Related papers: Two-Path Operators, Triadic Decompositions, and Sa…
Using diagrammatic methods, we show how the Ward identity can be used to constrain the ladder kernel in transport coefficient calculations. More specifically, we use the Ward identity to determine the necessary diagrams that must be…
String diagrams turn algebraic equations into topological moves that have recurring shapes, involving the sliding of one diagram past another. We individuate, at the root of this fact, the dual nature of polygraphs as presentations of…
Connectivity is a fundamental structural feature of a network that determines the outcome of any dynamics that happens on top of it. However, an analytical approach to obtain connection probabilities between nodes associated to paths of…
This note is devoted to the study of Hyt\"{o}nen's extrapolation theorem of compactness on weighted Lebesgue spaces. Two criteria of compactness of linear operators in the two-weight setting are obtained. As applications, we obtain…
In the present paper, the first in a series of two, we propose a model of universal quantum computation using a fermionic/bosonic multi-particle continuous-time quantum walk with two internal states (e.g., the spin-up and down states of an…
We study the behaviors of quantum groups under an edge contraction. We show that there exists an explicit embedding induced by an edge contraction operation. We further conjecture that this explicit embedding is a section of an explicit…
Graph learning architectures based on the k-dimensional Weisfeiler-Leman (k-WL) hierarchy offer a theoretically well-understood expressive power. However, such architectures often fail to deliver solid predictive performance on real-world…
We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. We extend the Wigner-In\"on\"u method of Lie algebra…
The theory of combinatorial designs has recently been used in order to build switch-centric data centre networks incorporating a large number of servers, in comparison with the popular Fat-Tree data centre network. The construction…
$k$-point crossover operators and their recombination sets are studied from different perspectives. We show that transit functions of $k$-point crossover generate, for all $k>1$, the same convexity as the interval function of the underlying…
(see paper for full abstract) We show that the Edge-Disjoint Paths problem is W[1]-hard parameterized by the number $k$ of terminal pairs, even when the input graph is a planar directed acyclic graph (DAG). This answers a question of…
Learning representations of nodes in a low dimensional space is a crucial task with many interesting applications in network analysis, including link prediction and node classification. Two popular approaches for this problem include matrix…
The complexity of a reasoning task over a graphical model is tied to the induced width of the underlying graph. It is well-known that the conditioning (assigning values) on a subset of variables yields a subproblem of the reduced complexity…
A weighted graph is a graph in which every edge is assigned a non-negative real number. In a weighted graph, the weight of a path is the sum of the weights of its edges, and the weighed degree of a vertex is the sum of the weights of the…
As one of the most fundamental concepts in transportation science, Wardrop equilibrium (WE) has always had a relatively weak behavioral underpinning. To strengthen this foundation, one must reckon with bounded rationality in human…
Future wireless networks are envisioned to integrate multi-hop, multi-operator, multi-technology (m3) components in order to meet the increasing traffic demand at an acceptable price for subscribers. The performance of such a network…
We propose a flexible framework for clustering hypergraph-structured data based on recently proposed random walks utilizing edge-dependent vertex weights. When incorporating edge-dependent vertex weights (EDVW), a weight is associated with…
Motivated by applications to spaces of embeddings and automorphisms of manifolds, we consider a tower of $\infty$-categories of truncated right-modules over a unital $\infty$-operad $\mathcal{O}$. We study monoidality and naturality…
This paper studies two fundamental problems in power systems: the economic dispatch problem (EDP) and load shedding. For the EDP, an extension of the problem considering the transmission losses is presented. Because the optimization problem…
Mobile-edge computing (MEC) has recently emerged as a cost-effective paradigm to enhance the computing capability of hardware-constrained wireless devices (WDs). In this paper, we first consider a two-user MEC network, where each WD has a…