The geographical distribution of production is getting an increased amount of attention in econom... more The geographical distribution of production is getting an increased amount of attention in economics. Distributed trade opens for production where it is cheapest, which in turn is reinforced by economies of scale. Using a simple agent-based model for the geographical interplay between transportation costs, economies of scale, as well as information costs, we address here the transition between local and distributed economies. The model naturally recapitulates that decreased transportation and information costs favor large companies. This suggests history dependence in the sense that new companies typically reemerge in the vicinity of old ones. Further, it suggests that company stability depends on transport costs, and that the transition from a local economy to a global economy is naturally driven by reduced transportation costs and an increased information horizon.
... Dr. Thomas Pellizzari Dr. Stefan Bornholdt University of Innsbruck University of Kiel Inst ..... more ... Dr. Thomas Pellizzari Dr. Stefan Bornholdt University of Innsbruck University of Kiel Inst ... John von Neumann's "self-reproducing automaton", and John Horton Conway's game of Life are perhaps the most widely known examples of cellular automata showing complex behavior on ...
Based on a recent model of evolving viruses competing with an adapting immune system [1], we stud... more 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.
Genetic regulatory networks control ontogeny. For fifty years Boolean networks have served as mod... more 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 subensemble 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.
A simple spin model is studied, motivated by the dynamics of traders in a market where expectatio... more 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 different scales: While ferromagnetic couplings connect each spin to its local neighborhood, an additional coupling relates each spin to the global magnetization. This new coupling is allowed to be anti-ferromagnetic. The resulting frustration causes a metastable dynamics with intermittency and phases of chaotic dynamics. The model reproduces main observations of real economic markets as power-law distributed returns and clustered volatility.
The "edge of chaos" phase transition in artificial neural networks is of renewed interest in ligh... more 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 neural systems, a recent study utilizing the excitationinhibition 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.
Zeitschrift Für Physik C Particles And Fields, Mar 1, 1993
The average potential is a scale dependent scalar effective potential. In a phase with spontaneou... more The average potential is a scale dependent scalar effective potential. In a phase with spontaneous symmetry breaking its inner region becomes flat as the averaging extends over infinite volume and the average potential approaches the convex effective potential. Fermion fluctuations affect the shape of the average potential in this region and its flattening with decreasing physical scale. They have to be taken into account to find the true minimum of the scalar potential which determines the scale of spontaneous symmetry breaking.
Opinion formation is a process with strong implications for public policy. In controversial debat... more 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.
Spin models of markets inspired by physics models of magnetism, as the Ising model, allow for the... more 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.
A learning algoritlu::p. based on genetic algorithms for asymmetric neural networks with an arbit... more A learning algoritlu::p. based on genetic algorithms for asymmetric neural networks with an arbitrary structure is presented. It is suited for the learrung of temporal patterns and leads to stable neural networks with feedback.. .
Methods of modeling cellular regulatory networks as diverse as differential equations and Boolean... more 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.
The stability of money value is an important requisite for a functioning economy, yet it critical... more 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 as a dynamical variable that results from trading between agents. The basic trading scenario can be recast into an Ising-type spin model and is studied on the hierarchical network structure of a Cayley tree. We solve this model analytically and observe a phase transition between a one-state phase, always allowing for a stable money value, and a two-state phase, where an unstable (in ationary) phase occurs. The onset of in ation is discontinuous and follows a ÿrst-order phase transition. The stable phase provides a parameter region where money value is robust and can be stabilized without ÿne tuning.
The average economic agent is often used to model the dynamics of simple markets, based on the as... more 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.
The problem of reliability of the dynamics in biological regulatory networks is studied in the fr... more 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 wellknown 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.
We study a genetic network model of eleven genes that coordinate the cell-cycle dynamics using a ... more 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.
Following the work of Krumov et al. [Eur. Phys. J. B 84, 535 (2011)] we revisit the question whet... more 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.
