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Search results for: CLASSIFICATION OF T-EQUIVARIANT MAPS
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Classification of homotopy classes of equivariant gradient maps
PublicationNiech V będzie ortogonalną reprezentacją zwartej grupy Liego Gi niech S(V),D(V) oznaczają sferę jednostkową i kulę jednostkową V.Jeżeli F jest G-niezmienniczą funkcją rzeczywistą klasy C^1 na Vto mówimy, że grad F (gradient F) jest dopuszczalny, jeżeli(grad F)(x) jest różny od zera dla x należących do S(V). Pracapoświęcona jest homotopijnej klasyfikacji dopuszczalnychG-niezmienniczych odwzorowań gradientowych.
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Degree of T-equivariant maps in R^n
PublicationW pracy przedstawiona jest konstrukcja niezmienniczego stopnia topologicznego dla odwzorowań z symetriami działających na przestrzeni euklidesowej z inwolucją. Udowodnione jest twierdzenie, że dwa dopuszczalne i gradientowe odwzorowania niezmiennicze są niezmienniczo homotopijne wtedy i tylko wtedy, gdy są one homotopijne niezmienniczo i gradientowo.
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A Hopf type theorem for equivariant local maps
PublicationWe study otopy classes of equivariant local maps and prove a Hopf type theorem for such maps in the case of a real finite-dimensional orthogonal representation of a compact Lie group.
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On the space of equivariant local maps
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Otopy classes of equivariant maps
PublicationW artykule definiuje się stopień topologiczny niezmienniczych odwzorowań lokalnych w przypadku gradientowym i niegradientowym. Wyniki dotyczą relacji pomiędzy tymi dwoma niezmiennikami topologicznymi.
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The Hopf type theorem for equivariant gradient local maps
PublicationWe construct a degree-type otopy invariant for equivariant gradient local maps in the case of a real finite-dimensional orthogonal representation of a compact Lie group. We prove that the invariant establishes a bijection between the set of equivariant gradient otopy classes and the direct sum of countably many copies of Z.
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Fixed orbit index for equivariant maps
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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublicationConsider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...
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Fixed point index for $G$-equivariant multivalued maps
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Equivariant degree of convex-valued maps applied to set-valued BVP
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Standard of living in Poland at regional level - classification with Kohonen self-organizing maps
PublicationThe standard of living is spatially diversified and its analyzes enable shaping regional policy. Therefore, it is crucial to assess the standard of living and to classify regions due to their standard of living, based on a wide set of determinants. The most common research methods are those based on composite indicators, however, they are not ideal. Among the current critiques moved to the use of composite...
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Ecotoxicity and chemical sediment data classification by the useof self-organising maps
PublicationArtykuł dotyczy przedstawiania nowej interpretacji szacowania jakości osadów. To oryginalne podejście bada powiązania między parametrami ekotoksyczności (ostrej i chronicznej) i składnikami chemicznymi (zanieczyszczenia takie jak polichlorowane bifenyle, pestycydy, wielopierścieniowe węglowodory aromatyczne, metale ciężkie) próbek osadów Jeziora Turawskiego (Polska) poprzez zastosowanie samoorganizujących się map (SOM) wobec badanego...
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Towards classification of patients based on surface EMG data of temporomandibular joint muscles using self-organising maps
PublicationThe study considers the need for an effective method of classification of patients with a temporomandibular joint disorder (TMD). The self-organising map method (SOM) was applied to group patients and used together with the cross-correlation approach to interpret the processed (rectified and smoothed by using root mean square (RMS) algorithm) surface electromyography signal (sEMG) obtained from testing the muscles (two temporal...
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Towards classification of patients based on surface EMG data of temporomandibular joint muscles using self-organising maps
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On relations between gradient and classical equivariant homotopy groups of spheres
PublicationWe investigate relations between stable equivariant homotopy groups of spheres in classical and gradient categories. To this end, the auxiliary category of orthogonal equivariant maps, a natural enlargement of the category of gradient maps, is used. Our result allows for describing stable equivariant homotopy groups of spheres in the category of orthogonal maps in terms of classical stable equivariant groups of spheres with shifted...
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Self-organizing maps classification of epidemiological data and toenail selenium content monitored on cancer and healthy patients from Poland
PublicationW pracy przedstawiono wyniki wielowymiarowej analizy danych pomiarowych (przy wykorzystaniu techniki samoorganizującej sie mapy (SOM))nad oszacowaniem zawartości selenu w próbkach paznokci pobranych od mieszkańców Województwa Pomorskiego ((w tym od grupy osób zdrowych i ze zdiagnozowaną chorobą nowotworową) i Lubuskiego. W wyniku przeprowadzonej analizy uzyskano podział uczestników ze zdiagnozowanym nowotworem na trzy różne grupy:1...
