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    Tytuł:
    Théorèmes de factorisation dans les algèbres normées complètes non associatives
    Autorzy:
    Akkar, M.
    Laayouni, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/966861.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Jordan-Banach algebras
    factorization
    Źródło:
    Colloquium Mathematicum; 1996, 70, 2; 253-264
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Note on cyclic decompositions of complete bipartite graphs into cubes
    Autorzy:
    Fronček, Dalibor
    Powiązania:
    https://bibliotekanauki.pl/articles/744154.pdf
    Data publikacji:
    1999
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    hypercubes
    bipartite graphs
    factorization
    Opis:
    So far, the smallest complete bipartite graph which was known to have a cyclic decomposition into cubes $Q_d$ of a given dimension d was $K_{d2^{d-1}, d2^{d-2}}$. We improve this result and show that also $K_{d2^{d-2}, d2^{d-2}}$ allows a cyclic decomposition into $Q_d$. We also present a cyclic factorization of $K_{8,8}$ into Q₄.
    Źródło:
    Discussiones Mathematicae Graph Theory; 1999, 19, 2; 219-227
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Unique prime factorization in a partial semigroup of matrix-polynomials
    Autorzy:
    Kaltenbäck, Michael
    Woracek, Harald
    Powiązania:
    https://bibliotekanauki.pl/articles/729169.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    partial semigroup
    unique prime factorization
    Opis:
    We establish a unique factorization result into irreducibel elements in the partial semigroup of 2 × 2-matrices with entries in K[x] whose determinant is equal to 1, where K is a field, and where multiplication is defined as the usual matrix-multiplication if the degrees of the factors add up. This investigation is motivated by a result on matrices of entire functions.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2006, 26, 1; 21-43
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A method of approximate factorization of positive definite matrix functions
    Autorzy:
    Janashia, Gigla
    Lagvilava, Edem
    Powiązania:
    https://bibliotekanauki.pl/articles/1216256.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    positive definite matrix function
    factorization
    Opis:
    An algorithm of factorization of positive definite matrix functions of second order is proposed.
    Źródło:
    Studia Mathematica; 1999, 137, 1; 93-100
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solution to the problem of Kubesa
    Autorzy:
    Meszka, Mariusz
    Powiązania:
    https://bibliotekanauki.pl/articles/743037.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    tree
    T-factorization
    degree sequence
    Opis:
    An infinite family of T-factorizations of complete graphs $K_{2n}$, where 2n = 56k and k is a positive integer, in which the set of vertices of T can be split into two subsets of the same cardinality such that degree sums of vertices in both subsets are not equal, is presented. The existence of such T-factorizations provides a negative answer to the problem posed by Kubesa.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2008, 28, 2; 375-378
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On twin edge colorings of graphs
    Autorzy:
    Andrews, Eric
    Helenius, Laars
    Johnston, Daniel
    VerWys, Jonathon
    Zhang, Ping
    Powiązania:
    https://bibliotekanauki.pl/articles/30148690.pdf
    Data publikacji:
    2014-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    edge coloring
    vertex coloring
    factorization
    Opis:
    A twin edge $k$-coloring of a graph $G$ is a proper edge coloring of $G$ with the elements of $\mathbb{Z}_k$ so that the induced vertex coloring in which the color of a vertex $v$ in $G$ is the sum (in $\mathbb{Z}_k$) of the colors of the edges incident with $v$ is a proper vertex coloring. The minimum $k$ for which $G$ has a twin edge $k$-coloring is called the twin chromatic index of $G$. Among the results presented are formulas for the twin chromatic index of each complete graph and each complete bipartite graph
    Źródło:
    Discussiones Mathematicae Graph Theory; 2014, 34, 3; 613-627
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Decomposing complete graphs into cubes
    Autorzy:
    El-Zanati, Saad
    Eynden, C.
    Powiązania:
    https://bibliotekanauki.pl/articles/743903.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph decomposition
    graph factorization
    d-cube
    Opis:
    This paper concerns when the complete graph on n vertices can be decomposed into d-dimensional cubes, where d is odd and n is even. (All other cases have been settled.) Necessary conditions are that n be congruent to 1 modulo d and 0 modulo $2^d$. These are known to be sufficient for d equal to 3 or 5. For larger values of d, the necessary conditions are asymptotically sufficient by Wilson's results. We prove that for each odd d there is an infinite arithmetic progression of even integers n for which a decomposition exists. This lends further weight to a long-standing conjecture of Kotzig.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2006, 26, 1; 141-147
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Cyclic decompositions of complete graphs into spanning trees
    Autorzy:
    Froncek, Dalibor
    Powiązania:
    https://bibliotekanauki.pl/articles/744515.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph factorization
    graph labelling
    spanning trees
    Opis:
    We examine decompositions of complete graphs with an even number of vertices, $K_{2n}$, into n isomorphic spanning trees. While methods of such decompositions into symmetric trees have been known, we develop here a more general method based on a new type of vertex labelling, called flexible q-labelling. This labelling is a generalization of labellings introduced by Rosa and Eldergill.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2004, 24, 2; 345-353
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Distributed accelerated projection-based consensus decomposition
    Autorzy:
    Maj, Wiktor
    Powiązania:
    https://bibliotekanauki.pl/articles/2197532.pdf
    Data publikacji:
    2022
    Wydawca:
    Politechnika Gdańska
    Tematy:
    factorization approximation
    numerical optimization
    distributed computing
    acceleration
    Opis:
    With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using distinctive optimization algorithms, iterative methods, or heuristics. A new variant of the Accelerated Projection-Based Consensus (APC) iterative method is proposed, which is faster than its classical version while handling large sparse matrices in distributed settings. The algorithm is proposed, and its description and implementation in a high-level programming language are presented. Convergence tests measuring acceleration factors based on real-world datasets are done, and their results are promising. The results of this research can be used as an alternative to solving numerical optimization problems.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2022, 26, 2; 32-38
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Unique factorisation of additive induced-hereditary properties
    Autorzy:
    Farrugia, Alastair
    Richter, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/744519.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    additive and hereditary graph classes
    unique factorization
    Opis:
    An additive hereditary graph property is a set of graphs, closed under isomorphism and under taking subgraphs and disjoint unions. Let ₁,...,ₙ be additive hereditary graph properties. A graph G has property (₁∘...∘ₙ) if there is a partition (V₁,...,Vₙ) of V(G) into n sets such that, for all i, the induced subgraph $G[V_i]$ is in $_i$. A property is reducible if there are properties , such that = ∘ ; otherwise it is irreducible. Mihók, Semanišin and Vasky [8] gave a factorisation for any additive hereditary property into a given number dc() of irreducible additive hereditary factors. Mihók [7] gave a similar factorisation for properties that are additive and induced-hereditary (closed under taking induced-subgraphs and disjoint unions). Their results left open the possiblity of different factorisations, maybe even with a different number of factors; we prove here that the given factorisations are, in fact, unique.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2004, 24, 2; 319-343
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Ascending Subgraph Decompositions of Oriented Graphs that Factor into Triangles
    Autorzy:
    Austin, Andrea D.
    Wagner, Brian C.
    Powiązania:
    https://bibliotekanauki.pl/articles/32304154.pdf
    Data publikacji:
    2022-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    ascending subgraph decomposition
    graph factorization
    Oberwolfach problem
    Opis:
    In 1987, Alavi, Boals, Chartrand, Erdős, and Oellermann conjectured that all graphs have an ascending subgraph decomposition (ASD). In a previous paper, Wagner showed that all oriented complete balanced tripartite graphs have an ASD. In this paper, we will show that all orientations of an oriented graph that can be factored into triangles with a large portion of the triangles being transitive have an ASD. We will also use the result to obtain an ASD for any orientation of complete multipartite graphs with 3n partite classes each containing 2 vertices (a K(2 : 3n)) or 4 vertices (a K(4 : 3n)).
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 3; 811-822
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Moving cast shadow detection using block nonnegative matrix factorization
    Autorzy:
    Yang, X.
    Liu, D.
    Zhou, D.
    Yang, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/200448.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    moving cast shadow detection
    video surveillance
    nonnegative matrix factorization
    block nonnegative matrix factorization
    nadzór wideo
    nieujemna faktoryzacja macierzy
    Opis:
    In recent years, moving cast shadow detection has become a critical challenge in improving the accuracy of moving object detection in video surveillance. In this paper, we propose two novel moving cast shadow detection methods based on nonnegative matrix factorization (NMF) and block nonnegative matrix factorization (BNMF). First, the algorithm of moving cast shadow detection using NMF is given and the key points such as the determination of moving shadow areas and the choice of discriminant function are specified. Then BNMF are introduced so that the new training samples and new classes can be added constantly with lower computational complexity. Finally, the improved shadow detection method is detailed described according to BNMF. The effectiveness of proposed methods is evaluated in various scenes. Experimental results demonstrate that the method achieves high detection rate and outperforms several state-of-the-art methods.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 2; 229-234
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Gregarious Kite Factorization of Tensor Product of Complete Graphs
    Autorzy:
    Tamil Elakkiya, A.
