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Wyniki wyszukiwania dla: QUADRATIC STOCHASTIC OPERATORS
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On mixing in the class of quadratic stochastic operators
PublikacjaWe study different types of limit behavior of quadratic stochastic operators acting on ℓ^1 (or ℓ^1_d) spaces in both strong and uniform topologies. The main motif of the paper is to express the uniform and strong asymptotic stability of the quadratic stochastic operator in terms of convergence of the associated (linear) nonhomogeneous Markov chain. We also examine which type of uniform convergence of iterates of the quadratic...
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Quadratic stochastic operators on Banach lattices
PublikacjaWe study the convergence of iterates of quadratic stochastic operators that are mean monotonic. They are defined on the convex set of probability measures concentrated on a weakly compact order interval S = [0, f] of a fixed Banach lattice F. We study their regularity and identify the limits of trajectories either as the “infimum” or “supremum” of the support of initial distributions.
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Weak Stability of Centred Quadratic Stochastic Operators
PublikacjaWe consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offspring’s trait is equal to an additively perturbed arithmetic mean of the parents’ traits. It is shown that for the existence of a weak limit, it...
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Prevalence Problem in the Set of Quadratic Stochastic Operators Acting on L1
PublikacjaThis paper is devoted to the study of the problem of prevalence in the class of quadratic stochastic operators acting on the L1 space for the uniform topology. We obtain that the set of norm quasi-mixing quadratic stochastic operators is a dense and open set in the topology induced by a very natural metric. This shows the typical long-term behaviour of iterates of quadratic stochastic operators.
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Asymptotic properties of quadratic stochastic operators acting on the L1 space
PublikacjaQuadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introduced and studied recently in the ℓ1 space. It turns out that in principle most of the results can be carried over to the L1 space. However, due to topological properties of this space one has to restrict in some situations to kernel quadratic stochastic operators. In this article we study the uniform and strong asymptotic...
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Quadratic stochastic operators as a tool in modelling the dynamics of a distribution of a population trait
PublikacjaQuadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introduced and studied recently. In the present work we discuss biological interpretations that can be attributed to them. We also propose a computer simulation method to illustrate the behaviour of iterates of quadratic stochastic operators.
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A Noether theorem for stochastic operators on Schatten classes
PublikacjaWe prove that a stochastic (Markov) operator S acting on a Schatten class C_1 satisfies the Noether condition S'(A) = A and S'(A^2) = A^2, where A is a Hermitian bounded linear operator on a complex Hilbert space H, if and only if, S(E(G)XE(G)) = E(G)S(X)E(G) holds true for every Borel subset G of the real line R, where E(G) denotes the orthogonal projection coming from the spectral resolution of A. Similar results are obtained...
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Asymptotic behaviour in the set of nonhomogeneous chains of stochastic operators
PublikacjaWe study different types of asymptotic behaviour in the set of (infinite dimensional) nonhomogeneous chains of stochastic operators acting on L1(μ) spaces. In order to examine its structure we consider different norm and strong operator topologies. To describe the nature of the set of nonhomogeneous chains of Markov operators with a particular limit behaviour we use the category theorem of Baire. We show that the geometric structure...
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Mieszanie w klasie niejednorodnych łańcuchów Markowa i kwadratowych operatorów stochastycznych
PublikacjaRozprawa doktorska poświęcona jest zagadnieniu asymptotycznych własności w klasie nieskończenie wymiarowych niejednorodnych łańcuchów Markowa z czasem dyskretnym oraz w klasie kwadratowych operatorów stochastycznych. W pierwszej kolejności definiowane są różne rodzaje asymptotycznego zachowania (mieszania) niejednorodnych łańcuchów Markowa odpowiadające zbieżności w normowej i mocnej topologii operatorowej oraz omówione są relacje...
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Rigorous numerics for critical orbits in the quadratic family
PublikacjaWe develop algorithms and techniques to compute rigorous bounds for finite pieces of orbits of the critical points, for intervals of parameter values, in the quadratic family of one-dimensional maps fa(x)=a−x2. We illustrate the effectiveness of our approach by constructing a dynamically defined partition P of the parameter interval Ω=[1.4,2] into almost 4 million subintervals, for each of which we compute to high precision the...
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PLC-based Implementation of Stochastic Optimization Method in the Form of Evolutionary Strategies for PID, LQR, and MPC Control
PublikacjaProgrammable logic controllers (PLCs) are usually equipped with only basic direct control algorithms like proportional-integral-derivative (PID). Modules included in engineering software running on a personal computer (PC) are usually used to tune controllers. In this article, an alternative approach is considered, i.e. the development of a stochastic optimizer based on the (μ,λ) evolution strategy (ES) in a PLC. For this purpose,...