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Degree product formula in the case of a finite group action
PublicationLet V, W be finite dimensional orthogonal representations of a finite group G. The equivariant degree with values in the Burnside ring of G has been studied extensively by many authors. We present a short proof of the degree product formula for local equivariant maps on V and W.
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Analysis of 2D Feature Spaces for Deep Learning-based Speech Recognition
Publicationconvolutional neural network (CNN) which is a class of deep, feed-forward artificial neural network. We decided to analyze audio signal feature maps, namely spectrograms, linear and Mel-scale cepstrograms, and chromagrams. The choice was made upon the fact that CNN performs well in 2D data-oriented processing contexts. Feature maps were employed in the Lithuanian word recognition task. The spectral analysis led to the highest word...
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Interpretable deep learning approach for classification of breast cancer - a comparative analysis of multiple instance learning models
PublicationBreast cancer is the most frequent female cancer. Its early diagnosis increases the chances of a complete cure for the patient. Suitably designed deep learning algorithms can be an excellent tool for quick screening analysis and support radiologists and oncologists in diagnosing breast cancer.The design of a deep learning-based system for automated breast cancer diagnosis is not easy due to the lack of annotated data, especially...
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Offshore benthic habitat mapping based on object-based image analysis and geomorphometric approach. A case study from the Slupsk Bank, Southern Baltic Sea
PublicationBenthic habitat mapping is a rapidly growing field of underwater remote sensing studies. This study provides the first insight for high-resolution hydroacoustic surveys in the Slupsk Bank Natura 2000 site, one of the most valuable sites in the Polish Exclusive Zone of the Southern Baltic. This study developed a quick and transparent, automatic classification workflow based on multibeam echosounder and side-scan sonar surveys to...
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Spike patterns and chaos in a map-based neuron model
PublicationThe work studies the well-known map-based model of neuronal dynamics introduced in 2007 by Courbage, Nekorkin and Vdovin, important due to various medical applications. We also review and extend some of the existing results concerning β-transformations and (expanding) Lorenz mappings. Then we apply them for deducing important properties of spike-trains generated by the CNV model and explain their implications for neuron behaviour....
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Visual Features for Improving Endoscopic Bleeding Detection Using Convolutional Neural Networks
PublicationThe presented paper investigates the problem of endoscopic bleeding detection in endoscopic videos in the form of a binary image classification task. A set of definitions of high-level visual features of endoscopic bleeding is introduced, which incorporates domain knowledge from the field. The high-level features are coupled with respective feature descriptors, enabling automatic capture of the features using image processing methods....
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Attention-Based Deep Learning System for Classification of Breast Lesions—Multimodal, Weakly Supervised Approach
PublicationBreast cancer is the most frequent female cancer, with a considerable disease burden and high mortality. Early diagnosis with screening mammography might be facilitated by automated systems supported by deep learning artificial intelligence. We propose a model based on a weakly supervised Clustering-constrained Attention Multiple Instance Learning (CLAM) classifier able to train under data scarcity effectively. We used a private...
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Equivariant Morse equation
PublicationThe paper is concerned with the Morse equation for flows in a representation of a compact Lie group. As a consequence of this equation we give a relationship between the equivariant Conley index of an isolated invariant set of the flow given by x˙ = − ∇f(x) and the gradient equivariant degree of ∇f. Some multiplicity results are also presented.
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Surface water quality assessment by the use of combination of multivariate statistical classification and expert information
PublicationThe present study deals with the assessment of surface water quality from an industrial-urban region located in northern Poland near to the city of Gdansk. Concentrations of thirteen chemicals includingtotal polycyclic aromatic hydrocarbons (PAHs), halogenated volatile organic compounds (HVOCs) and major ions in the samples collected at five sampling points during six campaigns were used as variablesthroughout the study. The originality...
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MACHINE LEARNING–BASED ANALYSIS OF ENGLISH LATERAL ALLOPHONES
PublicationAutomatic classification methods, such as artificial neural networks (ANNs), the k-nearest neighbor (kNN) and selforganizing maps (SOMs), are applied to allophone analysis based on recorded speech. A list of 650 words was created for that purpose, containing positionally and/or contextually conditioned allophones. For each word, a group of 16 native and non-native speakers were audio-video recorded, from which seven native speakers’...
