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We establish the Hao-Ng isomorphism for generalized gauge actions of locally compact abelian groups on product systems over abelian lattice orders and we then use it to explore Takai duality in this context. As an application we generalize…
Following recent work of the author, partly in collaboration with T. Dupuy and M. Barrett, we describe arithmetic analogues of some key concepts from Riemannian geometry such as: metrics, Chern connections, curvature, etc. Theorems are…
Web spaces, wide web spaces and worldwide web spaces (alias C-spaces) provide useful generalizations of continuous domains. We present new characterizations of such spaces and their patch spaces, obtained by joining the original topology…
We make use of multiplicative degree-based topological indices $X_\Pi(G)$ to perform a detailed analytical and statistical study of random networks $G=(V(G),E(G))$. We consider two classes of indices: $X_\Pi(G) = \prod_{u \in V(G)}…
The properties and applications of kronecker product in quantum theory is studied thoroughly. The use of kronecker product in quantum information theory to get the exact spin Hamiltonian is given. The proof of non-commutativity of matrices,…
We give necessary and sufficient conditions for a family of inner products in a finite-dimensional vector space $V$ over an arbitrary field $\mathbb{K}$ to have an orthogonal basis relative to all the inner products. Some applications to…
After a short review of some basic facts on g-frames, we analyze in details the so-called (alternate) dual g-frames. We end the paper by introducing what we call {\em g-coherent states} and studying their properties.
To make Robotics and Augmented Reality applications robust to illumination changes, the current trend is to train a Deep Network with training images captured under many different lighting conditions. Unfortunately, creating such a training…
Motivated by constructions from applied topology, there has been recent interest in the homological algebra of linear representations of posets, particularly in the context of homological algebra relative to non-standard exact structures. A…
We give complete descriptions of the tracial states on both the universal and reduced crossed products of a C*-dynamical system consisting of a unital C*-algebra and a discrete group. In particular, we also answer the question of when the…
We use a characterization of the graph C*-algebras C*(E) as the Stacey crossed product C*(E)^\gamma \times_{\beta_E} N, to study its ideal properties in terms of the (non-classical) C*-dynamical system (C*(E)^\gamma, \beta_E)
We propose a new technique for visual attribute transfer across images that may have very different appearance but have perceptually similar semantic structure. By visual attribute transfer, we mean transfer of visual information (such as…
Modern Generative Adversarial Networks are capable of creating artificial, photorealistic images from latent vectors living in a low-dimensional learned latent space. It has been shown that a wide range of images can be projected into this…
We study three intriguing properties of contrastive learning. First, we generalize the standard contrastive loss to a broader family of losses, and we find that various instantiations of the generalized loss perform similarly under the…
We discuss special properties of the spaces of characters and positive definite functions, as well as their associated dynamics, for arithmetic groups of product type. Axiomatizing these properties, we define the notions of charmenability…
Various tasks in decision making and decision support systems require selecting a preferred subset of a given set of items. Here we focus on problems where the individual items are described using a set of characterizing attributes, and a…
Deep generative models learned through adversarial training have become increasingly popular for their ability to generate naturalistic image textures. However, aside from their texture, the visual appearance of objects is significantly…
Prior studies have generally suggested that Artificial Neural Networks (ANNs) are superior to conventional statistical models in predicting consumer buying behavior. There are, however, contradicting findings which raise question over…
We introduce an equivalence relation, called stable equivalence, on knot diagrams and closed curves on surfaces. We give bijections between the set of abstract knots, the set of virtual knots, and the set of the stable equivalence classes…
We introduce a new threshold model of social networks, in which the nodes influenced by their neighbours can adopt one out of several alternatives. We characterize the graphs for which adoption of a product by the whole network is possible…