Related papers: An All-Encompassing Global Convergence Result for …
This paper focuses on flow-adapted point-shifts of point processes on topological groups, which map points of a point process to other points of the point process in a translation invariant way. Foliations and connected components generated…
A general polarizable embedded (PE) quantum mechanics/molecular mechanics scheme for periodic systems is presented, describing mutual polarization of the two subsystems. The QM system, described with density functional theory (DFT), is…
Intercellular exchange networks are essential for the adaptive capabilities of populations of cells. While diffusional exchanges have traditionally been difficult to map, recent advances in nanotechnology enable precise probing of exchange…
Mass-conservative reaction-diffusion systems have recently been proposed as a general framework to describe intracellular pattern formation. These systems have been used to model the conformational switching of proteins as they cycle from…
We study the stirring process with $N-1$ species on a generic graph $G=(V,\mathcal{E})$ with reservoirs. The multispecies stirring process generalizes the symmetric exclusion process, which is recovered in the case $N=2$. We prove the…
In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the…
The oversampling multiscale finite element method (MsFEM) is one of the most popular methods for simulating composite materials and flows in porous media which may have many scales. But the method may be inapplicable or inefficient in some…
We show that very simple molecular systems, modeled as chemical reaction networks, can have behaviors that exhibit dramatic phase transitions at certain population thresholds. Moreover, the magnitudes of these thresholds can thwart attempts…
Mathematical models are increasingly being used to understand complex biochemical systems, to analyze experimental data and make predictions about unobserved quantities. However, we rarely know how robust our conclusions are with respect to…
All living systems -- from the origin of life to modern cells -- rely on a set of biochemical reactions that are simultaneously self-sustaining and autocatalytic. This notion of an autocatalytic set has been formalized graph-theoretically…
From ancient philosophers to modern economists, biologists, and other researchers, there has been a continuous effort to unveil causal relations. The most formidable challenge lies in deducing the nature of the causal relationship: whether…
Biomolecular condensates are commonly organized by a small number of scaffold molecules that drive phase separation together with client molecules that do not condense on their own but become selectively recruited into the dense phase. A…
Chemical reactions often proceed through the formation and the consumption of intermediate species. An example is the creation and subsequent degradation of the substrate-enzyme complexes in an enzymatic reaction. In this paper we provide a…
Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is a set of nodes which exist in several layers, with each…
Every realistic instance of a percolation problem is faced with some degree of polydispersity, e.g., the pore-size distribution of an inhomogeneous medium, the size distribution of filler particles in composite materials, or the vertex…
The quantitative convergence to equilibrium for reaction-diffusion systems arising from complex balanced chemical reaction networks with mass action kinetics is studied by using the so-called entropy method. In the first part of the paper,…
To unveil the logic of cell from a level of chemical reaction dynamics, we need to clarify how ensemble of chemicals can autonomously produce the set of chemical, without assuming a specific external control echanism. A cell consists of a…
We consider a model of extracellular signal-regulated kinase (ERK) regulation by dual-site phosphorylation and dephosphorylation, which exhibits bistability and oscillations, but loses these properties in the limit in which the mechanisms…
Scaffold proteins organize cellular processes by bringing signaling molecules into interaction, sometimes by forming large signalosomes. Several of these scaffolds are known to polymerize. Their assemblies should therefore not be understood…
For a theoretical understanding of the reactivity of complex chemical systems, relative energies of stationary points on potential energy hypersurfaces need to be calculated to high accuracy. Due to the large number of intermediates present…