Related papers: On the classification of CW complexes with prescri…
Several interdisciplinary areas have appeared at the interface between biological and physical sciences. In this work, we suggest a complex network-based methodology for analyzing the interrelationships between some of these…
A weak chord index $Ind'$ is constructed for self crossing points of virtual links. Then a new writhe polynomial $W$ of virtual links is defined by using $Ind'$. $W$ is a generalization of writhe polynomial defined in [6]. Based on $W$,…
The goal of this paper is to discover a set of discriminative patches which can serve as a fully unsupervised mid-level visual representation. The desired patches need to satisfy two requirements: 1) to be representative, they need to occur…
We incorporate quandle cocycle information into the quandle coloring quivers we defined in arXiv:1807.10465 to define weighted directed graph-valued invariants of oriented links we call \textit{quandle cocycle quivers}. This construction…
for representing, characterizing, and modeling an ample range of structures and phenomena from both theoretical and applied perspectives. The present work describes the application of the recently introduced real-valued Jaccard and…
Many real-world complex networks are best modeled as bipartite (or 2-mode) graphs, where nodes are divided into two sets with links connecting one side to the other. However, there is currently a lack of methods to analyze properly such…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
In this paper we give a complete classification of cyclically graded semisimple Lie algebras that afford cuspidal character sheaves and determine the support of the cuspidal character sheaves. This constitutes a major step towards the…
A concept of implicit links for Complex Networks has been defined and a new value - cohesion factor, which allows to evaluate numerically the presence of such connection between any two nodes, has been introduced. We introduce a…
In this paper we study the use of cross-correlations between multiple gravitational wave (GW) data streams for detecting long-lived periodic signals. Cross-correlation searches between data from multiple detectors have traditionally been…
Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…
We outline the main features of the definitions and applications of crossed complexes and cubical $\omega$-groupoids with connections. These give forms of higher homotopy groupoids, and new views of basic algebraic topology and the…
The recent high level of interest in weighted complex networks gives rise to a need to develop new measures and to generalize existing ones to take the weights of links into account. Here we focus on various generalizations of the…
Topological properties of networks are widely applied to study the link-prediction problem recently. Common Neighbors, for example, is a natural yet efficient framework. Many variants of Common Neighbors have been thus proposed to further…
The science of complexity is far from being fully understood and even its foundations are not well established. On the other hand, during the last decade, the random motion of particles or waves - the so-called diffusion - has been known…
The vision of the Semantic Web (SW) is gradually unfolding and taking shape through a web of linked data, a part of which is built by capturing semantics stored in existing knowledge organization systems (KOS), subject metadata and resource…
This is a work in progress, far from being in its final form whose purpose is to investigate thoroughly the structure of Berkovich analytic curves and its relation with the semi-stable reduction theorem (of which a new proof is given here,…
A general introduction to lattice QCD suitable for graduate students in experimental and theoretical particle physics. Aimed at those who want to know how lattice calculations are done, and what the pitfalls are, without having to do the…
Let $C$ be a smooth irreducible projective algebraic curve defined over the complex numbers. The notion of the Clifford index of $C$ was extended a few years ago to semistable bundles of any rank. Recent work has been focussed mainly on the…
In this paper, we study the curvature properties of random complex plane curves. We bound from below the probability that a uniform proportion of the area of a random complex degree $d$ plane curve has a curvature smaller than $-d/8$. Our…