Topological Decomposition Research Articles

Using the method of image decomposition based on topological features for processing satellite images

The problem of interpretation of spatial data on satellite images is considered in the article. It is proposed to use the decomposition of images by topological features to highlight objects of interest, global and detailed structures on satellite images. The description of the method and the features of its implementation for creating a software product with effective algorithms for processing big data are given. The functionality of the developed software, which includes the classification of objects on satellite images, segmentation, binarization, noise removal is described. It is shown that these algorithms are built on a single theoretical basis in the form of a topological decomposition. Examples of using the program for segmentation and binarization of satellite images from urban neighborhoods are demonstrated.

A Distributed Gradient Descent Method for Node Localization on Large-Scale Wireless Sensor Network

A distributed iterative method is proposed to solve the problem of node (sensor) localization for large-scale wireless sensor network (WSN), by leveraging the graph topology decomposition and gradient descent method. First, the undirected graph representing the WSN is divided into several overlapping subgraphs. Based on the decomposition subgraphs, the localization problem is splitting into a series of subproblems each of which reside on one subgraph. The iterative procedure is proceeded on the subgraphs and each iteration consists of two operators. The first operator is solving the subproblem in every subgraph by using the gradient descent method which possesses light computational cost, and the second operator is to fuse and average the local positions of nodes in the overlapping region of adjacent subgraphs. In order to enrich the available information of localization, the positions of the target nodes with high localization accuracy are used as the (pseudo) anchor nodes for the subsequent iteration. Owing to that the operators are accomplished on subgraphs with small sizes, the proposed distributed iterative method possesses low computational cost, making it suitable for large-scale WSN. Numerical results are included to demonstrate the effectiveness of the proposed localization method.

Electromagnetic Steklov eigenvalues: existence and distribution in the self-adjoint case

In previous works, it was suggested to use Steklov eigenvalues for Maxwell equations as target signature for nondestructive testing, and it was recognized that this eigenvalue problem cannot be reformulated as a standard eigenvalue problem for a compact operator. Consequently, a modified eigenvalue problem with the desired properties was proposed. We report that apart for a countable set of particular frequencies, the spectrum of the original self-adjoint eigenvalue problem consists of three disjoint parts: The essential spectrum consisting of the origin, an infinite sequence of positive eigenvalues which accumulate only at infinity and an infinite sequence of negative eigenvalues which accumulate only at zero. The analysis is based on a suitable topological decomposition, a representation of the operator as block operator and Schur-factorizations. For each Schur-complement, the existence of an infinite sequence of eigenvalues is proven via an intermediate value technique. The modified eigenvalue problem arises as limit of one Schur-complement.

Machine learning the trilinear and light-quark Yukawa couplings from Higgs pair kinematic shapes

Revealing the Higgs pair production process is the next big challenge in high energy physics. In this work, we explore the use of interpretable machine learning and cooperative game theory for extraction of the trilinear Higgs self-coupling in Higgs pair production. In particular, we show how a topological decomposition of the gluon-gluon fusion Higgs pair production process can be used to simplify the machine learning analysis flow. Furthermore, we extend the analysis to include qoverline{q} → hh production, which is strongly suppressed in the Standard Model, to extract the trilinear Higgs coupling and to bound large deviations of the light-quark Yukawa couplings from the Standard Model values. The constraints on the rescaling of the trilinear Higgs self-coupling, κλ, and the rescaling of light-quark Yukawa couplings, κu and κd, at HL-LHC (FCC-hh) from single parameter fits are:κλ=0.531.70.971.03κu=−470430−5855κd=−360360−2628\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\displaystyle \\begin{array}{c}{\\kappa}_{\\lambda }=\\left[0.53,1.7\\right]\\ \\left(\\left[0.97,1.03\\right]\\right)\\\\ {}{\\kappa}_u=\\left[-470,430\\right]\\ \\left(\\left[-58,55\\right]\\right)\\\\ {}{\\kappa}_d=\\left[-360,360\\right]\\ \\left(\\left[-26,28\\right]\\right)\\end{array}} $$\\end{document}We show that the simultaneous modification of the Yukawa couplings can dilute the constraints on the trilinear coupling significantly. We perform similar analyses for FCC-hh. We discuss some motivated flavourful new physics scenarios where such an analysis prevails.

