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    Wyświetlanie 1-7 z 7
    Tytuł:
    Model based analysis of signaling pathways
    Autorzy:
    Śmieja, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/907948.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    ścieżka sygnalizacyjna
    układ dynamiczny
    biologia systemów
    interferon-beta
    signaling pathways
    dynamical system
    systems biology
    Opis:
    The paper is concerned with application of mathematical modeling to the analysis of signaling pathways. Two issues, deterministic modeling of gene transcription and model-driven discovery of regulatory elements, are dealt with. First, the biological background is given and the importance of the stochastic nature of biological processes is addressed. The assumptions underlying deterministic modeling are presented. Special emphasis is put on describing gene transcription. A framework for including unknown processes activating gene transcription by means of first-order lag elements is introduced and discussed. Then, a particular interferon-ß induced pathway is introduced, limited to early events that precede activation of gene transcription. It is shown how to simplify the system description based on the goals of modeling. Further, a computational analysis is presented, facilitating better understanding of the mechanisms underlying regulation of key components in the pathway. The analysis is illustrated by a comparison of simulation and experimental data.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2008, 18, 2; 139-145
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Time to the convergence of evolution in the space of population states
    Autorzy:
    Karcz-Dulęba, I.
    Powiązania:
    https://bibliotekanauki.pl/articles/907643.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    ewolucja fenotypowa
    układ dynamiczny
    punkt stały
    phenotypic evolution
    dynamical system
    time to convergence
    fixed points
    Opis:
    Phenotypic evolution of two-element populations with proportional selection and normally distributed mutation is considered. Trajectories of the expected location of the population in the space of population states are investigated. The expected location of the population generates a discrete dynamical system. The study of its fixed points, their stability and time to convergence is presented. Fixed points are located in the vicinity of optima and saddles. For large values of the standard deviation of mutation, fixed points become unstable and periodical orbits arise. In this case, fixed points are also moved away from optima. The time to convergence to fixed points depends not only on the mutation rate, but also on the distance of the points from unstability. Results show that a population spends most time wandering slowly towards the optimum with mutation as the main evolution factor.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2004, 14, 3; 279-287
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Procedural generation of aesthetic patterns from dynamics and iteration processes
    Autorzy:
    Gdawiec, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/329905.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    dynamical system
    dynamics process
    iteration process
    aesthetic pattern
    układ dynamiczny
    proces dynamiczny
    proces iteracji
    wzorzec estetyczny
    Opis:
    Aesthetic patterns are widely used nowadays, e.g., in jewellery design, carpet design, as textures and patterns on wallpapers, etc. Most of the work during the design stage is carried out by a designer manually. Therefore, it is highly useful to develop methods for aesthetic pattern generation. In this paper, we present methods for generating aesthetic patterns using the dynamics of a discrete dynamical system. The presented methods are based on the use of various iteration processes from fixed point theory (Mann, S, Noor, etc.) and the application of an affine combination of these iterations. Moreover, we propose new convergence tests that enrich the obtained patterns. The proposed methods generate patterns in a procedural way and can be easily implemented on the GPU. The presented examples show that using the proposed methods we are able to obtain a variety of interesting patterns. Moreover, the numerical examples show that the use of the GPU implementation with shaders allows the generation of patterns in real time and the speed-up (compared with a CPU implementation) ranges from about 1000 to 2500 times.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2017, 27, 4; 827-837
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection
    Autorzy:
    Obaid, H. A.
    Ouifki, R.
    Patidar, K. C.
    Powiązania:
    https://bibliotekanauki.pl/articles/331053.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    HIV infection
    dynamical system
    nonstandard finite difference methods
    equilibria
    stability
    zakażenie HIV
    układ dynamiczny
    metoda różnic skończonych
    równowaga
    Opis:
    We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves the positivity of the solution, which is one of the essential requirements when modeling epidemic diseases. Robust numerical results confirming theoretical investigations are provided. Comparisons are also made with the other conventional approaches that are routinely used for such problems.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2013, 23, 2; 357-372
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Generalized practical stability analysis of discontinuous dynamical systems
    Autorzy:
    Zhai, G.
    Michel, A. N.
    Powiązania:
    https://bibliotekanauki.pl/articles/907305.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    układ dynamiczny nieciągły
    analiza ilościowa
    funkcja Lyapunova
    discontinuous dynamical system
    quantitative analysis
    generalized practical stability
    Lyapunov-like function
    Opis:
    In practice, one is not only interested in the qualitative characterizations provided by the Lyapunov stability, but also in quantitative information concerning the system behavior, including estimates of trajectory bounds, possibly over finite time intervals. This type of information has been ascertained in the past in a systematic manner using the concept of practical stability. In the present paper, we give a new definition of generalized practical stability (abbreviated as GP-stability) and establish some sufficient conditions concerning GP-stability for a wide class of discontinuous dynamical systems. As in the classical Lyapunov theory, our results constitute a Direct Method, making use of auxiliary scalar-valued Lyapunov-like functions. These functions, however, have properties that differ significantly from the usual Lyapunov functions. We demonstrate the applicability of our results by means of several specific examples.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2004, 14, 1; 5-12
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On a stable solution of the problem of disturbance reduction
    Autorzy:
    Maksimov, Vyacheslav I.
    Powiązania:
    https://bibliotekanauki.pl/articles/1838215.pdf
    Data publikacji:
    2021
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    disturbance reduction
    dynamical controlled system
    guaranteed control theory
    redukcja zakłóceń
    system sterowany dynamicznie
    teoria sterowania
    Opis:
    We study the problem of active reduction of the influence of a disturbance on the output of a linear control system. We consider a system of linear differential equations under the action of an unknown disturbance and a control to be formed. Our goal is to design an algorithm for reducing the disturbance by means of an appropriate control on the basis of inaccurate measurements of the system phase coordinates. This algorithm should form a feedback control that would guarantee that the trajectory of a given system tracks the trajectory of the reference system, i.e., the system described by the same differential equations but with zero control and disturbance. We present an algorithm for solving this problem. The algorithm, based on the constructions of guaranteed control theory, is stable with respect to informational noises and computational errors.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2021, 31, 2; 187-194
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Derivation of physically motivated constraints for efficient interval simulations applied to the analysis of uncertain dynamical systems
    Autorzy:
    Freihold, M.
    Hofer, E. P.
    Powiązania:
    https://bibliotekanauki.pl/articles/930126.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    system Hamiltona
    algorytm rozgałęzienia
    system dynamiczny
    VALENCIA-IVP
    consistency tests for the reduction of overestimation
    identification of dynamical constraints
    Hamiltonian systems
    branch algorithm
    prune algorithm
    Opis:
    Interval arithmetic techniques such as VALENCIA-IVP allow calculating guaranteed enclosures of all reachable states of continuous-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Considering the fact that, in naive implementations of interval algorithms, overestimation might lead to unnecessarily conservative results, suitable consistency tests are essential to obtain the tightest possible enclosures. In this contribution, a general framework for the use of constraints based on physically motivated conservation properties is presented. The use of these constraints in verified simulations of dynamical systems provides a computationally efficient procedure which restricts the state enclosures to regions that are physically eaningful. A branch and prune algorithm is modified to a consistency test, which is based on these constraints. Two application scenarios are studied in detail. First, the total energy is employed as a conservation property for the analysis of mechanical systems. It is shown that conservation properties, such as the energy, are applicable to any Hamiltonian system. The second scenario is based on constraints that are derived from decoupling properties, which are considered for a high-dimensional compartment model of granulopoiesis in human blood cell dynamics.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2009, 19, 3; 485-499
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-7 z 7

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