Domain wall generation by fermion self-interaction and light particles

A possible explanation for the appearance of light fermions and Higgs bosons on the four-dimensional domain wall is proposed. The mechanism of light particle trapping is accounted for by a strong self-interaction of five-dimensional pre-quarks. We obtain the low-energy effective action which exhibits the invariance under the so called \tau-symmetry. Then we find a set of vacuum solutions which break that symmetry and the five-dimensional translational invariance. One type of those vacuum solutions gives rise to the domain wall formation with consequent trapping of light massive fermions and Higgs-like bosons as well as massless sterile scalars, the so-called branons. The induced relations between low-energy couplings for Yukawa and scalar field interactions allow to make certain predictions for light particle masses and couplings themselves, which might provide a signature of the higher dimensional origin of particle physics at future experiments. The manifest translational symmetry breaking, eventually due to some gravitational and/or matter fields in five dimensions, is effectively realized with the help of background scalar defects. As a result the branons acquire masses, whereas the ratio of Higgs and fermion (presumably top-quark) masses can be reduced towards the values compatible with the present-day phenomenology. Since the branons do not couple to fermions and the Higgs bosons do not decay into branons, the latter ones are essentially sterile and stable, what makes them the natural candidates for the dark matter in the Universe.Comment: 34 pages, 2 figures, JHEP style,few important refs. adde

The Review of Spatial Objects Recognition Models and Algorithms

AbstractThe article considers the problem of spatial objects recognition in geographic information systems. The solutions for this problem are given, a classification of the methods and algorithms already available is executed and the ways of development in search of the optimum decision on the matter are offered. Firstly, it is the improvement in the quality of recognition. Secondly, it is the creation of general rules of sufficient accuracy rating to prevent erratic classification of objects of a certain type. Thirdly, it is the establishment of rules defining correlations of spatial objects of different classes.Models and algorithms of spatially distributed objects recognition can be classified based on the following directions: with using external and internal topological relations, with application of neural network approach and mixed methods. Not only the issue of object recognition importance, but also the importance of accounting of their relative positioning and determination of spatial characteristics in relation to each other is considered

An algorithm for matching spatial objects of different-scale maps based on topological data analysis

A problem of automatic comparison of spatial objects on maps with different scales for the same locality is considered in the article. It is proposed that this problem should be solved using methods of topological data analysis. The initial data of the algorithm are spatial objects that can be obtained from maps with different scales and subjected to deformations and distortions. Persistent homology allows us to identify the general structure of such objects in the form of topological features. The main topological features in the study are the connectivity components and holes in objects. The paper gives a mathematical description of the persistent homology method for representing spatial objects. A definition of a barcode for spatial data, which contains a description of the object in the form of topological features is given. An algorithm for comparing feature barcodes was developed. It allows us to find the general structure of objects. The algorithm is based on the analysis of data from the barcode. An index of objects similarity in terms of topological features is introduced. Results of the research of the algorithm for comparing maps of natural and municipal objects with different scales, generalization and deformation are shown. The experiments confirm the high quality of the proposed algorithm. The percentage of similarity in the comparison of natural objects, while taking into account the scale and deformation, is in the range from 85 to 92, and for municipal objects, after stretching and distortion of their parts, was from 74 to 87. Advantages of the proposed approach over analogues for the comparison of objects with significant deformation at different scales and after distortion are demonstrated.</jats:p

Algorithm for constructing three-dimensional Barcodes to represent nD spatial objects in GIS

В статье рассмотрен алгоритм создания трехмерных Баркодов для представления nD пространственных объектов. Алгоритм основан на методах компьютерной топологии с использованием алгоритма 3D sweep hull для вычисления выпуклых оболочек и триангуляции Делоне. Результатом работы алгоритма являются 3D Баркоды пространственных объектов. Также были построены графики 3D Баркодов, которые отражают их различия во времени. Алгоритм построения 3D Баркодов позволит анализировать пространственные nD объекты в разные временные интервалы. The article describes the algorithm for creating three-dimensional Barcodes to represent nD features. The algorithm is based on computer topology methods using the 3D sweep hull algorithm for computing convex hulls and Delaunay triangulation. The result of the algorithm are 3D Barcodes of features. Were also constructed 3D Barcode graphics, which reflect their differences in time. The algorithm for constructing 3D Barcodes will allow analyzing spatial nD objects at different time intervals.Исследование выполнено при финансовой поддержке РФФИ и администрации Владимирской области в рамках научного проекта № 17-47-330387

Algorithm for encoding nD spatial objects into GIS

В статье предлагается применить методы компьютерной топологии для создания эффективных структур данных, которые позволят хранить и обрабатывать пространственные сцены в n-мерном пространстве. Основой для представления nD-геообъектов являются n-мерные симплексы. Например, представление пространственных данных высокой размерности позволит описать топологические отношения между 3D-объектами во времени. Разработаны математические основы и программное обеспечение для представления и обработки пространственных данных высокой размерности. Алгоритм кодирования пространственных объектов nD в ГИС предоставит возможность решать широкий круг задач для обработки сложной графической информации. The development of GIS technologies in the modern world is moving towards the use of 3D maps, multiscale, as well as time components. However, today the data of some regularities are kept separately. For high dimensions, those algorithms that work well for 2D and 3D maps are not applicable. The integration of dimensions raises new requirements for creating new methods and algorithms for processing spatial data. The use of topological data analysis is a promising direction in GIS. In this paper, it is proposed to apply computer topology methods to create efficient data structures that will allow storing and processing spatial scenes in a single n-dimensional space. The basis for the representation of nD geoobjects is n-dimensional simplexes. For example, the representation of spatial data of high dimension will allow us to describe the topological relationships between 3D objects in time. There is a need to develop mathematical bases and software for the presentation and processing of spatial data of high dimensionality. The algorithm for encoding nD spatial objects into GIS will provide an opportunity to solve a wide range of tasks for processing complex graphic information.Исследование выполнено при финансовой поддержке РФФИ и администрации Владимирской области в рамках научного проекта № 17-47-330387. Исследование выполнено при финансовой поддержке администрации Владимирской области согласно договору №326 от 29.09.2017