    Muthusamy, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/31804152.pdf
    Data publikacji:
    2020-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    tensor product
    kite
    decomposition
    gregarious factor
    factorization
    Opis:
    A kite factorization of a multipartite graph is said to be gregarious if every kite in the factorization has all its vertices in different partite sets. In this paper, we show that there exists a gregarious kite factorization of Km × Kn if and only if mn ≡ 0 (mod 4) and (m − 1)(n − 1) ≡ 0 (mod 2), where × denotes the tensor product of graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 1; 7-24
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A newly developed method for computing reliability measures in a water supply network
    Autorzy:
    Malinowski, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/406322.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
    Tematy:
    water supply network
    reliability
    series-parallel aggregation
    factorization
    Opis:
    A reliability model of a water supply network has beens examined. Its main features are: a topology that can be decomposed by the so-called state factorization into a (relatively)small number of derivative networks, each having a series-parallel structure (1), binary-state components (either operative or failed) with given flow capacities (2), a multi-state character of the whole network and its sub-networks – a network state is defined as the maximal flow between a source (sources) and a sink (sinks) (3), all capacities (component, network, and sub-network) have integer values (4). As the network operates, its state changes due to component failures, repairs, and replacements. A newly developed method of computing the inter-state transition intensities has been presented. It is based on the so-called state factorization and series-parallel aggregation. The analysis of these intensities shows that the failure-repair process of the considered system is an asymptotically homogenous Markov process. It is also demonstrated how certain reliability parameters useful for the network maintenance planning can be determined on the basis of the asymptotic intensities. For better understanding of the presented method, an illustrative example is given.
    Źródło:
    Operations Research and Decisions; 2016, 26, 4; 49-64
    2081-8858
    2391-6060
    Pojawia się w:
    Operations Research and Decisions
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On unique factorization semilattices
    Autorzy:
    Silva, Pedro
    Powiązania:
    https://bibliotekanauki.pl/articles/728874.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    semilattice
    factorization
    principal ideal
    semilattice embedding
    Munn semigroup
    Opis:
    The class of unique factorization semilattices (UFSs) contains important examples of semilattices such as free semilattices and the semilattices of idempotents of free inverse monoids. Their structural properties allow an efficient study, among other things, of their principal ideals. A general construction of UFSs from arbitrary posets is presented and some categorical properties are derived. The problem of embedding arbitrary semilattices into UFSs is considered and complete characterizations are obtained for particular classes of semilattices. The study of the Munn semigroup for regular UFSs is developed and a complete characterization is accomplished with respect to being E-unitary.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 1; 97-120
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Orthogonal double covers of complete graphs by fat caterpillars
    Autorzy:
    Froncek, Dalibor
    Leck, Uwe
    Powiązania:
    https://bibliotekanauki.pl/articles/743983.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    ODC
    orthogonal double cover
    graph decomposition
    self-orthogonal factorization
    Opis:
    An orthogonal double cover (ODC) of the complete graph Kₙ by some graph G is a collection of n spanning subgraphs of Kₙ, all isomorphic to G, such that any two of the subgraphs share exactly one edge and every edge of Kₙ is contained in exactly two of the subgraphs. A necessary condition for such an ODC to exist is that G has exactly n-1 edges. We show that for any given positive integer d, almost all caterpillars of diameter d admit an ODC of the corresponding complete graph.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2006, 26, 2; 343-349
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    RSA Keys Quality in a Real-world Organizational Certificate Dataset: a Practical Outlook
    Autorzy:
    Kamiński, Konrad
    Mazurczyk, Wojciech
    Powiązania:
    https://bibliotekanauki.pl/articles/27311954.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    certificates
    X.509
    RSA keys
    PKI
    vulnerabilities
    RSA factorization
    Opis:
    This research investigates the intricacies of X.509 certificates within a comprehensive corporate infrastructure. Spanning over two decades, the examined enterprise has heavily depended on its internal certificate authority and Public Key Infrastructure (PKI) to uphold its data and systems security. With the broad application of these certificates, from personal identification on smart cards to device and workstation authentication via Trusted Platform Modules (TPM), our study seeks to address a pertinent question on how prevalent are weak RSA keys within such a vast internal certificate repository. Previous research focused primarily on key sets publicly accessible from TLS and SSH servers or PGP key repositories. On the contrary, our investigation provides insights into the private domain of an enterprise, introducing new dimensions to this problem. Among our considerations are the trustworthiness of hardware and software solutions in generating keys and the consequential implications of identified vulnerabilities on organizational risk management. The obtained results can contribute to enhancing security strategies in enterprises.
    Źródło:
    International Journal of Electronics and Telecommunications; 2023, 69, 4; 803--810
    2300-1933
    Pojawia się w:
    International Journal of Electronics and Telecommunications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Multiplicative Algorithm for Correntropy-Based Nonnegative Matrix Factorization
    Autorzy:
    Hosseini-Asl, E.
    Zurada, J. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/108758.pdf
    Data publikacji:
    2013
    Wydawca:
    Społeczna Akademia Nauk w Łodzi
    Tematy:
    Nonnegative Matrix Factorization (NMF)
    Correntropy
    Multiplicative Algorithm
    Document Clustering
    Opis:
    Nonnegative matrix factorization (NMF) is a popular dimension reduction technique used for clustering by extracting latent features from highdimensional data and is widely used for text mining. Several optimization algorithms have been developed for NMF with different cost functions. In this paper we evaluate the correntropy similarity cost function. Correntropy is a nonlinear localized similarity measure which measures the similarity between two random variables using entropy-based criterion, and is especially robust to outliers. Some algorithms based on gradient descent have been used for correntropy cost function, but their convergence is highly dependent on proper initialization and step size and other parameter selection. The proposed general multiplicative factorization algorithm uses the gradient descent algorithm with adaptive step size to maximize the correntropy similarity between the data matrix and its factorization. After devising the algorithm, its performance has been evaluated for document clustering. Results were compared with constrained gradient descent method using steepest descent and L-BFGS methods. The simulations show that the performance of steepest descent and LBFGS convergence are highly dependent on gradient descent step size which depends on σ parameter of correntropy cost function. However, the multiplicative algorithm is shown to be less sensitive to σ parameterand yields better clustering results than other algorithms. The results demonstrate that clustering performance measured by entropy and purity improve the clustering. The multiplicative correntropy-based algorithm also shows less variation in accuracy of document clusters for variable number of clusters. The convergence of each algorithm is also investigated, and the experiments have shown that the multiplicative algorithm converges faster than L-BFGS and steepest descent method.
    Źródło:
    Journal of Applied Computer Science Methods; 2013, 5 No. 2; 89-104
    1689-9636
    Pojawia się w:
    Journal of Applied Computer Science Methods
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On solvability of some difference-discrete equations
    Autorzy:
    Vasilyev, A. V.
    Vasilyev, V. B.
    Powiązania:
    https://bibliotekanauki.pl/articles/254700.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    multidimensional difference-discrete equation
    symbol
    factorization
    periodic Riemann problem
    Opis:
    Multidimensional difference equations in a discrete half-space are considered. Using the theory of periodic Riemann problems a general solution and solvability conditions in discrete Lebesgue spaces are obtained. Some statements of boundary value problems of discrete type are given.
    Źródło:
    Opuscula Mathematica; 2016, 36, 4; 525-539
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Factorization through Hilbert space and the dilation of L(X,Y)-valued measures
    Autorzy:
    Mandrekar, V.
    P., P.
    Powiązania:
    https://bibliotekanauki.pl/articles/1292450.pdf
    Data publikacji:
    1993
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    spectral dilation of operator-valued measure
    Hilbertian operators
    factorization
    Opis:
    We present a general necessary and sufficient algebraic condition for the spectral dilation of a finitely additive L(X,Y)-valued measure of finite semivariation when X and Y are Banach spaces. Using our condition we derive the main results of Rosenberg, Makagon and Salehi, and Miamee without the assumption that X and/or Y are Hilbert spaces. In addition we relate the dilation problem to the problem of factoring a family of operators through a single Hilbert space.
    Źródło:
    Studia Mathematica; 1993, 107, 2; 101-113
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Unique factorization theorem for object-systems
    Autorzy:
    Mihók, Peter
    Semanišin, Gabriel
    Powiązania:
    https://bibliotekanauki.pl/articles/743977.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    object-system
    unique factorization
    graph
    hypergraph
    formal concept analysis
    Opis:
    The concept of an object-system is a common generalization of simple graph, digraph and hypergraph. In the theory of generalised colourings of graphs, the Unique Factorization Theorem (UFT) for additive induced-hereditary properties of graphs provides an analogy of the well-known Fundamental Theorem of Arithmetics. The purpose of this paper is to present UFT for object-systems. This result generalises known UFT for additive induced-hereditary and hereditary properties of graphs and digraphs. Formal Concept Analysis is applied in the proof.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2011, 31, 3; 559-575
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On determinant of certain pentadiagonal matrix
    Autorzy:
    Borowska, J.
    Łacińska, L.
