Related papers: A characterization of positive spanning sets with …
Many large, real-world complex networks have rich community structure that a network scientist seeks to understand. These communities may overlap or have intricate internal structure. Extracting communities with particular topological…
For a continuous flow on a compact metric space, the aim of this paper is to prove a Conley-type decomposition of the strong chain recurrent set. We first discuss in details the main properties of strong chain recurrent sets. We then…
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…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. The distinguishing feature of these diagrams is that edges need not be connected to…
We study the partial orderings of the form $\langle {\mathbb P} ({\mathbb X}), \subset \rangle $, where ${\mathbb X}$ is a binary relational structure with the connectivity components isomorphic to a strongly connected structure ${\mathbb…
A discrete subset $S$ of a topologically gyrogroup $G$ is called a {\it suitable set} for $G$ if $S\cup \{1\}$ is closed and the subgyrogroup generated by $S$ is dense in $G$, where $1$ is the identity element of $G$. In this paper, we…
In this paper we consider how the strong-coupling scale, or perturbative cutoff, in a multi-gravity theory depends upon the presence and structure of interactions between the different fields. This can elegantly be rephrased in terms of the…
In this survey we overview known results and get several new results on digraph compositions which generalize several classes of digraphs, such as quasi-transitive digraphs. After an introductory section, the paper is divided into six…
Structural approximations to positive, but not completely positive maps are approximate physical realizations of these non-physical maps. They find applications in the design of direct entanglement detection methods. We show that many of…
We introduce deep scale-spaces (DSS), a generalization of convolutional neural networks, exploiting the scale symmetry structure of conventional image recognition tasks. Put plainly, the class of an image is invariant to the scale at which…
Let $ G $ be a finite group of order $ n$. The strong power graph $\mathcal{P}_s(G) $ of $G$ is the undirected graph whose vertices are the elements of $G$ such that two distinct vertices $a$ and $b$ are adjacent if $a^{{m}_1}$=$b^{{m}_2}$…
In this paper we study the set of tensors that admit a special type of decomposition called an orthogonal tensor train decomposition. Finding equations defining varieties of low-rank tensors is generally a hard problem, however, the set of…
Signed networks provide a principled framework for representing systems in which interactions are not merely present or absent but qualitatively distinct: friendly or antagonistic, supportive or conflicting, excitatory or inhibitory. This…
This paper connects a vector-based composition model to a formal semantics, the Dependency-based Compositional Semantics (DCS). We show theoretical evidence that the vector compositions in our model conform to the logic of DCS.…
This work explores new classes of nonstationary stochastic sequences associated with polynomial hypergroups. Their covariance structures are analyzed through positive definite kernels and corresponding Hilbert spaces. Novel consistent…
We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…
We define "BPS graphs" on punctured Riemann surfaces associated with $A_{N-1}$ theories of class $\mathcal{S}$. BPS graphs provide a bridge between two powerful frameworks for studying the spectrum of BPS states: spectral networks and BPS…
Let $T$ be a digraph with vertices $u_1, \dots, u_t$ ($t\ge 2$) and let $H_1, \dots, H_t$ be digraphs such that $H_i$ has vertices $u_{i,j_i},\ 1\le j_i\le n_i.$ Then the composition $Q=T[H_1, \dots, H_t]$ is a digraph with vertex set…
Completely positive graphs have been employed to associate with completely positive matrices for characterizing the intrinsic zero patterns. As tensors have been widely recognized as a higher-order extension of matrices, the…
The search of spanning trees with interesting disjunction properties has led to the introduction of edge-disjoint spanning trees, independent spanning trees and more recently completely independent spanning trees. We group together these…