Related papers: An All-Encompassing Global Convergence Result for …
We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which…
The existence of a global attractor for the solution semiflow of the extended Brusselator system in the $L^2$ phase space is proved, which is a cubic-autocatalytic and partially reversible reaction-diffusion system with linear coupling…
We study the long-time behavior of the solutions of a two-component reaction-diffusion system on the real line, which describes the basic chemical reaction $A <=> 2 B$. Assuming that the initial densities of the species $A, B$ are bounded…
The goal of this paper is to analyse the asymptotic behavior of the cycle process and the total number of cycles of weighted and generalized weighted random permutations which are relevant models in physics and which extend the Ewens…
We prove existence and uniqueness of global solutions for a class of reaction-advection-anisotropic-diffusion systems whose reaction terms have a "triangular structure". We thus extend previous results to the case of time-space dependent…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
Molecular self-assembly plays a very important role in various aspects of technology as well as in biological systems. Governed by the covalent, hydrogen or van der Waals interactions - self-assembly of alike molecules results in a large…
Protein folding, peptide aggregation and crystallization, as well as adsorption of molecules on soft or solid substrates have an essential feature in common: In all these processes, structure formation is guided by a collective, cooperative…
A biochemical network can be simulated by a set of ordinary differential equations (ODE) under well stirred reactor conditions, for large numbers of molecules, and frequent reactions. This is no longer a robust representation when some…
We introduce a generalized concept of solutions for reaction-diffusion systems and prove their global existence. The only restriction on the reaction function beyond regularity, quasipositivity and mass control is special in that it merely…
The fundamental decomposition of a chemical reaction network (also called its "$\mathscr{F}$-decomposition") is the set of subnetworks generated by the partition of its set of reactions into the "fundamental classes" introduced by Ji and…
The convergence to equilibrium of mass action reaction-diffusion systems arising from networks of chemical reactions is studied. The considered reaction networks are assumed to satisfy the detailed balance condition and have no boundary…
We show systematically that a steady-state ensemble of mesoscopic inclusions of a solute-rich fluid can emerge in liquid solutions well outside the region of stability of the solute-rich phase. Unanticipated by conventional treatments, this…
Phosphorylation is a prototypical example of post-translational modifications (PTMs) that dynamically modulate protein func-tion, where dysregulation is often implicated in disease. NMR provides information on the exact location and time…
We consider a class of multi-type particle systems having similar structure to the contact process and show that additivity is equivalent to the existence of a dual process, extending a result of Harris. We give two additional…
Gaussian process regression has recently emerged as a powerful, system-agnostic tool for building global potential energy surfaces (PES) of polyatomic molecules. While the accuracy of GP models of PES increases with the number of potential…
For dynamical systems arising from chemical reaction networks, persistence is the property that each species concentration remains positively bounded away from zero, as long as species concentrations were all positive in the beginning. We…
The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a mathematical model is an important challenge…
The neural-network denoising functions which form the backbone of image diffusion models are remarkably consistent in their generalization behaviour across a wide variety of network architectures and training procedure hyperparameters. A…
Many drug delivery systems suffer from undesirable interactions with the host immune system. It has been experimentally established that covalent attachment (irreversible adsorption) of suitable macromolecules to the surface of the drug…