    Rychlewska, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/122492.pdf
    Data publikacji:
    2013
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    tridiagonal matrix
    pentadiagonal matrix
    determinant
    LU factorization
    determinanta
    rozkład LU
    Opis:
    In this paper, using the LU factorization, the relation between the determinant of a certain pentadiagonal matrix and the determinant of a corresponding tridiagonal matrix will be derived. Moreover, it will be shown that determinant of this special pentadiagonal matrix can be calculated by applying the fourth order homogeneous linear difference equation.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2013, 12, 3; 21-26
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Quantum Factorization of Integers 21 and 91 using Shor’s Algorithm
    Autorzy:
    Ardhyamath, Poornima
    Naghabhushana, N. M.
    Ujjinimatad, Rohitha
    Powiązania:
    https://bibliotekanauki.pl/articles/1070857.pdf
    Data publikacji:
    2019
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Euclidean Algorithm
    Factorization
    GCD
    Quantum Fourier Transform
    Shor’s Algorithm
    Opis:
    In this paper we focused on the factorization of integer in detail using well known Shor’s algorithm and its quantum part realization. The algorithm finds prime factors any integer more efficiently than any known classical algorithm. It is based on prior knowledge of the answer to the factorization problem. Algorithm includes finding gcd using polynomial time Euclidean algorithm, determination of unknown period from quantum computer and continued fraction expansion approach. Factorization of two integers 21 and 91 are shown in this paper with all steps. Quantum part of the factorization described mathematically.
    Źródło:
    World Scientific News; 2019, 123; 102-113
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Model-Based Method for Acoustic Echo Cancelation and Near-End Speaker Extraction: Non-negative Matrix Factorization
    Autorzy:
    Agrawal, P.
    Shandilya, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/958086.pdf
    Data publikacji:
    2018
    Wydawca:
    Instytut Łączności - Państwowy Instytut Badawczy
    Tematy:
    adaptive algorithms
    convergence
    echo cancellation
    non-negative matrix factorization (NMF)
    Opis:
    Rapid escalation of wireless communication and hands-free telephony creates a problem with acoustic echo in full-duplex communication applications. In this paper a simulation of model-based acoustic echo cancelation and near-end speaker extraction using statistical methods relying on nonnegative matrix factorization (NMF) is proposed. Acoustic echo cancelation using the NMF algorithm is developed and its implementation is presented, along with all positive, real time elements and factorization techniques. Experimental results are compared against the widely used existing adaptive algorithms which have a disadvantage in terms of long impulse response, increased computational load and wrong convergence due to change in near-end enclosure. All these shortcomings have been eliminated in the statistical method of NMF that reduces echo and enhances audio signal processing.
    Źródło:
    Journal of Telecommunications and Information Technology; 2018, 2; 15-22
    1509-4553
    1899-8852
    Pojawia się w:
    Journal of Telecommunications and Information Technology
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    About special properties of the hidden structure of triangular numbers for immediate factorization
    Autorzy:
    Samojluk, Artur
    Powiązania:
    https://bibliotekanauki.pl/articles/2133934.pdf
    Data publikacji:
    2022
    Wydawca:
    Uniwersytet Warmińsko-Mazurski w Olsztynie
    Tematy:
    factorization algorithm
    RSA
    cryptography
    numerical experiments
    triangular numbers
    number theory
    Opis:
    The factorization problem belongs to a group of problems important in the security of information systems and cryptography. The article describes a new number factorization algorithm designed based on numerical experiments. We present an extension of number factorization using triangular numbers features. The described algorithm can be used to increase the security of key generation for the RSA algorithm.
    Źródło:
    Technical Sciences / University of Warmia and Mazury in Olsztyn; 2022, 25(1); 35--57
    1505-4675
    2083-4527
    Pojawia się w:
    Technical Sciences / University of Warmia and Mazury in Olsztyn
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Automatic extractive and generic document summarization based on NMF
    Autorzy:
    Aghdam, Mehdi Hosseinzadeh
    Powiązania:
    https://bibliotekanauki.pl/articles/2201319.pdf
    Data publikacji:
    2023
    Wydawca:
    Społeczna Akademia Nauk w Łodzi. Polskie Towarzystwo Sieci Neuronowych
    Tematy:
    text summarization
    latent topics
    non-negative matrix factorization
    updating rules
    Opis:
    Nowadays, textual information grows exponentially on the Internet. Text summarization (TS) plays a crucial role in the massive amount of textual content. Manual TS is time-consuming and impractical in some applications with a huge amount of textual information. Automatic text summarization (ATS) is an essential technology to overcome mentioned challenges. Non-negative matrix factorization (NMF) is a useful tool for extracting semantic contents from textual data. Existing NMF approaches only focus on how factorized matrices should be modeled, and neglect the relationships among sentences. These relationships provide better factorization for TS. This paper suggests a novel non-negative matrix factorization for text summarization (NMFTS). The proposed ATS model puts regularizes on pairwise sentences vectors. A new cost function based on the Frobenius norm is designed, and an algorithm is developed to minimize this function by proposing iterative updating rules. The proposed NMFTS extracts semantic content by reducing the size of documents and mapping the same sentences closely together in the latent topic space. Compared with the basic NMF, the convergence time of the proposed method does not grow. The convergence proof of the NMFTS and empirical results on the benchmark data sets show that the suggested updating rules converge fast and achieve superior results compared to other methods.
    Źródło:
    Journal of Artificial Intelligence and Soft Computing Research; 2023, 13, 1; 37--49
    2083-2567
    2449-6499
    Pojawia się w:
    Journal of Artificial Intelligence and Soft Computing Research
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The geometry of Darlington synthesis
    Autorzy:
    Dewilde, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/908125.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    Darlington synthesis
    Hankel operator
    time varying systems
    contractive operators
    coprime factorization
    Opis:
    We revisit the classical problem of `Darlington synthesis', or Darlington embedding. Although traditionally it is solved using analytic means, a more natural way to approach it is to use the geometric properties of a well-chosen Hankel map. The method yields surprising results. In the first place, it allows us to formulate necessary and sufficient conditions for the existence of the embedding in terms of systems properties of the transfer operation to be embedded. In addition, the approach allows us to extend the solution to situations where no analytical transform is available. The paper has a high review content, as all the results presented have been obtained during the last twenty years and have been published. However, we make a systematic attempt at formulating them in a geometric way, independent of an accidental parametrization. The benefit is clarity and generality.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2001, 11, 6; 1379-1386
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Outer factorization of operator valued weight functions on the torus
    Autorzy:
    Cheng, Ray
    Powiązania:
    https://bibliotekanauki.pl/articles/1290317.pdf
    Data publikacji:
    1994
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    outer factorization
    Toeplitz operator
    prediction theory
    Szegö's infimum
    multivariate stationary process
    Opis:
    An exact criterion is derived for an operator valued weight function $W(e^{is},e^{it})$ on the torus to have a factorization $W(e^{is},e^{it}) = Φ(e^{is},e^{it})*Φ(e^{is},e^{it})$, where the operator valued Fourier coefficients of Φ vanish outside of the Helson-Lowdenslager halfplane $Λ = {(m,n) ∈ ℤ^2: m ≥ 1} ∪ {(0,n): n ≥ 0}$, and Φ is "outer" in a related sense. The criterion is expressed in terms of a regularity condition on the weighted space $L^2(W)$ of vector valued functions on the torus. A logarithmic integrability test is also provided. The factor Φ is explicitly constructed in terms of Toeplitz operators and other structures associated with W. The corresponding version of Szegö's infimum is given.
    Źródło:
    Studia Mathematica; 1994, 110, 1; 19-34
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Projective nonnegative matrix factorization based on α-divergence
    Autorzy:
    Yang, Z.
    Oja, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/91672.pdf
    Data publikacji:
    2011
    Wydawca:
    Społeczna Akademia Nauk w Łodzi. Polskie Towarzystwo Sieci Neuronowych
    Tematy:
    Nonnegative Matrix Factorization
    NMF
    α-divergence
    PNMF
    α-NMF
    α-PNMF
    Opis:
    The well-known Nonnegative Matrix Factorization (NMF) method can be provided with more flexibility by generalizing the non-normalized Kullback-Leibler divergence to α- divergences. However, the resulting α-NMF method can only achieve mediocre sparsity for the factorizing matrices. We have earlier proposed a variant of NMF, called Projective NMF (PNMF) that has been shown to have superior sparsity over standard NMF. Here we propose to incorporate both merits of α-NMF and PNMF. Our α-PNMF method can produce a much sparser factorizing matrix, which is desired in many scenarios. Theoretically, we provide a rigorous convergence proof that the iterative updates of α-PNMF monotonically decrease the α-divergence between the input matrix and its approximate. Empirically, the advantages of α-PNMF are verified in two application scenarios: (1) it is able to learn highly sparse and localized part-based representations of facial images; (2) it outperforms α-NMF and PNMF for clustering in terms of higher purity and smaller entropy.
