Related papers: Evolutionary Foundations of Mathematics
In this paper we start with a simple question, how is it possible that humans can recognize different movements over skin with only a prior visual experience of them? Or in general, what is the representation of spatial sequences that are…
Grammatical inference is a classical problem in computational learning theory and a topic of wider influence in natural language processing. We treat grammars as a model of computation and propose a novel neural approach to induction of…
A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…
Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative…
This brief discusses evolutionary game theory as a powerful and unified mathematical tool to study evolution of collective behaviours. It summarises some of my recent research directions using evolutionary game theory methods, which include…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
We introduce a novel evolutionary algorithm (EA) with a semantic network-based representation. For enabling this, we establish new formulations of EA variation operators, crossover and mutation, that we adapt to work on semantic networks.…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
Habituation - a phenomenon in which a dynamical system exhibits a diminishing response to repeated stimulations that eventually recovers when the stimulus is withheld - is universally observed in living systems from animals to unicellular…
We consider an integro-differential model for evolutionary game theory which describes the evolution of a population adopting mixed strategies. Using a reformulation based on the first moments of the solution, we prove some analytical…
We give a survey of the foundations of statistical queries and their many applications to other areas. We introduce the model, give the main definitions, and we explore the fundamental theory statistical queries and how how it connects to…
Natural selection explains how life has evolved over millions of years from more primitive forms. The speed at which this happens, however, has sometimes defied formal explanations when based on random (uniformly distributed) mutations.…
It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in…
In the work two ways of evolutionary interpretation of entropy model for correspondence matrix calculation are proposed. Both approaches based on the stochastic chemical kinetic evolution under the detailed balance condition. The first…
Building invariance to non-meaningful transformations is essential to building efficient and generalizable machine learning models. In practice, the most common way to learn invariance is through data augmentation. There has been recent…
Organisms and algorithms learn probability distributions from previous observations, either over evolutionary time or on the fly. In the absence of regularities, estimating the underlying distribution from data would require observing each…
We formulate the search for phenomenological models of synaptic plasticity as an optimization problem. We employ Cartesian genetic programming to evolve biologically plausible human-interpretable plasticity rules that allow a given network…
Based on Darwin's natural selection, we developed "machine scientists" to discover the laws of nature by learning from raw data. "Machine scientists" construct physical theories by applying a logic tree (state Decision Tree) and a value…
Networks are fundamental building blocks for representing data, and computations. Remarkable progress in learning in structurally defined (shallow or deep) networks has recently been achieved. Here we introduce evolutionary exploratory…
Economists model knowledge use and acquisition as a cause-and-effect calculus associating observations made by a decision-maker about their world with possible underlying causes. Knowledge models are well-established for static contexts,…