arXiv subjects

Dan Braha

Publications and source records attributed to Dan Braha.

At least 19 recordsLinked to original sources

arXiv2026

What sets the critical genome length for sympatric speciation? A closed form and asymptotic theory

In the Derrida--Higgs model of sympatric speciation, a sexually reproducing population with finite binary genomes can mate only when the genetic overlap between two individuals exceeds a threshold $q_{\min}$. Depending on the genome length $L$, the population either remains genetically connected or fragments into reproductively isolated species. A central problem is therefore to predict the critical genome length $L_c$ at which fragmentation begins. At finite $L$, fluctuations broaden the overlap distribution and allow genetically distant regions of the population to remain connected. A previously proposed transient variance criterion captures this effect, but its evaluation requires numerical iteration of coupled moment equations. Here we first correct the unrestricted moment equations by removing a previously implicit assumption and then derive an explicit closed form expression for $L_c$. The resulting formula shows that the critical genome length is determined, at the time the mean overlap reaches $q_{\min}$, by the competition between deterministic separation from the unrestricted equilibrium and the transient genealogical variance of the overlap distribution. This expression permits a systematic asymptotic analysis. When the deterministic contribution dominates, $L_c$ becomes essentially independent of the population size $M$ and scales as $μ^{-2}$. When the transient genealogical variance dominates, $L_c$ grows as $M^{3/2}$ or as $\sqrt{M}/μ$, depending on how $M$ and the mutation rate $μ$ jointly vary. Simulations support all predicted behaviors. Our results identify transient genealogical variance as the principal mechanism linking finite genome fluctuations to the onset of reproductive fragmentation and provide a practical analytical prediction for the critical genome length.

q-bio.PE↗

arXiv2026

Majority Correctness in Social Networks: From Well-Mixed Electorates to Complex Networks

We study majority correctness when voting is preceded by sustained social interaction on a social network. Motivated by the Condorcet Jury Theorem, we consider a binary choice with an objectively correct alternative, where uninformed voters revise their vote intentions through repeated interaction in the presence of competing committed leaders (zealots). In this zealot--contrarian voter model, voters may either imitate or oppose the views they encounter. For fully mixed electorates, we characterize the long-run distribution of votes and the correlation structure induced among voters, and we show that Erdős--Rényi networks exhibit the same majority-correctness behavior after an appropriate rescaling of leader influence. Building on these results, we establish a finite-electorate Condorcet-type guarantee: when post-deliberation individual correctness exceeds random choice, a strict majority is more likely to select the correct alternative than a randomly chosen voter. At the same time, we identify an aggregation failure: social interaction can reduce majority accuracy relative to a no-deliberation benchmark in which voters respond only to zealots. As the electorate size tends to infinity, this finite-electorate advantage disappears unless social updating is purely conformist, revealing a tipping point at full conformity: any persistent contrarian updating drives both individual and majority correctness to the random choice level of one half. Simulations on scale-free, ring, and small-world networks further show that topology matters because it shapes the vote correlations generated by social influence: hub-dominated structures generate stronger positive correlations and lower majority accuracy, whereas spatially structured networks generate weaker correlations, preserve a larger effective number of independent judgments, and improve majority accuracy.

cs.SI↗

arXiv2026

Selection Mechanisms, Stationary Distributions, and Reversibility in Multiallelic Moran Models

The Moran process with selection and recurrent mutation is a classical model in population genetics, yet how the placement of selection within the update rule shapes the stationary distribution has received little attention. We study a finite, well-mixed haploid population of constant size $n$ with $m$ labeled alleles, parent-independent mutation, and allele-specific fitnesses. Within this common framework we compare three Moran update kernels that differ only in the stage at which selection acts: during reproduction, when the offspring copies one of two sampled parents (Scheme~I); through fitness-biased mate choice, followed by neutral copying (Scheme~II); and at death, so that fitter individuals are less likely to be replaced (Scheme~III). Although all three favor fitter alleles, they define different Markov chains. For two alleles, each scheme reduces to a birth-death chain and admits an exact stationary law, but the three laws differ. For $m\ge 3$, the placement of selection becomes decisive: Schemes~I and~II are generally nonreversible when fitnesses are unequal, so no detailed-balance product form exists, whereas Scheme~III remains reversible for every $m$ and has a closed stationary distribution -- a Dirichlet-multinomial core modified by an explicit fitness factor. We further show that all three mechanisms can act simultaneously in the two-allele case without losing exact solvability, and we derive weak-selection expansions that make explicit how small fitness differences tilt the neutral beta-binomial and Dirichlet-multinomial benchmarks. Together, these results clarify when neutral stationary structure survives the introduction of selection and when multiallelic Moran dynamics become genuinely nonreversible

q-bio.PE↗

arXiv2026

The multi-allelic Moran process as a multi-zealot voter model: exact results and consequences for diversity thresholds

