arXiv subjects

Stefan Bornholdt

Publications and source records attributed to Stefan Bornholdt.

At least 37 records · Page 2Linked to original sources

arXiv2013

Spontaneous centralization of control in a network of company ownerships

We introduce a model for the adaptive evolution of a network of company ownerships. In a recent work it has been shown that the empirical global network of corporate control is marked by a central, tightly connected "core" made of a small number of large companies which control a significant part of the global economy. Here we show how a simple, adaptive "rich get richer" dynamics can account for this characteristic, which incorporates the increased buying power of more influential companies, and in turn results in even higher control. We conclude that this kind of centralized structure can emerge without it being an explicit goal of these companies, or as a result of a well-organized strategy.

physics.soc-ph↗

arXiv2013

Econophysics of adaptive power markets: When a market does not dampen fluctuations but amplifies them

The average economic agent is often used to model the dynamics of simple markets, based on the assumption that the dynamics of many agents can be averaged over in time and space. A popular idea that is based on this seemingly intuitive notion is to dampen electric power fluctuations from fluctuating sources (as e.g. wind or solar) via a market mechanism, namely by variable power prices that adapt demand to supply. The standard model of an average economic agent predicts that fluctuations are reduced by such an adaptive pricing mechanism. However, the underlying assumption that the actions of all agents average out on the time axis is not always true in a market of many agents. We numerically study an econophysics agent model of an adaptive power market that does not assume averaging a priori. We find that when agents are exposed to source noise via correlated price fluctuations (as adaptive pricing schemes suggest), the market may amplify those fluctuations. In particular, small price changes may translate to large load fluctuations through catastrophic consumer synchronization. As a result, an adaptive power market may cause the opposite effect than intended: Power fluctuations are not dampened but amplified instead.

q-fin.TR↗

arXiv2013

The citation wake of publications detects Nobel laureates' papers

For several decades, a leading paradigm of how to quantitatively assess scientific research has been the analysis of the aggregated citation information in a set of scientific publications. Although the representation of this information as a citation network has already been coined in the 1960s, it needed the systematic indexing of scientific literature to allow for impact metrics that actually made use of this network as a whole improving on the then prevailing metrics that were almost exclusively based on the number of direct citations. However, besides focusing on the assignment of credit, the paper citation network can also be studied in terms of the proliferation of scientific ideas. Here we introduce a simple measure based on the shortest-paths in the paper's in-component or, simply speaking, on the shape and size of the wake of a paper within the citation network. Applied to a citation network containing Physical Review publications from more than a century, our approach is able to detect seminal articles which have introduced concepts of obvious importance to the further development of physics. We observe a large fraction of papers co-authored by Nobel Prize laureates in physics among the top-ranked publications.

physics.soc-ph↗

arXiv2013

No need for conspiracy: Self-organized cartel formation in a modified trust game

We investigate the dynamics of a trust game on a mixed population where individuals with the role of buyers are forced to play against a predetermined number of sellers, whom they choose dynamically. Agents with the role of sellers are also allowed to adapt the level of value for money of their products, based on payoff. The dynamics undergoes a transition at a specific value of the strategy update rate, above which an emergent cartel organization is observed, where sellers have similar values of below optimal value for money. This cartel organization is not due to an explicit collusion among agents; instead it arises spontaneously from the maximization of the individual payoffs. This dynamics is marked by large fluctuations and a high degree of unpredictability for most of the parameter space, and serves as a plausible qualitative explanation for observed elevated levels and fluctuations of certain commodity prices.

q-fin.GN↗

arXiv2012

Mean-field-like behavior of the generalized voter-model-class kinetic Ising model

We analyze a kinetic Ising model with suppressed bulk noise which is a prominent representative of the generalized voter model phase transition. On the one hand we discuss the model in the context of social systems, and opinion formation in the presence of a tunable social temperature. On the other hand we characterize the abrupt phase transition. The system shows non-equilibrium dynamics in the presence of absorbing states. We slightly change the system to get a stationary state model variant exhibiting the same kind of phase transition. Using a Fokker-Planck description and comparing to mean field calculations, we investigate the phase transition, finite size effects and the effect of the absorbing states resulting in a dynamic slowing down.