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Distribution and extent of benthic habitats in Puck Bay (Gulf of Gdańsk, southern Baltic Sea)
PublicationThe majority of the southern Baltic Sea seabed encompasses homogenous soft-bottom sediments of limited productivity and low biological diversity, but shallow productive areas in the coastal zone such as wetlands, vegetated lagoons and sheltered bays show a high variety of benthic habitat types offering favourable biotopic conditions for benthic fauna. Within Polish marine areas, semi-enclosed Puck Bay (the western part of the...
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Multibeam Sonar Characterisation of Seafloor in the Context of Visualisation and Dissemination of Marine Data
PublicationThe paper presents the seafloor characterisation method based on multibeam sonar data. it relies on using three types of multibeam seafloor sensing data: 1) the grey-level sonar images (echograms) of seabed, 2) the 3D model of the seabed surface which consists of high resolution bathymetric data, 3) the set of time domain bottom echo envelopes received in the consecutive sonar beams. The classification is performed by utilisation...
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INWESTYCJE ALTERNATYWNE – OPŁACALNOŚĆ A RYZYKO
PublicationW rozprawie określono pojęcie oraz miejsce inwestycji alternatywnych na rynku inwestycyjnym. Wskazane zostały atrybuty tych inwestycji. Zbudowano klasyfikację inwestycji alternatywnych w podziale na kategorie oraz typy wraz ze wskazaniem powiązań pomiędzy poszczególnymi produktami. Dokonano autorskiego podziału analizowanych inwestycji na aktywne i pasywne. Zbadano stopę zwrotu i ryzyko pięćdziesięciu inwestycji alternatywnych,...
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The equivariant spectral flow and bifurcation of periodic solutions of Hamiltonian systems
PublicationWe define a spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the orthogonal action of a compact Lie group as an element of the representation ring of the latter. This G-equivariant spectral flow shares all common properties of the integer valued classical spectral flow, and it can be non-trivial even if the classical spectral flow vanishes. Our main theorem uses the G-equivariant spectral flow...
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Wild oscillations in a nonlinear neuron model with resets: (II) Mixed-mode oscillations
PublicationThis work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation and spike emission. We show that these models can generically display a form of mixed-mode oscillations (MMOs), which are trajectories featuring an alternation of small oscillations with spikes or bursts (multiple consecutive spikes). The mechanism by...
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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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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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Chemical composition of water from roof in Gdańsk, Poland
PublicationThis study deals with the assessment of roof runoff waters from the region of Gdansk collected during the winter season (2007/2008). The chemical analysis includes 16 chemical variables: major ions, PAHs and PCBs measured at 3 sampling sites for 6-14 rain events. Although the data set is of limited volume the statistical data treatment using self-organizing maps (SOM) reveals the main factors controlling roof runoff water quality...
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Software for calculation of noise maps implemented on the supercomputer
PublicationThis paper presents investigation results relevant to the implementation of the algorithms for the calculation of noise maps. The aim of the implementation of the algorithms on the computer cluster is explained. Selected implementation details of the software called the noise propagation model are described. The interaction of the software with the data acquisition system is presented. Noise maps obtained by exploitation of the...
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On structural physical approximations and entanglement breaking maps
PublicationVery recently, a conjecture saying that the so-called structural physical approximations (SPAs) to optimal positive maps (optimal entanglement witnesses) give entanglement breaking (EB) maps (separable states) has been posed (Korbicz et al 2008 Phys. Rev. A 78 062105). The main purpose of this contribution is to explore this subject. First, we extend the set of entanglement witnesses supporting the conjecture. Then, we ask whether...
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AI in the creation of the satellite maps
PublicationSatellite and aerial imagery acquisition is a very useful source of information for remote monitoring of the Earth’s surface. Modern satellite and aerial systems provide data about the details of the site topography, its characteristics due to different criteria (type of terrain, vegetation cover, soil type and moisture content), or even information about emergency situations or disasters. The paper proposes and discusses the process...
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Creating Acoustic Maps Employing Supercomputing Cluster
PublicationThe implemented online urban noise pollution monitoring system is presented with regard to its conceptual assumptions and technical realization. A concept of the noise source parameters dynamic assessment is introduced. The idea of noise modeling, based on noise emission characteristics and emission simulations, was developer and practically utilized in the system. Furthermore, the working system architecture and the data acquisition...
