arXiv subjects

James Holehouse

Publications and source records attributed to James Holehouse.

15 recordsLinked to original sources

arXiv2026

The Origins of Transient Bimodality

Many dynamical systems exhibit diverse modes of behavior. In biology, such modes can represent individual or cell fates. While the emergence of multimodality is commonly studied, transient bimodality is much less well understood. Under transient bimodality, a system moving from a well-defined initial to a final state transiently undergoes a bifurcation into multiple probability modes. This noise-driven phenomenon can significantly impact processes such as cell differentiation and speciation in the presence of changing environmental conditions. We detail a theoretical approach for understanding transient bimodality connecting results from ecology, optics, chemical reaction networks and cell biology, propose a ``minimal model'' of transient bimodality and derive a general criterion for its presence. We show that fast-to-slow dynamics can lead to transient bimodality in addition to the well-known case of slow-to-fast dynamics. Finally, we discuss the role of transient bimodality across the scientific literature, with emphasis on biochemical kinetics and gene regulation.

q-bio.SC↗

arXiv2026

Three Centuries of the Laws of Cricket Reveal Core Principles of the Evolution of Regulatory Mechanisms

Rules, regulations, and regulatory systems are central to societies, institutions, and organisms, yet surprisingly little is known about their evolution over long timescales. The Laws of Cricket, the world's second most popular sport, offer a unique insight into this fundamental question. Their 268-year history constitutes the longest continuous rule-set record yet assembled. Our quantitative analysis reveals generic features including rule-book size growing exponentially in time but scaling sublinearly with matches played; new situations stimulate new rules, but at a decelerating rate; regulatory structures exhibit abrupt phase transitions, increasing rule specificity, interconnectivity and complexity with central rules shifting from gameplay to officiating. These provide a framework for understanding how governance evolves from simple collections of rules to complex regulatory architectures across social, legal, and biological domains.

physics.soc-ph↗

arXiv2026

Branching under First-Passage Resetting

Many biological processes, from cell division to viral lysis, are triggered when an internal stochastic variable reaches a threshold. Here we introduce Branching under First-Passage Resetting, a general framework in which replication events arise endogenously from first-passage dynamics rather than from externally imposed lifetime clocks. We show that the resulting population dynamics obey an exact renewal equation linking single-trajectory first-passage statistics to the population growth rate. This mapping shows that, for fixed offspring number and fixed mean replication time, stochastic timing fluctuations necessarily enhance growth relative to a deterministic clock. When offspring yield depends on the first-passage time, however, fluctuations have non-trivial effects and expose a fundamental yield-delay trade-off: waiting longer can increase the number of descendants, but delays all future lineages. Our framework allows us to address this optimization problem analytically, and upon application to bacteriophage lysis, gives an optimal lysis time and growth rate consistent with empirical data.

q-bio.PE↗

arXiv2026

How is gene-regulatory evolution affected by cell-to-cell variability?

The evolutionary origins of structural features in reconstructed gene-regulatory networks (GRNs) remain poorly understood, especially given the random aspects of gene expression. Here, we extend a classical model of GRN evolution to allow a single network to express a distribution of phenotypes through noisy developmental dynamics. Inspired by Hopfield networks, we introduce an alignment score that quantifies the cohesion of gene-gene interactions in the network to support a target stable phenotype. Overall, evolved populations optimized their fitness and reduced the length of their developmental paths. Increased noise levels promoted alignment, enriched coherent feedforward and positive feedback loops relative to non-evolved and noiseless controls, and buffered against mutational perturbations. Alignment provides intuitive interpretations because an increased number of appropriately signed gene-gene interactions is more redundant and thus more robust against developmental noise and mutations. Together, these results demonstrate that cell-to-cell variability exerts strong selective pressure, driving the evolution of aligned, robust, and motif-enriched GRN architectures.

q-bio.PE↗

arXiv2025

Closed-form solution of a general three-term recurrence relation: applications to Heun functions and social choice models

We derive a concise closed-form solution for a linear three-term recurrence relation. Such recurrence relations are very common in the quantitative sciences, and describe finite difference schemes, solutions to problems in Markov processes and quantum mechanics, and coefficients in the series expansion of Heun functions and other higher-order functions. Our solution avoids the usage of continued fractions and relies on a linear algebraic approach that makes use of the properties of lower-triangular and tridiagonal matrices, allowing one to express the terms in the recurrence relation in closed-form in terms of a finite set of orthogonal polynomials. We pay particular focus to the power series coefficients of Heun functions, which are often found as solutions in eigenfunction problems in quantum mechanics and general relativity and have also been found to describe time-dependent dynamics in both biology and economics. Finally, we apply our results to find equations describing the relaxation times to steady state behaviour in social choice models.

