Related papers: Technical details of distributed localization
Optimization of thin-walled structures like an aircraft wing, aircraft fuselage or submarine hull often involves dividing the shell surface into numerous localized panels, each characterized by its own set of design variables. The process…
In this paper,we develop a local-to-global and measure-theoretical approach to understand datasets. The idea is to take network models with restricted domains as local charts of datasets. We develop the mathematical foundations for these…
Statistical pattern classification methods based on data-random graphs were introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the data points from various classes.…
Properties and examples of the dual transformation between two planes, which is such that the coordinates of a point in the original plane give the coefficients of a line in the dual plane and the coefficients of a line in the original…
In engineering practice one often encounters planar problems, where the corresponding vector space of forces, velocities or (infinitesimal) displacements is three dimensional. This paper shows how these spaces can be factorized, such that…
A relaxed factorization is used to obtain many of the properties obeyed by the confluent hypergeometric functions. Their implications on the analytical solutions of some interesting physical problems are also studied. It is quite remarkable…
The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement…
The use of data-random graphs in statistical testing of spatial patterns is introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the points from various classes.…
We prove spectral and dynamical localization for the multi-dimensional random displacement model near the bottom of its spectrum by showing that the approach through multiscale analysis is applicable. In particular, we show that a…
The Discrete Dislocation (DD) analysis and its computional modeling have been advanced significantly over the past decade. This progress has been further magnified by the idea to couple DD with continuum mechanics analysis in association…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
Distributed data aggregation is an important task, allowing the decentralized determination of meaningful global properties, that can then be used to direct the execution of other applications. The resulting values result from the…
The local analysis is an established approach to the study of singularities and mobility of linkages. Key result of such analyses is a local picture of the finite motion through a configuration. This reveals the finite mobility at that…
We use contraction method in probabilistic metric spaces to prove existence and uniqueness of selfsimilar random fractal measures.
Several algebraic criteria, reflecting displacement properties of transformation groups, have been used in the past years to prove vanishing of bounded cohomology and stable commutator length. Recently, the authors introduced the property…
In this article we introduce Variable exponent Fock spaces and study some of their basic properties such as the boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality.
This work was intended as an attempt to extend the results on localization of Fourier-Laplace series to the spectral expansions of distributions on the unit sphere. It is shown that the spectral expansions of the distribution on the unit…
Many tools and techniques measure local structure in materials in contexts ranging from biology to geology. We provide a survey of those tools and metrics that are especially useful for analyzing particulate soft matter. The metrics we…
The aim of this paper is to show a possibility to identify multivariate distribution by means of specially constructed one-dimensional random variable. We give some inequalities which may appear to helpful for a construction of multivariate…
The structural properties of confined single-file hard-disk fluids are studied analytically by means of a mapping of the original system onto a one-dimensional mixture of non-additive hard rods, the mapping being exact in the polydisperse…