Related papers: Weak uniform structures on probability distributio…
The asymptotic distribution of a wide class of V- and U-statistics with estimated parameters is derived in the case when the kernel is not necessarily differentiable along the parameter. The results have their application in goodness-of-fit…
In Functional Analysis, certain conclusions apply to sequences, but they cannot be carried over when we consider nets. In fact, some nets, including sequences, can behave unexpectedly. In this paper we are interested in exploring the…
We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…
This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the…
Random geometric graphs are widely used in modeling geometry and dependence structure in networks. In a random geometric graph, nodes are independently generated from some probability distribution $F$ over a metric space, and edges link…
In the In recent times, the research community has explored diverse structures and novel fabrication methods for amorphous solids. This work investigates structural trends among different classes of amorphous materials to identify universal…
We study the approximation of non-negative multi-variate couplings in the uniform norm while matching given single-variable marginal constraints.
The capability of recurrent neural networks to approximate trajectories of a random dynamical system, with random inputs, on non-compact domains, and over an indefinite or infinite time horizon is considered. The main result states that…
In this paper we find asymptotic distribution for some unreliable networks. Using Markov Additive Structure and Adan, Foley, McDonald method, we find the exact asymptotic for the stationary distribution. With the help of MA structure and…
In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number…
This paper explores a variety of strategies for understanding the formation, structure, efficiency and vulnerability of water distribution networks. Water supply systems are studied as spatially organized networks for which the practical…
In this article we continue the study of the quenched distributions of transient, one-dimensional random walks in a random environment. In a previous article we showed that while the quenched distributions of the hitting times do not…
We develop tame topology over dp-minimal structures equipped with definable uniformities satisfying certain assumptions. Our assumptions are enough to ensure that definable sets are tame: there is a good notion of dimension on definable…
Any symmetric affinity function $w: V\times V \to \mathbb{R}_+$ defined on a discrete set $V$ induces Euclidean space structure on $V$. In particular, an undirected graph specified by an affinity (or adjacency) matrix can be considered as a…
We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of…
Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing…
Neural networks are one of the most popularly used methods in machine learning and artificial intelligence nowadays. Due to the universal approximation theorem (Hornik et al. (1989)), a neural network with one hidden layer can approximate…
In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…