Related papers: The Combinatorics of Alternating Tangles: from the…
We completely generalize previous results related to the counting of connected Feynman diagrams. We use a generating function approach, which encodes the Wick contraction combinatorics of the respective connected diagrams. Exact solutions…
A recent study characterizing failures in computer networks shows that transient single element (node/link) failures are the dominant failures in large communication networks like the Internet. Thus, having the routing paths globally…
We introduce the notion of an \emph{asymptotic triangulation} of the annulus. We show that asymptotic triangulations can be mutated as the usual triangulations and describe their exchange graph. Viewing asymptotic triangulations as limits…
Tandem duplication is an evolutionary process whereby a segment of DNA is replicated and proximally inserted. The different configurations that can arise from this process give rise to some interesting combinatorial questions. Firstly, we…
Tangle machines are a topologically inspired diagrammatic formalism to describe information flow in networks. This paper begins with an expository account of tangle machines motivated by the problem of describing `covariance intersection'…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
This paper discusses the enumeration of independent sets in king graphs of size $m \times n$, based on the tensor network contractions algorithm given in reference~\cite{tilEnum}. We transform the problem into Wang tiling enumeration within…
In the paper we introduce and study a classification of finite (simple, undirected, loopless) graphs with respect to a switch-equivalence (`local-complement' equivalence of \cite{pascvebl}, an analogue of the complement-equivalence of…
We develop the theory of sparse multiplex networks with partially overlapping links based on their local tree-likeness. This theory enables us to find the giant mutually connected component in a two-layer multiplex network with arbitrary…
We study the following combinatorial problem. Given a set of $n$ y-monotone wires, a tangle determines the order of the wires on a number of horizontal layers such that the orders of the wires on any two consecutive layers differ only in…
A method of resummation of infinite series of perturbation theory diagrams is applied for studying the properties of random band matrices. The topological classification of Feynman diagrams, which was actively used in last years for matrix…
Tanglegrams are drawings of two rooted binary phylogenetic trees and a matching between their leaf sets. The trees are drawn crossing-free on opposite sides with their leaf sets facing each other on two vertical lines. Instead of minimizing…
In this paper, the transfer matrix technique using the $k$-matching vector is developed to compute the number of $k$-matchings in an arbitrary graph which can be constructed by successive amalgamations over sets of cardinality two. This…
The appearance of numbers enumerating alternating sign matrices in stationary states of certain stochastic processes is reviewed. New conjectures concerning nest distribution functions are presented as well as a bijection between certain…
Consider the collection of edge bicolorings of a graph that is cellularly embedded on an orientable surface. In this work, we count the number of equivalence classes of such colorings under two relations: reversing colors around a face and…
The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…
We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the…
We establish a connection between linear codes and hyperplane arrangements using the Thomas decomposition of polynomial systems and the resulting counting polynomial. This yields both a generalization and a refinement of the weight…
Model merging has emerged as a cost-efficient approximation to multitask learning. Among merging strategies, task arithmetic is notable for its simplicity and effectiveness. In this work, we provide a theoretical motivation for task vectors…
A pair of complementary algorithms are presented. One of the pair is a fast method for connecting graphs with an edge. The other is a fast method for removing edges from a graph. Both algorithms employ the same tree based graph…