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Stochastic resonance in measurements
PublikacjaNoise is usually associated with the negative phenomenon, hampering the measurements data and their analysis. This view has been broken in the '80s when the phenomenon of stochastic resonance (Stochastic Resonance - SR) was discovered. It is a phenomenon that occurs in nonlinear dynamic measurement systems when the selected input noise can optimize system performance. SR became a way to improve efficiency of weak signals detection....
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Fractional differential equations with causal operators
PublikacjaWe study fractional differential equations with causal operators. The existence of solutions is obtained by applying the successive approximate method. Some applications are discussed including also the case when causal operator Q is a linear operator. Examples illustrate some results.
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Directed electromagnetic pulse dynamics: projecting operators method
PublikacjaIn this article, we consider a one-dimensional model of electromagnetic pulse propagation in isotropic media, takinginto account a nonlinearity of the third order. We introduce a method for Maxwell's equation transformation on thebasis of a complete set of projecting operators. The operators correspond to wave dispersion branches including thedirection of propagation. As the simplest result of applying the method, we derive a system...
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Text-mining Similarity Approximation Operators for Opinion Mining in BI tools
PublikacjaThe concept of the Text-mining Similarity Approximation Operators for Opinion Mining as extensions to Natural Language Interface Database is defined. The new operators: “keywords of” dimension; subsetting operator “about C is q”; aggregation operator “by similar C” are proposed. These operators are based on the Latent Semantic Analysis and Social Network Analysis
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Neural Approximators for Variable-Order Fractional Calculus Operators (VO-FC)
PublikacjaThe paper presents research on the approximation of variable-order fractional operators by recurrent neural networks. The research focuses on two basic variable-order fractional operators, i.e., integrator and differentiator. The study includes variations of the order of each fractional operator. The recurrent neural network architecture based on GRU (Gated Recurrent Unit) cells functioned as a neural approximation for selected...
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Distortional buckling of thin-walled columns of closed quadratic cross-section
PublikacjaThe elastic stability of axially compressed column related to the cross-section distortion is investigated. Two kinds of closed quadratic cross-sections are taken into consideration with internal walls and without it. The governing differential equation is derived with aid of the principle of stationary total potential energy. The critical loads for the simply supported columns are found in an analytical form and compared with...
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Evolutionary Sets of Safe Ship Trajectories: problem dedicated operators
PublikacjaThe paper presents the optimization process of the evolutionary sets of safe ship trajectories method, with a focus on its problem-dedicated operators. The method utilizes a customized evolutionary algorithm to solve a constrained optimization problem. This problem is defined as finding a set of cooperating trajectories (a set is an evolutionary individual) of all the ships involved in the encounter situation. The resulting trajectories...
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Multi-state vibronic interactions in the fluorobenzene radical cation: The importance of quadratic coupling terms
PublikacjaThe multi-mode multi-state vibronic interactions in the set of X^2B_1 - D^2A_1 electronic states of the monofluoro benzene radical cation are investigated theoretically, based on a quadratic vibronic coupling approach. The underlying ionization potentials and coupling constants are obtained from ab initio coupled-cluster calculations. Previous investigations (relying on the linear coupling approach) are extended by including all...
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Dynamical nonlocality in quantum time via modular operators
PublikacjaWe formalize the concept of the modular energy operator within the Page and Wootters timeless framework. As a result, this operator is elevated to the same status as the more studied modular operators of position and momentum. In analogy with dynamical nonlocality in space associated with the modular momentum, we introduce and analyze the nonlocality in time associated with the modular energy operator. Some applications of our...
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Enhancing rheological muscle models with stochastic processes
PublikacjaPurpose: Biological musculoskeletal systems operate under variable conditions. Muscle stiffness, activation signals, and loads change during each movement. The presence of noise and different harmonic components in force production significantly influences the behaviour of the muscular system. Therefore, it is essential to consider these factors in numerical simulations. Methods: This study aims to develop a rheological mathematical...
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On noncausal identification of nonstationary stochastic systems
PublikacjaIn this paper we consider the problem of noncausal identification of nonstationary,linear stochastic systems, i.e., identification based on prerecorded input/output data. We show how several competing weighted least squares parameter smoothers, differing in memory settings, can be combined together to yield a better and more reliable smoothing algorithm. The resulting parallel estimation scheme automatically adjusts its smoothing...
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Elastic distortional buckling of thin-walled bars of closed quadratic cross-section
PublikacjaIn this study a thin-walled bar with closed quadratic cross-section is considered. The elastic stability of axially compressed bar related to the cross-section distortion is investigated. The governing differential equation is derived with aid of the principle of stationary total potential energy. The critical load for the simply supported bar is found in analytical form and it is compared with the FEM solution. Sufficient accuracy...
