arXiv subjects

Alexandre V. Morozov

Publications and source records attributed to Alexandre V. Morozov.

At least 19 recordsLinked to original sources

arXiv2026

Fluctuation theorems and exact multi-allele fixation probabilities

A mutant gene that appears in a finite population will, in the long run, either disappear from it or become fixed, so that all members of the population will carry a copy of the mutant gene. Determining the fixation probability of a mutant gene is thus a prerequisite for modeling evolutionary dynamics in finite populations. Within the diffusion theory framework, the mutant's competition with the wild-type genes is described by the closed-form solution of a one-dimensional backward Kolmogorov equation for the mutant fixation probability, derived by Motoo Kimura in 1962. However, in asexual populations the rate of adaptation and the relative importance of alternative evolutionary pathways are shaped by clonal interference - the competition between several lineages arising from distinct beneficial or deleterious mutations. Quantitative descriptions of clonal interference require computing fixation probabilities in populations where multiple alleles are present simultaneously - a formidable mathematical problem which amounts to solving a multi-dimensional backward Kolmogorov equation. Here, we employ fluctuation theorems (a set of exact equalities in non-equilibrium statistical mechanics) in order to re-derive Kimura's fixation probability formula. When extended to multi-allele systems, fluctuation theorems provide a constraint which must be satisfied by any valid set of fixation probabilities. Moreover, we present a recursive analytical solution of the multi-allele fixation probability problem. We use our formalism to study the fate of a novel beneficial mutation in a clonal interference scenario, discovering substantial deviations between our exact treatment and the mean-field approximation in which the target mutation competes with a single effective genotype. Our formalism can be used to replace both explicit simulations and approximate analytical results in models of asexual evolution.

q-bio.PE↗

arXiv2026

A Hybrid State-Space Approach for Census-Tract Population Estimation

Sequence models---the architecture family behind large language models and, increasingly, state-of-the-art image recognition---have redefined how machines learn from high-dimensional data. Yet population estimation from satellite imagery, a task that underpins infrastructure planning, public health, and disaster response, has scarcely benefited: leading systems still bind population to a uniform raster, disaggregating census counts onto grid cells through weighting surfaces built from ancillary data (e.g., in WorldPop and LandScan), which can introduce systematic spatial bias, and predicting population per grid cell with convolutional neural networks. In this approach, the administrative-unit structure in which the census was actually collected is discarded. We close this gap with MambaPop, which renders each administrative unit as a single polygon-masked satellite image and treats tract-level population estimation as a sequence-modeling problem over its image patches, pairing each tract image directly with its population label and eliminating the disaggregation step entirely. Built on the hybrid state-space--attention MambaVision backbone, MambaPop is, to our knowledge, the first method to learn population directly from an administrative unit's own image as well as the first to apply a state-space based (Mamba) hybrid architecture to the population estimation task. Across all $\sim$84{,}000 contiguous-US census tracts of the 2020 census, MambaPop attains a mean absolute error (MAE) of $1{,}141$ persons per tract, matching the strongest convolutional baseline (YOLOv11, MAE $1{,}122$).

cs.CV↗

arXiv2026

Attention as In-Context Empirical Bayes: A Two-Stage View via Particle Dynamics

We study minimal attention-only transformers under all-token corruption and show they admit a two-stage empirical Bayes interpretation. A single attention step computes a kernel-weighted posterior mean with respect to the empirical distribution defined by the context. Depth refines this distribution through particle dynamics (Stage 1), while a long-range skip-connection carries the noisy input as a query for posterior inference (Stage 2), revealing distinct statistical roles for depth and attention residuals. The framework isolates a minimal setting in which the context itself induces a depth-dependent energy landscape governing in-context inference. We show that effective denoising can emerge without an explicit noise schedule: a fixed kernel bandwidth and finite integration horizon suffice, yielding a principled depth-noise relationship. We further establish a posterior-mean recovery guarantee for a class of well-behaved priors, where the empirical estimator converges to the Bayes-optimal predictor under asymptotic conditions. Connecting these dynamics to reverse-diffusion limits, our results provide a statistical interpretation of attention as in-context inference via sample-based posterior estimation, without explicit density modeling.

