biology.

q-bio.MN↗

arXiv2018

A system-wide network reconstruction of gene regulation and metabolism in Escherichia coli

Genome-scale metabolic models have become a fundamental tool for examining metabolic principles. However, metabolism is not solely characterized by the underlying biochemical reactions and catalyzing enzymes, but also affected by regulatory events. Since the pioneering work of Covert and co-workers as well as Shlomi and co-workers it is debated, how regulation and metabolism synergistically characterize a coherent cellular state. The first approaches started from metabolic models which were extended by the regulation of the encoding genes of the catalyzing enzymes. By now, bioinformatics databases in principle allow addressing the challenge of integrating regulation and metabolism on a system-wide level. Collecting information from several databases we provide a network representation of the integrated gene regulatory and metabolic system for Escherichia coli, including major cellular processes, from metabolic processes via protein modification to a variety of regulatory events. Besides transcriptional regulation, we also take into account regulation of translation, enzyme activities and reactions. Our network model provides novel topological characterizations of system components based on their positions in the network. We show that network characteristics suggest a representation of the integrated system as three network domains (regulatory, metabolic and interface networks) instead of two. This new three-domain representation reveals the structural centrality of components with known high functional relevance. This integrated network can serve as a platform for understanding coherent cellular states as active subnetworks and to elucidate crossover effects between metabolism and gene regulation.

q-bio.MN↗

arXiv2017

Inhibition as a determinant of activity and criticality in dynamical networks

A certain degree of inhibition is a common trait of dynamical networks in nature, ranging from neuronal and biochemical networks, to social and technological networks. We study here the role of inhibition in a representative dynamical network model, characterizing the dynamics of random threshold networks with both excitatory and inhibitory links. Varying the fraction of excitatory links has a strong effect on the network's population activity and its sensitivity to perturbation. The average degree $K$, known to have a strong effect on the dynamics when small, loses its influence on the dynamics as its value increases. Instead, the strength of inhibition is a determinant of dynamics and sensitivity here, allowing for criticality only in a specific corridor of inhibition. This criticality corridor requires that excitation dominates, while the balance region corresponds to maximum sensitivity to perturbation. We develop mean-field approximations of the population activity and sensitivity and find that the network dynamics is independent of degree distribution for high $K$. In a minimal model of an adaptive threshold network we demonstrate how the dynamics remains robust against changes in the topology. This adaptive model can be extended in order to generate networks with a controllable activity distribution and specific topologies.

nlin.AO↗

arXiv2017

The interdependent network of gene regulation and metabolism is robust where it needs to be

The major biochemical networks of the living cell, the network of interacting genes and the network of biochemical reactions, are highly interdependent, however, they have been studied mostly as separate systems so far. In the last years an appropriate theoretical framework for studying interdependent networks has been developed in the context of statistical physics. Here we study the interdependent network of gene regulation and metabolism of the model organism Escherichia coli using the theoretical framework of interdependent networks. In particular we aim at understanding how the biological system can consolidate the conflicting tasks of reacting rapidly to (internal and external) perturbations, while being robust to minor environmental fluctuations, at the same time. For this purpose we study the network response to localized perturbations and find that the interdependent network is sensitive to gene regulatory and protein-level perturbations, yet robust against metabolic changes. This first quantitative application of the theory of interdependent networks to systems biology shows how studying network responses to localized perturbations can serve as a useful strategy for analyzing a wide range of other interdependent networks.

q-bio.MN↗

arXiv2014

Avalanches in self-organized critical neural networks: A minimal model for the neural SOC universality class

The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting that this homeostasis of brain activity could occur even without a central regulator, via self-organization on the level of neurons and their interactions, alone. Such physical mechanisms from the class of self-organized criticality exhibit characteristic dynamical signatures, similar to seismic activity related to earthquakes. Measurements of cortex rest activity showed first signs of dynamical signatures potentially pointing to self-organized critical dynamics in the brain. Indeed, recent more accurate measurements allowed for a detailed comparison with scaling theory of non-equilibrium critical phenomena, proving the existence of criticality in cortex dynamics. We here compare this new evaluation of cortex activity data to the predictions of the earliest physics spin model of self-organized critical neural networks. We find that the model matches with the recent experimental data and its interpretation in terms of dynamical signatures for criticality in the brain. The combination of signatures for criticality, power law distributions of avalanche sizes and durations, as well as a specific scaling relationship between anomalous exponents, defines a universality class characteristic of the particular critical phenomenon observed in the neural experiments. The spin model is a candidate for a minimal model of a self-organized critical adaptive network for the universality class of neural criticality. As a prototype model, it provides the background for models that include more biological details, yet share the same universality class characteristic of the homeostasis of activity in the brain.

cond-mat.dis-nn↗

arXiv2014

Motif-based success scores in coauthorship networks are highly sensitive to author name disambiguation

Following the work of Krumov et al. [Eur. Phys. J. B 84, 535 (2011)] we revisit the question whether the usage of large citation datasets allows for the quantitative assessment of social (by means of coauthorship of publications) influence on the progression of science. Applying a more comprehensive and well-curated dataset containing the publications in the journals of the American Physical Society during the whole 20th century we find that the measure chosen in the original study, a score based on small induced subgraphs, has to be used with caution, since the obtained results are highly sensitive to the exact implementation of the author disambiguation task.

physics.soc-ph↗

arXiv2014

Do Bitcoins make the world go round? On the dynamics of competing crypto-currencies

Bitcoins have emerged as a possible competitor to usual currencies, but other crypto-currencies have likewise appeared as competitors to the Bitcoin currency. The expanding market of crypto-currencies now involves capital equivalent to $10^{10}$ US Dollars, providing academia with an unusual opportunity to study the emergence of value. Here we show that the Bitcoin currency in itself is not special, but may rather be understood as the contemporary dominating crypto-currency that may well be replaced by other currencies. We suggest that perception of value in a social system is generated by a voter-like dynamics, where fashions form and disperse even in the case where information is only exchanged on a pairwise basis between agents.

physics.soc-ph↗