Generalized PT Symmetry in Non-Hermitian Wireless Power Transfer Systems.

We show that, by using a saturable gain g_{sat}, generalized PT (GPT) symmetry can be achieved in the intrinsically unbalanced (non-PT-symmetric) high-order wireless power transfer systems. A topology decomposition approach is implemented to analyze the parity of the high-order wireless power transfer systems. In the coupling parametric space, a global GPT-symmetric eigenstate is observed along with the spontaneous phase transition of the local GPT-symmetric eigenstates on the exceptional contour. GPT symmetry guarantees a highly efficient and stable power transfer across the distinct coupling regions, which introduces a new paradigm for a broad range of application scenarios involving asymmetric coupling.

Therapeutic Neuromodulation toward a Critical State May Serve as a General Treatment Strategy.

Brain disease has become one of this century’s biggest health challenges, urging the development of novel, more effective treatments. To this end, neuromodulation represents an excellent method to modulate the activity of distinct neuronal regions to alleviate disease. Recently, the medical indications for neuromodulation therapy have expanded through the adoption of the idea that neurological disorders emerge from deficits in systems-level structures, such as brain waves and neural topology. Connections between neuronal regions are thought to fluidly form and dissolve again based on the patterns by which neuronal populations synchronize. Akin to a fire that may spread or die out, the brain’s activity may similarly hyper-synchronize and ignite, such as seizures, or dwindle out and go stale, as in a state of coma. Remarkably, however, the healthy brain remains hedged in between these extremes in a critical state around which neuronal activity maneuvers local and global operational modes. While it has been suggested that perturbations of this criticality could underlie neuropathologies, such as vegetative states, epilepsy, and schizophrenia, a major translational impact is yet to be made. In this hypothesis article, we dissect recent computational findings demonstrating that a neural network’s short- and long-range connections have distinct and tractable roles in sustaining the critical regime. While short-range connections shape the dynamics of neuronal activity, long-range connections determine the scope of the neuronal processes. Thus, to facilitate translational progress, we introduce topological and dynamical system concepts within the framework of criticality and discuss the implications and possibilities for therapeutic neuromodulation guided by topological decompositions.

Topological transition and helicity conversion of vortex knots and links

Topological transition and helicity conversion of vortex torus knots and links are studied using direct numerical simulations of the incompressible Navier–Stokes equations. We find three topological transitional routes (viz. merging, reconnection and transition to turbulence) in the evolution of vortex knots and links over a range of torus aspect ratios and winding numbers. The topological transition depends not only on the initial topology but also on the initial geometry of knots/links. For small torus aspect ratios, the initially knotted or linked vortex tube rapidly merges into a vortex ring with a complete helicity conversion from the writhe and link components to the twist. For large torus aspect ratios, the vortex knot or link is untied into upper and lower coiled loops via the first vortex reconnection, with a helicity fluctuation including loss of writhe and link, and generation of twist. Then, the relatively unstable lower loop can undergo a secondary reconnection to split into multiple small vortices with a similar helicity fluctuation. Surprisingly, for moderate torus aspect ratios, the incomplete reconnection of tangled vortex loops together with strong vortex interactions triggers transition to turbulence, in which the topological helicity decomposition fails due to the breakdown of vortex core lines.

