Related papers: Meanders: A Direct Enumeration Approach
We propose a path for making quantitative analyses of mean-square displacement curves of polymer chains in the melt or in solution. The approach invokes a general functional form that accurately describes $g(t) \equiv \langle (\Delta…
In the context of countable groups of polynomial volume growth, we consider a large class of random walks that are allowed to take long jumps along multiple subgroups according to power law distributions. For such a random walk, we study…
Predicting unobserved entries of a partially observed matrix has found wide applicability in several areas, such as recommender systems, computational biology, and computer vision. Many scalable methods with rigorous theoretical guarantees…
Modeling of polymer chains has received a lot of attention in mathematics. In fact, probabilistic models that naturally arise in statistical mechanics have been widely studied by mathematicians for the very challenging and novel problems…
Many simple hydrologic models are based on parametric statistical relations between the river flow and catchment properties such as its area, precipitation rates, soil properties, etc., fitted to the available data. The main objective of…
Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more…
A flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and negative binomial model, as well as to more general models accounting for excess zeros that…
In meandering rivers, interactions between flow, sediment transport, and bed topography affect diverse processes, including bedform development and channel migration. Predicting how these interactions affect the spatial patterns and…
This paper describes the isothermal die swell using our recent quasi-1D model for fast (high Deborah number) contraction flows of polymers melts. Because the model analyzes the flow in several flow regions as one continuous process, it…
In Parts I-III we showed that the number of ways to place $q$ nonattacking queens or similar chess pieces on an $n\times n$ chessboard is a quasipolynomial function of $n$ whose coefficients are essentially polynomials in $q$. In this part…
We address the task of estimating multiple trajectories from unlabeled data. This problem arises in many settings, one could think of the construction of maps of transport networks from passive observation of travellers, or the…
We use Ratner's theorem to compute the asymptotics of the number of (cylinders of) periodic trajectories in a rectangle with a barrier, assuming that the location p/q of the barrier is rational. We also show that as q tends to infinity, the…
This paper introduces a spatially continuous force-based model for simulating pedestrian dynamics. The main intention of this work is the quantitative description of pedestrian movement through bottlenecks and in corridors. Measurements of…
This paper introduces a space-continuous force-based model for simulating pedestrian dynamics. The main interest of this work is the quantitative description of pedestrian movement through a bottleneck. Measurements of flow and density will…
We study the conformational properties of charged polymers in a solvent in the presence of structural obstacles correlated according to a power law $\sim x^{-a}$. We work within the continuous representation of a model of linear chain…
Prudent walks are special self-avoiding walks that never take a step towards an already occupied site, and \emph{$k$-sided prudent walks} (with $k=1,2,3,4$) are, in essence, only allowed to grow along $k$ directions. Prudent polygons are…
We consider a system consisting of a planar random walk on a square lattice, submitted to stochastic elementary local deformations. Depending on the deformation transition rates, and specifically on a parameter $\eta$ which breaks the…
Machine learning, deep learning, and NLP methods on knowledge graphs are present in different fields and have important roles in various domains from self-driving cars to friend recommendations on social media platforms. However, to apply…
We study a random fragmentation process and its associated random tree. The process has earlier been studied by Dean and Majumdar (J. Phys. A: Math. Gen., vol. 35, L501--L507), who found a phase transition: the number of fragmentations is…
In this article we study a \emph{non-directed polymer model} on $\mathbb Z$, that is a one-dimensional simple random walk placed in a random environment. More precisely, the law of the random walk is modified by the exponential of the sum…