Sorin Solomon

• Professor (Full) at Hebrew University of Jerusalem

Abstract The spread of information, opinions, preferences, and behavior across social media is a crucial feature of the current functioning of our economy, politics, and culture. One of the emerging channels for spreading social collective action and funding of novelty in all these domains is Crowdfunding on various platforms such as Kickstarter, I...

We present a platform for stochastic agent-based simulation of the role of labor in the economy (SABLE). The platform facilitates heterogeneous agents: a large number of firms, workers, and banks are represented as individual agents. It allows the agents to have fixed or random reactions to the other agents and to pursue goals through decisions wit...

The Kiyotaki and Wright(1989) (henceforth KW) model of money emergence as a medium of exchange has been studied from various perspectives in recent papers. In the present work we propose a minimalistic model for the behavior of agents in the KW framework, which may either reproduce the theoretical predictions of Kiyotaki and Wright(1989) on the eme...

To quantify the mechanism of a complex network growth we focus on the network of citations of scientific papers and use a combination of the theoretical and experimental tools to uncover microscopic details of this network growth. Namely, we develop a stochastic model of citation dynamics based on copying/redirection/triadic closure mechanism. In a...

Solomon and Golo [1] have recently proposed an autocatalytic (self-reinforcing) feedback model which couples a macroscopic system parameter (the interest rate), a microscopic parameter that measures the distribution of the states of the individual agents (the number of firms in financial difficulty) and a peer-to-peer network effect (contagion acro...

We propose a novel approach and an empirical procedure to test direct contagion of growth rate in a trade credit network of firms. Our hypotheses are that the use of trade credit contributes to contagion (from many customers to a single supplier - “many to one” contagion) and amplification (through their interaction with the macrocopic variables, s...

Ecosystems greatly vary in their species composition and interactions, yet they all show remarkable resilience to external influences. Recent experiments have highlighted the significant effects of spatial structure and connectivity on the extinction and survival of species. It has also been emphasized lately that in order to study extinction dynam...

We demonstrate a comprehensive framework that accounts for citation dynamics of scientific papers and for the age distribution of references. We show that citation dynamics of scientific papers is nonlinear and this nonlinearity has far-reaching consequences, such as diverging citation distributions and runaway papers. We propose a nonlinear stocha...

It is generally accepted that neighboring nodes in financial networks are negatively assorted with respect to the correlation between their degrees. This feature would play an important 'damping' role in the market during downturns (periods of distress) since this connectivity pattern between firms lowers the chances of auto-amplifying (the propaga...

We study analytically and numerically Minsky instability as a combination of top-down, bottom-up and peer-to-peer positive feedback loops. The peer-to-peer interactions are represented by the links of a network formed by the connections between firms, contagion leading to avalanches and percolation phase transitions propagating across these links....

The primordial confrontation underlying the existence of our Universe can be conceived as the battle between entropy and complexity. The law of ever-increasing entropy (Boltzmann H-theorem) evokes an irreversible, one-directional evolution (or rather involution) going uniformly and monotonically from birth to death. Since the 19th century, this con...

Masanao Aoki developed a new methodology for a basic problem of economics: deducing rigorously the macroeconomic dynamics as emerging from the interactions of many individual agents. This includes deduction of the fractal / intermittent fluctuations of macroeconomic quantities from the granularity of the mezo-economic collective objects (large indi...

Agent-based models (ABMs) are quite new in the modeling landscape; they emerged on the scene in the 1990s. ABMs have a clear advantage over other approaches: they create the capacity to manage learning processes in agents and discover novelties in their behavior. In addition to bounded rationality assumptions, ABMs share a number of peculiar charac...

Masanao Aoki developed a new methodology for a basic problem of economics: deducing rigorously the macroeconomic dynamics as emerging from the interactions of many individual agents. This includes deduction of the fracta/intermittent fluctuations of macroeconomic quantities from the granularity of the mezo-economic collective objects (large individ...

Solomon and Golo [1] have recently proposed an autocatalytic (self-reinforcing) feedback model which couples a macroscopic system parameter (the interest rate), a microscopic parameter that measures the distribution of the states of the individual agents (the number of firms in financial difficulty) and a peer-to-peer network effect (contagion acro...

Opinion dynamics is studied through a minimal Ising model with three main influences (fields): personal conservatism (power-law distributed), inter-personal and group pressure, and a global field incorporating peer-to-peer and mass communications, which is generated bottom-up from the faction supporting the new opinion. A rich phase diagram appears...