Surface Integrity of Pre-sintered Ceramics and Composites Used for Dental Prostheses After CAD/CAM Abrasive Milling

All-ceramic fixed partial dental restorations are milled by CAD/CAM process. The significant challenges for such prostheses manufacturing are respecting functional and aesthetic requirements. Specific surface integrity (SI) might be manufactured in different anatomical and assembly prosthesis areas. Aesthetics, biological and mechanical responses require a low surface roughness. Contrariwise, the surface to be bonded needs to be sufficiently rough. The CAD/CAM process’s influence on prosthesis SI is not investigated in the industrial and scientific restorative dentistry community. This paper evaluates the influence of tools, biomaterials, and milling parameters on SI, especially the roughness, leading to topological decomposition of the prosthesis shape.

A Modular Method for Mechanical Error Analysis of Planar Linkages Composed of Class II Assur Group Kinematic Chains

Abstract This paper presents a modular method for the mechanical error analysis of complex planar linkages. The topology of the linkage under investigation is decomposed into several class II Assur group kinematic chains (AGKCs) combined in a given sequence. Therefore, the mechanical error of the whole linkage can be analyzed by investigating the error propagations of adopted AGKCs in successive order. Because class II AGKCs are first served as modules, the mechanical error equations of these AGKCs in terms of each error in link lengths and joint variables can be pre-formulated and embedded in form of subroutines in any programmable language. Once the AGKCs constituting the linkage topology are identified, the corresponding subroutines are introduced to compute the error propagations in the linkage. Therefore, the presented modular approach can facilitate the analysis by concentrating on the topology decomposition instead of the algebraic derivation. Numerical examples are provided to illustrate the advantage and flexibility of the modular approach.

Currents, systoles, and compactifications of character varieties

We study the Weyl chamber length compactification both of the Hitchin and of the maximal character varieties and determine therein an open set of discontinuity for the action of the mapping class group. This result is obtained as a consequence of a canonical decomposition of a geodesic current on a surface of finite type arising from a topological decomposition of the surface along special geodesics. We show that each component either is associated to a measured lamination or has positive systole. For a current with positive systole, we show that the intersection function on the set of closed curves is bilipschitz equivalent to the length function with respect to a hyperbolic metric.

Topological Decompositions of the Pauli Group and their Influence on Dynamical Systems

In the present paper we show that it is possible to obtain the well known Pauli group P = 〈X,Y,Z | X2 = Y2 = Z2 = 1,(YZ)4 = (ZX)4 = (XY )4 = 1〉 of order 16 as an appropriate quotient group of two distinct spaces of orbits of the three dimensional sphere S3. The first of these spaces of orbits is realized via an action of the quaternion group Q8 on S3; the second one via an action of the cyclic group of order four mathbb {Z}(4) on S3. We deduce a result of decomposition of P of topological nature and then we find, in connection with the theory of pseudo-fermions, a possible physical interpretation of this decomposition.

TO THE PROBLEM OF DETERMINING AIR VELOCITY FIELD IN TUNNEL STRUCTURES OF A SUBWAY LINE USING CIRCULAR MODELS AS A METHOD OF TOPOLOGICAL DECOMPOSITION

Underground subway structures represent crowded public areas; therefore, they are subject to high requirements for maintaining the standard microclimate parameters at stations and in tunnels, including the content of suspended dust in the air. To maintain dust concentration within specifications, it is proposed to use air filters installed in station ventilation connections in the stream of air from the piston effect of trains. To study the piston effect by aerogasdynamic computational methods, a method is proposed for the topological decomposition of a subway line - transition froma complete linear model to a closed circular model by isolating several lines and closing them into a circle, which allows reducing the size of discrete model of the design section, while maintaining the influence of neighboring lines and stations as well as calculation accuracy. As a result of a numerical experiment, the parameters of transient air distribution from the piston effect of trains and the structure of air stream at the places of filter installation are determined for further study of their geometric, structural and operational parameters.

