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We survey the distributional properties of progressively dilating sets under projection by covering maps, focusing on manifolds of constant sectional curvature. In the Euclidean case, we review previously known results and formulate some…
We develop a new interior-point algorithm for solving multiconic optimization problems using the parabolic target space approach. The feasible cone in these problems is composed as a direct product of many small-dimensional cones. Our…
In this paper, a unified nonlocal rational continuum enrichment technique is presented for improving the dispersive characteristics of some well known classical continuum equations on the basis of atomistic dispersion relations. This type…
Cylindrical Algebraic Decomposition (CAD) has long been one of the most important algorithms within Symbolic Computation, as a tool to perform quantifier elimination in first order logic over the reals. More recently it is finding…
Canonical Correlation Analysis (CCA) has been widely applied to jointly embed multiple views of data in a maximally correlated latent space. However, the alignment between various data perspectives, which is required by traditional…
The lattice studies in QCD demonstrate the nontrivial localization behavior of the eigenmodes of the 4D Euclidean Dirac operator considered as Hamiltonian of $4+1$ dimensional disordered system. We use the holographic viewpoint to provide…
We extend a previously introduced semi-analytical representation of a decomposition of CA dynamics in arbitrary dimensions and neighborhood schemes via the use of certain universal maps in which CA rule vectors are derivable from the…
The notion of the characteristic Lie algebra of the discrete hyperbolic type equation is introduced. An effective algorithm to compute the algebra for the equation given is suggested. Examples and further applications are discussed.
This paper studies complexity of recognition of classes of bounded configurations by a generalization of conventional cellular automata (CA) -- finite dynamic cellular automata (FDCA). Inspired by the CA-based models of biological and…
Motivated by a model for the perception of textures by the visual cortex in primates, we analyse the bifurcation of periodic patterns for nonlinear equations describing the state of a system defined on the space of structure tensors, when…
A new approach is introduced for deriving a mixed variational formulation for Kirchhoff plate bending problems with mixed boundary conditions involving clamped, simply supported, and free boundary parts. Based on a regular decomposition of…
We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on…
We introduce decorated piecewise hyperbolic and spherical surfaces and discuss their discrete conformal equivalence. A decoration is a choice of circle about each vertex of the surface. Our decorated surfaces are closely related to…
Simplicial complexes are increasingly used to understand the topology of complex systems as different as brain networks and social interactions. It is therefore of special interest to extend the study of percolation to simplicial complexes.…
We study a formulation of lattice gravity defined via Euclidean dynamical triangulations (EDT). After fine-tuning a non-trivial local measure term we find evidence that four-dimensional, semi-classical geometries are recovered at long…
We aim to analyze the relation between two random vectors that may potentially have both different number of attributes as well as realizations, and which may even not have a joint distribution. This problem arises in many practical…
We show how it is possible to formulate Euclidean two-dimensional quantum gravity as the scaling limit of an ordinary statistical system by means of dynamical triangulations, which can be viewed as a discretization in the space of…
The perturbative QCD approach to multiparticle production assuming Local Parton Hadron Duality (LPHD) and some recent results are discussed. Finite asymptotic scaling limits are obtained for various observables, after an appropriate…
Due to the rapid growth of smart agents such as weakly connected computational nodes and sensors, developing decentralized algorithms that can perform computations on local agents becomes a major research direction. This paper considers the…
Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as…