    Źródło:
    Journal of Artificial Intelligence and Soft Computing Research; 2011, 1, 1; 7-16
    2083-2567
    2449-6499
    Pojawia się w:
    Journal of Artificial Intelligence and Soft Computing Research
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Properties of reducible polynomials
    Własności wielomianów redukowalnych
    Autorzy:
    Borowska, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/404051.pdf
    Data publikacji:
    2015
    Wydawca:
    Polskie Towarzystwo Symulacji Komputerowej
    Tematy:
    irreducible polynomials
    factorization
    cryptography
    elliptic curves
    wielomian nieredukowalny
    faktoryzacja
    kryptografia
    krzywe eliptyczne
    Opis:
    We consider polynomials p(x) over the 2-element field F2. If p(x) of degree n is irreducible, then a set of polynomials of degree less than n together with operations (of addition and multiplication) modulo p(x) forms the finite field GF(2n). If p(x) of degree n is reducible, then the set of all polynomials of degree less than n contains several groups with respect to multiplication modulo p(x). Properties of these groups are described in Section 3. In Section 4 is presented a polynomial factorization algorithm. Irreducible polynomials are widely used (for instance in cryptography) due to the possibility of an efficient representation of all the elements from GF(2n) on a fixed number of bits.
    Analizowano wielomiany z jedną zmienną nad ciałem skończonym F2. Jeśli wielomian p(x) stopnia n jest nierozkładalny, to zbiór wielomianów stopnia mniejszego od n wraz z operacjami (dodawania i mnożenia) modulo p(x) tworzy ciało skończone GF(2n). Jeżeli p(x) stopnia n jest rozkładalny, w zbiorze wielomianów stopnia mniejszego od n można wyróżnić kilka podzbiorów, które wraz z działaniem *p (mnożenie modulo p(x)) tworzą grupy. Własności tych grup (oparte na wykonanych testach) opisano w sekcji 3. W sekcji 4 zaproponowano algorytm faktoryzacji wielomianów. Wydajność zapisywania elementów GF(2n) na ustalonej liczbie bitów zachęca do wykorzystywania wielomianów nierozkładalnych na przykład w kryptografii.
    Źródło:
    Symulacja w Badaniach i Rozwoju; 2015, 6, 3; 175-184
    2081-6154
    Pojawia się w:
    Symulacja w Badaniach i Rozwoju
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Application of high-performance techniques for solving linear systems of algebraic equations
    Autorzy:
    Grzonka, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/307729.pdf
    Data publikacji:
    2013
    Wydawca:
    Instytut Łączności - Państwowy Instytut Badawczy
    Tematy:
    Advanced Vector Extension
    conjugate gradient method
    incomplete Cholesky factorization
    preconditioning
    vector registers
    Opis:
    Solving many problems in mechanics, engineering, medicine and other (e.g., diffusion tensor magnetic resonance imaging or finite element modeling) requires the efficient solving of algebraic equations. In many cases, such systems are very complex with a large number of linear equations, which are symmetric positive-defined (SPD). This paper is focused on improving the computational efficiency of the solvers dedicated for the linear systems based on incomplete and noisy SPD matrices by using preconditioning technique – Incomplete Cholesky Factorization, and modern set of processor instructions – Advanced Vector Extension. Application of these techniques allows to fairly reduce the computational time, number of iterations of conventional algorithms and improve the speed of calculation.
    Źródło:
    Journal of Telecommunications and Information Technology; 2013, 4; 85-91
    1509-4553
    1899-8852
    Pojawia się w:
    Journal of Telecommunications and Information Technology
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Preconditioned Conjugate Gradient Method for Solution of Large Finite Element Problems on CPU and GPU
    Autorzy:
    Fialko, S. Y.
    Zeglen, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/307602.pdf
    Data publikacji:
    2016
    Wydawca:
    Instytut Łączności - Państwowy Instytut Badawczy
    Tematy:
    conjugate gradient
    incomplete Cholesky factorization
    iterative solvers
    NVIDIA CUDA
    preconditioned conjugate gradient
    Opis:
    In this article the preconditioned conjugate gradient (PCG) method, realized on GPU and intended to solution of large finite element problems of structural mechanics, is considered. The mathematical formulation of problem results in solution of linear equation sets with sparse symmetrical positive definite matrices. The authors use incomplete Cholesky factorization by value approach, based on technique of sparse matrices, for creation of efficient preconditioning, which ensures a stable convergence for weakly conditioned problems mentioned above. The research focuses on realization of PCG solver on GPU with using of CUBLAS and CUSPARSE libraries. Taking into account a restricted amount of GPU core memory, the efficiency and reliability of GPU PCG solver are checked and these factors are compared with data obtained with using of CPU version of this solver, working on large amount of RAM. The real-life large problems, taken from SCAD Soft collection, are considered for such a comparison.
    Źródło:
    Journal of Telecommunications and Information Technology; 2016, 2; 26-33
    1509-4553
    1899-8852
    Pojawia się w:
    Journal of Telecommunications and Information Technology
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Factorization of Nonnegative Matrices by the Use of Elementary Operation
    Autorzy:
    Kaczorek, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/386810.pdf
    Data publikacji:
    2012
    Wydawca:
    Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
    Tematy:
    faktoryzacja
    nieujemna macierz
    procedura
    obliczanie
    factorization
    nonnegative matrix
    positive rank
    procedure
    computation
    Opis:
    A method based on elementary column and row operations of the factorization of nonnegative matrices is proposed. It is shown that the nonnegative matrix R×( ? ) has positive full column rank if and only if it can be transformed to a matrix with cyclicstructure. A procedure for computation of nonnegative matrices ? R ×, ? R × ( ? rank (,)) satisfying = is proposed.
    Źródło:
    Acta Mechanica et Automatica; 2012, 6, 4; 15-18
    1898-4088
    2300-5319
    Pojawia się w:
    Acta Mechanica et Automatica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Positive definite functions and dual pairs of locally convex spaces
    Autorzy:
    Alpay, D.
    Gabriyelyan, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/255413.pdf
    Data publikacji:
    2018
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    positive definite function locally convex space
    dual pair
    factorization property
    dilation theory
    Opis:
    Using pairs of locally convex topological vector spaces in duality and topologies defined by directed families of sets bounded with respect to the duality, we prove general factorization theorems and general dilation theorems for operator-valued positive definite functions.
    Źródło:
    Opuscula Mathematica; 2018, 38, 4; 463-482
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Pseudo-differential equations and conical potentials: 2-dimensional case
    Autorzy:
    Vasilyev, Vladimir B.
    Powiązania:
    https://bibliotekanauki.pl/articles/255700.pdf
    Data publikacji:
    2019
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    pseudo-differential equation
    wave factorization
    Dirichlet problem
    system of linear integral equations
    Opis:
    We consider two-dimensional elliptic pseudo-differential equation in a plane sector. Using a special representation for an elliptic symbol and the formula for a general solution we study the Dirichlet problem for such equation. This problem was reduced to a system of linear integral equations and then after some transformations to a system of linear algebraic equations. The unique solvability for the Dirichlet problem was proved in Sobolev-Slobodetskii spaces and a priori estimate for the solution is given.
    Źródło:
    Opuscula Mathematica; 2019, 39, 1; 109-124
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical analysis of the orthotropic sample for conductivity tests
    Analiza numeryczna pola temperatury w ortotropowej próbce
    Autorzy:
    Tokarski, Mieszko
    Powiązania:
    https://bibliotekanauki.pl/articles/101685.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Śląska. Wydział Inżynierii Środowiska i Energetyki. Instytut Techniki Cieplnej
    Tematy:
    MATLAB
    Ansys
    FEM
    Neumann's Boundary Condition
    Factorization
    ANSYS
    Warunek Brzegowy Neumann'a
    faktoryzacja
    Opis:
    This work describes the development of a program based on the Finite Element Method for the calculation of a temperature field in orthotropic sample with use of the Neumann's Boundary Condition. Such a program has been created for the purposes of the project carrying out in the Intitute of Thermal Technology in Gliwice, Poland. It is an important part of the fully – automated algorithm for determining the sample's thermal conductivity by fitting numerically obtained temperature field with its counterpart provided by the measurements. Because of the specific nature of the measurement process as well as the main algorithm itself, the developed program is characterized by high efficiency (comparable to Ansys), sufficient accuracy and preparation for cooperation with the mentioned before fully – automated algorithm. Most important features of the program are: module for geometry data import (data is provided by the Ansys), module for the results export, the two control text files for easy management by external procedures, logging and error reporting module.
    W pracy tej opisano proces tworzenia pogramu opartego na Metodzie Elementów Skończonych a służącego do obliczania pola temperatury w ortotropowej próbce z wykorzystaniem warunku brzegowego Neumann'a. Program ten został stworzony na potrzeby projektu prowadzonego w Instytucie Techniki Cieplnej w Gliwicach. Stanowi on ważną część zautomatyzowanej procedury mającej wyznaczać współczynnik przewodzenia ciepła badanej próbki poprzez dopasowanie rozkładu temperatury otrzymanego na drodze obliczeń numerycznych z rozkładem temperatury otrzymanym z pomiarów. Z racji specyfiki pomiarów oraz samej procedury sterującej całą analizą, stworzony program charakteryzuje się dużą wydajnością porównywalną do wydajności Ansysa (dla tego samego przypadku), wystarczającą dokładnością oraz przygotowaniem do sprzęgnięcia z głównym algorytmem. Najważniejszymi cechami tego programu są: moduł do importu geometrii z Ansysa, moduł do eksportu danych dla algorytmu sterującego, dwa pliki tekstowe umożliwiające łatwe zarządzanie tym kodem (zwłaszcza w przypadku sterowania przez zewnętrzny program), logowanie działania programu oraz raportowanie o błędach.