We discuss microscopic mechanisms of complex network growth, with the special emphasis of how these mechanisms can be evaluated from the measurements on real networks. As an example we consider the network of citations to scientific papers. Contrary to common belief that its growth is determined by the linear preferential attachment, our microscopi...

The dynamics of collective decision making is not yet well understood. Its practical relevance however can be of utmost importance, as experienced by people who lost their fortunes in turbulent moments of financial markets. In this paper we show how spontaneous collective "moods" or "biases" emerge dynamically among human participants playing a tra...

Optimal solution of the $-Game. (DOC)

Instructions given to the subjects in experiments on humans (history m = 3). (DOC)

Screenshot of a representative game in time step t = 1. (TIF)

Screenshot of a representative game in time step t = 3. (TIF)

Screenshot of a representative game in time step t = 5. (TIF)

Screenshot of a representative game in time step t = 6. (TIF)

Screenshot of a representative game in time step t = 2. (TIF)

Screenshot of a representative game in time step t = 4. (TIF)

We perform experimental verification of the preferential attachment model that is commonly accepted as a generating mechanism of the scale-free complex networks. To this end we chose citation network of Physics papers and traced citation history of 40,195 papers published in one year. Contrary to common belief, we found that citation dynamics of th...

Revolution dynamics is studied through a minimal Ising model with three main influences (fields): personal conservatism (power-law distributed), inter-personal and group pressure, and a global field incorporating peer-to-peer and mass communications, which is generated bottom-up from the revolutionary faction. A rich phase diagram appears separatin...

Statistical distributions with heavy tails are ubiquitous in natural and social phenomena. Since the entries in heavy tail have disproportional significance, the knowledge of its exact shape is very important. Citations of scientific papers form one of the best-known heavy tail distributions. Even in this case there is a considerable debate whether...

We propose a general scheme for constructing an action principle for arbitrary consistent overdetermined systems of nonlinear field equations. The principal tool is the BFV-BRST formalism. There is no need for star-product nor Chern-Simons forms. The main application of this general construction is the derivation of a superspace action in terms of...

We study the effect of external intervention on the self-organized jamming phase transition. The classical traffic model of Biham, Middleton, and Levine (BML) is modified to give priority to longer queues. It is shown that this lowers the critical density at which the jamming transition takes place (in comparison to the original model).

We have performed high precision finite size scaling measurements of the critical behavior of the Ising model on dynamically triangulated surfaces of genus 0. The results are in perfect agreement with the matrix model predictions. 1,2 Values of the critical exponents equal to the regular lattice 2D Ising model are excluded by our error bars. In ord...

Language comprehension is a complex task that involves a wide network of brain regions. We used topological measures to qualify and quantify the functional connectivity of the networks used under various comprehension conditions. To that aim we developed a technique to represent functional networks based on EEG recordings, taking advantage of their...

The inference of past demographic parameters from current genetic polymorphism is a fundamental problem in population genetics. The standard techniques utilize a reconstruction of the gene-genealogy, a cumbersome process that may be applied only to small numbers of sequences. We present a method that compares the total number of haplotypes (distinc...

The generation mechanisms of real world networks have been described using multiple models. The mathematical features of these models are usually extrapolated from statistical properties of a snapshot of these networks. We here propose an alternative method based on direct measurement of a sequence of consecutive snapshots to uncover the dynamics u...

Information received by the human cortex is supplied by two main sources: extrinsic stimuli delivered by the external environment and intrinsic information regarding the body and self. We reanalyzed electrophysiological data involving the same external stimuli, but manipulating the degree of 'self-projection' to locations inside and outside the bod...

A formal model that captures the basic processes at work in the development and transformation of intractable conflict is presented. The formal model translates the insights of the Crude Law, which distills the principles underlying a highly diverse set of ideas and research finding into parameters that can be instantiated in computer simulations....

We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during times of recession and recovery. We then argue that this equation is the response function of the economy to isolated shocks, hence that it can be used to detect...

We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during times of recession and recovery. We then argue that this equation is the response function of the economy to isolated shocks, hence that it can be used to detect...

Perfect synchronicity in $N$-player games is a useful theoretical dream, but communication delays are inevitable and may result in asynchronous interactions. Some systems such as financial markets are asynchronous by design, and yet most theoretical models assume perfectly synchronized actions. We propose a general method to transform standard mode...

