Related papers: Complex Scaling and Geometric Analysis of Several …
In this mini-review we summarize the progress of modeling, simulation and analysis of shock responses of heterogeneous materials in our group in recent years. The basic methodology is as below. We first decompose the problem into different…
For many finite groups, the Inverse Galois Problem can be approached through modular/automorphic Galois representations. This is a report explaining the basic strategy, ideas and methods behind some recent results. It focusses mostly on the…
The Random Parameters model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we…
We investigate various types of symmetries and their mutual relationships in Hamiltonian systems defined on manifolds with different geometric structures: symplectic, cosymplectic, contact and cocontact. In each case we pay special…
Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^\beta$ with a nontrivial value of the exponent $\beta$, usually determined by regression…
Motivated by applications in moduli theory, we introduce a flexible and powerful language for expressing lower bounds on relative dimension of morphisms of schemes, and more generally of algebraic stacks. We show that the theory is robust…
The purpose of this thesis is to study classical combinatorial objects, such as polytopes, polytopal complexes, and subspace arrangements, using tools that have been developed in combinatorial topology, especially those tools developed in…
Cartograms combine statistical and geographical information in thematic maps, where areas of geographical regions (e.g., countries, states) are scaled in proportion to some statistic (e.g., population, income). Cartograms make it possible…
Physical understanding of how the interplay between symmetries and nonlinear effects can control the scaling and multiscaling properties in a coupled driven system, such as magnetohydrodynamic turbulence or turbulent binary fluid mixtures,…
We introduce several highness notions on degrees related to the problem of computing isomorphisms between structures, provided that isomorphisms exist. We consider variants along axes of uniformity, inclusion of negative information, and…
We classify proper holomorphic mappings between generalized pseudoellipsoids of different dimensions. Those domains are parametrized by the exponents. The relations among them are also obtained. Main tool is the orthogonal decomposition of…
Various aspects of Supersymmetry in 1-dimensional systems are analyzed.
We give a thoroughful explanation of the general properties of different, general scales, corresponding to different (all possible) mathematical functions f(x), we mention and analyse many examples. These observations and statements might…
Multidimensional Scaling (MDS) is a classic technique that seeks vectorial representations for data points, given the pairwise distances between them. However, in recent years, data are usually collected from diverse sources or have…
Scaling of the conductances and the finite-size localization lengths is generalized to anisotropic systems and tested in two dimensional systems. Scaling functions of isotropic systems are recovered once the dimension of the system in each…
The lack of generalization in learning-based autonomous driving applications is shown by the narrow range of road scenarios that vehicles can currently cover. A generalizable approach should capture many distinct road structures and…
With the rapid adoption of machine learning techniques for large-scale applications in science and engineering comes the convergence of two grand challenges in visualization. First, the utilization of black box models (e.g., deep neural…
Exactly solvable two-dimensional polygon models, counted by perimeter and area, are described by $q$-algebraic functional equations. We provide techniques to extract the scaling behaviour of these models up to arbitrary order and apply them…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
The concept of scaling algebra provides a novel framework for the general structural analysis and classification of the short distance properties of algebras of local observables in relativistic quantum field theory. In the present article…