    Źródło:
    Archiwum Instytutu Techniki Cieplnej; 2016, 1; 153-204
    2451-277X
    Pojawia się w:
    Archiwum Instytutu Techniki Cieplnej
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Factorization of weakly continuous holomorphic mappings
    Autorzy:
    González, Manuel
    Gutiérrez, Joaqín
    Powiązania:
    https://bibliotekanauki.pl/articles/1287688.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    weakly continuous holomorphic mapping
    factorization of holomorphic mappings
    polynomial
    weakly continuous multilinear mapping
    Opis:
    We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly uniformly} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Hervés and Valdivia for polynomials between Banach spaces, and it also holds if the weak topology is replaced by a coarser one. However, we show that it need not be true for a stronger topology, thus answering a question raised by Aron. As an application of the first result, we prove that a holomorphic mapping ƒ between complex Banach spaces is weakly uniformly continuous on bounded subsets if and only if it admits a factorization of the form f = g∘S, where S is a compact operator and g a holomorphic mapping.
    Źródło:
    Studia Mathematica; 1996, 118, 2; 117-133
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Cohens proof of the Factorization Theorem
    Autorzy:
    Kisyński, Jan
    Powiązania:
    https://bibliotekanauki.pl/articles/1207918.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    factorization for a representation of a Banach algebra with a bounded approximate identity
    Opis:
    Various proofs of the Factorization Theorem for representations of Banach algebras are compared with its original proof due to P. Cohen.
    Źródło:
    Annales Polonici Mathematici; 2000, 75, 2; 177-192
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Factorizations of properties of graphs
    Autorzy:
    Broere, Izak
    Teboho Moagi, Samuel
    Mihók, Peter
    Vasky, Roman
    Powiązania:
    https://bibliotekanauki.pl/articles/744148.pdf
    Data publikacji:
    1999
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    factorization
    property of graphs
    irreducible property
    reducible property
    lattice of properties of graphs
    Opis:
    A property of graphs is any isomorphism closed class of simple graphs. For given properties of graphs ₁,₂,...,ₙ a vertex (₁, ₂, ...,ₙ)-partition of a graph G is a partition {V₁,V₂,...,Vₙ} of V(G) such that for each i = 1,2,...,n the induced subgraph $G[V_i]$ has property $_i$. The class of all graphs having a vertex (₁, ₂, ...,ₙ)-partition is denoted by ₁∘₂∘...∘ₙ. A property is said to be reducible with respect to a lattice of properties of graphs if there are n ≥ 2 properties ₁,₂,...,ₙ ∈ such that = ₁∘₂∘...∘ₙ; otherwise is irreducible in . We study the structure of different lattices of properties of graphs and we prove that in these lattices every reducible property of graphs has a finite factorization into irreducible properties.
    Źródło:
    Discussiones Mathematicae Graph Theory; 1999, 19, 2; 167-174
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On generating sets of induced-hereditary properties
    Autorzy:
    Semanišin, Gabriel
    Powiązania:
    https://bibliotekanauki.pl/articles/743561.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    induced-hereditary property of graphs
    additivity
    reducibility
    generating sets
    maximal graphs
    unique factorization
    Opis:
    A natural generalization of the fundamental graph vertex-colouring problem leads to the class of problems known as generalized or improper colourings. These problems can be very well described in the language of reducible (induced) hereditary properties of graphs. It turned out that a very useful tool for the unique determination of these properties are generating sets. In this paper we focus on the structure of specific generating sets which provide the base for the proof of The Unique Factorization Theorem for induced-hereditary properties of graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2002, 22, 1; 183-192
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The revision and extension of the RMS ring for time delay systems
    Autorzy:
    Pekař, L.
    Prokop, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/200559.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    time delay system
    ring
    Bézout domain
    coprime factorization
    system opóźniania
    pierścień
    domena Bézout
    Opis:
    This paper is aimed at reviewing the ring of retarded quasipolynomial meromorphic functions (RMS) that was recently introduced as a convenient control design tool for linear, time-invariant time delay systems (TDS). It has been found by the authors that the original definition does not constitute a ring and has some essential deficiencies, and hence it could not be used for an algebraic control design without a thorough reformulation which i.a. extends the usability to neutral TDS and to those with distributed delays. This contribution summarizes the original definition of RMS simply highlights its deficiencies via examples, and suggests a possible new extended definition. Hence, the new ring of quasipolynomial meromorphic functions RQM is established to avoid confusion. The paper also investigates and introduces selected algebraic properties supported by some illustrative examples and concisely outlines its use in controller design.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2017, 65, 3; 341-349
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Factorization of the Popov Function of a Multivariable Linear Distributed Parameter System in the Non-Coercive Case: a Penalization Approach
    Autorzy:
    Pandolfi, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/908131.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    system elastyczny
    system rozpraszający
    linear distributed systems
    dissipative systems
    factorization
    outer factor
    Popov function
    Opis:
    We study the construction of an outer factor to a positive definite Popov function Pi(iomega) of a distributed parameter system. We assume that Pi(iomega) is a non-negative definite matrix with non-zero determinant. Coercivity is not assumed. We present a penalization approach which gives an outer factor just in the case when there exists any outer factor.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2001, 11, 6; 1249-1260
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Trees with α-labelings and decompositions of complete graphs into non-symmetric isomorphic spanning trees
    Autorzy:
    Kubesa, Michael
    Powiązania:
    https://bibliotekanauki.pl/articles/744369.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph decomposition and factorization
    graph labeling
    α-labeling
    flexible q-labeling
    α-like labeling
    Opis:
    We examine constructions of non-symmetric trees with a flexible q-labeling or an α-like labeling, which allow factorization of $K_{2n}$ into spanning trees, arising from the trees with α-labelings.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2005, 25, 3; 311-324
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Exponential machines
    Autorzy:
    Novikov, A.
    Trofimov, M.
    Oseledets, I.
    Powiązania:
    https://bibliotekanauki.pl/articles/201849.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    tensor decomposition
    tensor train
    factorization machines
    Riemannian optimization
    optymalizacja
    dekompozycja tensorowa
    tensor metryczny Riemanna
    Opis:
    Modeling interactions between features improves the performance of machine learning solutions in many domains (e.g. recommender systems or sentiment analysis). In this paper, we introduce Exponential machines (ExM), a predictor that models all interactions of every order. The key idea is to represent an exponentially large tensor of parameters in a factorized format called tensor train (TT). The tensor train format regularizes the model and lets you control the number of underlying parameters. To train the model, we develop a stochastic Riemannian optimization procedure, which allows us to fit tensors with ¼ 256 entries. We show that the model achieves state-of-the-art performance on synthetic data with high-order interactions and that it works on par with high-order factorization machines on a recommender system dataset MovieLens 100 K.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 6; 789-797
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Factoring an odd abelian group by lacunary cyclic subsets
    Autorzy:
    Szabó, Sándor
    Powiązania:
    https://bibliotekanauki.pl/articles/729053.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    factorization of finite abelian groups
    periodic subsets
    cyclic subsets
    lacunary cyclic subsets
    Hajós-Rédei theory
    Opis:
    It is a known result that if a finite abelian group of odd order is a direct product of lacunary cyclic subsets, then at least one of the factors must be a subgroup. The paper gives an elementary proof that does not rely on characters.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2010, 30, 2; 137-146
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The reactance wave diffraction problem by a strip in a scale of Bessel potential spaces
    Autorzy:
    Castro, L. P.
    Natroshvili, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/255627.pdf
    Data publikacji:
    2006
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Helmholtz equation
    boundary-transmission problem
    wave diffraction
    convolution type operator
    Wiener-Hopf operator
    Fredholm property
    factorization
    Opis:
    We consider a boundary-transmission problem for the Helmholtz equation, in a Bessel potential space setting, which arises within the context of wave diffraction theory. The boundary under consideration consists of a strip, and certain reactance conditions are assumed on it. Operator theoretical methods are used to deal with the problem and, as a consequence, several convolution type operators are constructed and associated to the problem. At the end, the well-posedness of the problem is shown for a range of regularity orders of the Bessel potential spaces, and for a set of possible reactance numbers (dependent on the wave number).