Despite intense research on intractable conflicts their dynamical properties are not well understood, and in many respects they appear paradoxical. The defining characteristic of intractable conflicts is stability and resistance to intervention, yet this stability is maintained by underlying volatile dynamics. The dynamical systems approach provide...

We present a dynamical model of the emergence of firms as opposed to a flat labour market where entrepreneurs would recruit workers for each business opportunity. The model uses a preferential choice of partners based on previous collaborations experience. A sharp transition in the parameter space separates an ordered regime, where preferential lin...

Proving the existence of speculative financial bubbles even a posteriori has proven exceedingly difficult so anticipating a speculative bubble ex ante would at first seem an impossible task. Still as illustrated by the recent turmoil in financial markets initiated by the so called subprime crisis there is clearly an urgent need for new tools in our...

The stabilizing effects of local enrichment are revisited. Diffusively coupled host–parasitoid and predator–prey metapopulations are shown to admit a stable fixed point, limit cycle or stable torus with a rich bifurcation structure. A linear toy model that yields many of the basic qualitative features of this system is presented. The further nonlin...

P.W. Anderson proposed the concept of complexity in order to describe the emergence and growth of macroscopic collective patterns out of the simple interactions of many microscopic agents. In the physical sciences this paradigm was implemented systematically and confirmed repeatedly by successful confrontation with reality. In the social sciences h...

The stabilizing effects of local enrichment are revisited. Diffusively coupled host-parasitoid and predator-prey metapopulations are shown to admit a stable fixed point, limit cycle or stable torus with a rich bifurcation structure. A linear toy model that yields many of the basic qualitative features of this system is presented. The further nonlin...

We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during times of recession and recovery. We then argue that this equation is the response function of the economy to isolated shocks, hence that it can be used to detect...

In this paper, we show how simple logistic growth that was studied intensively during the last 200 years in many domains of science could be extended in a rather simple way and with these extensions is capable to produce a collection of behaviors widely observed in an enormous number of real-life systems in Economics, Sociology, Biology, Ecology an...

We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during the times of recession and recovery. We then argue that it can be used to detect shocks and discuss its predictive power. Finally, a two-sector theoretical model...

P.W. Anderson proposed the concept of complexity in order to describe the emergence and growth of macroscopic collective patterns out of the simple interactions of many microscopic agents. In the physical sciences this paradigm was implemented systematically and confirmed repeatedly by successful confrontation with reality. In the social sciences h...

The rapid accumulation of knowledge and the recent emergence of new dynamic and practically unmoderated information repositories have rendered the classical concept of the hierarchal knowledge structure irrelevant and impossible to impose manually. This led to modern methods of data location, such as browsing or searching, which conceal the underly...

The survival of autocatalytic agents in hostile environments depends on their ability to adapt their spatial configuration to local fluctuations. A model of diffusive reactants that extract the advantage of spatio-temporal fluctuations associated with the stochastic wandering of diffusive catalysts is discussed. Two arguments are presented for the...

Statistical regularities at the top end of the wealth distribution in the United States are examined using the Forbes 400 lists of richest Americans, published between 1988 and 2003. It is found that the wealths are distributed according to a power-law (Pareto) distribution. This result is explained using a simple stochastic model of multiple inves...

We describe the main idea and the conceptual architecture of a platform for simulating a large number of asynchronously interacting agents in continuous time. We show how the generic capabilities of the platform apply to the simulation of realistic stock market interactions. A particular example of a very dramatic market event that took place in Fi...

Unlabelled: We study two kinds of networks: genetic regulatory networks and the World Wide Web. We systematically test microscopic mechanisms to find the set of such mechanisms that optimally explain each networks' specific properties. In the first case we formulate a model including mainly random unbiased gene duplications and mutations. In the s...

Statistical regularities at the top end of the wealth distribution are examined using the Forbes 400 lists during 1988–2003. We find that the wealth is distributed according to a Pareto (power-law) distribution with an average exponent of α = 1.49.

We present a novel agent based simulation platform designed for general-purpose modeling in social sciences. Beyond providing convenient environment for modeling, debugging, simulation and analysis, the platform automatically enforces many of the properties inherent to the reality (such as causality and precise timing of events). A unique formalism...

Although computer viruses cause tremendous economic loss, defence mechanisms fail to adapt to their rapid evolution. Previous immunization strategies have been characterized as being static and centralized, which has made virus containment difficult or even impossible. We suggest, instead, to propagate the immunization agent as an epidemic. The mai...

