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Search results for: discrete green's function
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Morse decompositions for a population model with harvesting. Case Hj-Se: Harvesting juveniles only, equal survival rates of juveniles and adults
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Morse decompositions for a population model with harvesting. Case Hj-S1: Harvesting juveniles only, survival rates of juveniles and adults add up to 1
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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A DISCRETE-CONTINUOUS METHOD OF MECHANICAL SYSTEM MODELLING
PublicationThe paper describes a discrete-continuous method of dynamic system modelling. The presented approach is hybrid in its nature, as it combines the advantages of spatial discretization methods with those of continuous system modelling methods. In the proposed method, a three-dimensional system is discretised in two directions only, with the third direction remaining continuous. The thus obtained discrete-continuous model is described...
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Numerical Test for Stability Evaluation of Discrete-Time Systems
PublicationIn this paper, a new numerical test for stability evaluation of discrete-time systems is presented. It is based on modern root-finding techniques at the complex plane employing the Delaunay triangulation and Cauchy's Argument Principle. The method evaluates if a system is stable and returns possible values and multiplicities of unstable zeros of the characteristic equation. For state-space discrete-time models, the developed test...
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PROTEINS-STRUCTURE FUNCTION AND BIOINFORMATICS
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On the Characteristic Graph of a Discrete Symmetric Channel
PublicationWe present some characterizations of characteristic graphs of row and/or column symmetric channels. We also give a polynomial-time algorithm that decides whether there exists a discrete symmetric channel whose characteristic graph is equal to a given input graph. In addition, we show several applications of our results.
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Discrete-continuous optimisation of an axial flow blood pump
PublicationThis paper presents results of discrete-continuous optimisation of an axial flow blood pump. Evolution Strategies (ES) are used as a global optimisation method in order to localise the optimal solution in relatively short time. The whole optimisation process is fully automated. This also applies to geometry modelling. Numerical simulations of the flow inside the pump is performed by means of the Reynolds-Average Navier-Stokes...
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The Discrete-Continuous, Global Optimisation of an Axial Flow Blood Pump
PublicationThis paper presents the results of the discrete-continuous optimisation of an axial flow blood pump. Differential evolution (DE) is used as a global optimisation method in order to localise the optimal solution in a relatively short time. The whole optimisation process is fully automated. This also applies to geometry modelling. Numerical simulations of the flow inside the pump are performed by means of the Reynolds-Average Navier-Stokes...
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Discrete convolution based on polynomial residue representation
PublicationThis paper presents the study of fast discrete convolution calculation with use of the Polynomial Residue Number System (PRNS). Convolution can be based the algorithm similar to polynomial multiplication. The residue arithmetic allows for fast realization of multiplication and addition, which are the most important arithmetic operations in the implementation of convolution. The practical aspects of hardware realization of PRNS...
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Discrete and continuous fractional persistence problems – the positivity property and applications
PublicationIn this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
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Discrete Modelling of Micro-structural Phenomena in Granular Shear Zones
PublicationThe micro-structure evolution in shear zones in cohesionless sand for quasi-static problems was analyzed with a discrete element method (DEM). The passive sand failure for a very rought retaining wall undergoing horizontal translation towards the sand backfill was discussed. To simulate the behaviour of sand, the spherical discrete element model was used with elements in the form of rigid spheres with contacts moments.
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The smoothness test for a density function
PublicationThe problem of testing hypothesis that a density function has no more than μ derivatives versus it has more than μ derivatives is considered. For a solution, the L2 norms of wavelet orthogonal projections on some orthogonal ‘‘differences’’ of spaces from a multiresolution analysis is used. For the construction of the smoothness test an asymptotic distribution of a smoothness estimator is used. To analyze that asymptotic distribution,...
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A procedure for elastoplastic hardening function identification.
PublicationThe inverse analysis method for identifying a nonlinear hardening function,which governs a plastic yielding of soil and rock materials in the framework of elastoplastic theory is presented. A concept of two stage finite element based on spatial discretization of computational space and hardening function space is introduced. The proposed inverse analysis can be classified as the output least squares method. The Levenberg Marquard...
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Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
PublicationIn this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained...
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Stability of softly switched multiregional dynamic output controllers with a static antiwindup filter: A discrete-time case
PublicationThis paper addresses the problem of model-based global stability analysis of discrete-time Takagi–Sugeno multiregional dynamic output controllers with static antiwindup filters. The presented analyses are reduced to the problem of a feasibility study of the Linear Matrix Inequalities (LMIs), derived based on Lyapunov stability theory. Two sets of LMIs are considered candidate derived from the classical common quadratic Lyapunov...
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Discrete-time estimation of nonlinear continuous-time stochastic systems
PublicationIn this paper we consider the problem of state estimation of a dynamic system whose evolution is described by a nonlinear continuous-time stochastic model. We also assume that the system is observed by a sensor in discrete-time moments. To perform state estimation using uncertain discrete-time data, the system model needs to be discretized. We compare two methods of discretization. The first method uses the classical forward Euler...