    Źródło:
    Opuscula Mathematica; 2006, 26, 2; 289-303
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Overview of adaptive and low-rank approximation algorithms for modeling influence of electromagnetic waves generated by cellphone antenna on human head
    Autorzy:
    Głut, Barbara
    Paszyński, Maciej
    Powiązania:
    https://bibliotekanauki.pl/articles/2097964.pdf
    Data publikacji:
    2021
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    mesh generation
    mesh adaptation
    Pennes bioheat equations
    time-harmonic Maxwell equations
    sparse factorization
    low rank approximation
    Opis:
    This paper presents an overview of formulations and algorithms that are dedicated to modeling the influence of electromagnetic waves on the human head. We start from h adaptive approximation of a three-dimensional MRI scan of the human head. Next, we solve the time-harmonic Maxwell equations with a 1.8 GHz cellphone antenna. We compute the specific absorption rate used as the heat source for the Pennes bioheat equation modeling the heat generated by EM waves inside the head. We propose an adaptive algorithm mixed with time-stepping iterations where we simultaneously refine the computational mesh, solve the Maxwell and Pennes equations, and iterate the time steps. We employ the sparse Gaussian elimination algorithm with the low-rank compres-sion of the off-diagonal matrix blocks for the factorization of the matrices. We conclude with the statement that 15 minutes of talking with a 1.8 GHz antenna with one watt of power results in increased brain tissue temperatures (up to 38.4◦C).
    Źródło:
    Computer Science; 2021, 22 (4); 433--461
    1508-2806
    2300-7036
    Pojawia się w:
    Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    FILTRACJA FINANSOWYCH SZEREGÓW CZASOWYCH METODAMI NIEUJEMNEJ FAKTORYZACJI MACIERZY
    FILTRATION OF FINANCIAL TIME SERIES USING NON-NEGATIVE MATRIX FACTORIZATION METHODS
    Autorzy:
    Szupiluk, Ryszard
    Rubach, Paweł
    Powiązania:
    https://bibliotekanauki.pl/articles/453792.pdf
    Data publikacji:
    2018
    Wydawca:
    Szkoła Główna Gospodarstwa Wiejskiego w Warszawie. Katedra Ekonometrii i Statystyki
    Tematy:
    filtracja szeregów czasowych
    estymacja trendów
    nieujemna faktoryzacja macierzy
    time-series filtration
    trend estimation
    non-negative matrix factorization
    Opis:
    W niniejszym artykule przedstawimy metodę wielowy¬miarowej filtracji do eliminacji szumów oraz estymacji trendów z finansowych szeregów czasowych. Jednym z istotnych elementów procesu filtracji będzie dekompozycja szeregów czasowych przy wykorzystaniu nieujemnej faktoryzacji macierzy. Prezentowana metoda może być wykorzystana w wielu praktycznych obszarach finansów i zarządzania jak analiza techniczna rynków, systemy inwestycyjne czy modele ryzyka.
    In this paper, we will present a method of multivariate filtration that may be used to eliminate noise and estimate trends in financial time-series. A significant element of the filtration process is the decomposition of time-series using nonnegative matrix factorization. The presented method may be applied in many practical aspects of finance and management, in particular for use in technical analysis of financial markets, trading systems or risk models.
    Źródło:
    Metody Ilościowe w Badaniach Ekonomicznych; 2018, 19, 3; 284-292
    2082-792X
    Pojawia się w:
    Metody Ilościowe w Badaniach Ekonomicznych
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The UD RLS Algorithm for Training Feedforward Neural Networks
    Autorzy:
    Bilski, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/908480.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    sieć neuronowa
    algorytm uczenia
    metoda najmniejszych kwadratów
    neural networks
    learning algorithms
    recursive least squares method
    UD factorization
    Opis:
    A new algorithm for training feedforward multilayer neural networks is proposed. It is based on recursive least squares procedures and U-D factorization, which is a well-known technique in filter theory. It will be shown that due to the U-D factorization method, our algorithm requires fewer computations than the classical RLS applied to feedforward multilayer neural network training.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2005, 15, 1; 115-123
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Unique factorization theorem
    Autorzy:
    Mihók, Peter
    Powiązania:
    https://bibliotekanauki.pl/articles/743745.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    induced-hereditary
    additive property of graphs
    reducible property of graphs
    unique factorization
    uniquely partitionable graphs
    generating sets
    Opis:
    A property of graphs is any class of graphs closed under isomorphism. A property of graphs is induced-hereditary and additive if it is closed under taking induced subgraphs and disjoint unions of graphs, respectively. Let ₁,₂, ...,ₙ be properties of graphs. A graph G is (₁,₂,...,ₙ)-partitionable (G has property ₁ º₂ º... ºₙ) if the vertex set V(G) of G can be partitioned into n sets V₁,V₂,..., Vₙ such that the subgraph $G[V_i]$ of G induced by V_i belongs to $_i$; i = 1,2,...,n. A property is said to be reducible if there exist properties ₁ and ₂ such that = ₁ º₂; otherwise the property is irreducible. We prove that every additive and induced-hereditary property is uniquely factorizable into irreducible factors. Moreover the unique factorization implies the existence of uniquely (₁,₂, ...,ₙ)-partitionable graphs for any irreducible properties ₁,₂, ...,ₙ.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2000, 20, 1; 143-154
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A method for solving a system of linear equations with a symmetric indefinite coefficient matrix
    Autorzy:
    Czochralska, Izabela
    Powiązania:
    https://bibliotekanauki.pl/articles/748583.pdf
    Data publikacji:
    2006
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Gaussian elimination, triangular and triangular-diagonal factorization of a matrix, numerically stable diagonalization of a symmetric indefinite matrix.
    Opis:
    The subject of this article is a numerically stable method for solving nonsingular Cramerian systems of linear equations, with a symmetric indefinite coefficient matrix. It consists in adapting the algorithm presented in [1] that can stably and effectively diagonalize any indefinite symmetric matrix. It is in fact some modification of the Gaussian symmetric elimination procedure.
    Źródło:
    Mathematica Applicanda; 2006, 34, 48/07
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Influence of preconditioning and blocking on accuracy in solving Markovian models
    Autorzy:
    Bylina, B.
    Bylina, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/907654.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    kondycjonowanie
    równanie liniowe
    metoda blokowania
    łańcuch Markowa
    rozkład WZ
    preconditioning
    linear equations
    blocking methods
    Markov chains
    WZ factorization
    Opis:
    The article considers the effectiveness of various methods used to solve systems of linear equations (which emerge while modeling computer networks and systems with Markov chains) and the practical influence of the methods applied on accuracy. The paper considers some hybrids of both direct and iterative methods. Two varieties of the Gauss elimination will be considered as an example of direct methods: the LU factorization method and the WZ factorization method. The Gauss-Seidel iterative method will be discussed. The paper also shows preconditioning (with the use of incomplete Gauss elimination) and dividing the matrix into blocks where blocks are solved applying direct methods. The motivation for such hybrids is a very high condition number (which is bad) for coefficient matrices occuring in Markov chains and, thus, slow convergence of traditional iterative methods. Also, the blocking, preconditioning and merging of both are analysed. The paper presents the impact of linked methods on both the time and accuracy of finding vector probability. The results of an experiment are given for two groups of matrices: those derived from some very abstract Markovian models, and those from a general 2D Markov chain.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2009, 19, 2; 207-217
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A factorization of elements in PSL(2, F), where F = Q, R
    Autorzy:
    Ambrosiewicz, Jan
    Powiązania:
    https://bibliotekanauki.pl/articles/728836.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    factorization of linear groups
    linear groups
    matrix representations of groups
    sets of elements of the same order in groups
    Opis:
    Let G be a group and Kₙ = {g ∈ G: o(g) = n}. It is prowed: (i) if F = ℝ, n ≥ 4, then PSL(2,F) = Kₙ²; (ii) if F = ℚ,ℝ, n = ∞, then PSL(2,F) = Kₙ²; (iii) if F = ℝ, then PSL(2,F) = K₃³; (iv) if F = ℚ,ℝ, then PSL(2,F) = K₂³ ∪ E, E ∉ K₂³, where E denotes the unit matrix; (v) if F = ℚ, then PSL(2,F) ≠ K₃³.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 2; 159-167
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Regularized nonnegative matrix factorization: Geometrical interpretation and application to spectral unmixing
    Autorzy:
    Zdunek, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/329732.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    blind source separation
    nonnegative matrix factorization
    active set algorithm
    regularized NMF
    polytope approximation
    ślepa separacja sygnału
    nieujemna faktoryzacja macierzy
    Opis:
    Nonnegative Matrix Factorization (NMF) is an important tool in data spectral analysis. However, when a mixing matrix or sources are not sufficiently sparse, NMF of an observation matrix is not unique. Many numerical optimization algorithms, which assure fast convergence for specific problems, may easily get stuck into unfavorable local minima of an objective function, resulting in very low performance. In this paper, we discuss the Tikhonov regularized version of the Fast Combinatorial NonNegative Least Squares (FC-NNLS) algorithm (proposed by Benthem and Keenan in 2004), where the regularization parameter starts from a large value and decreases gradually with iterations. A geometrical analysis and justification of this approach are presented. The numerical experiments, carried out for various benchmarks of spectral signals, demonstrate that this kind of regularization, when applied to the FC-NNLS algorithm, is essential to obtain good performance.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2014, 24, 2; 233-247
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A study on new right/left inverses of nonsquare polynomial matrices
    Autorzy:
    Hunek, W. P.
    Latawiec, K. J.