The Moran process is a foundational model of genetic drift and mutation in finite populations. In its standard two-allele form with population size $n$, allele counts, and hence allele frequencies, change through stochastic replacement and mutation, yet converge to a stationary distribution. This distribution undergoes a qualitative transition at the \emph{critical mutation rate} $μ_c=1/(2n)$: at $μ=μ_c$ it is exactly uniform, so that the probability of observing $k$ copies of allele~1 (and $n-k$ of allele~2) is $π(k)=1/(n+1)$ for $k=0,\dots,n$. For $μ<μ_c$ diversity is low: the stationary distribution places most of its mass near $k=0$ and $k=n$, and the population is therefore typically dominated by one allele. For $μ>μ_c$, on the other hand, diversity is high: the distribution concentrates around intermediate values, so that both alleles are commonly present at comparable frequencies. Recently, the two-allele Moran process was shown to be exactly equivalent to the voter model with two candidates and $α_1$ and $α_2$ committed voters (\emph{zealots}) in a population of $n+α_1+α_2$, where mutation is played by zealot influence. Here we extend this equivalence to multiple alleles and multiple candidates. Using the mapping, we derive the exact stationary distribution of allele counts for well-mixed populations with an arbitrary number $m$ of alleles, and obtain the critical mutation rate $μ_c = 1/(m+2n-2)$, which depends explicitly on $m$. We then analyze the Moran process on randomly connected populations and show that both the stationary distribution and $μ_c$ are invariant to network structure and coincide with the well-mixed results. Finally, simulations on general network topologies show that structural heterogeneity can substantially reshape the stationary allele distribution and, consequently, the level of genetic diversity.

q-bio.PE↗

arXiv2025

Generalizing Condorcet's Jury Theorem to Social Networks

We generalize Condorcet's jury theorem (CJT) to socially connected populations in which agents revise discrete choices on a network in the presence of zealots. Free agents receive privately informative signals about the correct alternative and, at each update, either retain their state or imitate a uniformly chosen neighbor (free or zealot). For finite networks, we derive closed-form stationary laws for vote counts, and we characterize the corresponding vote-share limits as the number of free voters tends to infinity. For majority rule -- both in binary and multi-alternative settings -- we obtain an exact accuracy limit in closed form via the regularized incomplete beta function. For plurality rule, we establish sharp closed-form lower bounds on accuracy, expressed in terms of regularized incomplete beta functions. Under an absolute-majority condition for the correct alternative, both majority and plurality accuracies strictly exceed the accuracy of any single voter, showing that informative signals, coupled through social interaction, are amplified at the group level. These results extend CJT beyond independence and provide closed-form accuracy benchmarks for networked decision systems in social, biological, and engineered settings.

physics.soc-ph↗

arXiv2025

Emergence of Collective Accuracy in Socially Connected Networks

We analyze the accuracy of collective decision-making in socially connected populations, where agents update binary choices through local interactions on a network. Each agent receives a private signal that is biased -- even marginally -- toward the correct alternative, and social influence mediates the aggregation of these signals. We show analytically that, in the large-population limit, the probability of a correct majority converges to a nontrivial expression involving the regularized incomplete beta function. Remarkably, this collective accuracy surpasses that of any individual agent whenever private signals are better than random, revealing that network-mediated influence can enhance, rather than impair, group performance. Our findings may inform the design of resilient decision-making systems in social, biological, and engineered networks, where accuracy must emerge from interdependent and noisy agents.

stat.ME↗

arXiv2023

Phase Transitions of Civil Unrest across Countries and Time

Phase transitions, characterized by abrupt shifts between macroscopic patterns of organization, are ubiquitous in complex systems. Despite considerable research in the physical and natural sciences, the empirical study of this phenomenon in societal systems is relatively underdeveloped. The goal of this study is to explore whether the dynamics of collective civil unrest can be plausibly characterized as a sequence of recurrent phase shifts, with each phase having measurable and identifiable latent characteristics. Building on previous efforts to characterize civil unrest as a self-organized critical system, we introduce a macro-level statistical model of civil unrest and evaluate its plausibility using a comprehensive dataset of civil unrest events in 170 countries from 1946 to 2017. Our findings demonstrate that the macro-level phase model effectively captures the characteristics of civil unrest data from diverse countries globally and that universal mechanisms may underlie certain aspects of the dynamics of civil unrest. We also introduce a scale to quantify a country's long-term unrest per unit of time and show that civil unrest events tend to cluster geographically, with the magnitude of civil unrest concentrated in specific regions. Our approach has the potential to identify and measure phase transitions in various collective human phenomena beyond civil unrest, contributing to a better understanding of complex social systems.