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Elastic distortional buckling of thin-walled bars of closed quadratic cross-section
PublikacjaIn this study a tin-walled bar with closed quadratic cross-section is considered. The elastic stability of axially compressed bar related to the cross-section distortion is investigated. The governing differential equatio is derived with aid of the principle of stationary potential energy. The critical load for simply supported bar is found in an analytical form and it is copared with the FEM solution. Sufficient accuracy of the...
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Estimation of a Stochastic Burgers' Equation Using an Ensemble Kalman Filter
PublikacjaIn this work, we consider a difficult problem of state estimation of nonlinear stochastic partial differential equations (SPDE) based on uncertain measurements. The presented solution uses the method of lines (MoL), which allows us to discretize a stochastic partial differential equation in a spatial dimension and represent it as a system of coupled continuous-time ordinary stochastic differential equations (SDE). For such a system...
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Quadratic Cohen representations in spectral analysis of serration process in Al–Mg alloys
PublikacjaImportant from mechanical point of view the Portevin–Le Chatelier serration phenomenon is being characterized by a complicated spectral profile. As a typical example of nonstationary processes it demands a special treatment allowing to follow the evolution of energy of stress fluctuations as a function of strain. The authors suggest the utilization of a compact system of quadratic transformations, known as Cohen class, as a technique...
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On DoA estimation for rotating arrays using stochastic maximum likelihood approach
PublikacjaThe flexibility needed to construct DoA estimators that can be used with rotating arrays subject to rapid variations of the signal frequency is offered by the stochastic maximum likelihood approach. Using a combination of analytic methods and Monte Carlo simulations, we show that for low and moderate source correlations the stochastic maximum likelihood estimator that assumes noncorrelated sources has accuracy comparable to the...
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An idea of an approach to self-testing of mixed signal systems based on a quadratic function stimulation
PublikacjaA new approach to self-testing of the analog parts of mixed-signal electronic systems controlled by microcontrollers equipped with an ADC and a DAC is presented. It is based on a BIST and a new fault diagnosis method. A novelty is the use of the DAC as a component of the BIST, allowing to generate a stimulating signal with a quadratic function shape. It contributes to a better extraction of information about the state of the circuit...
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Stochastic equivalence scales in log-normal distributions of expenditures
PublikacjaIn the paper, the properties of the stochastic equivalence scales (SES) are analysed when expenditure distributions are log-normal. The SES provides the equivalent distribution of expenditures when the population of households is heterogeneous with respect to such attributes as household size, demographic cpmposition, etc. For log-normal expenditure distributions, the non-parametric SES deflators are proportional to the ration...
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Saturation of Bernstein Schnabl operators.
PublikacjaW pracy dowodzi się twierdzenia o nasyceniu dla operatorów Bernsteina-Schnabla nad sympleksem Bauera w przestrzeni Banacha.
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Fast Basis Function Estimators for Identification of Nonstationary Stochastic Processes
PublikacjaThe problem of identification of a linear nonsta-tionary stochastic process is considered and solved using theapproach based on functional series approximation of time-varying parameter trajectories. The proposed fast basis func-tion estimators are computationally attractive and yield resultsthat are better than those provided by the local least squaresalgorithms. It is shown that two...
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Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures
PublikacjaVarious equicontinuity properties for families of Markov operators have been – and still are – used in the study of existence and uniqueness of invariant probability for these operators, and of asymptotic stability. We prove a general result on equivalence of equicontinuity concepts. It allows comparing results in the literature and switching from one view on equicontinuity to another, which is technically convenient in proofs....
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Asynchronous Networked Estimation System for Continuous Time Stochastic Processes
PublikacjaIn this paper we examine an asynchronous networked estimation system for state estimation of continuous time stochastic processes. Such a system is comprised of several estimation nodes connected using a possibly incomplete communication graph. Each of the nodes uses a Kalman filter algorithm and data from a local sensor to compute local state estimates of the process under observation. It also performs data fusion of local estimates...
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On noncausal weighted least squares identification of nonstationary stochastic systems
PublikacjaIn this paper, we consider the problem of noncausal identification of nonstationary, linear stochastic systems, i.e., identification based on prerecorded input/output data. We show how several competing weighted (windowed) least squares parameter smoothers, differing in memory settings, can be combined together to yield a better and more reliable smoothing algorithm. The resulting parallel estimation scheme automatically adjusts...
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Investigation of long-range dependencies in the stochastic part of daily GPS solutions
PublikacjaThe long-range dependence (LRD) of the stochastic part of GPS-derived topocentric coordinates change (North, East, Up) results with relatively high autocorrelation values with a focus on self-similarity. One of the reasons for such self-similarity in the GPS time series are noises that are commonly recognised to prevail in the form of the flicker noise model. To prove the self-similarity of the stochastic part of GPS time series...