cs.LG↗

arXiv2026

Coarse-grained Shannon entropy of random walks with shrinking steps

In one-dimensional diffusive processes with discrete steps characterized by geometrically decaying magnitudes, the usual Gaussian broadening familiar from Brownian motion is replaced by bounded probability distributions over particle positions that are characterized by multi-scale fractal structures. In this work, we study random walks with shrinking steps (known as Bernoulli convolutions), focusing on their behavior in the vicinity of the dyadic contraction ratio 1/2. Our analytical and numerical results show that the coarse-grained Shannon entropy of particle distributions induced by Bernoulli convolutions exhibits a local maximum at the dyadic ratio, arising from the competition between diffusive spreading, which increases entropy, and emergent fine structure, which tends to decrease it. This entropy maximum is a general property of systems driven by non-Gaussian discrete noise, whose dynamics near stable fixed points can be viewed as an autoregressive process - an approximation that is mathematically equivalent to unbiased random walks with shrinking steps. We discuss potential implications of Bernoulli convolution dynamics for protocell self-replication and vesicle proliferation, establishing a link between our information-theoretic approach and biophysical models of cell division.

cond-mat.stat-mech↗

arXiv2026

Neural network optimization strategies and the topography of the loss landscape

Neural networks are trained by optimizing multi-dimensional sets of fitting parameters on non-convex loss landscapes. Low-loss regions of the landscapes correspond to the parameter sets that perform well on the training data. A key issue in machine learning is the performance of trained neural networks on previously unseen test data. Here, we investigate neural network training by stochastic gradient descent (SGD) - a non-convex global optimization algorithm which relies only on the gradient of the objective function. We contrast SGD solutions with those obtained via a non-stochastic quasi-Newton method, which utilizes curvature information to determine step direction and Golden Section Search to choose step size. We use several computational tools to investigate neural network parameters obtained by these two optimization methods, including kernel Principal Component Analysis and a novel, general-purpose algorithm for finding low-height paths between pairs of points on loss or energy landscapes, FourierPathFinder. We find that the choice of the optimizer profoundly affects the nature of the resulting solutions. SGD solutions tend to be separated by lower barriers than quasi-Newton solutions, even if both sets of solutions are regularized by early stopping to ensure adequate performance on test data. When allowed to fit extensively on the training data, quasi-Newton solutions occupy deeper minima on the loss landscapes that are not reached by SGD. These solutions are less generalizable to the test data however. Overall, SGD explores smooth basins of attraction, while quasi-Newton optimization is capable of finding deeper, more isolated minima that are more spread out in the parameter space. Our findings help understand both the topography of the loss landscapes and the fundamental role of landscape exploration strategies in creating robust, transferrable neural network models.

cs.LG↗

arXiv2026

Poisson Log-Normal Process for Count Data Prediction

Modeling count data is important in physics and other scientific disciplines, where measurements often involve discrete, non-negative quantities such as photon or neutrino detection events. Traditional parametric approaches can be trained to generate integer-count predictions but may struggle with capturing complex, non-linear dependencies often observed in the data. Gaussian process (GP) regression provides a robust non-parametric alternative to modeling continuous data; however, it cannot generate integer outputs. We propose the Poisson Log-Normal (PoLoN) process, a framework that employs GP to model Poisson log-rates. As in GP regression, our approach relies on the correlations between data points captured via GP kernel structure rather than explicit functional parameterizations. We demonstrate that the PoLoN predictive distribution is Poisson-LogNormal and provide an algorithm for optimizing kernel hyperparameters. Furthermore, we adapt the PoLoN approach to the problem of detecting weak localized signals superimposed on a smoothly varying background - a task of considerable interest in many areas of science and engineering. Our framework allows us to predict the strength, location and width of the detected signals. We evaluate PoLoN's performance using both synthetic and real-world datasets, including the open dataset from CERN which was used to detect the Higgs boson at the Large Hadron Collider. Our results indicate that the PoLoN process can be used as a non-parametric alternative for analyzing, predicting, and extracting signals from integer-valued data.

physics.data-an↗

arXiv2026

To clean or not to clean: The free-rider problem in sequentially shared resources