physics.soc-ph↗

arXiv2025

Quantifying Broken Detailed Balance in Transcription

For the canonical two-state model of transcription, we derive exact analytic expressions for the entropy production rate of transcription at steady state, and assess detailed balance breaking in transcription. Our analytics allow us to easily evaluate the entropy production rate of thousands of genes across seven datasets of two-state model parameters without needing to evaluate the entropy production rate from trajectory-based computation. A data-driven approach then exposes that most genes avoid parameter regimes associated with large entropy production rates, akin to a mesoscopic version of energy expenditure minimization. Importantly, we show that this is not a thermodynamic phenomenon, since the entropy production rate from the two state gene model provides only a weak bound on the housekeeping energy needed to power transcription. Finally, we show that cell-to-cell variability can make mRNA expression seem more or less irreversible than a ``representative cell'' would imply.

q-bio.SC↗

arXiv2025

A generative model of function growth explains hidden self-similarities across biological and social systems

From genomes and ecosystems to bureaucracies and cities, the growth of complex systems occurs by adding new types of functions and expanding existing ones. We present a simple generative model that generalizes the Yule-Simon process by including: (i) a size-dependent probability of introducing new functions, and (ii) a generalized preferential attachment mechanism for expanding existing ones. We uncover a shared underlying structure that helps explain how function diversity evolves in empirical observations, such as prokaryotic proteomes, U.S. federal agencies, and urban economies. We show that real systems are often best represented as having non-Zipfian rank-frequency distributions, driven by sublinear preferential attachment, whilst still maintaining power-law scaling in their abundance distributions. Furthermore, our analytics explain five distinct phases of the organization of functional elements across complex systems. The model integrates empirical findings regarding the logarithmic growth of diversity in cities and the self-similarity of their rank-frequency distributions. Self-similarity previously observed in the rank-frequency distributions of cities is not observed in cells and federal agencies -- however, under a rescaling relative to the total diversity, all systems admit self-similar structures predicted by our theory.

physics.soc-ph↗

arXiv2025

A Century of Evolution in the Complexity of the United States Legal Code

As societies confront increasingly complex regulatory demands in domains such as digital governance, climate policy, and public health, there is a pressing need to understand how legal systems evolve, where they concentrate regulatory attention, and how their institutional architectures shape capacity for adaptation. Yet, the long-term structural dynamics of law remain empirically underexplored. Here, we provide a versioned, machine-readable record of the United States Code (U.S. Code), the primary compilation of federal statutory law in the United States, covering the entire history of the Code from 1926 to 2023. We include not only the curated text in Code but also its structural and linguistic complexity: word counts, vocabulary statistics, hierarchical organization (titles, chapters, sections, subsections), and cross-references among titles. In this way, the dataset offers an empirical foundation for large-scale and long-term interdisciplinary analysis of the growth, reorganization, and internal logic of statutory systems. The dataset is released on GitHub with comprehensive documentation to support reuse across legal studies, data science, complexity research, and institutional analysis.

physics.soc-ph↗

arXiv2023

First-passage on disordered intervals

We investigate the first-passage properties of nearest-neighbor hopping on a finite interval with disordered hopping rates. We develop an approach that relies on the backward equation, in conjunction with probability generating functions, to obtain all moments, as well as the distribution of first-passage times. Our approach is simpler than previous approaches that are based on either the forward equation or recursive method, in which the $m^{\rm th}$ moment requires all preceding moments. For the interval with two absorbing boundaries, we elucidate the disparity in the first-passage times between different realizations of the hopping rates and also unexpectedly find that the distribution of first-passage times can be \emph{bimodal} for certain realizations of the hopping rates.

cond-mat.stat-mech↗

arXiv2022

Scaling Laws for Function Diversity and Specialization Across Socioeconomic and Biological Complex Systems

Function diversity, the range of tasks individuals perform, and specialization, the distribution of function abundances, are fundamental to complex adaptive systems. In the absence of overarching principles, these properties have appeared domain-specific. Here, we introduce an empirical framework and a mathematical model for the diversification and specialization of functions across disparate systems, including bacteria, federal agencies, universities, corporations, and cities. We find that the number of functions grows sublinearly with system size, with exponents from 0.35 to 0.57, consistent with Heaps' Law. In contrast, cities exhibit logarithmic scaling. To explain these empirical findings, we generalize the Yule-Simon model by introducing two key parameters: a diversification parameter that characterizes how existing functions inhibit the creation of new ones, and a specialization parameter that describes how a function's attractiveness depends on its abundance. Our model enables cross-system comparisons, from microorganisms to metropolitan areas. The analysis suggests that what drives the creation of new functions depends on the system's goals and structure: federal agencies tend to ensure comprehensive coverage of necessary functions; cities tend to slow the creation of new occupations as existing ones expand; and cells occupy an intermediate position. Once functions are introduced, their growth follows a remarkably universal pattern across all systems.