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Discrete-time estimation of nonlinear continuous-time stochastic systems
PublicationIn this paper we consider the problem of state estimation of a dynamic system whose evolution is described by a nonlinear continuous-time stochastic model. We also assume that the system is observed by a sensor in discrete-time moments. To perform state estimation using uncertain discrete-time data, the system model needs to be discretized. We compare two methods of discretization. The first method uses the classical forward Euler...
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Brain Structure & Function
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CELL STRUCTURE AND FUNCTION
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Journal of Function Spaces
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TREES-STRUCTURE AND FUNCTION
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Periodic Properties of 1D FE Discrete Models in High Frequency Dynamics
PublicationFinite element discrete models of various engineering 1D structures may be considered as structures of certain periodic characteristics. The source of this periodicity comes from the discontinuity of stress/strain field between the elements. This behaviour remains unnoticeable, when low frequency dynamics of these structures is investigated. At high frequency regimes, however, its influence may be strong enough to dominate calculated...
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Green function diagonal for a class of heat equations
PublicationA construction of the heat kernel diagonal is considered as element of generalized zeta function theory, which gradient at the origin defines determinant of a differential operator in a technique for regularizing quadratic path integral. Some classes of explicit expressions of the Green function in the case of finite-gap potential coefficient of the heat equation are constructed. An algorithm and program for Mathematica are presented...
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Connection matrix theory for discrete dynamical systems
PublicationIn [C] and [F1] the connection matrix theory for Morse decomposition is developedin the case of continuous dynamical systems. Our purpose is to study the case of discrete timedynamical systems.
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Index filtrations and Morse decomposition for discrete dynamical systems
PublicationOn a Morse decomposition of an isolated invariant set of a homeomorphism(discrete dynamical system) there are partial orderings defined by the homeomorphism.These are called admissible orderings of the...
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Matematyka Dyskretna (Discrete Mathematics) 2021/22
e-Learning CoursesMateriały do przedmiotów: - Matematyka Dyskretna, kier: informatyka niestac. inż. rok 2. sem.3.
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Matematyka Dyskretna (Discrete Mathematics) Lato 2022
e-Learning CoursesMateriały do przedmiotów: - Matematyka Dyskretna, kier: informatyka inż. rok 1. sem.2.
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Local basis function method for identification of nonstationary systems
PublicationThis thesis is focused on the basis function method for the identification of nonstationary processes. The first chapter describes a group of models that can be identified using the basis function method. The next chapter describes the basic version of the basis function method, including its algebraic and statistical properties. The following section introduces the local basis function (LBF) method: its properties are described...
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Discrete Optimization
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Discrete Analysis
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THE FUNCTION OF GREENERY IN A SKYSCRAPER: THE PLACEMENT AND ITS INFLUENCE
PublicationThe contrast between the high rise buildings; with their mostly geometric shapes, and the organic form of the greenery was visible even in the idea of a skyscraper. Yet the realizations and recent projects show emerging interest and the link between them. To better understand the developing function of the greenery in the context of a skyscraper, both literature and case studies are conducted. The aim is to relate the location...
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Gordon Decomposition of the Magnetizability of a Dirac One-Electron Atom in an Arbitrary Discrete Energy State
PublicationWe present analytical derivation of formulas for diamagnetic and paramagnetic contributions to magnetizabilities of relativistic hydrogenlike atoms being in an arbitrary discrete energy eigenstate.
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Quasi-discrete modelling of PMSM phase currents in drives with low switching-to-fundamental frequency ratio
PublicationThis study proposes a new quasi-discrete approach to modelling the permanent magnet synchronous motor (PMSM). The quasi-discrete modelling reflects the impact of continuous rotor movement, which takes place during a control cycle, on the shape of motor current waveforms. This provides much improvement in current modelling accuracy under inverter low switching-to-fundamental frequency operation. The proposed approach may be used...
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Port-based approach to distributed transfer function method
PublicationIn the paper there is presented an uniform, port-based approach to modeling of both lumped and distributed parameter systems. Port-based model of distributed system has been defined by application of distributed transfer function method (DTFM). The approach proposed combines versatility of port - based modeling and accuracy of distributed transfer function method. It enables to formulate appropriate input data for computer analysis...
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The Concept of Using the Decision-Robustness Function in Integrated Navigation Systems
PublicationThe diversity and non-uniformity of the positioning systems available in maritime navigation systems often impede the watchkeeping officer in the selection of the appropriate positioning system, in particular, in restricted basins. Thus, it is necessary to introduce a mathematical apparatus to suggest, in an automated manner, which of the available systems should be used at the given moment of a sea trip. Proper selection of the...
