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Information theory and Shannon entropy are essential for quantifying irregularity in complex systems or signals. Recently, two-dimensional entropy methods, such as two-dimensional sample entropy, distribution entropy, and permutation…
In close binary systems the atmosphere of one or both components can be significantly influenced by irradiation from the companion. Often the irradiated atmosphere is simulated with a single-temperature approximation for the entire…
Many time series in smart energy systems exhibit two different timescales. On the one hand there are patterns linked to daily human activities. On the other hand, there are relatively slow trends linked to seasonal variations. In this paper…
Rendering 3D human appearance from a single image in real-time is crucial for achieving holographic communication and immersive VR/AR. Existing methods either rely on multi-camera setups or are constrained to offline operations. In this…
Over the past decade, various matrix completion algorithms have been developed. Thresholded singular value decomposition (SVD) is a popular technique in implementing many of them. A sizable number of studies have shown its theoretical and…
For the problem of 3D object recognition, researchers using deep learning methods have developed several very different input representations, including "multi-view" snapshots taken from discrete viewpoints around an object, as well as…
A flexible, scalable and affordable virtual reality software system architecture is proposed. This solution can be easily implemented on different hardware configurations: on a single computer or on a computer cluster. The architecture is…
Neural networks have been shown to be an effective tool for learning algorithms over graph-structured data. However, graph representation techniques---that convert graphs to real-valued vectors for use with neural networks---are still in…
Many iterative methods in applied mathematics can be thought of as fixed-point iterations, and such algorithms are usually analyzed analytically, with inequalities. In this paper, we present a geometric approach to analyzing contractive and…
This paper consists of a description of the variety of two dimensional associative algebras within the framework of Nonstandard Analysis. By decomposing each algebra in A^2 as sum of a Jordan algebra and a Lie algebra, we calculate the…
A key problem in the modern study of AI is predicting and understanding emergent capabilities in models during training. Inspired by methods for studying reactions in quantum chemistry, we present the ``2-datapoint reduced density matrix".…
We explore the use of tools from Riemannian geometry for the analysis of symmetric positive definite matrices (SPD). An SPD matrix is a versatile data representation that is commonly used in chemical engineering (e.g.,…
Data visualizations summarize high-dimensional distributions in two or three dimensions. Dimensionality reduction entails a loss of information, and what is preserved differs between methods. Existing methods preserve the local or the…
This paper presents a new technique for the virtual reality (VR) visu-alization of complex volume images obtained from computer tomography (CT) and Magnetic Resonance Imaging (MRI) by combining three-dimensional (3D) mesh processing and…
A divide-and-conquer based approach for computing the Moore-Penrose pseudo-inverse of the combinatorial Laplacian matrix $(\bb L^+)$ of a simple, undirected graph is proposed. % The nature of the underlying sub-problems is studied in detail…
Automated analysis of imaged phenotypes enables fast and reproducible quantification of biologically relevant features. Despite recent developments, recordings of complex, networked structures, such as: leaf venation patterns, cytoskeletal…
This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous…
In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for physicists dealing, for instance, with optimization problems, with data analysis, with the…
The automorphisms of all 4-dimensional, real Lie Algebras are presented in a comprehensive way. Their action on the space of $4\times 4$, real, symmetric and positive definite, matrices, defines equivalence classes which are used for the…
Graph Representation Learning (GRL) is an upcoming and promising area in recommendation systems. In this paper, we revisit the Singular Value Decomposition (SVD) of adjacency matrix for embedding generation of users and items and use a…