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Search results for: topological invariants
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Topological invariants for equivariant flows: Conley index and degree
PublicationAbout forty years have passed since Charles Conley defined the homotopy index. Thereby, he generalized the ideas that go back to the calculus of variations work of Marston Morse. Within this long time the Conley index has proved to be a valuable tool in nonlinear analysis and dynamical systems. A significant development of applied methods has been observed. Later, the index theory has evolved to cover such areas as discrete dynamical...
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Seiberg-Witten invariants the topological degree and wall crossing formula
PublicationFollowing S. Bauer and M. Furuta we investigate finite dimensional approximations of a monopole map in the case b 1 = 0. We define a certain topological degree which is exactly equal to the Seiberg-Witten invariant. Using homotopy invariance of the topological degree a simple proof of the wall crossing formula is derived.
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Topological extraordinary optical transmission
PublicationΤhe incumbent technology for bringing light to the nanoscale, the near-field scanning optical microscope, has notoriously small throughput efficiencies of the order of 10^4-10^5 or less. We report on a broadband, topological, unidirectionally guiding structure, not requiring adiabatic tapering and, in principle, enabling near-perfect (∼100%) optical transmission through an unstructured single arbitrarily subdiffraction slit at...
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Construction of phylogenetic trees with topological constraints
PublicationThis paper proposes a method of reconstruction of phylogenetic trees based on heuristic search with topological constraints. Using topological constraints it is possible to reduce the set of solutions as well as to enforce that the result is consistent with a given hypothesis about the evolution process within some group of species. Along with this work a number of algorithms used for phylogenetic analysis were implemented. Those...
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Weak forms of shadowing in topological dynamics
PublicationWe consider continuous maps of compact metric spaces. It is proved that every pseudotrajectory with sufficiently small errors contains a subsequence of positive density that is point-wise close to a subsequence of an exact trajectory with the same indices. Also, we study homeomor- phisms such that any pseudotrajectory can be shadowed by a finite number of exact orbits. In terms of numerical methods this property (we call it multishadowing)...
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On Invariants of Fluid Mechanics Tensors
PublicationThis paper presents physical interpretations of the first and second invariants of tensors of fluid mechanics. Some examples of elementary applications and meanings are also given.
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Combinatorial-topological framework for the analysis of global dynamics
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Naval electromagnetic compatibility investigations by use of topological model
PublicationPublikacja przedstawia zagadnienie uwarunkowań kompatybilnościowych na statkach. Ze względu na trudności jakie stwarza analiza EMC dużych obiektów, środowisko elektromagnetyczne okrętów jest zwykle dzielone na fragmenty analizowane oddzielnie. Referat przedstawia topologiczny model środowiska elektromagnetycznego w formie macierzowej, który pozwala na kompleksową analizę zagadnień kompatybilnościowych wielu systemów pracujących...
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On thermal stability of topological qubit in Kitaev's 4D model
PublicationWe analyse stability of the four-dimensional Kitaev model-a candidate for scalable quantum memory - in finite temperature within the weak coupling Markovian limit. It is shown that, below a critical temperature, certain topological qubit observables X and Z possess relaxation times exponentially long in the size of the system. Their construction involves polynomial in system size algorithm which uses as an input the results of...
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Magnetotransport properties of the correlated topological nodal-line semimetal YbCdGe
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Multi-objective optimization for assessment of topological modification in UWB antennas
PublicationThis paper addresses an issue of systematic and rigorous assessment of effects of topological modifications on the performance of compact UWB antennas. Application of fast surrogate-assisted multi-objective optimization procedures allows us for obtaining, in a practically acceptable timeframe, a set of designs representing the best possible trade-offs between conflicting objectives (here, antenna size minimization and reduction...
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Topological Behaviour of Solutions of Vibro-Impact Systems in the Neighborhood of Grazing
PublicationThe grazing bifurcation is considered for the Newtonian model of vibro-impact systems. A brief review on the conditions, sufficient for the existence of a grazing family of periodic solutions, is given. The properties of these periodic solutions are discussed. A plenty of results on the topological structure of attractors of vibro-impact systems is known. However, since the considered system is strongly nonlinear, these attractors...
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Topological-numerical analysis of a two-dimensional discrete neuron model
PublicationWe conduct computer-assisted analysis of a two-dimensional model of a neuron introduced by Chialvo in 1995 [Chaos, Solitons Fractals 5, 461–479]. We apply the method of rigorous analysis of global dynamics based on a set-oriented topological approach, introduced by Arai et al. in 2009 [SIAM J. Appl. Dyn. Syst. 8, 757–789] and improved and expanded afterward. Additionally, we introduce a new algorithm to analyze the return times...
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Product Graph Invariants with Applications in the Theory of Information
PublicationThere are a large number of graph invariants. In the paper, we consider some of them, e.g. the independence and chromatic numbers. It is well know that we cannot efficiently calculate these numbers for arbitrary graphs. In the paper we present relations between these invariants and concepts from the theory of information. Concepts such as source coding and transmission over a noisy channel with zero probability of error are modeled...
