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In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…

Disordered Systems and Neural Networks · Physics 2011-05-16 Markus Brede

We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent…

Computation · Statistics 2021-05-04 Scott N. Walsh , Tim M. Wildey , John D. Jakeman

The substantial increase in AI model training has considerable environmental implications, mandating more energy-efficient and sustainable AI practices. On the one hand, data-centric approaches show great potential towards training…

Machine Learning · Computer Science 2024-02-20 Mohammed Alswaitti , Roberto Verdecchia , Grégoire Danoy , Pascal Bouvry , Johnatan Pecero

We present an algebraic approach to evolutionary accumulation modelling (EvAM). EvAM is concerned with learning and predicting the order in which evolutionary features accumulate over time. Our approach is complementary to the more common…

Applications · Statistics 2026-04-29 Jessica Renz , Frederik Witt , Iain G. Johnston

All living things exhibit adaptations that enable them to survive and reproduce in the natural environment that they inhabit. From a biological standpoint, it has long been understood that adaptation comes from natural selection, whereby…

Biological Physics · Physics 2016-06-22 Nikolai Perunov , Robert Marsland , Jeremy England

In a constantly changing world, animals must account for environmental volatility when making decisions. To appropriately discount older, irrelevant information, they need to learn the rate at which the environment changes. We develop an…

Neurons and Cognition · Quantitative Biology 2017-01-12 Adrian E Radillo , Alan Veliz-Cuba , Kresimir Josic , Zachary P Kilpatrick

Organisms and ecological groups accumulate evidence to make decisions. Classic experiments and theoretical studies have explored this process when the correct choice is fixed during each trial. However, we live in a constantly changing…

Neurons and Cognition · Quantitative Biology 2015-10-01 Alan Veliz-Cuba , Zachary P. Kilpatrick , Kresimir Josic

We revisit the Ornstein-Uhlenbeck (OU) process as the fundamental mathematical description of linear irreversible phenomena, with fluctuations, near an equilibrium. By identifying the underlying circulating dynamics in a stationary process…

Statistical Mechanics · Physics 2015-09-22 Yi-An Ma , Hong Qian

Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…

Methodology · Statistics 2023-02-03 Nicholas W. Barendregt , Emily G. Webb , Zachary P. Kilpatrick

This paper presents a statistically sound method for measuring the accuracy with which a probabilistic model reflects the growth of a network, and a method for optimising parameters in such a model. The technique is data-driven, and can be…

Networking and Internet Architecture · Computer Science 2009-04-07 Richard Clegg , Raul Landa , Uli Harder , Miguel Rio

We propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been…

Populations and Evolution · Quantitative Biology 2015-11-18 Alex McAvoy

There has been a long debate on how new levels of organization have evolved. It might seem unlikely, as cooperation must prevail over competition. One well-studied example is the emergence of autocatalytic sets, which seem to be a…

Populations and Evolution · Quantitative Biology 2026-02-16 Sean P. Maley , Carlos Gershenson , Stuart A. Kauffman

Genetic algorithms are high-level heuristic optimization methods which enjoy great popularity thanks to their intuitive description, flexibility, and, of course, effectiveness. The optimization procedure is based on the evolution of…

Probability · Mathematics 2026-03-27 Giacomo Borghi

By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation, and genetic drift. This requires us to track only four macroscopic variables,…

Populations and Evolution · Quantitative Biology 2010-11-18 Harold P. de Vladar , Nick Barton

Population-based evolutionary algorithms (EAs) have been widely applied to solve various optimization problems. The question of how the performance of a population-based EA depends on the population size arises naturally. The performance of…

Neural and Evolutionary Computing · Computer Science 2013-05-13 Jun He , Tianshi Chen , Boris Mitavskiy

Stochastic differential equations such as the Ornstein-Uhlenbeck process have long been used to model realworld probablistic events such as stock prices and temperature fluctuations. While statistical methods such as Maximum Likelihood…

Machine Learning · Computer Science 2026-02-05 Aroon Sankoh , Victor Wickerhauser

Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been…

Populations and Evolution · Quantitative Biology 2017-08-16 Benjamin Allen , Gabor Lippner , Yu-Ting Chen , Babak Fotouhi , Naghmeh Momeni , Martin A. Nowak , Shing-Tung Yau

We study the evolution of artificial learning systems by means of selection. Genetic programming is used to generate a sequence of populations of algorithms which can be used by neural networks for supervised learning of a rule that…

Biological Physics · Physics 2009-11-07 Juan Pablo Neirotti , Nestor Caticha

To study population dynamics, ecologists and wildlife biologists use relative abundance data, which are often subject to temporal preferential sampling. Temporal preferential sampling occurs when sampling effort varies across time. To…

Methodology · Statistics 2022-12-14 Michael R. Schwob , Mevin B. Hooten , Travis McDevitt-Galles

We investigate the evolutionary dynamics of a finite population of sequences adapting to NK fitness landscapes. We find that, unlike in the case of an infinite population, the average fitness in a finite population is maximized at a small…

Biological Physics · Physics 2009-11-07 Paulo R. A. Campos , Christoph Adami , Claus O. Wilke
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