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MODEL OF MULTILEVEL STOCHASTIC ANALYSIS OF ROAD SAFETY ON REGIONAL LEVEL
PublikacjaIn this paper multilevel approach to the issue of road safety level on the road network of European regions, classified as NUTS 2 in statistical databases of the European Union, has been presented. Following the pattern of many publications on road safety it has been assumed that the risk calculated as the number of death casualties in road accidents per 100,000 inhabitants of a given region has Poisson distribution. Therefore,...
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Discrete-time estimation of nonlinear continuous-time stochastic systems
PublikacjaIn 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
PublikacjaIn 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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Application of a stochastic compartmental model to approach the spread of environmental events with climatic bias
PublikacjaWildfires have significant impacts on both environment and economy, so understanding their behaviour is crucial for the planning and allocation of firefighting resources. Since forest fire management is of great concern, there has been an increasing demand for computationally efficient and accurate prediction models. In order to address this challenge, this work proposes applying a parameterised stochastic model to study the propagation...
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Asynchronous distributed state estimation for continuous-time stochastic processes
PublikacjaWe consider the problem of state estimation of a continuous-time stochastic process using an asynchronous distributed multi-sensor estimation system (ADES). In an ADES the state of a process of interest is estimated by a group of local estimators. Each local estimator based, for example, on a Kalman filter, performs single sensor filtration but also fusion of its local results and results from other (remote) processors to compute...
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Variations of Ship’s Deck Elevation Due to Stochastic Process of Containers Loading
PublikacjaThe stochastic process of container loading is described in the paper with special emphasis to ship motion when she is lying at a quay. The 3 DOF system was applied to describe rolling, pitching and heaving of a vessel which may cause a significant variations of momentary deck elevation. The realistic range of such variations are assessed for a variety of cargo locations on-board and a phase shift between two independent gantries...
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Locally Adaptive Cooperative Kalman Smoothing and Its Application to Identification of Nonstationary Stochastic Systems
PublikacjaOne of the central problems of the stochastic approximation theory is the proper adjustment of the smoothing algorithm to the unknown, and possibly time-varying, rate and mode of variation of the estimated signals/parameters. In this paper we propose a novel locally adaptive parallel estimation scheme which can be used to solve the problem of fixed-interval Kalman smoothing in the presence of model uncertainty. The proposed solution...
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Boundary value problems with causal operators
PublikacjaPraca dotyczy istnienia rozwiązań dla równań różniczkowych z nieliniowymi dwu-punktowymi warunkami brzegowymi. Podano warunki dostateczne na istnienie rozwiązań takich zagadnień stosując metodę iteracji monotonicznych. Dyskutowano też nierówności różniczkowe rzędu pierwszego z dodatnimi operatorami liniowymi oraz problem rozwiązań ekstremalnych.
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On residualities in the set of Markov operators on C1
PublikacjaDowodzi się, że zbiór operatorów Markowa na klasie Schattena 1, które są mieszające w normie, jest normowo gęsty, otwarty. Natomiast w topologii mocno operatorowej operatory Markowa mocno mieszające są zbiorem I kategorii.
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Shift invariant operators and a saturation theorem.
PublikacjaPraca jest kontynuacją wcześniejszych dwóch prac wydanych w Appl. Math. w latach 2001 i 2002. Główny wynik dotyczy wygładzania specjalnego ciągu zbieżnego słabo, tak iż dostajemy ciąg zbieżny w normie supremum.
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HCI-Based Wireless System for Measuring the Concentration of Mining Machinery and Equipment Operators
PublikacjaMaintaining stable and reliable working conditions is a matter of vital importance for various companies, especially those involving heavy machinery. Due to human exhaustion, as well as unpredicted hazards and dangerous situations, the personnel has to take actions and wisely plan each move. This paper presents a human–computer interaction (HCI)-based system that uses a concentration level measurement function to increase the safety...
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Comparative analysis of numerical with optical soliton solutions of stochastic Gross–Pitaevskii equation in dispersive media
PublikacjaThis article deals with the stochastic Gross–Pitaevskii equation (SGPE) perturbed with multiplicative time noise. The numerical solutions of the governing model are carried out with the proposed stochastic non-standard finite difference (SNSFD) scheme. The stability of the scheme is proved by using the Von-Neumann criteria and the consistency is shown in the mean square sense. To seek exact solutions, we applied the Sardar subequation...
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Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family
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Quadratic programming approach to coupled resonator filter cad
PublikacjaArtykuł prezentuje technikę komputerowego wspomagania procesu projektowania filtrów zbliżeniowych. Polega ona na sformułowaniu macierzy sprzężeń jako problemu programowania kwadratowego (QP). Dzięki zdefiniowaniu procedury optymalizacyjnej jako problemu QP, przy założeniu liniowej zależności współczynników sprzężeń od wymiarów geometrycznych struktury, uzyskano znaczącą redukcję liczby pełnofalowych symulacji prowadzących do uzyskania...
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On the decomposition of stochastic cellular automata
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