Related papers: A growth model based on the arithmetic $Z$-game
This article studies the Gram random matrix model $G=\frac1T\Sigma^{\rm T}\Sigma$, $\Sigma=\sigma(WX)$, classically found in the analysis of random feature maps and random neural networks, where $X=[x_1,\ldots,x_T]\in{\mathbb R}^{p\times…
A big challenge in current biology is to understand the exact self-organization mechanism underlying complex multi-physics coupling developmental processes. With multiscale computations of from subcellular gene expressions to cell…
We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values…
Golomb's sequence is the unique nondecreasing sequence of positive integers in which each $n$ appears exactly $a(n)$ times. It satisfies the global self-referential rule \[ a\bigl(a(n)+a(n-1)+\cdots+a(1)\bigr)=n, \] grows smoothly like a…
We consider a time-continuous branching random walk on a one-dimensional lattice on which there is one center (lattice point) of particle generation, called branching source. The generation of particles in the branching source is described…
This paper reports on patterns exhibiting self-replication with spontaneous, inheritable mutations and exponential genetic drift in Neural Cellular Automata. Despite the models not being explicitly trained for mutation or inheritability,…
We give a comprehensive rate equation description for the irreversible growth of aggregates by migration from small to large aggregates. For a homogeneous rate K(i;j) at which monomers migrate from aggregates of size i to those of size j,…
An analytical model for the evolution of the boundary of the new phase in transformations ruled by nucleation and growth is presented. Both homogeneous and heterogeneous nucleation have been considered: The former includes transformations…
In our previous studies, we developed discrete-space Birth, Death and Innovation Models (BDIM) of genome evolution. These models explain the origin of the characteristic Pareto distribution of paralogous gene family sizes in genomes, and…
Let G be a group generated by $r$ elements $g_1,g_2,..., g_r.$ Among the reduced words in $g_1,g_2,..., g_r$ of length $n$ some, say $\gamma_n,$ represent the identity element of the group $G.$ It has been shown in a combinatorial way that…
We introduce a novel evolutionary formulation of the problem of finding a maximum independent set of a graph. The new formulation is based on the relationship that exists between a graph's independence number and its acyclic orientations.…
We consider an infinite locally finite system (configuration) $\gamma$ of particles distributed over a Euclidean space $X$. Each particle located at $x\in X$ carries an internal parameter (mark, or ``spin'') $\sigma_{x}\in S=\mathbb{R}.$…
In this paper we unify, simplify, and extend previous work on the evolutionary dynamics of symmetric $N$-player matrix games with two pure strategies. In such games, gains from switching strategies depend, in general, on how many other…
Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabilistically in stochastic models) the…
In this paper, we develop a set of genetic programming operators and an initialization population process based on concepts of functional programming rewriting for boosting inductive genetic programming. Such genetic operators are used…
We investigate the growth of needles from a flat substrate. We focus on the situation when needles suddenly begin to grow from the seeds randomly distributed on the line. The width of needles is ignored and we additionally assume that (i)…
A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating function. The extraction of its coefficients…
We propose TD-GEN, a graph generation framework based on tree decomposition, and introduce a reduced upper bound on the maximum number of decisions needed for graph generation. The framework includes a permutation invariant tree generation…
We consider the optimization problem of constructing a binary orthogonal array (OA) starting from a bigger one, by removing a specified amount of lines. In particular, we develop a genetic algorithm (GA) where the underlying chromosomes are…
As artificial intelligence systems (AIs) become increasingly produced by recursive self-improvement, a form of evolution may emerge, with the traits of AI systems shaped by the success of earlier AIs in designing and propagating their…