Simulations of artificial stock markets were considered as early as 1964 and multi-agent ones were introduced as early as 1989. Starting the early 90's, collaborations of economists and physicists produced increasingly realistic simulation platforms. Currently, the market stylized facts are easily reproduced and one has now to address the realistic...

We discuss the influence of information contagion on the dynamics of choices in social networks of heterogeneous buyers. In the case of non-adaptive agents, the dynamics results in either the contagion process being stuck and very few agents actually buying (flops) or in a ‘hit’ where most agents a priori interested in getting the product actually...

We present Postext (pronounced POS-TEH) – a platform for collective thinking. This generic system was originally created in order to assist the community of complexity research to self-organize (the system is operative and can be found at http://complexity.huji.ac.il). In this paper we describe the basic philosophical ideas that promoted its creati...

We propose a Statistical-Mechanics inspired framework for modeling economic systems. Each agent composing the economic system is characterized by a few variables of distinct nature (e.g. saving ratio, expectations, etc.). The agents interact locally by their individual variables: for example, people working in the same office may influence their pe...

In our innovation-driven world we tend to lay concepts that have lost their attractiveness to rest and rush to embrace the next giant leap. However, in most fields of creation, patterns of reawakening of old, extinct innovations can be found. It often looks as if new technological and social concepts have a life of their own, survival instincts and...

We are fascinated by the idea of giving life to the inanimate. The fields of Artificial Life and Artificial Intelligence (AI) attempt to use a scientific approach to pursue this desire. The first steps on this approach hark back to Turing and his suggestion of an imitation game as an alternative answer to the question "can machines think?".1 To tes...

Many new products fail, despite preliminary market surveys having determined considerable potential market share. This effect is too systematic to be attributed to bad luck. We suggest an explanation by presenting a new percolation theory model for product propagation, where agents interact over a social network. In our model, agents who do not ado...

We propose a Statistical-Mechanics inspired framework for modeling economic systems. Each agent composing the economic system is characterized by a few variables of distinct nature (e.g. saving ratio, expectations, etc.). The agents interact locally by their individual variables: for example, people working in the same office may influence their pe...

The Pareto (power-law) wealth distribution, which is empirically observed in many countries, implies rather extreme wealth inequality. For instance, in the U.S. the top 1% of the population holds about 40% of the total wealth. What is the source of this inequality? The answer to this question has profound political, social, and philosophical implic...

This paper discusses some consequences of the discovery that antigen receptors are degenerate: Immune specificity, in contrast to the tenets of the clonal selection paradigm, must be generated by the immune response down-stream of initial antigen recognition; and specificity is a property of a collective of cells and not of single clones.

We propose a stochastic model of interactive formation of individual expectations regarding the business climate in an industry. Our model is motivated by a business climate survey cond ucted since 1960 in Germany by the Ifo-institute (www.ifo.de). In accordance with the data structure of this survey, in our model there is asso ciated to each econo...

Consider an infinite 2 dimensional world inhabited by 2 types of particles (“creatures”): A (“angels”): They do not die, are not born and can only diffuse (jump randomly from one location to a neighboring one) with a probability rate DA. Assume they are initially distributed uniformly with a density R. B (“mortals”): They diffuse too (with a probab...

We propose a stochastic generalization of the Lotka-Volterra-Eigen-Schuster systems. In the generalized system, the set of dynamical variables is divided into several subsets, such that the variables within each subset interact with each other more strongly than with those in other subsets. It is shown that the size distribution of the dynamical va...

Introduced in 1994, the Levy-Levy-Solomon (LLS) model developed into a standard tool to study in realistic detail the emergence of complex dynamics of stock markets with heterogeneous quasi-rational partially informed investors. We review the main features of this model and several of its extensions. We study the effects of investor heterogeneity a...

We consider the emergence of power-law tails in the returns distribution of limit-order driven markets. We explain a previously observed clash between the theoretical and numerical studies of such models. We introduce a solvable model that interpolates between the previous studies and agrees with each of them in the relevant limit.

We study the emergence of collective spatio-temporal objects in biological systems by representing individually the elementary interactions between their microscopic components. We use the immune system as a prototype for such interactions. The results of this detailed explicit analysis are compared with the traditional procedure of representing th...