Shared resources enhance productivity yet at the same time provide channels for biological and digital contamination, turning physical or digital hygiene into a cooperation dilemma prone to free-riding. Here we introduce a game of sequential sharing of common resources, an empirically parameterized evolutionary model of population dynamics in sequential-use settings such as gyms and shared workspaces. The success of the strategies implemented in the model, such as cleaning equipment before or after use, are based on the trade-offs between cleaning costs, contamination risk, and social incentives to mitigate disease transmission. We find that cooperative hygiene can be achieved by lowering the effective costs of cleaning, strengthening pro-social incentives, and monitoring population-level noncompliance. Remarkably, stability of fully altruistic populations is primarily affected by the cleaning costs. In contrast, increasing effective infection costs, for example through punishment, appears less important in this case. The model's evolutionary dynamics exhibit multi-stability, hysteresis, and abrupt shifts in strategy composition, broadly consistent with empirical observations from shared-use facilities. Our framework offers testable predictions and is amenable to quantitative calibration with behavioral and environmental data. Our predictions can be used to inform the design of cost-effective public health and digital security policies.

physics.soc-ph↗

arXiv2023

An adaptive Bayesian approach to gradient-free global optimization

Many problems in science and technology require finding global minima or maxima of various objective functions. The functions are typically high-dimensional; each function evaluation may entail a significant computational cost. The importance of global optimization has inspired development of numerous heuristic algorithms based on analogies with physical, chemical or biological systems. Here we present a novel algorithm, SmartRunner, which employs a Bayesian probabilistic model informed by the history of accepted and rejected moves to make a decision about the next random trial. Thus, SmartRunner intelligently adapts its search strategy to a given objective function and moveset, with the goal of maximizing fitness gain (or energy loss) per function evaluation. Our approach can be viewed as adding a simple adaptive penalty to the original objective function, with SmartRunner performing hill ascent or descent on the modified landscape. This penalty can be added to many other global optimization algorithms. We explored SmartRunner's performance on a standard set of test functions, finding that it compares favorably against several widely-used alternatives: simulated annealing, stochastic hill climbing, evolutionary algorithm, and taboo search. Interestingly, adding the adaptive penalty to the first three of these algorithms considerably enhances their performance. We have also employed SmartRunner to study the Sherrington-Kirkpatrick (SK) spin glass model and Kauffman's NK fitness model - two NP-hard problems characterized by numerous local optima. In systems with quenched disorder, SmartRunner performs well compared to the other global optimizers. Moreover, in finite SK systems it finds close-to-optimal ground-state energies averaged over disorder.

physics.data-an↗

arXiv2022

Network community detection and clustering with random walks

We present a novel approach to partitioning network nodes into non-overlapping communities - a key step in revealing network modularity and hierarchical organization. Our methodology, applicable to networks with both weighted and unweighted symmetric edges, uses random walks to explore neighboring nodes in the same community. The walk-likelihood algorithm (WLA) produces an optimal partition of network nodes into a given number of communities. The walk-likelihood community finder (WLCF) employs WLA to predict both the optimal number of communities and the corresponding network partition. We have extensively benchmarked both algorithms, finding that they outperform or match other methods in terms of the modularity of predicted partitions and the number of links between communities. Making use of the computational efficiency of our approach, we investigated a large-scale map of roads and intersections in the state of Colorado. Our clustering yielded geographically sensible boundaries between neighboring communities.

physics.soc-ph↗

arXiv2022

Model selection and signal extraction using Gaussian Process regression

We present a novel computational approach for extracting weak signals, whose exact location and width may be unknown, from complex background distributions with an arbitrary functional form. We focus on datasets that can be naturally presented as binned integer counts, demonstrating our approach on the CERN open dataset from the ATLAS collaboration at the Large Hadron Collider, which contains the Higgs boson signature. Our approach is based on Gaussian Process (GP) regression - a powerful and flexible machine learning technique that allowed us to model the background without specifying its functional form explicitly, and to separate the background and signal contributions in a robust and reproducible manner. Unlike functional fits, our GP-regression-based approach does not need to be constantly updated as more data becomes available. We discuss how to select the GP kernel type, considering trade-offs between kernel complexity and its ability to capture the features of the background distribution. We show that our GP framework can be used to detect the Higgs boson resonance in the data with more statistical significance than a polynomial fit specifically tailored to the dataset. Finally, we use Markov Chain Monte Carlo (MCMC) sampling to confirm the statistical significance of the extracted Higgs signature.

hep-ex↗

arXiv2018

Rapid Bayesian Inference of Global Network Statistics Using Random Walks

We propose a novel Bayesian methodology which uses random walks for rapid inference of statistical properties of undirected networks with weighted or unweighted edges. Our formalism yields high-accuracy estimates of the probability distribution of any network node-based property, and of the network size, after only a small fraction of network nodes has been explored. The Bayesian nature of our approach provides rigorous estimates of all parameter uncertainties. We demonstrate our framework on several standard examples, including random, scale-free, and small-world networks, and apply it to study epidemic spreading on a scale-free network. We also infer properties of the large-scale network formed by hyperlinks between Wikipedia pages.