    Powiązania:
    https://bibliotekanauki.pl/articles/907786.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    układ wielowymiarowy
    macierz wielomianowa
    sterowanie minimalnowariancyjne
    multivariable systems
    right/left inverses of polynomial matrices
    Smith factorization
    minimum variance control
    Opis:
    This paper presents several new results on the inversion of full normal rank nonsquare polynomial matrices. New analytical right/left inverses of polynomial matrices are introduced, including the so-called [...]-inverses, [...]-inverses and, in particular, S-inverses, the latter providing the most general tool for the design of various polynomial matrix inverses. The application-oriented problem of selecting stable inverses is also solved. Applications in inverse-model control, in particular robust minimum variance control, are exploited, and possible applications in signal transmission/recovery in various types of MIMO channels are indicated.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2011, 21, 2; 331-348
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Matrix Quadratic Equations, Column/row Reduced Factorizations and an Inertia Theorem for Matrix Polynomials
    Autorzy:
    Karelin, I.
    Lerer, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/908122.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    macierz
    równanie różniczkowe Riccatiego
    matrix quadratic equations
    Bezoutians
    inertia
    column (row) reduced polynomials
    factorization
    algebraic Riccati equation
    extremal solutions
    Opis:
    It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial G(lambda) (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of G(lambda). The proof of these results depends heavily on a new inertia theorem for matrix polynomials which is also one of the main results in this paper.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2001, 11, 6; 1285-1310
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Classification of Music Genres Based on Music Separation into Harmonic and Drum Components
    Autorzy:
    Rosner, A.
    Schuller, B.
    Kostek, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/177566.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    music information retrieval
    musical sound separation
    drum separation
    music genre classification
    support vector machine (SVM)
    co-training
    nonnegative matrix factorization
    Opis:
    This article presents a study on music genre classification based on music separation into harmonic and drum components. For this purpose, audio signal separation is executed to extend the overall vector of parameters by new descriptors extracted from harmonic and/or drum music content. The study is performed using the ISMIS database of music files represented by vectors of parameters containing music features. The Support Vector Machine (SVM) classifier and co-training method adapted for the standard SVM are involved in genre classification. Also, some additional experiments are performed using reduced feature vectors, which improved the overall result. Finally, results and conclusions drawn from the study are presented, and suggestions for further work are outlined.
    Źródło:
    Archives of Acoustics; 2014, 39, 4; 629-638
    0137-5075
    Pojawia się w:
    Archives of Acoustics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Predicting pairwise relations with neural similarity encoders
    Autorzy:
    Horn, F.
    Müller, K. R.
    Powiązania:
    https://bibliotekanauki.pl/articles/200921.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    neural networks
    kernel PCA
    dimensionality reduction
    matrix factorization
    SVD
    similarity preserving embeddings
    sieci neuronowe
    jądro
    PCA
    redukcja wymiarowości
    faktoryzacja macierzy
    Opis:
    Matrix factorization is at the heart of many machine learning algorithms, for example, dimensionality reduction (e.g. kernel PCA) or recommender systems relying on collaborative filtering. Understanding a singular value decomposition (SVD) of a matrix as a neural network optimization problem enables us to decompose large matrices efficiently while dealing naturally with missing values in the given matrix. But most importantly, it allows us to learn the connection between data points’ feature vectors and the matrix containing information about their pairwise relations. In this paper we introduce a novel neural network architecture termed similarity encoder (SimEc), which is designed to simultaneously factorize a given target matrix while also learning the mapping to project the data points’ feature vectors into a similarity preserving embedding space. This makes it possible to, for example, easily compute out-of-sample solutions for new data points. Additionally, we demonstrate that SimEc can preserve non-metric similarities and even predict multiple pairwise relations between data points at once.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 6; 821-830
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A factor graph based genetic algorithm
    Autorzy:
    Helmi, B. H.
    Rahmani, A. T.
    Pelikan, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/330811.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    optimization problem
    genetic algorithm
    estimation
    distribution algorithm
    factor graph
    matrix factorization
    problem optymalizacji
    algorytm genetyczny
    algorytm estymacji rozkładu
    faktoryzacja macierzy
    Opis:
    We propose a new linkage learning genetic algorithm called the Factor Graph based Genetic Algorithm (FGGA). In the FGGA, a factor graph is used to encode the underlying dependencies between variables of the problem. In order to learn the factor graph from a population of potential solutions, a symmetric non-negative matrix factorization is employed to factorize the matrix of pair-wise dependencies. To show the performance of the FGGA, encouraging experimental results on different separable problems are provided as support for the mathematical analysis of the approach. The experiments show that FGGA is capable of learning linkages and solving the optimization problems in polynomial time with a polynomial number of evaluations.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2014, 24, 3; 621-633
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Using the Moore-Penrose Generalized Inverse in Cryptography
    Autorzy:
    Kanan, Asmaa M.
    Zayd, Zaleekha Abu
    Powiązania:
    https://bibliotekanauki.pl/articles/1031200.pdf
    Data publikacji:
    2020
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Cipher text
    Cryptography
    Full Column Rank
    Full Rank Factorization
    Full Row Rank
    Plain text
    Rectangular Matrix
    The Moore-Penrose Generalized Inverse
    Opis:
    In this work, we introduce a new method in cryptography. It is using the Moore-Penrose generalized inverse of a rectangular matrix to the cryptographic system. We use a rectangular matrix which has the Moore-Penrose generalized inverse as a key. We mean, the rectangular matrix which has full row rank, or the rectangular matrix which has full column rank, or the rectangular matrix which has full factorization.
    Źródło:
    World Scientific News; 2020, 148; 1-14
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Studying OpenMP thread mapping for parallel linear algebra kernels on multicore system
    Autorzy:
    Bylina, B.
    Bylina, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/200778.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    computation performance
    OpenMP standard
    nonnegative matrix factorization
    thread mapping
    energy consumption
    wydajność obliczeniowa
    Standard OpenMP
    nieujemna faktoryzacja macierzy
    mapowanie
    zużycie energii
    Opis:
    Thread mapping is one of the techniques which allow for efficient exploiting of the potential of modern multicore architectures. The aim of this paper is to study the impact of thread mapping on the computing performance, the scalability, and the energy consumption for parallel dense linear algebra kernels on hierarchical shared memory multicore systems. We consider the basic application, namely a matrix-matrix product (GEMM), and two parallel matrix decompositions (LU and WZ). Both factorizations exploit parallel BLAS (basic linear algebra subprograms) operations, among others GEMM. We compare differences between various thread mapping strategies for these applications. Our results show that the choice of thread mapping has the measurable impact on the performance, the scalability, and energy consumption of the GEMM and two matrix factorizations.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 6; 981-990
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Local fault detection of rolling element bearing components by spectrogram clustering with semi-binary NMF
    Wykrywanie uszkodzeń lokalnych elementów łożysk tocznych poprzez klasteryzację spektrogramu za pomocą półbinarnej nieujemnej faktoryzacji macierzy
    Autorzy:
    Wodecki, J.
    Zdunek, R.
    Wyłomańska, A.
    Zimroz, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/327868.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Polskie Towarzystwo Diagnostyki Technicznej PAN
    Tematy:
    vibration data
    time-frequency analysis
    nonnegative matrix factorization
    local damage detection
    dane drganiowe
    analiza czasowo-częstotliwościowa
    nieujemna faktoryzacja macierzy
    wykrywanie uszkodzeń lokalnych
    Opis:
    Information extraction is a very important problem nowadays. In diagnostics, it is particularly useful when one desires to isolate information about machine damage from a measured diagnostic signal. The method presented in this paper utilizes the idea that is based on a very important topic in numerical algebra, which is nonnegative matrix factorization. When applied to the matrix of multidimensional representation of the measured data, it can extract very useful information about the events which occur in the signal and are not recognizable otherwise. In the presented methodology, we use the algorithm called Semi-Binary Nonnegative Matrix Factorization (SB-NMF), and apply it to a time-frequency representation of the real-life vibration signal measured on faulty bearing operating in a belt conveyor driving station. Detected impulses of local damage are clearly identifiable. Performance of the algorithm is very satisfying in terms of time efficiency and output signal quality.
    Ekstrakcja informacji jest aktualnym kierunkiem badań. Jest ona szczególnie użyteczna, kiedy próbuje się wyizolować informację na temat uszkodzenia maszyny z zarejestrowanego sygnału diagnostycznego. Metoda zaprezentowana w niniejszej pracy bazuje na bardzo ważnym zagadnieniu algebry numerycznej, jakim jest nieujemna faktoryzacja macierzy. Kiedy jest ona zastosowana do analizy macierzy będącej wielowymiarową reprezentacją sygnału wejściowego, może wyizolować informację istotną z punktu widzenia procesów zachodzących w sygnale, a która nie jest rozpoznawalna w inny sposób. Przedstawiona metodologia korzysta z algorytmu znanego jako półbinarna nieujemna faktoryzacja macierzy, zastosowanego do reprezentacji czasowo-częstotliwościowej rzeczywistego sygnału drganiowego, zmierzonego na uszkodzonym łożysku pracującym w stacji napędowej przenośnika taśmowego. Wykryte impulsy związane z uszkodzeniem lokalnym zostały wyraźnie zidentyfikowane. Działanie algorytmu jest satysfakcjonujące w kwestii wydajności obliczeniowej oraz jakości otrzymanego wyniku.
