arXiv subjects

S. Redner

Publications and source records attributed to S. Redner.

At least 19 recordsLinked to original sources

arXiv2026

Universal fluctuations of first discoveries in competitive exploration

Random exploration is usually quantified by how fast new space is found, from the range of a single walker to the territory collectively covered by many walkers. In competitive exploration, first arrival secures an exclusive resource, as when foragers compete for food items or agents capture distributed targets. It is then no longer enough to know which sites have been discovered: one must determine, for each discovered site, which searcher reached it first. We introduce the discovery share $X_n$, the fraction of the first $n$ collective discoveries secured by a tagged searcher. For two identical competitors, exchange symmetry fixes $\langle X_n\rangle=1/2$, but the central question is whether this equal split emerges in each long exploration history or only on average, i.e. whether early competitive advantages are erased or persist. Here we show that the answer is controlled by the spectral dimension $d_s$, defined by the large-time decay of the probability that a single searcher is at its starting point after $t$ steps, $p_0(t)\sim t^{-d_s/2}$. Across ordinary diffusion, long-range superdiffusion and subdiffusion induced by crowding or memory, $d_s$ separates persistent randomness in recurrent exploration $(d_s<2)$, anomalously slow non-Gaussian concentration for $2\le d_s<3$, and Gaussian concentration, logarithmically corrected at $d_s=3$, for $d_s\ge3$. For $d_s\ge2$, we derive exact asymptotic variances, including prefactors, and the discovery scale on which competitive imbalances are erased. Two-point correlations of first-discovery labels identify the memory mechanism behind these regimes. The same phase structure persists under changes in geometry, competitor heterogeneity, number of competitors and memory, revealing a general fluctuation theory of first-arrival inequalities.

cond-mat.stat-mech↗

arXiv2026

Anomalous scaling in redirection networks

In networks that grow by isotropic redirection (IR), a new node selects an initial target node uniformly at random and attaches to a randomly chosen neighbor of the target. The emerging networks exhibit leaf proliferation, in which the number of nonleaves scales sublinearly as $N^\mu$ and the degree distribution has an algebraic tail with exponent $1+\mu$. To understand these mysterious properties, we introduce a class of models with redirection to leaves whenever possible. The resulting networks exhibit qualitatively similar phenomenology to IR networks, but avoid the inherent non-locality of the IR growth rule. These networks admit an analytical description of the leaf degree distribution, from which we extract the exponent $\mu$.

cond-mat.stat-mech↗

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

One pathogen does not an epidemic make: A review of interacting contagions, diseases, beliefs, and stories

From pathogens and computer viruses to genes and memes, contagion models have found widespread utility across the natural and social sciences. Despite their success and breadth of adoption, the approach and structure of these models remain surprisingly siloed by field. Given the siloed nature of their development and widespread use, one persistent assumption is that a given contagion can be studied in isolation, independently from what else might be spreading in the population. In reality, countless contagions of biological and social nature interact within hosts (interacting with existing beliefs, or the immune system) and across hosts (interacting in the environment, or affecting transmission mechanisms). Additionally, from a modeling perspective, we know that relaxing these assumptions has profound effects on the physics and translational implications of the models. Here, we review mechanisms for interactions in social and biological contagions, as well as the models and frameworks developed to include these interactions in the study of the contagions. We highlight existing problems related to the inference of interactions and to the scalability of mathematical models and identify promising avenues of future inquiries. In doing so, we highlight the need for interdisciplinary efforts under a unified science of contagions and for removing a common dichotomy between social and biological contagions.

physics.soc-ph↗

arXiv2024

Self-reinforcing cascades: A spreading model for beliefs or products of varying intensity or quality

Models of how things spread often assume that transmission mechanisms are fixed over time. However, social contagions--the spread of ideas, beliefs, innovations--can lose or gain in momentum as they spread: ideas can get reinforced, beliefs strengthened, products refined. We study the impacts of such self-reinforcement mechanisms in cascade dynamics. We use different mathematical modeling techniques to capture the recursive, yet changing nature of the process. We find a critical regime with a range of power-law cascade size distributions with non-universal scaling exponents. This regime clashes with classic models, where criticality requires fine tuning at a precise critical point. Self-reinforced cascades produce critical-like behavior over a wide range of parameters, which may help explain the ubiquity of power-law distributions in empirical social data.

physics.soc-ph↗

arXiv2024

How much regulation do we need from genomes to society?