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Topological modifications for performance improvement and size reduction of wideband antenna structures
PublicationCompact antennas belong to the key components of modern communication systems. Their miniaturization is often achieved by introducing appropriate topological changes such as simple ground plane slots or tapered feeds. More sophisticated modifications are rarely considered in the literature because they normally lead to significant increase of the number of tunable parameters, which makes the antenna design process more challenging....
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TOPOLOGICAL CLUES FOR PREDICTING OUTCOMES OF MULTIPLAYER ONLINE BATTLE ARENA GAMES
PublicationWith 27 million people playing League of Legends every day, e-sports became more and more important part of our everyday life. Rise of its popularity builds a demand for better understanding e-sports mechanics on a deeper level. In the article, we test a hypothesis that it is possible to predict an outcome of Multiplayer Online Battle Arena game based on topological clues only (such as area of polygon where vertices are players...
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Topological, nonreciprocal, and multiresonant slow light beyond the time-bandwidth limit
PublicationTopologically protected transport has recently emerged as an effective means to address a recurring problem hampering the field of slow light for the past two decades: its keen sensitivity to disorders and structural imperfections. With it, there has been renewed interest in efforts to overcome the delay-time-bandwidth limitation usually characterizing slow-light devices, on occasion thought to be a fundamental limit. What exactly...
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Shift invariant operators and a saturation theorem.
PublicationPraca jest kontynuacją wcześniejszych dwóch prac wydanych w Appl. Math. w latach 2001 i 2002. Główny wynik dotyczy wygładzania specjalnego ciągu zbieżnego słabo, tak iż dostajemy ciąg zbieżny w normie supremum.
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Topological Model of an Electromagnetic Environment Inside a Ship for Electromagnetic Compatibility (EMC) Analysis
PublicationThe mutual electromagnetic (EM) interactions between electrical and electronic devices in a segmented space, such as a ship's environment, ared described. Firstly, the topological structure of a ship's segmented internal environment, which consists of many electrical screening walls (shielding planes), is presented. Then, taking into account the ship's topological structure, a general description of the EM disturbance distribution,...
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Topological behavior mimicking ethylene–hexene copolymers using branched lactones and macrolactones
PublicationPolyolefins are of paramount importance in the world of polymers due to their technological and economic potential.1 However, their nonpolar character significantly restricts the compatibility and adhesion properties, which consequently limits their versatility. Moreover, an intensified demand for materials from renewable resources can also become a problematic venture for the current polyolefin industry.2 Although Braskem and...
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Rotationally invariant bipartite states and bound entanglement
PublicationW pracy rozważano stany kwantowe niezmiennicze na działanie grupy SO(3). Pokazano, że w przypadku, gdy pierwszy podukład ma parzysty wymiar większy lub równy cztery oraz drugi podukład ma wymiar dowolny, większy niż pierwszy to pośród takich stanów zawsze istnieje splątanie związane.
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A Note on Shannon Capacity for Invariant and Evolving Channels
PublicationIn the paper we discuss the notion of Shannon capacity for invariant and evolving channels. We show how this notion is involved in information theory, graph theory and Ramsey theory.
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Invariant Measures for Uncountable Random Interval Homeomorphisms
PublicationA necessary and sufficient condition for the iterated function system { f (·, ω) | ω ∈ } with probability P to have exactly one invariant measure μ∗ with μ∗((0, 1)) = 1 is given. The main novelty lies in the fact that we only require the transformations f (·, ω) to be increasing homeomorphims, without any smoothness condition, nei- ther we impose conditions on the cardinality of . In particular, positive Lyapunov exponents conditions...
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Topological degree for equivariant gradient perturbations of an unbounded self-adjoint operator in Hilbert space
PublicationWe present a version of the equivariant gradient degree defined for equivariant gradient perturbations of an equivariant unbounded self-adjoint operator with purely discrete spectrum in Hilbert space. Two possible applications are discussed.
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Large nonsaturating magnetoresistance, weak anti-localization, and non-trivial topological states in SrAl2Si2
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Algorytmy samostabilizujące w sieciach o wybranych topologiach
PublicationIdea algorytmów samostabilizujących została zapoczątkowana przez E. Dijkstrę artykułem pt. „Self-stabilizing systems in spite of distributed control” (Communications of the ACM, 1974). W rozprawie został położony nacisk na algorytmy samostabilizujące działające w sieciach o pewnych specyficznych topologiach, jak na przykład w grafach maksymalnych zewnętrznie planarnych, iloczynach kartezjańskich tych grafów ze ścieżkami i w drzewach. Wykorzystując...
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Insight into the influence of polymer topological structure on the exfoliation of clay in polystyrene matrix via annealing process
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Generic invariant measures for iterated systems of interval homeomorphisms
PublicationIt is well known that iterated function systems generated by orientation preserving homeomorphisms of the unit interval with positive Lyapunov exponents at its ends admit a unique invariant measure on (0, 1) provided their action is minimal. With the additional requirement of continuous differentiability of maps on a fixed neighbourhood of {0,1} { 0 , 1 } , we present a metric in the space of such systems which renders it complete....
