Related papers: Weaves, webs and flows
This paper aims to develop a mathematical foundation to model knitting with graphs. We provide a precise definition for knit objects with a knot theoretic component and propose a simple undirected graph, a simple directed graph, and a…
Sticky Brownian motion is the simplest example of a diffusion process that can spend finite time both in the interior of a domain and on its boundary. It arises in various applications such as in biology, materials science, and finance.…
Chain graphs combine directed and undirected graphs and their underlying mathematics combines properties of the two. This paper gives a simplified definition of chain graphs based on a hierarchical combination of Bayesian (directed) and…
Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously…
Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes…
The flow of ideas has been extensively studied by physicists, psychologists, and machine learning engineers. This paper adopts specific tools from microrheology to investigate the similarity-based flow of ideas. We introduce a random walker…
This is the first of a series of papers devoted to a thorough analysis of the class of gradient flows in a metric space $(X,\mathsf{d})$ that can be characterized by Evolution Variational Inequalities. We present new results concerning the…
Conventional deep learning prioritizes unconstrained optimization, yet biological systems operate under strict metabolic constraints. We propose that these physical constraints shape dynamics to function not as limitations, but as a…
Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber reinforced materials are also common in technology. An important characteristic of such materials is their…
Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…
For the directed landscape, the putative universal space-time scaling limit object in the (1+1) dimensional Kardar-Parisi-Zhang (KPZ) universality class, consider the geodesic tree -- the tree formed by the coalescing semi-infinite…
We show the existence of periodic traveling waves at the free surface of a two dimensional, infinitely deep, and constant vorticity flow, under gravity, whose profiles are overhanging, including one which intersects itself to enclose a…
Graph classification is a fundamental but challenging issue for numerous real-world applications. Despite recent great progress in image/video classification, convolutional neural networks (CNNs) cannot yet cater to graphs well because of…
Over the last two decades, network theory has shown to be a fruitful paradigm in understanding the organization and functioning of real-world complex systems. One technique helpful to this endeavor is identifying functionally influential…
There has been much research on network flows over time due to their important role in real world applications. This has led to many results, but the more challenging continuous time model still lacks some of the key concepts and techniques…
The behavior of a non-spherical particle in a viscous, plane channel flow is studied by means of a combination of analytical technique and geometrical reasoning. An efficient implementation of Lamb's general solution is adopted, allowing…
Network embedding techniques are powerful to capture structural regularities in networks and to identify similarities between their local fabrics. However, conventional network embedding models are developed for static structures, commonly…
We explore a simple mathematical model of network computation, based on Markov chains. Similar models apply to a broad range of computational phenomena, arising in networks of computers, as well as in genetic, and neural nets, in social…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
We extend the theory of gradient flows beyond metric spaces by studying evolution variational inequalities (EVIs) driven by general cost functions $c$, including Bregman and entropic transport divergences. We establish several properties of…