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Local basis function estimators for identification of nonstationary systems
PublicationThe problem of identification of a nonstationary stochastic system is considered and solved using local basis function approximation of system parameter trajectories. Unlike the classical basis function approach, which yields parameter estimates in the entire analysis interval, the proposed new identification procedure is operated in a sliding window mode and provides a sequence of point (rather than interval) estimates. It is...
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Anti-plane surface waves in media with surface structure: Discrete vs. continuum model
PublicationWe present a comparison of the dispersion relations derived for anti-plane surface waves using the two distinct approaches of the surface elasticity vis-a-vis the lattice dynamics. We consider an elastic half-space with surface stresses described within the Gurtin–Murdoch model, and present a formulation of its discrete counterpart that is a square lattice half-plane with surface row of particles having mass and elastic bonds different...
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Tuning the work function of graphite nanoparticles via edge termination
PublicationGraphite nanoparticles are important in energy materials applications such as lithium-ion batteries (LIBs), supercapacitors and as catalyst supports. Tuning the work function of the nanoparticles allows local control of lithiation behaviour in LIBs, and the potential of zero charge of electrocatalysts and supercapacitors. Using large scale density functional theory (DFT) calculations, we find that the surface termination of multilayer...
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Clonal selection in discrete optimization
PublicationW rozprawie zajmujemy się efektywnymi metodami przybliżonego rozwiązywania problemów optymalizacji dyskretnej, a w szczególności algorytmami opartymi na metodzie selekcji klonalnej (SK), należącymi do kategorii sztucznych systemów immunologicznych. Techniki optymalizacji to znaczące pole badań w informatyce, a niektóre ze starszych technik, takie jak algorytmy genetyczne, symulowane wyżarzanie czy przeszukiwanie tabu, stały się...
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Roughness evaluation of turned composite surfaces by analysis of the shape of Autocorrelation Function
PublicationIn this paper, the application of an Autocorrelation Function for the characterisation of surface topography was validated. The roughness evaluation of turned composite surfaces was supported by sophisticated studies of the Autocorrelation Function properties, considering especially the shape of the function. Details were measured with the optical method. The selection of the surface roughness evaluation procedures was carried...
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Validation of dynamic electrochemical impedance spectrograms using autocorrelation function
PublicationValidation of impedance data is essential for checking the reliability of experimental data. Kramers – Kronig transformation is used to verify data obtained from classical Electrochemical Impedance Spectroscopy (EIS) measurements. Data obtained from Dynamic Electrochemical Impedance Spectroscopy (DEIS) could be validated in the same way, but in this case, there is no information about internal consistency between every single spectrum...
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Regularized Local Basis Function Approach to Identification of Nonstationary Processes
PublicationThe problem of identification of nonstationary stochastic processes (systems or signals) is considered and a new class of identification algorithms, combining the basis functions approach with local estimation technique, is described. Unlike the classical basis function estimation schemes, the proposed regularized local basis function estimators are not used to obtain interval approximations of the parameter trajectory, but provide...
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SIMULATIONS OF FRACTURE IN CONCRETE BEAMS UNDER BENDING USING A CONTINUUM AND DISCRETE APPROACH
PublicationThe paper describes two-dimensional meso-scale results of fracture in notched concrete beams under bending. Concrete was modelled as a random heterogeneous 4-phase material composed of aggregate particles, cement matrix, interfacial transitional zones and air voids. Within continuum mechanics, the simulations were carried out with the finite element method based on a isotropic damage constitutive model enhanced by a characteristic...
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Topological-numerical analysis of a two-dimensional discrete neuron model
PublicationWe conduct computer-assisted analysis of a two-dimensional model of a neuron introduced by Chialvo in 1995 [Chaos, Solitons Fractals 5, 461–479]. We apply the method of rigorous analysis of global dynamics based on a set-oriented topological approach, introduced by Arai et al. in 2009 [SIAM J. Appl. Dyn. Syst. 8, 757–789] and improved and expanded afterward. Additionally, we introduce a new algorithm to analyze the return times...
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Computational Methods and Function Theory
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Journal of Function Spaces and Applications
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublicationIn this article, specific methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublicationIn this study, dedicated methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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Single and Series of Multi-valued Decision Diagrams in Representation of Structure Function
PublicationStructure function, which defines dependency of performance of the system on performance of its components, is a key part of system description in reliability analysis. In this paper, we compare two approaches for representation of the structure function. The first one is based on use of a single Multi-valued Decision Diagram (MDD) and the second on use of a series of MDDs. The obtained results indicate that the series of MDDs...
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Follow-up assessment of the microvascular function in patients with long COVID
PublicationLong COVID is a complex pathophysiological condition. However, accumulating data suggests that COVID-19 is a systemic microvascular endothelial dysfunction with different clinical manifestations. In this study, a microvascular function was assessed in long COVID patients (n = 33) and healthy controls (n = 30) using flow-mediated skin fluorescence technique (FMSF), based on measurements of nicotinamide adenine dinucleotide fluorescence...