The geographical distribution of production is getting an increased amount of attention in econom... more The geographical distribution of production is getting an increased amount of attention in economics. Distributed trade opens for production where it is cheapest, which in turn is reinforced by economies of scale. Using a simple agent-based model for the geographical interplay between transportation costs, economies of scale, as well as information costs, we address here the transition between local and distributed economies. The model naturally recapitulates that decreased transportation and information costs favor large companies. This suggests history dependence in the sense that new companies typically reemerge in the vicinity of old ones. Further, it suggests that company stability depends on transport costs, and that the transition from a local economy to a global economy is naturally driven by reduced transportation costs and an increased information horizon.
... Dr. Thomas Pellizzari Dr. Stefan Bornholdt University of Innsbruck University of Kiel Inst ..... more ... Dr. Thomas Pellizzari Dr. Stefan Bornholdt University of Innsbruck University of Kiel Inst ... John von Neumann's "self-reproducing automaton", and John Horton Conway's game of Life are perhaps the most widely known examples of cellular automata showing complex behavior on ...
Based on a recent model of evolving viruses competing with an adapting immune system [1], we stud... more 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.
Genetic regulatory networks control ontogeny. For fifty years Boolean networks have served as mod... more 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 subensemble 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.
A simple spin model is studied, motivated by the dynamics of traders in a market where expectatio... more 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 different scales: While ferromagnetic couplings connect each spin to its local neighborhood, an additional coupling relates each spin to the global magnetization. This new coupling is allowed to be anti-ferromagnetic. The resulting frustration causes a metastable dynamics with intermittency and phases of chaotic dynamics. The model reproduces main observations of real economic markets as power-law distributed returns and clustered volatility.
The "edge of chaos" phase transition in artificial neural networks is of renewed interest in ligh... more 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 neural systems, a recent study utilizing the excitationinhibition 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.
Zeitschrift Für Physik C Particles And Fields, Mar 1, 1993
The average potential is a scale dependent scalar effective potential. In a phase with spontaneou... more The average potential is a scale dependent scalar effective potential. In a phase with spontaneous symmetry breaking its inner region becomes flat as the averaging extends over infinite volume and the average potential approaches the convex effective potential. Fermion fluctuations affect the shape of the average potential in this region and its flattening with decreasing physical scale. They have to be taken into account to find the true minimum of the scalar potential which determines the scale of spontaneous symmetry breaking.
Opinion formation is a process with strong implications for public policy. In controversial debat... more 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.
Spin models of markets inspired by physics models of magnetism, as the Ising model, allow for the... more 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.
A learning algoritlu::p. based on genetic algorithms for asymmetric neural networks with an arbit... more A learning algoritlu::p. based on genetic algorithms for asymmetric neural networks with an arbitrary structure is presented. It is suited for the learrung of temporal patterns and leads to stable neural networks with feedback.. .
Methods of modeling cellular regulatory networks as diverse as differential equations and Boolean... more 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.
The stability of money value is an important requisite for a functioning economy, yet it critical... more 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 as a dynamical variable that results from trading between agents. The basic trading scenario can be recast into an Ising-type spin model and is studied on the hierarchical network structure of a Cayley tree. We solve this model analytically and observe a phase transition between a one-state phase, always allowing for a stable money value, and a two-state phase, where an unstable (in ationary) phase occurs. The onset of in ation is discontinuous and follows a ÿrst-order phase transition. The stable phase provides a parameter region where money value is robust and can be stabilized without ÿne tuning.
The average economic agent is often used to model the dynamics of simple markets, based on the as... more 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.
The problem of reliability of the dynamics in biological regulatory networks is studied in the fr... more 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 wellknown 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.
We study a genetic network model of eleven genes that coordinate the cell-cycle dynamics using a ... more 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.
Following the work of Krumov et al. [Eur. Phys. J. B 84, 535 (2011)] we revisit the question whet... more 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.
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Papers by Stefan Bornholdt