The formation of vegetation patterns in the arid and the semiarid climatic zones is studied. Threshold for the biomass of the perennial flora is shown to be a relevant factor, leading to a frozen disordered pattern in the arid zone. In this "glassy" state, vegetation appears as singular plant spots separated by irregular distances, and an indirect...

The manifest destiny and the ultimate fron-tier for physicists on the financial markets continent is to investigate the emergence of complex macroscopic market dynamics out of the individual traders'microscopic inter-actions [1]. Their main tool is statistical mechanics, which has lately been routinely used by physicists for expansion into vari-ous...

Economic and cultural globalization is one of the most important processes humankind has been undergoing lately. This process is assumed to be leading the world into a wealthy society with a better life. However, the current trend of globalization is not unprecedented in human history, and has had some severe consequences in the past. By applying a...

The formation of vegetation patterns in the arid and the semi-arid climatic zones is studied. Threshold for the biomass of the perennial flora is shown to be a relevant factor, leading to a frozen disordered patterns in the arid zone. In this ``glassy'' state, vegetation appears as a singular plant spots separated by irregular distances, and an ind...

The dynamics of generalized Lotka-Volterra systems is studied by theoretical techniques and computer simulations. These systems describe the time evolution of the wealth distribution of individuals in a society, as well as of the market values of firms in the stock market. The individual wealths or market values are given by a set of time dependent...

The dynamics of generalized Lotka-Volterra systems is studied by theoretical techniques and computer simulations. These systems describe the time evolution of the wealth distribution of individuals in a society, as well as of the market values of firms in the stock market. The individual wealths or market values are given by a set of time dependent...

Financial time series typically exhibit strong fluctuations that cannot be described by a Gaussian distribution. In recent empirical studies of stock market indices it was examined whether the distribution P(r) of returns r(tau) after some time tau can be described by a (truncated) Levy-stable distribution L_{alpha}(r) with some index 0 < alpha <=...

We study a stochastic multiplicative system composed of finite asynchronous elements to describe the wealth evolution in financial markets. We find that the wealth fluctuations or returns of this system can be described by a walk with correlated step sizes obeying truncated Lévy-like distribution, and the cross-correlation between relative updated...

The generalized Lotka–Voltera (GLV) formalism has been introduced in order to explain the power law distributions in the individual wealth (wi(t)) (Pareto law) and financial markets returns (fluctuations) (r) as a result of the auto-catalytic (multiplicative random) character of the individual capital dynamics.As long as the multiplicative random f...

We study a stochastic multiplicative system composed of finite asynchronous elements to describe the wealth evolution in financial markets. We find that the wealth fluctuations or returns of this system can be described by a walk with correlated step sizes obeying truncated Levy-like distribution, and the cross-correlation between relative updated...

Using the Generalized Lotka Volterra model adapted to deal with mutiagent systems we can investigate economic systems from a general viewpoint and obtain generic features common to most economies. Assuming only weak generic assumptions on capital dynamics, we are able to obtain very specific predictions for the distribution of social wealth. First,...

Financial time series typically exhibit strong fluctuations that cannot be described by a Gaussian distribution. Recent empirical studies of stock market indices examined whether the distribution P(r) of returns r(tau) after some time tau can be described by a (truncated) Lévy-stable distribution L(alpha)(r) with some index 0<alpha< or =2. While th...

Biological systems, unlike physical or chemical systems, are characterized by the very inhomogeneous distribution of their components. The immune system, in particular, is notable for self-organizing its structure. Classically, the dynamics of natural systems have been described using differential equations. But, differential equation models fail t...

Is there “music platonism”—universal music—awaiting discovery? The Perspectives by P. M. Gray et al. ([1][1]) and M. J. Tramo ([2][2]) are relevant to this question. In searching for music platonism, should we pursue a unified theory of external effects (involving whales, birds, etc.)? Does

We study the finite-size effects in some scaling systems, and show that the finite number of agents N leads to a cut-off in the upper value of the Pareto law for the relative individual wealth. The exponent α of the Pareto law obtained in stochastic multiplicative market models is crucially affected by the fact that N is always finite in real syste...

We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws in the size distribution of their individual elements. The exponents of these power laws are time independent...

We study the finite-size effects in some scaling systems, and show that the finite number of agents N leads to a cut-off in the upper value of the Pareto law for the relative individual wealth. The exponent $\alpha$ of the Pareto law obtained in stochastic multiplicative market models is crucially affected by the fact that N is always finite in rea...