A Formula for the Möbius Function of the Permutation Poset Based on a Topological Decomposition

The poset P of all permutations ordered by pattern containment is a fundamental object of study in the field of permutation patterns. This poset has a very rich and complex topology and an understanding of its Möbius function has proved particularly elusive, although results have been slowly emerging in the last few years. Using a variety of topological techniques we present a two term formula for the Mo ̈bius function of intervals in P. The first term in this formula is, up to sign, the number of so called normal occurrences of one permutation in another. Our definition of normal occurrences is similar to those that have appeared in several variations in the literature on the Möbius function of this and other posets, but simpler than most of them. The second term in the formula is (still) complicated, but we conjecture that it equals zero for a significant proportion of intervals. We present some cases where the second term vanishes and others where it is nonzero. Computing the Möbius function recursively from its definition has exponential complexity, whereas the computation of the first term in our formula is polynomial and the exponential part is isolated to the second term, which seems to often vanish. This is thus the first polynomial time formula for the Möbius function of what appears to be a large proportion of all intervals of P.

Projective and Non-Projective Varieties of Topological Decomposition of Groups with Embeddings

In general, the group decompositions are formulated by employing automorphisms and semidirect products to determine continuity and compactification properties. This paper proposes a set of constructions of novel topological decompositions of groups and analyzes the behaviour of group actions under the topological decompositions. The proposed topological decompositions arise in two varieties, such as decomposition based on topological fibers without projections and decomposition in the presence of translated projections in topological spaces. The first variety of decomposition introduces the concepts of topological fibers, locality of group operation and the partitioned local homeomorphism resulting in formulation of transitions and symmetric surjection within the topologically decomposed groups. The reformation of kernel under decomposed homeomorphism and the stability of group action with the existence of a fixed point are analyzed. The first variety of decomposition does not require commutativity maintaining generality. The second variety of projective topological decomposition is formulated considering commutative as well as noncommutative projections in spaces. The effects of finite translations of topologically decomposed groups under projections are analyzed. Moreover, the embedding of a decomposed group in normal topological spaces is formulated in this paper. It is shown that Schoenflies homeomorphic embeddings preserve group homeomorphism in the decomposed embeddings within normal topological spaces. This paper illustrates that decomposed group embedding in normal topological spaces is separable. The applications aspects as well as parametric comparison of group decompositions based on topology, direct product and semidirect product are included in the paper.

Application of 3D Virtual Ocean Image Simulation in Ship Vision

Li, D.-B., 2019. Application of 3d virtual ocean image simulation in ship vision. In: Gong, D.; Zhu, H., and Liu, R. (eds.), Selected Topics in Coastal Research: Engineering, Industry, Economy, and Sustainable Development. Journal of Coastal Research, Special Issue No. 94, pp. 530–534. Coconut Creek (Florida), ISSN 0749-0208.The marine battlefield situation is an important part of the marine geographical environment information. The three-dimensional visualization of the battlefield situation can give the intelligence officers and commanders a more realistic feeling, which makes them work more smoothly. It is an urgent task for the development of military electronic information systems. The simulation research on the virtual visual image system of the naval ship combat is an important means to analyze the situation of the ocean battlefield. In this paper, a three-dimensional virtual ocean simulation technology based on the mesh topology decomposition of ocean topology is proposed and applied in the ship vision system, this simulation technology makes the 3D virtual ocean have better real-time visual simulation rendering effect, and the viewpoint conversion and viewpoint control are smooth, which improves the authenticity of the ship visual simulation in the three-dimensional marine environment.