physics.soc-ph↗

arXiv2012

Opinion formation model for markets with a social temperature and fear

In the spirit of behavioral finance, we study the process of opinion formation among investors using a variant of the 2D Voter Model with a tunable social temperature. Further, a feedback acting on the temperature is introduced, such that social temperature reacts to market imbalances and thus becomes time dependent. In this toy market model, social temperature represents nervousness of agents towards market imbalances representing speculative risk. We use the knowledge about the discontinuous Generalized Voter Model phase transition to determine critical fixed points. The system exhibits metastable phases around these fixed points characterized by structured lattice states, with intermittent excursions away from the fixed points. The statistical mechanics of the model is characterized and its relation to dynamics of opinion formation among investors in real markets is discussed.

physics.soc-ph↗

arXiv2012

Self-organized criticality in neural network models

It has long been argued that neural networks have to establish and maintain a certain intermediate level of activity in order to keep away from the regimes of chaos and silence. Strong evidence for criticality has been observed in terms of spatio-temporal activity avalanches first in cultures of rat cortex by Beggs and Plenz (2003) and subsequently in many more experimental setups. These findings sparked intense research on theoretical models for criticality and avalanche dynamics in neural networks, where usually some dynamical order parameter is fed back onto the network topology by adapting the synaptic couplings. We here give an overview of existing theoretical models of dynamical networks. While most models emphasize biological and neurophysiological detail, our path here is different: we pick up the thread of an early self-organized critical neural network model by Bornholdt and Roehl (2001) and test its applicability in the light of experimental data. Keeping the simplicity of early models, and at the same time lifting the drawback of a spin formulation with respect to the biological system, we here study an improved model (Rybarsch and Bornholdt, 2012b) and show that it adapts to criticality exhibiting avalanche statistics that compare well with experimental data without the need for parameter tuning.

cond-mat.dis-nn↗

arXiv2012

Binary threshold networks as a natural null model for biological networks

Spin models of neural networks and genetic networks are considered elegant as they are accessible to statistical mechanics tools for spin glasses and magnetic systems. However, the conventional choice of variables in spin systems may cause problems in some models when parameter choices are unrealistic from a biological perspective. Obviously, this may limit the role of a model as a template model for biological systems. Perhaps less obviously, also ensembles of random networks are affected and may exhibit different critical properties. We consider here a prototypical network model that is biologically plausible in its local mechanisms. We study a discrete dynamical network with two characteristic properties: Nodes with binary states 0 and 1, and a modified threshold function with $Θ_0(0)=0$. We explore the critical properties of random networks of such nodes and find a critical connectivity $K_c=2.0$ with activity vanishing at the critical point. Finally, we observe that the present model allows a more natural implementation of recent models of budding yeast and fission yeast cell-cycle control networks.

cond-mat.dis-nn↗

arXiv2012

Evolution of robust network topologies: Emergence of central backbones

We model the robustness against random failure or intentional attack of networks with arbitrary large-scale structure. We construct a block-based model which incorporates --- in a general fashion --- both connectivity and interdependence links, as well as arbitrary degree distributions and block correlations. By optimizing the percolation properties of this general class of networks, we identify a simple core-periphery structure as the topology most robust against random failure. In such networks, a distinct and small "core" of nodes with higher degree is responsible for most of the connectivity, functioning as a central "backbone" of the system. This centralized topology remains the optimal structure when other constraints are imposed, such as a given fraction of interdependence links and fixed degree distributions. This distinguishes simple centralized topologies as the most likely to emerge, when robustness against failure is the dominant evolutionary force.

physics.soc-ph↗

arXiv2011

Spin models as microfoundation of macroscopic financial market models

Macroscopic price evolution models are commonly used for investment strategies. There are first promising achievements in defining microscopic agent based models for the same purpose. Microscopic models allow a deeper understanding of mechanisms in the market than the purely phenomenological macroscopic models, and thus bear the chance for better models for market regulation. We exemplify this strategy in a case study, deducing a macroscopic Langevin equation from a microscopic spin market model closely related to the Ising model. The interplay of the microscopic and the macroscopic view allows for a better understanding of the microscopic model, as well, and may guide the construction of agent based market models as basis of macroscopic price models.

q-fin.PR↗

arXiv2009

Morphogenesis by coupled regulatory networks: Reliable control of positional information and proportion regulation

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 networks of cells in a developing multicellular organism. As an example we study the developmental problems of domain formation and proportion regulation in the presence of noise, as well as in the presence of 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. Proportion regulation is scalable with system size and leads to sharp, precisely localized boundaries of gene expression domains, even for large numbers of cells. A detailed analysis of noise-induced dynamics, using a mean-field approximation, shows that noise in gene expression states stabilizes (rather than disrupts) the spatial pattern in the presence of cell movements, both for stationary as well as growing systems. Finally, we discuss how this mechanism could be realized in the highly dynamic environment of growing tissues in multi-cellular organisms.

