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We generalize a graph-based multiclass semi-supervised classification technique based on diffuse interface methods to multilayer graphs. Besides the treatment of various applications with an inherent multilayer structure, we present a very…
The use of tools from analysis to approach problems in graph theory has become an active area of research. Usually such methods are applied to problems involving dense graphs and hypergraphs; here we give the an extension of such methods to…
A recent method called Asymptotic Taylor expansion (ATEM) is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrodinger equation for the bistable potentials. Optimal…
Traditional analytical reflectance models, while compact and interpretable, lack the capacity to accurately represent physical measurements. Recent neural models, which closely fit input data, are less generalizable and often more expensive…
We give new positive and negative results (some conditional) on speeding up computational algebraic geometry over the reals: (1) A new and sharper upper bound on the number of connected components of a semialgebraic set. Our bound is novel…
We study the analyticity of bounded solutions of systems of analytic state-dependent delay differential equations. We obtain the analyticity of solutions by transforming the system of state-dependent delay equations into an abstract…
Let $S$ be the symmetric algebra of an algebraic Lie algebra. We provide a sufficient condition for the maximality of Poisson commutative subalgebras of $S$ obtained by the argument shift method.
Compounding is a highly productive word-formation process in some languages that is often problematic for natural language processing applications. In this paper, we investigate whether distributional semantics in the form of word…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
Nonlinear systems of the reaction-diffusion type, including Gierer-Meinhardt models of autocatalysis, are studied by using Lie algebras coming from the prolongation structure. The consequences of this analytical approach, as the…
Self-similarity techniques are booming in blind super-resolution (SR) due to accurate estimation of the degradation types involved in low-resolution images. However, high-dimensional matrix multiplication within self-similarity computation…
The algebraic method for computing the complete point symmetry group of a system of differential equations is extended to finding the complete equivalence group of a class of such systems. The extended method uses the knowledge of the…
In 1998 the Adapted Ordering Method was developed for the study of the representation theory of the superconformal algebras in two dimensions. It allows: to determine the maximal dimension for a given type of space of singular vectors, to…
A new efficient algorithm is proposed for factoring polynomials over an algebraic extension field. The extension field is defined by a polynomial ring modulo a maximal ideal. If the maximal ideal is given by its Groebner basis, no extra…
We study a bijective map from integer partitions to the prime factorizations of integers that we call the "supernorm" of a partition, in which the multiplicities of the parts of partitions are mapped to the multiplicities of prime factors…
We consider the problem of computing the Lebesgue volume of compact basic semi-algebraic sets. In full generality, it can be approximated as closely as desired by a converging hierarchy of upper bounds obtained by applying the Moment-SOS…
In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real…
We consider Borcherds superalgebras obtained from semisimple finite-dimensional Lie algebras by adding an odd null root to the simple roots. The additional Serre relations can be expressed in a covariant way. The spectrum of generators at…
Most, if not all, modern deep learning systems restrict themselves to a single dataset for neural network training and inference. In this article, we are interested in systematic ways to join datasets that are made of similar purposes.…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…