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In the study of random structures we often face a trade-off between realism and tractability, the latter typically enabled by assuming some form of independence. In this work we initiate an effort to bridge this gap by developing tools that…
Humans develop a common sense of style compatibility between items based on their attributes. We seek to automatically answer questions like "Does this shirt go well with that pair of jeans?" In order to answer these kinds of questions, we…
In this paper we develop a duality theory for all finite-dimensional near-vector spaces and introduce a notion of inner product tailored to the broad and natural class of strongly regular near-vector spaces. This generalized construction…
We present a novel method for image anomaly detection, where algorithms that use samples drawn from some distribution of "normal" data, aim to detect out-of-distribution (abnormal) samples. Our approach includes a combination of encoder and…
We introduce the notion of perturbations of quantum stochastic models using the series product, and establish the asymptotic convergence of sequences of quantum stochastic models under the assumption that they are related via a right series…
We define a general product of two $n$-dimensional tensors $\mathbb {A}$ and $\mathbb {B}$ with orders $m\ge 2$ and $k\ge 1$, respectively. This product is a generalization of the usual matrix product, and satisfies the associative law.…
In this expository paper we present a proof of the equivalence of the standard definition of descent data on schemes with another one mentioned in the literature that involves certain cartesian diagrams. Using this equivalence, we discuss…
We prove dimension formulas for arihmetic sums of regular Cantor sets, and, more generally, for images of cartesian products of regular Cantor sets by differentiable real maps.
In this work, the warped product of Hamilton spaces is introduced and it is shown that these spaces obtain Hamiltonian structure as well. Then, the geometric properties of warped product Hamilton spaces such as their nonlinear connections…
We study linkedness of Cartesian product of graphs and prove that the product of an $a$-linked and a $b$-linked graphs is $(a+b-1)$-linked if the graphs are sufficiently large. Further bounds in terms of connectivity are shown. We determine…
We survey the extensions of a group by a group using crossed products instead of exact sequences of groups. The approach has various advantages, one of them being that the crossed product is an universal object. Several new applications are…
In this paper, we present the outer product decomposition of a product of compatible linked networks. It provides a foundation for the fractional approach in network analysis. We discuss the standard and Newman's normalization of networks.…
The Jaccard similarity index has often been employed in science and technology as a means to quantify the similarity between two sets. When modified to operate on real-valued values, the Jaccard similarity index can be applied to compare…
This paper introduces the structure and axioms for a temporal digital topology (TDT) with the focus on digital connectedness, continuity and proximities in TDT spaces. Results are given for temporal digital adjacencies, connectedness and…
The notion of non-abelian Hom-Leibniz tensor product is introduced and some properties are established. This tensor product is used in the description of the universal ($\alpha$-)central extensions of Hom-Leibniz algebras. We also give its…
Digital Photo images are everywhere, on the covers of magazines, in newspapers, in courtrooms, and all over the Internet. We are exposed to them throughout the day and most of the time. Ease with which images can be manipulated; we need to…
This paper completes a fundamental construction in Alexandrov geometry. Previously we gave a new construction of metric spaces with curvature bounds either above or below, namely warped products with intrinsic metric space base and fiber,…
For continuous maps of compact metric spaces $f:X\to X$ and $g:Y\to Y$ and for various notions of topological recurrence, we study the relationship between recurrence for $f$ and $g$ and recurrence for the product map $f\times g:X\times Y…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
In quantum logical terms, Hardy-type arguments can be uniformly presented and extended as collections of intertwined contexts and their observables. If interpreted classically those structures serve as graph-theoretic "gadgets" that enforce…