Regulatory functions are essential in both socioeconomic and biological systems, from corporate managers to regulatory genes. Regulatory functions come with substantial costs and benefits, and the balance of the two is often taken for granted. A fundamental question for all complex systems becomes how much regulatory function do they need for their size and function? Here, we present empirical evidence that regulatory functions scale systematically across diverse systems: biological organisms (bacterial and eukaryotic genomes), human organizations (companies, federal agencies, universities), and decentralized entities (Wikipedia, cities). We combine an analysis of large data sets from each of these domains with a simple conceptual model. The model predicts that the scaling of regulatory costs shifts with system structure. Well-mixed small systems exhibit superlinear scaling between size and regulatory function, while modular large ones show sublinear or linear scaling, both in agreement with data. Finally, we find that socioeconomic systems that contain more diverse occupational functions tend to have more regulatory costs than expected from the scaling relationships, confirming the hypothesis that the type and complexity of interactions also play a role in regulatory costs. Our cross-system comparison offers a mechanistic framework for understanding regulatory function and can potentially guide efforts to analyze the costs and benefits of regulatory function in diverse systems.

nlin.AO↗

arXiv2024

Templating Aggregation

We introduce an aggregation process based on \emph{templating}, where a specified number of constituent clusters must assemble on a larger aggregate, which serves as a scaffold, for a reaction to occur. A simple example is a dimer scaffold, upon which two monomers meet and create another dimer, while dimers and larger aggregates undergo in irreversible aggregation with mass-independent rates. In the mean-field approximation, templating aggregation has unusual kinetics in which the cluster and monomer densities, $c(t)$ and $m(t)$ respectively, decay with time as $c\sim m^2\sim t^{-2/3}$. These starkly contrast to the corresponding behaviors in conventional aggregation, $c\sim \sqrt{m}\sim t^{-1}$. We then treat three natural extensions of templating: (a) the reaction in which $L$ monomers meet and react on an $L$-mer scaffold to create two $L$-mers, (b) multistage scaffold reactions, and (c) templated ligation, in which clusters of all masses serve as scaffolds and binary aggregation is absent.

cond-mat.soft↗

arXiv2024

Charged Aggregation

We introduce an aggregation process that begins with equal concentrations of positively and negatively `charged' monomers. Oppositely charged monomers merge to form neutral dimers. These dimers are the seeds for subsequent aggregation events in which neutral clusters of necessarily even mass join irreversibly to form neutral aggregates of ever-increasing size. In the mean-field approximation with mass independent reaction rates, we solve for the reaction kinetics and show that the concentration of clusters of mass $k$, $c_k(t)$, asymptotically scales as $A_k/t$, with $A_k$ having a non-trivial dependence on $k$. We also investigate the phenomenon of gelation in charged aggregation when the reaction rate equals the product of the two incident cluster masses. Finally, we generalize our model to the case of three and more types of monomers.

cond-mat.soft↗

arXiv2024

Catalytic Coagulation

We introduce an autocatalytic aggregation model in which the rate at which two clusters merge to form a cluster is controlled by the presence of a third "catalytic" cluster whose mass must equal to the mass of one of the reaction partners. The catalyst is unaffected by the joining event and is available to either participate in or catalyze subsequent reactions. This model is meant to mimic the self-replicating reactions that occur in models for the origin of life. We solve the kinetics of this catalytic coagulation model for the case of mass-independent rates and show that the total cluster density decays as $t^{-1/3}$, while the density of clusters of any fixed mass decays as $t^{-2/3}$. These behaviors contrast with the corresponding $t^{-1}$ and $t^{-2}$ scalings for classic aggregation. We extend our model to mass-dependent reaction rates, to situations where only "magic" mass clusters can catalyze reactions, and to include steady monomer input.

cond-mat.stat-mech↗

arXiv2023

Epidemic Forecast Follies

We introduce a simple multiplicative model to describe the temporal behavior and the ultimate outcome of an epidemic. Our model accounts, in a minimalist way, for the competing influences of imposing public-health restrictions when the epidemic is severe, and relaxing restrictions when the epidemic is waning. Our primary results are that different instances of an epidemic with identical starting points have disparate outcomes and each epidemic temporal history is strongly fluctuating.

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↗

arXiv2023

The Magic of Networks Grown by Redirection

We highlight intriguing features of complex networks that are grown by \emph{redirection}. In this mechanism, a target node is chosen uniformly at random from the pre-existing network nodes and the new node attaches either to this initial target or to a neighbor of this target. This exceedingly simple algorithm generates preferential attachment networks in an algorithmic time that is linear in the number of network nodes $N$. Even though preferential attachment ostensibly requires \emph{global knowledge} of the network, redirection requires only \emph{local knowledge}. We also show that changing just a \emph{single} attachment rate in linear preferential attachment leads to a non-universal degree distribution. Finally, we present unexpected consequences of redirection in networks with undirected links, where highly modular and non-sparse networks arise.