physics.soc-ph↗

arXiv2021

Shannon information criterion for low-high diversity transition in Moran and Voter models

Mutation and drift play opposite roles in genetics. While mutation creates diversity, drift can cause gene variants to disappear, especially when they are rare. In the absence of natural selection and migration, the balance between the drift and mutation in a well-mixed population defines its diversity. The Moran model captures the effects of these two evolutionary forces and has a counterpart in social dynamics, known as the Voter model with external opinion influencers. Two extreme outcomes of the Voter model dynamics are consensus and coexistence of opinions, which correspond to low and high diversity in the Moran model. Here we use a Shannon's information-theoretic approach to characterize the smooth transition between the states of consensus and coexistence of opinions in the Voter model. Mapping the Moran into the Voter model we extend the results to the mutation-drift balance and characterize the transition between low and high diversity in finite populations. Describing the population as a network of connected individuals we show that the transition between the two regimes depends on the network topology of the population and on the possible asymmetries in the mutation rates.

q-bio.PE↗

arXiv2018

Opinion Dynamics on Networks under Correlated Disordered External Perturbations

We study an influence network of voters subjected to correlated disordered external perturbations, and solve the dynamical equations exactly for fully connected networks. The model has a critical phase transition between disordered unimodal and ordered bimodal distribution states, characterized by an increase in the vote-share variability of the equilibrium distributions. The random heterogeneities in the external perturbations are shown to affect the critical behavior of the network relative to networks without disorder. The size of the shift in the critical behavior essentially depends on the total fluctuation of the external influence disorder. Furthermore, the external perturbation disorder also has the surprising effect of amplifying the expected support of an already biased opinion. We show analytically that the vote-share variability is directly related to the external influence fluctuations. We extend our analysis by considering a fat-tailed multivariate lognormal disorder, and present numerical simulations that confirm our analytical results. Simulations for other network topologies demonstrate the generalizability of our findings. Understanding the dynamic response of complex systems to disordered external perturbations could account for a wide variety of networked systems, from social networks and financial markets to amorphous magnetic spins and population genetics.

physics.soc-ph↗

arXiv2018

Complex Design Networks: Structure and Dynamics

Why was the $6 billion FAA air traffic control project scrapped? How could the 1977 New York City blackout occur? Why do large scale engineering systems or technology projects fail? How do engineering changes and errors propagate, and how is that related to epidemics and earthquakes? In this paper we demonstrate how the rapidly expanding science of complex design networks could provide answers to these intriguing questions. We review key concepts, focusing on non-trivial topological features that often occur in real-world large-scale product design and development networks; and the remarkable interplay between these structural features and the dynamics of design rework and errors, network robustness and resilience, and design leverage via effective resource allocation. We anticipate that the empirical and theoretical insights gained by modeling real-world large-scale product design and development systems as self-organizing complex networks will turn out to be the standard framework of a genuine science of design.

physics.soc-ph↗

arXiv2016

Voting Contagion

Social influence plays an important role in human behavior and decisions. The sources of influence can be generally divided into external, which are independent of social context, or as originating from peers, such as family and friends. An important question is how to disentangle the social contagion by peers from external influences. While a variety of experimental and observational studies provided insight into this problem, identifying the extent of social contagion based on large-scale observational data with an unknown network structure remains largely unexplored. By bridging the gap between the large-scale complex systems perspective of collective human dynamics and the detailed approach of the social sciences, we present a parsimonious model of social influence, and apply it to a central topic in political science -- elections and voting behavior. We provide an analytical expression of the county vote-share distribution in a two party system, which is in excellent agreement with 92 years of observed U.S. presidential election data. Analyzing the social influence topography over this period reveals an abrupt transition in the patterns of social contagion -- from low to high levels of social contagion. The results from our analysis reveal robust differences among regions of the United States in terms of their social influence index. In particular, we identify two regions of 'hot' and 'cold spots of social influence, each comprising states that are geographically close. These results suggest that social contagion effects are becoming more instrumental in shaping large scale collective political behavior, which is at the core of democratic societies.

physics.soc-ph↗

arXiv2012

A Universal Model of Global Civil Unrest

Civil unrest is a powerful form of collective human dynamics, which has led to major transitions of societies in modern history. The study of collective human dynamics, including collective aggression, has been the focus of much discussion in the context of modeling and identification of universal patterns of behavior. In contrast, the possibility that civil unrest activities, across countries and over long time periods, are governed by universal mechanisms has not been explored. Here, we analyze records of civil unrest of 170 countries during the period 1919-2008. We demonstrate that the distributions of the number of unrest events per year are robustly reproduced by a nonlinear, spatially extended dynamical model, which reflects the spread of civil disorder between geographic regions connected through social and communication networks. The results also expose the similarity between global social instability and the dynamics of natural hazards and epidemics.

