Related papers: Localization of directed polymers in continuous sp…
We investigate the effects of spatial discreteness of molecules in reaction-diffusion systems. It is found that discreteness within the so called Kuramoto length can lead to a localization of molecules, resulting in novel steady states that…
We study two types of probability measures on the set of integer partitions of $n$ with at most $m$ parts. The first one chooses the random partition with a chance related to its largest part only. We then obtain the limiting distributions…
In this work, we propose and investigate stable high-order collocation-type discretisations of the discontinuous Galerkin method on equidistant and scattered collocation points. We do so by incorporating the concept of discrete least…
We provide a topological classification of locally constant functions over subshifts of finite type via their zero-temperature measures. Our approach is to analyze the relationship between the distribution of the zero-temperature measures…
Quasiperiodic systems serve as fertile ground for studying localisation, due to their propensity already in one dimension to exhibit rich phase diagrams with mobility edges. The deterministic and strongly-correlated nature of the…
The main objective of this paper is to extend Morse-Forman theory to vector-valued functions. This is mostly motivated by the need to develop new tools and methods to compute multiparameter persistence. To generalize the theory, in addition…
We establish higher-order nonasymptotic expansions for a difference between probability distributions of sums of i.i.d. random vectors in a Euclidean space. The derived bounds are uniform over two classes of sets: the set of all Euclidean…
We consider a discrete time random walk in one dimension. At each time step the walker jumps by a random distance, independent from step to step, drawn from an arbitrary symmetric density function. We show that the expected positive maximum…
In the present article we consider a natural generalization of Hammersley's Last Passage Percolation (LPP) called Entropy-controlled Last Passage Percolation (E-LPP), where points can be collected by paths with a global (entropy) constraint…
Computing equilibrium concentrations of molecular complexes is generally analytically intractable and requires numerical approaches. In this work we focus on the polymer-monomer level, where indivisible molecules (monomers) combine to form…
In Euclidean space condensers with variable potential levels and the presence of a free part at the boundary are studied. The asymptotic formula of the modulus of such condenser is obtained when the plates are pulled into points. The…
Polymers in a melt may be subject to topological constraints, as in the example of unlinked polymer rings. How to do statistical mechanics in the presence of such constraints remains a fundamental open problem. We study the effect of…
Exactly soluble models in the theory of electromagnetic propagation and scattering are essentially restricted to horizontally stratified or spherically symmetric geometries, with results also available for certain waveguide geometries.…
We study the dynamics of a tracer particle, which performs a totally directed random walk in an adsorbed monolayer composed of mobile hard-core particles undergoing continuous exchanges with a vapour phase. In terms of a mean-field-type…
We consider continuous and discrete (1+1)-dimensional wetting models which undergo a localization/delocalization phase transition. Using a simple approach based on Renewal Theory we determine the precise asymptotic behavior of the partition…
A polymer-chain network is a collection of interconnected polymer-chains, made themselves of the repetition of a single pattern called a monomer. Our first main result establishes that, for a class of models for polymer-chain networks, the…
We study the problem of quantization of discrete probability distributions, arising in universal coding, as well as other applications. We show, that in many situations this problem can be reduced to the covering problem for the unit…
This article presents an innovative methodology for locating injection points in injection-molded parts using intelligent models with geometric algorithms for discrete topologies. The first algorithm calculates the center of mass of the…
Monte Carlo simulations of coarse-grained polymers provide a useful tool to deepen the understanding of conformational and statistical properties of polymers both in physical as well as in biological systems. In this study we sample compact…
Epanechnikov Mean Shift is a simple yet empirically very effective algorithm for clustering. It localizes the centroids of data clusters via estimating modes of the probability distribution that generates the data points, using the…