Related papers: Highly irregular separated nets
Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives [1, 2]. A critical property of a network is its resilience to random breakdown and failure [3-6], typically studied as a…
Examples are constructed of sparse subsequences of the integers for which the associated maximal averages operator is of weak type (1,1). A consequence, by transference, is that an almost everywhere L^1 -- type ergodic theorem holds for…
We consider robustness and percolation properties of the networks of networks, in which random nodes in different individual networks (layers) can be interdependent. We explore the emergence of the giant mutually connected component,…
In this paper we study nonlocal nonlinear equations of fractional $(s,p)$-Laplacian type on $\mathbf{R}^n$. We show that the irregular boundary points for the Dirichlet problem can be divided into two disjoint classes: semiregular and…
The success and superior performance of deep networks is spreading their popularity and use to an increasing number of applications. Very recent works, however, demonstrate that modern day deep networks suffer from irreproducibility (also…
Wigner limits are given formally as the difference between a lattice sum, associated to a positive definite quadratic form, and a corresponding multiple integral. To define these limits, which arose in work of Wigner on the energy of static…
We study the effects of nonreciprocity and network structure on percolation. To this end, we investigate nonreciprocal random networks - directed networks for which the probability of a link occurring from node i to node j differs from the…
Quantum network correlations have attracted strong interest as the emergency of the new types of violations of locality. Here we investigated network nonlocal sharing in the extended bilocal scenario via weak measurements. Interestingly,…
Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higher order interactions among…
As a fundamental challenge in vast disciplines, link prediction aims to identify potential links in a network based on the incomplete observed information, which has broad applications ranging from uncovering missing protein-protein…
We study the structural characteristics of complex networks using the representative eigenvectors of the adjacent matrix. The probability distribution function of the components of the representative eigenvectors are proposed to describe…
We consider divergent orbits of the group of diagonal matrices in the space of lattices in Euclidean space. We define two natural numerical invariants of such orbits: The discriminant - an integer - and the type - an integer vector. We then…
We study the problem of comparing a pair of geometric networks that may not be similarly defined, i.e., when they do not have one-to-one correspondences between their nodes and edges. Our motivating application is to compare power…
We study (strictly) join irreducible varieties in the lattice of subvarieties of residuated lattices. We explore the connections with well-connected algebras and suitable generalizations, focusing in particular on representable varieties.…
Given a finite point set $P$ in ${\mathbb R}^d$, and $\epsilon>0$ we say that $N\subseteq{ \mathbb R}^d$ is a weak $\epsilon$-net if it pierces every convex set $K$ with $|K\cap P|\geq \epsilon |P|$. We show that for any finite point set in…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
The correlations in quantum networks have attracted strong interest with new types of violations of the locality. The standard Bell inequalities cannot characterize the multipartite correlations that are generated by multiple sources. The…
Extensive research efforts have been put into characterizing and constructing maximally separating multiset and graph neural networks. However, recent empirical evidence suggests the notion of separation itself doesn't capture several…
It is found that there exist composite media that exhibit strong spatial dispersion even in the very large wavelength limit. This follows from the study of lattices of ideally conducting parallel thin wires (wire media). In fact, our…
We consider a neural network architecture with randomized features, a sign-splitter, followed by rectified linear units (ReLU). We prove that our architecture exhibits robustness to the input perturbation: the output feature of the neural…