physics.soc-ph↗

arXiv2011

Corporate competition: A self-organized network

A substantial number of studies have extended the work on universal properties in physical systems to complex networks in social, biological, and technological systems. In this paper, we present a complex networks perspective on interfirm organizational networks by mapping, analyzing and modeling the spatial structure of a large interfirm competition network across a variety of sectors and industries within the United States. We propose two micro-dynamic models that are able to reproduce empirically observed characteristics of competition networks as a natural outcome of a minimal set of general mechanisms governing the formation of competition networks. Both models, which utilize different approaches yet apply common principles to network formation give comparable results. There is an asymmetry between companies that are considered competitors, and companies that consider others as their competitors. All companies only consider a small number of other companies as competitors; however, there are a few companies that are considered as competitors by many others. Geographically, the density of corporate headquarters strongly correlates with local population density, and the probability two firms are competitors declines with geographic distance. We construct these properties by growing a corporate network with competitive links using random incorporations modulated by population density and geographic distance. Our new analysis, methodology and empirical results are relevant to various phenomena of social and market behavior, and have implications to research fields such as economic geography, economic sociology, and regional economic development.

physics.soc-ph↗

arXiv2011

Predicting economic market crises using measures of collective panic

Predicting panic is of critical importance in many areas of human and animal behavior, notably in the context of economics. The recent financial crisis is a case in point. Panic may be due to a specific external threat, or self-generated nervousness. Here we show that the recent economic crisis and earlier large single-day panics were preceded by extended periods of high levels of market mimicry --- direct evidence of uncertainty and nervousness, and of the comparatively weak influence of external news. High levels of mimicry can be a quite general indicator of the potential for self-organized crises.

q-fin.ST↗

arXiv2010

A dynamic model of time-dependent complex networks

The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness against failures, vulnerability to deliberate attacks, and diffusion properties. However, recent empirical research of large dynamic networks (characterized by connections that are irregular and evolve rapidly) has demonstrated that there is little continuity in degree centrality of nodes over time, even when their degree distributions follow a power law. This unexpected dynamic centrality suggests that the connections in these systems are not driven by preferential attachment or other known mechanisms. We present a novel approach to explain real-world dynamic networks and qualitatively reproduce these dynamic centrality phenomena. This approach is based on a dynamic preferential attachment mechanism, which exhibits a sharp transition from a base pure random walk scheme.

physics.soc-ph↗

arXiv2007

Dynamical Response of Networks under External Perturbations: Exact Results

We introduce and solve a general model of dynamic response under external perturbations. This model captures a wide range of systems out of equilibrium including Ising models of physical systems, social opinions, and population genetics. The distribution of states under perturbation and relaxation process reflects two regimes -- one driven by the external perturbation, and one driven by internal ordering. These regimes parallel the disordered and ordered regimes of equilibrium physical systems driven by thermal perturbations but here are shown to be relevant for non-thermal and non-equilibrium external influences on complex biological and social systems. We extend our results to a wide range of network topologies by introducing an effective strength of external perturbation by analytic mean-field approximation. Simulations show this generalization is remarkably accurate for many topologies of current interest in describing real systems.

nlin.SI↗

arXiv2007

Preferential Detachment in Broadcast Signaling Networks: Connectivity and Cost Trade-off

We consider a network of nodes distributed in physical space without physical links communicating through message broadcasting over specified distances. Typically, communication using smaller distances is desirable due to savings in energy or other resources. We introduce a network formation mechanism to enable reducing the distances while retaining connectivity. Nodes, which initially transmit signals at a prespecified maximum distance, subject links to preferential detachment by autonomously decreasing their transmission radii while satisfying conditions of zero communication loss and fixed maximum node-hopping distance for signaling. Applied to networks with various spatial topologies, we find cost reductions as high as 90% over networks that are restricted to have all nodes with equal transmission distance.

nlin.AO↗

arXiv2006

From Centrality to Temporary Fame: Dynamic Centrality in Complex Networks

We develop a new approach to the study of the dynamics of link utilization in complex networks using records of communication in a large social network. Counter to the perspective that nodes have particular roles, we find roles change dramatically from day to day. "Local hubs" have a power law degree distribution over time, with no characteristic degree value. Our results imply a significant reinterpretation of the concept of node centrality in complex networks, and among other conclusions suggest that interventions targeting hubs will have significantly less effect than previously thought.

physics.soc-ph↗