A Modular Design Approach to Provide Exhaustive Carrier-Based PWM Patterns for Multilevel ANPC Converters

The number of applicable carrier-based pulsewidth modulation (PWM) patterns increases with the growth of output levels in scalable multilevel topologies, such as active-neutral-point-clamped (ANPC) converters. Therefore, it is hard to optimize PWM for such topology, especially with large output levels. In this paper, a simplified and modular carrier-based PWM design approach for multilevel ANPC converters is proposed. Inspired by the decomposition theory, the topology decomposition is introduced in this paper to decompose an N -level ANPC converter into low-level subtopologies. Then, the complete set of applicable PWM patterns is derived based on ANPC operation principles, which makes it possible to optimize the performance based on the various requirements in applications. Meanwhile, the carrier-based PWM is implemented through the utilization of subtopologies with low-level modulation schemes, such that the design process of carrier-based PWM is greatly simplified and modularly realized. Both the complete PWM patterns and PWM design examples with experimental results of several ANPC converters are provided to show the feasibility and modularity of the proposed method.

The geometry of flip graphs and mapping class groups

The space of topological decompositions into triangulations of a surface has a natural graph structure where two triangulations share an edge if they are related by a so-called flip. This space is a sort of combinatorial Teichmüller space and is quasi-isometric to the underlying mapping class group. We study this space in two main directions. We first show that strata corresponding to triangulations containing a same multiarc are strongly convex within the whole space and use this result to deduce properties about the mapping class group. We then focus on the quotient of this space by the mapping class group to obtain a type of combinatorial moduli space. In particular, we are able to identity how the diameters of the resulting spaces grow in terms of the complexity of the underlying surfaces.

A Computer-Aided Tool to Predict Dental Crown Prosthesis Surface Integrity after Milling

The roughness of dental prostheses surfaces, manufactured by CAD/CAM, is one of the major components of surface integrity (SI) to insure clinical success. This article aims at evaluating and quantifying the influence of the milling process characteristics on the roughness. First, the experimental results emphasize an influence of the tool grit size, the tool/prosthesis inclination and the biomaterials used on roughness. Then, based on these results, the definition of performance indicators for multi-physical and multi-indicator SI evaluation are proposed and implemented on a computer-aided tool to predict roughness. The use of this tool might help to proceed a topological decomposition of the crown to better respect the prosthetic specifications and to provide valuable assistance to the practitioner or the laboratory technician.

Heuristic Topological Decomposition Algorithm for Optimal Energy-Resource-Efficient Routing of Complex Process Pipeline Systems

A heuristic topological decomposition algorithm for optimal energy-resource-efficient routing of complex process pipeline systems was developed. The algorithm is distinguished by using an automated procedure for constructing a topological model of a hydraulic circuit as a hydraulic structural graph, a modified algorithm for finding the shortest spanning tree of the initial structural graph, and a set of heuristic rules. The developed algorithm enables one to determine the optimal energy-resource-efficient route with minimum reduced cost.

Toric Geometry ofSL2(ℂ) Free Group Character Varieties from Outer Space

AbstractCuller and Vogtmann defined a simplicial spaceO(g), calledouter space, to study the outer automorphism group of the free groupFg. Using representation theoretic methods, we give an embedding ofO(g) into the analytification of X(Fg,SL2(ℂ)), theSL2(ℂ) character variety ofFg, reproving a result of Morgan and Shalen. Then we show that every pointvcontained in a maximal cell ofO(g) defines a flat degeneration of X(Fg,SL2(ℂ)) to a toric varietyX(PΓ). We relate X(Fg,SL2(ℂ)) andX(v) topologically by showing that there is a surjective, continuous, proper map Ξv:X(Fg,SL2(ℂ)) →X(v). We then show that this map is a symplectomorphism on a dense open subset of X(Fg, SL2(ℂ)) with respect to natural symplectic structures on X(Fg, SL2(ℂ)) andX(v). In this way, we construct an integrable Hamiltonian system in X(Fg, SL2(ℂ)) for each point in a maximal cell ofO(g), and we show that eachvdefines a topological decomposition of X(Fg, SL2(ℂ)) derived from the decomposition ofX(PΓ) by its torus orbits. Finally, we show that the valuations coming from the closure of a maximal cell inO(g) all arise as divisorial valuations built from an associated projective compactification of X(Fg, SL2(ℂ)).