physics.soc-ph↗

arXiv2016

Generalization of the Ewens sampling formula to arbitrary fitness landscapes

In considering evolution of transcribed regions, regulatory modules, and other genomic loci of interest, we are often faced with a situation in which the number of allelic states greatly exceeds the population size. In this limit, the population eventually adopts a steady state characterized by mutation-selection-drift balance. Although new alleles continue to be explored through mutation, the statistics of the population, and in particular the probabilities of seeing specific allelic configurations in samples taken from a population, do not change with time. In the absence of selection, probabilities of allelic configurations are given by the Ewens sampling formula, widely used in population genetics to detect deviations from neutrality. Here we develop an extension of this formula to arbitrary, possibly epistatic, fitness landscapes. Although our approach is general, we focus on the class of landscapes in which alleles are grouped into two, three, or several fitness states. This class of landscapes yields sampling probabilities that are computationally more tractable, and can form a basis for the inference of selection signatures from sequence data. We demonstrate that, for a sizeable range of mutation rates and selection coefficients, the steady-state allelic diversity is not neutral. Therefore, it may be used to infer selection coefficients, as well as other key evolutionary parameters, using high-throughput sequencing of evolving populations to collect data on locus polymorphisms. We also find that our theory remains sufficiently accurate even if the assumptions such as the infinite allele limit and the "full connectivity" assumption in which each allele can mutate into any other allele are relaxed. Thus, our framework establishes a theoretical foundation for inferring selection signatures from samples of sequences produced by evolution on epistatic fitness landscapes.

q-bio.PE↗

arXiv2015

Path statistics, memory, and coarse-graining of continuous-time random walks on networks

Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states, for example those employed in studies of molecular kinetics, and models with spatial disorder can give rise to memory and non-exponential distributions of waiting times and first-passage statistics. However, existing methods for analyzing CTRWs on complex energy landscapes do not address these effects. We therefore use statistical mechanics of the nonequilibrium path ensemble to characterize first-passage CTRWs on networks with arbitrary connectivity, energy landscape, and waiting time distributions. Our approach is valuable for calculating higher moments (beyond the mean) of path length, time, and action, as well as statistics of any conservative or non-conservative force along a path. For homogeneous networks we derive exact relations between length and time moments, quantifying the validity of approximating a continuous-time process with its discrete-time projection. For more general models we obtain recursion relations, reminiscent of transfer matrix and exact enumeration techniques, to efficiently calculate path statistics numerically. We have implemented our algorithm in PathMAN, a Python script that users can easily apply to their model of choice. We demonstrate the algorithm on a few representative examples which underscore the importance of non-exponential distributions, memory, and coarse-graining in CTRWs.

cond-mat.stat-mech↗

arXiv2015

Scaling properties of evolutionary paths in a biophysical model of protein adaptation

The enormous size and complexity of genotypic sequence space frequently requires consideration of coarse-grained sequences in empirical models. We develop scaling relations to quantify the effect of this coarse-graining on properties of fitness landscapes and evolutionary paths. We first consider evolution on a simple Mount Fuji fitness landscape, focusing on how the length and predictability of evolutionary paths scale with the coarse-grained sequence length and alphabet. We obtain simple scaling relations for both the weak- and strong-selection limits, with a non-trivial crossover regime at intermediate selection strengths. We apply these results to evolution on a biophysical fitness landscape that describes how proteins evolve new binding interactions while maintaining their folding stability. We combine the scaling relations with numerical calculations for coarse-grained protein sequences to obtain quantitative properties of the model for realistic binding interfaces and a full amino acid alphabet.

q-bio.PE↗

arXiv2014

Protein folding and binding can emerge as evolutionary spandrels through structural coupling

