Related papers: A Combinatorial Theory of Assembly Systems via Gen…
An explanatory model for the emergence of evolvable units must display emerging structures that (1) preserve themselves in time (2) self-reproduce and (3) tolerate a certain amount of variation when reproducing. To tackle this challenge,…
In this paper, we introduce a novel approach for generating random elements of a finite group given a set of generators of that. Our method draws upon combinatorial group theory and automata theory to achieve this objective. Furthermore, we…
How do we estimate the probability of an abundant objects' formation, with minimal context or assumption about is origin? To explore this we have previously introduced the concept of pathway assembly (as pathway complexity), in a graph…
Polymers consisting of more than one type of monomer, known as copolymers, are vital to both living and synthetic systems. Copolymerisation has been studied theoretically in a number of contexts, often by considering a Markov process in…
This work introduces a method for generating generalized structures of amorphous polymers using simulated polymerization and molecular dynamics equilibration, with a particular focus on amorphous polymers. The techniques and algorithms used…
We present assembly-theory, a Rust package for computing assembly indices of covalently bonded molecular structures. This is a key complexity measure of assembly theory, a recent theoretical framework quantifying selection across diverse…
In this talk, we present a procedure to systematically generate a large number of valid mass matrix textures from very generic assumptions. Compared to plain anarchy arguments, we postulate some structure for the theory, such as a possible…
The conference GASCom brings together researchers in combinatorics, algorithms, probabilities, and more generally mathematical computer science, around the theme of random and exhaustive generation of combinatorial structures, mostly…
Self-assembly in natural and synthetic molecular systems can create complex aggregates or materials whose properties and functionality rises from their internal structure and molecular arrangement. The key microscopic features that control…
A novel framework has recently been proposed for designing the molecular structure of chemical compounds with a desired chemical property using both artificial neural networks and mixed integer linear programming. In this paper, we design a…
Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made…
We consider a general concept of composition and decomposition of objects, and discuss a few natural properties one may expect from a reasonable choice thereof. It will be demonstrated how this leads to multiplication and co- multiplication…
It is described the group of arrowy permutations (that is extension of symmetric group) and the consequent process of generation of GL(n) and some its subgroups by this combinatoric group and its subgroups.
Active polymers are ubiquitous in nature, and often kicked by persistent noises that break detailed balance. In order to capture the out-of-equilibrium dynamics of such active polymers, we propose a simple yet reliable analytical framework…
A complete approach for the determination of the complex constitutive behaviour of textile composites through finite element simulation is presented in this paper. In this work, simulations of different loading cases are carried out on…
Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…
Component systems - ensembles of realizations built from a shared repertoire of modular parts - are ubiquitous in biological, ecological, technological, and socio-cultural domains. From genomes to texts, cities, and software, these systems…
Arithmetic combinatorics is often concerned with the problem of bounding the behaviour of arbitrary finite sets in a group or ring with respect to arithmetic operations such as addition or multiplication. Similarly, combinatorial geometry…
Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…
Let A be a class of objects, equipped with an integer size such that for all n the number a(n) of objects of size n is finite. We are interested in the case where the generating fucntion sum_n a(n) t^n is rational, or more generally…