Related papers: Weaves, webs and flows
We consider a stochastic flow in which individual particles follow skew Brownian motions, with each one of these processes driven by the same Brownian motion. One does not have uniqueness for the solutions of the corresponding stochastic…
We consider Brownian particles immersed in the fluid which flow is turbulent. We study the limit where the particles' inertia is weak and their velocity relaxes fast to the velocity of the flow. The trajectories of the particles in this…
We investigate a class of line ensembles whose local structure is described by independent geometric random walk bridges, which have been conditioned to interlace with each other. The latter arise naturally in the context Schur processes,…
Normalizing flows model complex probability distributions by combining a base distribution with a series of bijective neural networks. State-of-the-art architectures rely on coupling and autoregressive transformations to lift up invertible…
We introduce a new model called the Brownian Conga Line. It is a random curve evolving in time, generated when a particle performing a two dimensional Gaussian random walk leads a long chain of particles connected to each other by cohesive…
In many physical situations involving diverse length scales, waves or rays representing them travel through media characterized by spatially smooth, random, modest refactive index variations. "Primary" diffraction (by individual…
Network embedding which encodes all vertices in a network as a set of numerical vectors in accordance with it's local and global structures, has drawn widespread attention. Network embedding not only learns significant features of a…
There are many web-based visualization systems available to date, each having its strengths and limitations. The goals these systems set out to accomplish influence design decisions and determine how reusable and scalable they are. Weave is…
We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them…
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…
Network fluids are structured fluids consisting of chains and branches. They are characterized by unusual physical properties, such as, exotic bulk phase diagrams, interfacial roughening and wetting transitions, and equilibrium and…
The coalescing Brownian flow on $\mathbb{R}$ is a process which was introduced by Arratia [Coalescing Brownian motions on the line (1979) Univ. Wisconsin, Madison] and T\'{o}th and Werner [Probab. Theory Related Fields 111 (1998) 375-452],…
Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply.…
Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study continuous time random walks on combs and present a generic…
Increased attention has been paid over the last four years to dynamic network embedding. Existing dynamic embedding methods, however, consider the problem as limited to the evolution of a topology over a sequence of global, discrete states.…
Inspired by the work of Bemrose et al. \cite{Be16}, we delve into the study of weaving frames in Krein spaces. This paper presents a comprehensive exploration of various properties and characterizations of Krein space weaving frames. In…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
Woven fabrics play an essential role in everyday textiles for clothing/sportswear, water filtration, and retaining walls, to reinforcements in stiff composites for lightweight structures like aerospace, sporting, automotive, and marine…
We consider a planar geometric flow in which the normal velocity is a nonlocal variant of the curvature. The flow is not scaling invariant and in fact has different behaviors at different spatial scales, thus producing phenomena that are…