Binding interactions between proteins and other molecules mediate numerous cellular processes, including metabolism, signaling, and regulation of gene expression. These interactions evolve in response to changes in the protein's chemical or physical environment (such as the addition of an antibiotic), or when genes duplicate and diverge. Several recent studies have shown the importance of folding stability in constraining protein evolution. Here we investigate how structural coupling between protein folding and binding -- the fact that most proteins can only bind their targets when folded -- gives rise to evolutionary coupling between the traits of folding stability and binding strength. Using biophysical and evolutionary modeling, we show how these protein traits can emerge as evolutionary "spandrels" even if they do not confer an intrinsic fitness advantage. In particular, proteins can evolve strong binding interactions that have no functional role but merely serve to stabilize the protein if misfolding is deleterious. Furthermore, such proteins may have divergent fates, evolving to bind or not bind their targets depending on random mutation events. These observations may explain the abundance of apparently nonfunctional interactions among proteins observed in high-throughput assays. In contrast, for proteins with both functional binding and deleterious misfolding, evolution may be highly predictable at the level of biophysical traits: adaptive paths are tightly constrained to first gain extra folding stability and then partially lose it as the new binding function is developed. These findings have important consequences for our understanding of fundamental evolutionary principles of both natural and engineered proteins.

q-bio.PE↗

arXiv2013

Biophysical Fitness Landscapes for Transcription Factor Binding Sites

Evolutionary trajectories and phenotypic states available to cell populations are ultimately dictated by intermolecular interactions between DNA, RNA, proteins, and other molecular species. Here we study how evolution of gene regulation in a single-cell eukaryote S. cerevisiae is affected by the interactions between transcription factors (TFs) and their cognate genomic sites. Our study is informed by high-throughput in vitro measurements of TF-DNA binding interactions and by a comprehensive collection of genomic binding sites. Using an evolutionary model for monomorphic populations evolving on a fitness landscape, we infer fitness as a function of TF-DNA binding energy for a collection of 12 yeast TFs, and show that the shape of the predicted fitness functions is in broad agreement with a simple thermodynamic model of two-state TF-DNA binding. However, the effective temperature of the model is not always equal to the physical temperature, indicating selection pressures in addition to biophysical constraints caused by TF-DNA interactions. We find little statistical support for the fitness landscape in which each position in the binding site evolves independently, showing that epistasis is common in evolution of gene regulation. Finally, by correlating TF-DNA binding energies with biological properties of the sites or the genes they regulate, we are able to rule out several scenarios of site-specific selection, under which binding sites of the same TF would experience a spectrum of selection pressures depending on their position in the genome. These findings argue for the existence of universal fitness landscapes which shape evolution of all sites for a given TF, and whose properties are determined in part by the physics of protein-DNA interactions.

q-bio.PE↗

arXiv2013

Ubiquitous nucleosome unwrapping in the yeast genome

Nucleosome core particle is a dynamic structure -- DNA may transiently peel off the histone octamer surface due to thermal fluctuations or the action of chromatin remodeling enzymes. Partial DNA unwrapping enables easier access of DNA-binding factors to their target sites and thus may provide a dominant pathway for effecting rapid and robust access to DNA packaged into chromatin. Indeed, a recent high-resolution map of distances between neighboring nucleosome dyads in \emph{S.cerevisiae} shows that at least 38.7\% of all nucleosomes are partially unwrapped. The extent of unwrapping follows a stereotypical pattern in the vicinity of genes, reminiscent of the canonical pattern of nucleosome occupancy in which nucleosomes are depleted over promoters and well-positioned over coding regions. To explain these observations, we developed a biophysical model which employs a 10-11 base pair periodic nucleosome energy profile. The profile, based on the pattern of histone-DNA contacts in nucleosome crystal structures and the idea of linker length discretization, accounts for both nucleosome unwrapping and higher-order chromatin structure. Our model reproduces the observed genome-wide distribution of inter-dyad distances, and accounts for patterns of nucleosome occupancy and unwrapping around coding regions. At the same time, our approach explains \emph{in vitro} measurements of accessibility of nucleosome-covered binding sites, and of nucleosome-induced cooperativity between DNA-binding factors. We are able to rule out several alternative scenarios of nucleosome unwrapping as inconsistent with the genomic data.

q-bio.GN↗

arXiv2013

Statistical Physics of Evolutionary Trajectories on Fitness Landscapes

Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role in evolutionary theory. The topography of fitness landscapes and its effect on evolutionary dynamics have been extensively studied in the literature. We will survey the current research knowledge in this field, focusing on a recently developed systematic approach to characterizing path lengths, mean first-passage times, and other statistics of the path ensemble. This approach, based on general techniques from statistical physics, is applicable to landscapes of arbitrary complexity and structure. It is especially well-suited to quantifying the diversity of stochastic trajectories and repeatability of evolutionary events. We demonstrate this methodology using a biophysical model of protein evolution that describes how proteins maintain stability while evolving new functions.

q-bio.PE↗