physics.soc-ph↗

arXiv2022

Exact time-dependent dynamics of discrete binary choice models

We provide a generic method to find full dynamical solutions to binary decision models with interactions. In these models, agents follow a stochastic evolution where they must choose between two possible choices by taking into account the choices of their peers. We illustrate our method by solving Kirman and Föllmer's ant recruitment model for any number $N$ of agents and for any choice of parameters, recovering past results found in the limit $N\to \infty$. We then solve extensions of the ant recruitment model for increasing asymmetry between the two choices. Finally, we provide an analytical time-dependent solution to the standard voter model and a semi-analytical solution to the vacillating voter model.

cond-mat.stat-mech↗

arXiv2022

Non-equilibrium time-dependent solution to discrete choice with social interactions

We solve the binary decision model of Brock and Durlauf in time using a method reliant on the resolvent of the master operator of the stochastic process. Our solution is valid when not at equilibrium and can be used to exemplify path-dependent behaviours of the binary decision model. The solution is computationally fast and is indistinguishable from Monte Carlo simulation. Well-known metastable effects are observed in regions of the model's parameter space where agent rationality is above a critical value, and we calculate the time scale at which equilibrium is reached from first passage time theory to a much greater approximation than has been previously conducted. In addition to considering selfish agents, who only care to maximise their own utility, we consider altruistic agents who make decisions on the basis of maximising global utility. Curiously, we find that although altruistic agents coalesce more strongly on a particular decision, thereby increasing their utility in the short-term, they are also more prone to being subject to non-optimal metastable regimes as compared to selfish agents. The method used for this solution can be easily extended to other binary decision models, including Kirman's ant model, and under reinterpretation also provides a time-dependent solution to the mean-field Ising model. Finally, we use our time-dependent solution to construct a likelihood function that can be used on non-equilibrium data for model calibration. This is a rare finding, since often calibration in economic agent based models must be done without an explicit likelihood function. From simulated data, we show that even with a well-defined likelihood function, model calibration is difficult unless one has access to data representative of the underlying model.

econ.TH↗

arXiv2020

Steady-state fluctuations of a genetic feedback loop with fluctuating rate parameters using the unified colored noise approximation

A common model of stochastic auto-regulatory gene expression describes promoter switching via cooperative protein binding, effective protein production in the active state and dilution of proteins. Here we consider an extension of this model whereby colored noise with a short correlation time is added to the reaction rate parameters -- we show that when the size and timescale of the noise is appropriately chosen it accounts for fast reactions that are not explicitly modelled, e.g., in models with no mRNA description, fluctuations in the protein production rate can account for rapid multiple stages of nuclear mRNA processing which precede translation in eukaryotes. We show how the unified colored noise approximation can be used to derive expressions for the protein number distribution that is in good agreement with stochastic simulations. We find that even when the noise in the rate parameters is small, the protein distributions predicted by our model can be significantly different than models assuming constant reaction rates.

q-bio.SC↗

arXiv2019

Stochastic modeling of auto-regulatory genetic feedback loops: a review and comparative study

Auto-regulatory feedback loops are one of the most common network motifs. A wide variety of stochastic models have been constructed to understand how the fluctuations in protein numbers in these loops are influenced by the kinetic parameters of the main biochemical steps. These models differ according to (i) which sub-cellular processes are explicitly modelled; (ii) the modelling methodology employed (discrete, continuous or hybrid); (iii) whether they can be analytically solved for the steady-state distribution of protein numbers. We discuss the assumptions and properties of the main models in the literature, summarize our current understanding of the relationship between them and highlight some of the insights gained through modelling.

q-bio.SC↗

arXiv2018

Cross-situational learning of large lexicons with finite memory

Cross-situational word learning, wherein a learner combines information about possible meanings of a word across multiple exposures, has previously been shown to be a very powerful strategy to acquire a large lexicon in a short time. However, this success may derive from idealizations that are made when modeling the word-learning process. In particular, an earlier model assumed that a learner could perfectly recall all previous instances of a word's use and the inferences that were drawn about its meaning. In this work, we relax this assumption and determine the performance of a model cross-situational learner who forgets word-meaning associations over time. Our main finding is that it is possible for this learner to acquire a human-scale lexicon by adulthood with word-exposure and memory-decay rates that are consistent with empirical research on childhood word learning, as long as the degree of referential uncertainty is not too high or the learner employs a mutual exclusivity constraint. Our findings therefore suggest that successful word learning does not necessarily demand either highly accurate long-term tracking of word and meaning statistics or hypothesis-testing strategies.

physics.soc-ph↗