Related papers: Compositions of Functions and Permutations Specifi…
Reaction systems, introduced by Ehrenfeucht and Rozenberg, are elementary computational models based on biochemical reactions transpiring within the living cells. Numerous studies focus on mathematical aspects of minimal reaction systems…
Reaction system is a computing model inspired by the biochemical interaction taking place within the living cells. Various extended or modified frameworks motivated by biological, physical, or purely mathematically considerations have been…
The method proposed by Pratt to derive recursion relations for systems of degenerate fermions [Phys. Rev. Lett. 84, 4255 (2000), arXiv:nucl-th/9905055] relies on diagrammatic techniques. This efficient formalism assumes no explicit two-body…
We investigate a generalization of stacks that we call $\mathcal{C}$-machines. We show how this viewpoint rapidly leads to functional equations for the classes of permutations that $\mathcal{C}$-machines generate, and how these systems of…
We introduce an algebraic model, based on the determinantal expansion of the product of two matrices, to test combinatorial reductions of set functions. Each term of the determinantal expansion is deformed through a monomial factor in d…
At a crossroads of calculus and combinatorics, the generating function of secant and tangent numbers (Euler numbers) provides enumeration of alternating permutations. In this article, we present a new refinement of Euler numbers to answer…
Intracellular protein patterns govern essential cellular functions by dynamically redistributing proteins between membrane-bound and cytosolic states, conserving their total numbers. This review presents a theoretical framework for…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
This paper presents new results about the optimization based generation of chemical reaction networks (CRNs) of higher deficiency. Firstly, it is shown that the graph structure of the realization containing the maximal number of reactions…
We show that the class of Kalm\'ar elementary functions can be inductively generated from the addition, the integer remainder, and the base-two exponentiation, hence improving previous results by Marchenkov and Mazzanti. We also prove that…
We define two versions of compositions of matrix-valued rational functions of appropriate sizes and whenever analytic at infinity, offer a set of formulas for the corresponding state-space realization, in terms of the realizations of the…
We study the existence of segregated solutions to a class of reaction-diffusion systems with strong interactions, arising in many physical applications. These special solutions are obtained as weak limits of minimizers of a family of…
Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…
A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…
Let $S_n$ denote the group all permutations of $n$. For every permutation $\sigma$, we let $\mathrm{des}(\sigma)$ denote the number of descents in $\sigma$ and $\mathrm{LRMin}(\sigma)$ denote the number of left-to-right minima of $\sigma$.…
Molecular interactions are wired in a fascinating way resulting in complex behavior of biological systems. Theoretical modeling provides a useful framework for understanding the dynamics and the function of such networks. The complexity of…
A number system coding for the permutations generated by cyclic shift is described. The system allows to find the rank of a permutation given how it has been generated, and to determine a permutation given its rank. It defines a code…
It is a classical problem to compute a minimal set of invariant polynomial generating the invariant ring of a finite group as an algebra. We present here an algorithm for the computation of minimal generating sets in the non-modular case.…
Mass-action kinetics is frequently used in systems biology to model the behaviour of interacting chemical species. Many important dynamical properties are known to hold for such systems if they are weakly reversible and have a low…
In this paper, we define a set which has a finite group action and is generated by a finite color set, a set which has a finite group action, and a subset of the set of non negative integers. we state its properties to apply one of solution…