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Periodic Points for Sphere Maps Preserving MonopoleFoliations
PublicationLet S^2 be a two-dimensional sphere. We consider two types of its foliations with one singularity and maps f:S^2→S^2 preserving these foliations, more and less regular. We prove that in both cases f has at least |deg(f)| fixed points, where deg(f) is a topological degree of f. In particular, the lower growth rate of the number of fixed points of the iterations of f is at least log|deg(f)|. This confirms the Shub’s conjecture in...
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Improving depth maps of plants by using a set of five cameras
PublicationObtaining high-quality depth maps and disparity maps with the use of a stereo camera is a challenging task for some kinds of objects. The quality of these maps can be improved by taking advantage of a larger number of cameras. The research on the usage of a set of five cameras to obtain disparity maps is presented. The set consists of a central camera and four side cameras. An algorithm for making disparity maps called multiple...
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Data visualization of marine objects on digital maps
PublicationThe paper presents the implementation of two multithreaded applications for data visualization of marine objects written in C#, designed to run on operator consoles with 32-bit or 64-bit Windows 7 OS. The article describes the most important functionality and features of the developed C# .NET user controls for data visualization on digital maps and in the configurable tables.
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Lefschetz periodic point free self-maps of compact manifolds
PublicationLet f be a self-map of a compact connected manifold M. We characterize Lefschetz periodic point free continuous self-maps of M for several classes of manifolds and generalize the results of Guirao and Llibre [J.L.G. Guirao, J. Llibre, On the Lefschetz periodic point free continuous self-maps on connected compact manifolds,
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Music Mood Visualization Using Self-Organizing Maps
PublicationDue to an increasing amount of music being made available in digital form in the Internet, an automatic organization of music is sought. The paper presents an approach to graphical representation of mood of songs based on Self-Organizing Maps. Parameters describing mood of music are proposed and calculated and then analyzed employing correlation with mood dimensions based on the Multidimensional Scaling. A map is created in which...
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Lefschetz periodic point free self-maps of compact manifolds
PublicationLet f be a self-map of a compact connected manifold M. We characterize Lefschetz periodic point free continuous self-maps of M for several classes of manifolds and generalize the results of Guirao and Llibre [J.L.G. Guirao, J. Llibre, On the Lefschetz periodic point free continuous self-maps on connected compact manifolds, Topology Appl. 158 (16) (2011) 2165-2169].
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Application of two-dimensional intensity maps in high-accuracy polarimetry
PublicationWe propose the analysis of 2D intensity contour maps which is based on the optical transmission function for the polarizer-specimen-analyzer system. A small modification of the high-accuracy universal polarimeter (HAUP) technique was used to measure the intensity maps (HAUP maps) and determine the phase retardation, linear dichroism (LD) parameters, and multiple light reflection contribution in uniaxial crystals. We have performed...
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Physics augmented classification of fNIRS signals
PublicationBackground. Predictive classification favours performance over semantics. In traditional predictive classification pipelines, feature engineering is often oblivious to the underlying phenomena. Hypothesis. In applied domains such as functional Near Infrared Spectroscopy (fNIRS), the exploitation of physical knowledge may improve the discriminative quality of our observation set. Aims. Give exemplary evidence that intervening the...
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Shub’s conjecture for smooth longitudinal maps of S^m
PublicationLet f be a smooth map of the m-dimensional sphere Sm to itself, preserving the longitudinal foliation. We estimate from below the number of fixed points of the iterates of f , reduce Shub’s conjecture for longitudinal maps to a lower dimensional classical version, and prove the conjecture in case m = 2 and in a weak form for m = 3.
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Selections and approximations of convex-valued equivariant mappings
PublicationUdowodniono szereg twierdzeń o współzmienniczych selekcjach i aproksymacjach ciągłych, mierzalnych i typu Caratheodory'ego dla odwzorowań G-współzmienniczych o wartościach wypukłych, gdzie G jest grupą zwartą Liego. Tw. typu Michaela, Celliny, Browdera, Kuratowskiego-Ryll-Nardzewskiego, Castaing itd.
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Otopy Classification of Gradient Compact Perturbations of Identity in Hilbert Space
PublicationWe prove that the inclusion of the space of gradient local maps into the space of all local maps from Hilbert space to itself induces a bijection between the sets of the respective otopy classes of these maps, where by a local map we mean a compact perturbation of identity with a compact preimage of zero.
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Seabed classification using multibeam echosounder
PublicationThe method of seabed identification and classification from multibeam sonar echoes is presented. The proposed approach is based on calculation of a set of parameters of an echo envelope, similarly as in seafloor classification using single beam echosounder. These parameters are extracted for each consecutive beam allowing the estimation of their dependence on the seafloor incident angle. The relation between seabed type and calculated...