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Structural stability of invariant sets of vibro-impact systems
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Camera angle invariant shape recognition in surveillance systems
PublicationA method for human action recognition in surveillance systems is described. Problems within this task are discussed and a solution based on 3D object models is proposed. The idea is shown and some of its limitations are talked over. Shape description methods are introduced along with their main features. Utilized parameterization algorithm is presented. Classification problem, restricted to bi-nary cases is discussed. Support vector...
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New variants of the SDF classifier
PublicationPraca dotyczy problemów związanych z konstruowaniem klasyfikatorów, w których typowa wektorowa reprezentacja obrazu została zastapiona danymi o strukturze macierzowej. W pracy zaproponowano nowe algorytmy oparte na funkcji SDF. Zostały one przetestowane na obrazach przedstawiających cyfry pisane ręcznie oraz na zdjęciach twarzy. Przeprowadzone eksperymenty pozwalają stwierdzić, że wprowadzone modyfikacje istotnie zwiększyły skuteczność...
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Theological Intersections: Newman’s ‘Primacy of God’ in Modern Church Discourse
PublicationThis article critically examines the Catholic–Anglican theological dialogue, centering on John Henry Newman’s ‘Primacy of God’, Catholic synodality, and Anglican comprehensiveness. It illuminates the interconnectedness of these elements, revealing their potential to enhance ecumenical conversations. Newman’s concept of communal faith and divine primacy resonates across both traditions, advocating a transformative,...
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Specification-Oriented Automatic Design of Topologically Agnostic Antenna Structure
PublicationDesign of antennas for modern applications is a challenging task that combines cognition-driven development of topology intertwined with tuning of its parameters using rigorous numerical optimization. However, the process can be streamlined by neglecting the engineering insight in favor of automatic de-termination of structure geometry. In this work, a specification-oriented design of topologically agnostic antenna is considered....
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Performance Comparison of Automatically Generated Topologically Agnostic Patch Antennas
PublicationReal-world antenna design typically relies on empirical methods, where the development starts with structure synthesis followed by its iterative adjustments to achieve the desired performance. Although the outlined approach proved to be successful, it is also dependent on engineering experience. Alternatively, development can be performed automatically based on the specifications. In this work, an unsupervised design of topologically...
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Topological model of aptitude of the measurement circuits of main subassemblies of an internal combustion engine crankshaft-piston assembly
PublicationThe paper presents a topological model allowing to determine the probability of aptitude of the diagnosing system (SDG) individual measuring circuits and also to determine to what degree they influence the assessment of the technical condition of an arbitrary main subassembly of crankshaft-piston assemblies as a diagnosed system (SDN).
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Invariant measures for interval translations and some other piecewise continuous maps
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Chaotic invariant sets of vibro-impact systems with one degree of freedom
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RAILWAY WATER TOWERS OF WESTERN POLAND – HISTORIC NETWORKED ARCHITECTURAL RESOURCE AND ITS TYPOLOGICAL STRUCTURE
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Fourier transform symmetry and invariance for neurocontrol of NARMA models
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Computation of cubical homology, cohomology, and (co)homological operations via chain contraction
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Structures for parameterization, meshing and data exchange of topologically related surfaces of a ship hull
PublicationThis paper presents proposal of data structures for storage and processing of a parametric three-dimensional model of a midship hull sections. The model consists of coarse surfaces like: decks, frames, girders, stiffeners, brackets, partitions etc. bounded by topological relations. All workshop details are omitted as the model is intended for numeric calculations. Proposed data structures are prepared to facilitate changes in the...
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Osmotic MD and other membrane distillation variants
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Survivin splice variants expression in thyroid malignancy
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Evaluation of survivin splice variants in pituitary tumors
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Gauge-invariant theory of the Meissner effect in the lattice model of a superconductor with local pairing
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Common variants of DNA repair genes and malignant melanoma
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Environmental costs for exploitation variants of Racibórz dry polder
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Pose-Invariant Face Detection by Replacing Deep Neurons with Capsules for Thermal Imagery in Telemedicine
PublicationAbstract— The aim of this work was to examine the potential of thermal imaging as a cost-effective tool for convenient, non- intrusive remote monitoring of elderly people in different possible head orientations, without imposing specific behavior on users, e.g. looking toward the camera. Illumination and pose invariant head tracking is important for many medical applications as it can provide information, e.g. about vital signs, sensory...
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Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces
PublicationIn this paper we introduce a new compactness condition — Property-(C) — for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be developed. For example (regular) index pairs always exist for Property-(C) flows and a Conley index can be defined. An important class of flows satisfying the this compactness condition are LS-flows. We apply E-cohomology to index pairs of LS-flows and obtain...
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Algebraic periods and minimal number of periodic points for smooth self-maps of 1-connected 4-manifolds with definite intersection forms
PublicationLet M be a closed 1-connected smooth 4-manifolds, and let r be a non-negative integer. We study the problem of finding minimal number of r-periodic points in the smooth homotopy class of a given map f: M-->M. This task is related to determining a topological invariant D^4_r[f], defined in Graff and Jezierski (Forum Math 21(3):491–509, 2009), expressed in terms of Lefschetz numbers of iterations and local fixed point indices of...