Related papers: Special points of the Brownian net

The goal of this brief pedagogical article is to show that Binary Decision Diagrams are a special kind of Bayesian Net. This observation is obvious to workers in these two fields, but it might not be too obvious to others.

Robust and comprehensive characterization of the topological properties of complex networks requires the adoption of several respective measurements, among which the node degree has special importance. In the present work, we provide an…

One of aims of this note is to capture the interest of the mathematical community to a novel transformation, which we shall call Brownian symmetrization. This transformation arises from the solution of the planar Skorokhod embedding…

We can view Brownian sheet as a sequence of interacting Brownian motions or slices. Here we present a number of results about the slices of the sheet. A common feature of our results is that they exhibit phase transition. In addition, a…

Point cloud analysis has drawn broader attentions due to its increasing demands in various fields. Despite the impressive performance has been achieved on several databases, researchers neglect the fact that the orientation of those point…

Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based…

Brunnian links have been known for a long time in knot theory, whereas the idea of n-triviality is a recent innovation. We illustrate the relationship between the two concepts with four short theorems.

Networks are pervasive in the real world. Nature, society, economy, and technology are supported by ostensibly different networks that in fact share an amazing number of interesting structural properties. Network thinking exploded in the…

We study interacting systems of linear Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. Our main objective has been to study the long range behavior of the…

This paper proposes BPNet, a novel end-to-end deep learning framework to learn B\'ezier primitive segmentation on 3D point clouds. The existing works treat different primitive types separately, thus limiting them to finite shape categories.…

This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…

A recent work by Ramanujan et al. (2020) provides significant empirical evidence that sufficiently overparameterized, random neural networks contain untrained subnetworks that achieve state-of-the-art accuracy on several predictive tasks. A…

Data describing the three-dimensional structure of physical networks is increasingly available, leading to a surge of interest in network science to explore the relationship between the shape and connectivity of physical networks. We…

We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction and disappearance. In particular, we focus on the case where the individuals are initially prepared at equilibrium within a confined geometry.…

We define and study a new class of 4d N=1 superconformal quiver gauge theories associated with a planar bipartite network. While UV description is not unique due to Seiberg duality, we can classify the IR fixed points of the theory by a…

There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How various preferential linking mechanisms produce networks with different features? In this paper we…

Multinets are certain configurations of lines and points with multiplicities in the complex projective plane $\mathbb{P}^2$. They appear in the study of resonance and characteristic varieties of complex hyperplane arrangement complements…

We define what we call an on/off Brownian snake. We use this to construct on/off super Brownian motion recently introduced to the literature by Blath and Jacobi and which is a measure-valued branching process with a dormant state and an…

Network representations of systems from various scientific and societal domains are neither completely random nor fully regular, but instead appear to contain recurring structural building blocks. These features tend to be shared by…

We present a new theory which describes the collection of all tunnels of tunnel number 1 knots in the 3-sphere (up to orientation-preserving equivalence in the sense of Heegaard splittings) using the disk complex of the genus-2 handlebody…