q-bio.MN↗

arXiv2008

Self-organized criticality and adaptation in discrete dynamical networks

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 that lead to self-organization of network topology based on a local coupling between a dynamical order parameter and rewiring of network connectivity, with convergence towards criticality in the limit of large network size $N$. In particular, two adaptive schemes are discussed and compared in the context of Boolean Networks and Threshold Networks: 1) Active nodes loose links, frozen nodes aquire new links, 2) Nodes with correlated activity connect, de-correlated nodes disconnect. These simple local adaptive rules lead to co-evolution of network topology and -dynamics. Adaptive networks are strikingly different from random networks: They evolve inhomogeneous topologies and broad plateaus of homeostatic regulation, dynamical activity exhibits $1/f$ noise and attractor periods obey a scale-free distribution. The proposed co-evolutionary mechanism of topological self-organization is robust against noise and does not depend on the details of dynamical transition rules. Using finite-size scaling, it is shown that networks converge to a self-organized critical state in the thermodynamic limit. Finally, we discuss open questions and directions for future research, and outline possible applications of these models to adaptive systems in diverse areas.

nlin.AO↗

arXiv2008

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

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 of the fission yeast cell cycle control network, we here set the two approaches in relation to each other. We find that the Boolean network can be formulated as a specific coarse-grained limit of the more detailed differential network model for this system. This lays the mathematical foundation on which Boolean networks can be applied to biological regulatory networks in a controlled way.

q-bio.MN↗

arXiv2008

Reliability of regulatory networks and its evolution

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 artificial genetic networks such as the repressilator, we discuss concepts of reliability of rhythmic attractors. In a simple evolution process we investigate how overall network structure affects the reliability of the dynamics. In the course of the evolution, networks are selected for reliable dynamics. We find that most networks can be easily evolved towards reliable functioning while preserving the original function.

q-bio.MN↗

arXiv2008

Dynamic Effects Increasing Network Vulnerability to Cascading Failures

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 loads after an initial network failure (triggering event). It is found that considering the flow dynamics may imply reduced network robustness compared to previous static overload failure models. This is due to the transient oscillations or overshooting in the loads, when the flow dynamics adjusts to the new (remaining) network structure. We obtain {\em upper} and {\em lower} limits to network robustness, and it is shown that {\it two} time scales $τ$ and $τ_0$, defined by the network dynamics, are important to consider prior to accurately addressing network robustness or vulnerability. The robustness of networks showing cascading failures is generally determined by a complex interplay between the network topology and flow dynamics, where the ratio $χ=τ/τ_0$ determines the relative role of the two of them.

physics.soc-ph↗

arXiv2007

Reliability of genetic networks is evolvable

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 ask to what extent the property of a stochastic dynamical network to produce reliable dynamics is an evolvable trait. Using an evolutionary algorithm based on a deterministic selection criterion for the reliability of dynamical attractors, we evolve dynamical networks of noisy discrete threshold nodes. We find that, starting from any random network, reliability of the attractor landscape can often be achieved with only few small changes to the network structure. Further, the evolvability of networks towards reliable dynamics while retaining their function is investigated and a high success rate is found.

q-bio.MN↗

arXiv2007

Boolean network model predicts cell cycle sequence of fission yeast

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 the model in the computer, faithfully reproduces the known sequence of regulatory activity patterns along the cell cycle of the living cell. Contrary to existing differential equation models, no parameters enter the model except the structure of the regulatory circuitry. The dynamical properties of the model indicate that the biological dynamical sequence is robustly implemented in the regulatory network, with the biological stationary state G1 corresponding to the dominant attractor in state space, and with the biological regulatory sequence being a strongly attractive trajectory. Comparing the fission yeast cell-cycle model to a similar model of the corresponding network in S. cerevisiae, a remarkable difference in circuitry, as well as dynamics is observed. While the latter operates in a strongly damped mode, driven by external excitation, the S. pombe network represents an auto-excited system with external damping.

q-bio.MN↗

arXiv2007

Partitioning and modularity of graphs with arbitrary degree distribution

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 studying the problem in graphs with a Poissonian degree distribution had found a scaling with ^1/2 [Fu and Anderson, J. Phys. A: Math. Gen. 19, 1986]. The new results also generalize to the problem of q-partitioning. They can be used to find the expected modularity Q [Newman and Grivan, Phys. Rev. E, 69, 2004] of random graphs and allow for the assessment of statistical significance of the output of community detection algorithms.

cond-mat.dis-nn↗