    Źródło:
    Diagnostyka; 2017, 18, 1; 3-8
    1641-6414
    2449-5220
    Pojawia się w:
    Diagnostyka
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The parallel tiled WZ factorization algorithm for multicore architectures
    Autorzy:
    Bylina, Beata
    Bylina, Jarosław
    Powiązania:
    https://bibliotekanauki.pl/articles/331092.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    tiled algorithm
    WZ factorization
    solution of linear system
    Amdahl’s law
    high performance computing
    multicore architecture
    rozkład WZ
    układ liniowy
    prawo Amdahla
    architektura wielordzeniowa
    Opis:
    The aim of this paper is to investigate dense linear algebra algorithms on shared memory multicore architectures. The design and implementation of a parallel tiled WZ factorization algorithm which can fully exploit such architectures are presented. Three parallel implementations of the algorithm are studied. The first one relies only on exploiting multithreaded BLAS (basic linear algebra subprograms) operations. The second implementation, except for BLAS operations, employs the OpenMP standard to use the loop-level parallelism. The third implementation, except for BLAS operations, employs the OpenMP task directive with the depend clause. We report the computational performance and the speedup of the parallel tiled WZ factorization algorithm on shared memory multicore architectures for dense square diagonally dominant matrices. Then we compare our parallel implementations with the respective LU factorization from a vendor implemented LAPACK library. We also analyze the numerical accuracy. Two of our implementations can be achieved with near maximal theoretical speedup implied by Amdahl’s law.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2019, 29, 2; 407-419
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Rekonstrukcja niekompletnych obrazów za pomocą metod aproksymacji modelami niskiego rzędu
    Image completion with low-rank model approximation methods
    Autorzy:
    Sadowski, T.
    Zdunek, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/408844.pdf
    Data publikacji:
    2017
    Wydawca:
    Politechnika Lubelska. Wydawnictwo Politechniki Lubelskiej
    Tematy:
    rekonstrukcja obrazów
    aproksymacja niskiego rzędu
    nieujemna faktoryzacja macierzy
    dekompozycja tensorowa
    uzupełnianie elementów macierzy
    image completion
    low-rank approximation
    nonnegative matrix factorization
    tensor decomposition
    matrix completion
    Opis:
    W pracy badano zadanie rekonstrukcji brakujących pikseli w obrazach poddanych losowym zaburzeniom impulsowym w kanale transmisyjnym. Takie zadanie może być sformułowane w kontekście interpolacji obrazu na nieregularnej siatce lub aproksymacji niekompletnego obrazu za pomocą modeli dekompozycji obrazu na faktory niskiego rzędu. Porównano skuteczność czterech algorytmów opartych na dekompozycjach macierzy lub tensorów: SVT, SmNMF-MC, FCSA-TC i SPC-QV. Badania przeprowadzono na obrazach niekompletnych, otrzymanych z obrazów oryginalnych przez usunięcie losowo wybranych pikseli lub linii tworzących regularną siatkę. Najwyższą efektywność rekonstrukcji obrazu uzyskano gdy na estymowane faktory niskiego rzędu narzucano ograniczenia nieujemności i gładkości w postaci wagowej filtracji uśredniającej.
    The paper is concerned with the task of reconstructing missing pixels in images perturbed with impulse noise in a transmission channel. Such a task can be formulated in the context of image interpolation on an irregular grid or by approximating an incomplete image by low-rank factor decomposition models. We compared four algorithms that are based on the low-rank decomposition model: SVT, SmNMF-MC , FCSA-TC and SPC-QV. The numerical experiments are carried out for various cases of incomplete images, obtained by removing random pixels or regular grid lines from test images. The best performance is obtained if nonnegativity and smoothing constraints are imposed onto the estimated low-rank factors.
    Źródło:
    Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska; 2017, 7, 4; 44-48
    2083-0157
    2391-6761
    Pojawia się w:
    Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Using recommendation approaches for ratings matrixes in online marketing
    Zastosowanie zaleceń rekomendacji do oceny macierzy w marketingu online
    Autorzy:
    Nehrey, Maryna
    Hnot, Taras
    Powiązania:
    https://bibliotekanauki.pl/articles/591774.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Ekonomiczny w Katowicach
    Tematy:
    Matrix factorization
    Memory-based recommender systems
    Model-based recommender systems
    Recommender systems
    Faktoryzacja macierzowa
    Modele rekomendujące oparte na modelach
    Systemy rekomendujące
    Systemy rekomendujące oparte na pamięci
    Opis:
    The main objective of the study is detecting of advantages and disadvantages of different algorithms which are used when building recommender system. Recommender systems became so popular because of active development of online marketing and increase of sales through the Internet. Development and implementation of a strategy for recommending products cause effective use of resources and dynamic sales of the company. Recommender systems are one of the most effective tools: systems, which are built using memory-based algorithms, and systems with model-based algorithms. The best performance was shown by Matrix Factorization techniques with Stochastic Gradient Descend. When selecting a recommender system it is advisable to consider the purpose of use, product features, specifications and availability of customer data on their preferences. The use of one of the described recommender system will improve the efficiency of the product marketing.
    Głównym celem badania jest wykrycie zalet i wad różnych algorytmów wykorzystywanych podczas budowania systemu rekomendacji. Systemy rekomendujące stały się tak popularne ze względu na aktywny rozwój marketingu internetowego i wzrost sprzedaży za pośrednictwem Internetu. Opracowanie i wdrożenie strategii rekomendowania produktów powoduje efektywne wykorzystanie zasobów firmy i dynamiczną sprzedaż. Systemy rekomendujące są jednym z najbardziej efektywnych narzędzi – systemów, które są zbudowane przy użyciu algorytmów opartych na pamięci i systemów z algorytmami opartymi na modelach. Najlepszą wydajność pokazały techniki Matrix Factorization ze Stochastic Gradient Descend. Wybierając system rekomendujący, należy wziąć pod uwagę cel używania, cechy produktu, specyfikacje i dostępność danych klienta według ich preferencji. Korzystanie z jednego z opisanych systemów rekomendujących poprawi efektywność marketingu produktów.
    Źródło:
    Studia Ekonomiczne; 2017, 342; 115-130
    2083-8611
    Pojawia się w:
    Studia Ekonomiczne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Safety weaknesses of digital signature used for safety critical applications of e-government
    Autorzy:
    Franekova, M.
    Šutak, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/393832.pdf
    Data publikacji:
    2018
    Wydawca:
    Polskie Stowarzyszenie Telematyki Transportu
    Tematy:
    e-government
    safety-critical
    services
    eID card
    authorization
    qualified certificate
    digital signature
    RSA
    ECDSA
    complexity of factorization
    e-państwo
    karta eID
    autoryzacja
    podpis kwalifikowany
    podpis cyfrowy
    złożoność faktoryzacji
    Opis:
    The authors of this article focus on the analysis of safety weaks of digital signature schemes used within e-Government service in condition of Slovak republic. Main part is orientated on the possibility of attacks on eID card with using RSA digital signature scheme what was in the last months very frequently medialized in Slovakia. In the practical part on the base of mathematically description is analysed possible weaks of RSA digital signature schemes especially complexity of factorization problems dependence of length of key is describe and compare with more effectiveness ECDSA scheme. On the base of studies the authors mentioned the recommendations for parameters selection of very often used digital signature schemes focus on access to safety-critical applications supported during process of digitalization of e-Government in Slovak republic.
    Źródło:
    Archives of Transport System Telematics; 2018, 11, 3; 11-18
    1899-8208
    Pojawia się w:
    Archives of Transport System Telematics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Kryptosystemy oparte na problemach trudnych obliczniowo z wyszczególnieniem problemu faktoryzacji liczb całkowitych
    Cryprosystems based on difficult computational problems with specification of the prime factorization problem
    Autorzy:
    Kapcia, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/320370.pdf
    Data publikacji:
    2005
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    złożoność obliczeniowa
    bezpieczeństwo kryptosystemów klucza publicznego
    faktoryzacja liczb całkowitych
    logarytm dyskretny
    logarytm dyskretny na krzywych eliptycznych
    security of public key cryptosystems
    computational complexity
    prime factorization
    discrete logarithm
    elliptic curve discrete logarithm
    Opis:
    Publikacja przedstawia analizę złożoności obliczeniowej problemów matematycznych, na których opiera się konstrukcja, a zarazem bezpieczeństwo kryptosystemów klucza publicznego. Jednocześnie, na podstawie aktualnej wiedzy z obliczeniowej teorii liczb oraz informacji o możliwościach nowoczesnej techniki obliczeniowej, przedyskutowana została skuteczność algorytmów wykorzystywanych do rozwiązywania tych problemów.
    This paper presents analysis of computational complexity of mathematical problems on which construction and security of the public key cryptosystems could be based. Additionally on the basis of current knowledge sourcing from computational number and information theory, regarding possibilities of modern computational techniques, it has been discussed effectiveness of algorithms solving these problems.
    Źródło:
    Elektrotechnika i Elektronika; 2005, 24, 2; 148-157
    1640-7202
    Pojawia się w:
    Elektrotechnika i Elektronika
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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