physics.soc-ph↗

arXiv2022

Optimal Storage for Solar Energy Self-Sufficiency

We determine the energy storage needed to achieve self sufficiency to a given reliability as a function of excess capacity in a combined solar-energy generation and storage system. Based on 40 years of solar-energy data for the St.\ Louis region, we formulate a statistical model that we use to generate synthetic insolation data over millions of years. We use these data to monitor the energy depletion in the storage system near the winter solstice. From this information, we develop explicit formulas for the required storage and the nature of cost-optimized system configurations as a function of reliability and the excess of generation capacity. Minimizing the cost of the combined generation and storage system gives the optimal mix of these two constituents. For an annual failure rate of less than 3\%, it is sufficient to have a solar generation capacity that slightly exceeds the daily electrical load at the winter solstice, together with a few days of storage.

physics.soc-ph↗

arXiv2022

Universal exploration dynamics of random walks

The territory explored by a random walk is a key property that may be quantified by the number of distinct sites that the random walk visits up to a given time. The extent of this spatial exploration characterizes many important physical, chemical, and ecological phenomena. In spite of its fundamental interest and wide utility, the number of visited sites gives only an incomplete picture of this exploration. In this work, we introduce a more fundamental quantity, the elapsed time $\tau_n$ between visits to the $n^{\rm th}$ and the $(n+1)^{\rm st}$ distinct sites, from which the full dynamics about the visitation statistics can be obtained. To determine the distribution of these inter-visit times $\tau_n$, we develop a theoretical approach that relies on a mapping with a trapping problem, in which, in contrast to previously studied situations, the spatial distribution of traps is continuously updated by the random walk itself. Despite the geometrical complexity of the territory explored by a random walk (typically aspherical, as well as containing holes and islands at all scales), we find that the distribution of the $\tau_n$ can be accounted for by simple analytical expressions. Processes as varied as regular diffusion, anomalous diffusion, and diffusion in disordered media and fractals, fall into the same universality classes for the temporal history of distinct sites visited. We confirm our theoretical predictions by Monte Carlo and exact enumeration methods. We also determine additional basic exploration observables, such as the perimeter of the visited domain or the number of islands of unvisited sites enclosed within this domain, thereby illustrating the generality of our approach. Because of their fundamental character and their universality, these inter-visit times represent a promising tool to unravel many more aspects of the exploration dynamics of random walks.

cond-mat.stat-mech↗

arXiv2022

Birds on a Wire

We investigate the occupancy statistics of birds on a wire and on higher-dimensional substrates. In one dimension, birds land one by one on a wire and rest where they land. Whenever a newly arriving bird lands within a fixed distance of already resting birds, these resting birds immediately fly away. We determine the steady-state occupancy of the wire, the distribution of gaps between neighboring birds, and other basic statistical features of this process. We discuss conjectures for corresponding observables in higher dimensions.

cond-mat.stat-mech↗

arXiv2022

First-Passage-Driven Boundary Recession

We investigate a moving boundary problem for a Brownian particle on the semi-infinite line in which the boundary moves by a distance proportional to the time between successive collisions of the particle and the boundary. Phenomenologically rich dynamics arises. In particular, the probability for the particle to first reach the moving boundary for the $n^\text{th}$ time asymptotically scales as $t^{-(1+2^{-n})}$. Because the tail of this distribution becomes progressively fatter, the typical time between successive first passages systematically gets longer. We also find that the number of collisions between the particle and the boundary scales as $\ln\ln t$, while the time dependence of the boundary position varies as $t/\ln t$.

cond-mat.stat-mech↗

arXiv2022

A First Look at First-Passage Processes

These notes are based on the lectures that I gave (virtually) at the Bruneck Summer School in 2021 on first-passage processes and some applications of the basic theory. I begin by defining what is a first-passage process and presenting the connection between the first-passage probability and the familiar occupation probability. Some basic features of first passage on the semi-infinite line and a finite interval are then discussed, such as splitting probabilities and first-passage times. I also treat the fundamental connection between first passage and electrostatics. A number of applications of first-passage processes are then presented, including the hitting probability for a sphere in greater than two dimensions, reaction rate theory and its extension to receptors on a cell surface, first-passage inside an infinite absorbing wedge in two dimensions, stochastic hunting processes in one dimension, the survival of a diffusing particle in an expanding interval, and finally the dynamics of the classic birth-death process.

cond-mat.stat-mech↗

arXiv2022

How Smart Should a Forager Be?

We introduce an idealized model of an intelligent forager in which higher intelligence corresponds to a larger spatial range over which the forager can detect food. Such a forager diffuses randomly whenever the nearest food is more distant than the forager's detection range, $R$, and moves ballistically towards the nearest food inside its detection range. Concomitantly, the forager's metabolic energy cost per step is an increasing function of its intelligence. A dumb forager wanders randomly and may miss nearby food, thus making it susceptible to starvation. Conversely, a too-smart forager incurs a large metabolic cost per step during its search for food and is again susceptible to starvation. We show that the forager's lifetime is maximized at an optimal, intermediate level of intelligence.

physics.bio-ph↗