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Search results for: SMOOTH ORTHOGONAL PROJECTION SPHERE PARSEVAL FRAME ADAPTIVE ESTIMATOR TALAGRAND’S INEQUALITY BESOV SPACES PARAMETER OF SMOOTHNESS
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Harmonic Analysis
Open Research DataWe construct a decomposition of the identity operator on a Riemannian manifold M as a sum of smooth orthogonal projections subordinate to an open cover of M. This extends a decomposition on the real line by smooth orthogonal projection due to Coifman and Meyer (C. R. Acad. Sci. Paris, Sér. I Math., 312(3), 259–261 1991) and Auscher, Weiss, Wickerhauser...
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Parseval Wavelet Frames on Riemannian Manifold
PublicationWe construct Parseval wavelet frames in L 2 (M) for a general Riemannian manifold M and we show the existence of wavelet unconditional frames in L p (M) for 1 < p < ∞. This is made possible thanks to smooth orthogonal projection decomposition of the identity operator on L 2 (M), which was recently proven by Bownik et al. (Potential Anal 54:41–94, 2021). We also show a characterization of Triebel–Lizorkin F sp,q (M) and Besov B...
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Smooth orthogonal projections on sphere.
PublicationWe construct a decomposition of the identity operator on the sphere S^d as a sum of smooth orthogonal projections subordinate to an open cover of S^d. We give applications of our main result in the study of function spaces and Parseval frames on the sphere.
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Marcinkiewicz Averages of Smooth Orthogonal Projections on Sphere
PublicationWe construct a single smooth orthogonal projection with desired localization whose average under a group action yields the decomposition of the identity operator. For any full rank lattice \Gamma ⊂ R^d , a smooth projection is localized in a neighborhood of an arbitrary precompact fundamental domain R^d / \Gamma. We also show the existence of a highly localized smooth orthogonal projection, whose Marcinkiewicz average under the...
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Multiresolution analysis and adaptive estimation on a sphere using stereographic wavelets
PublicationWe construct an adaptive estimator of a density function on d dimensional unit sphere Sd (d ≥ 2), using a new type of spherical frames. The frames, or as we call them, stereografic wavelets are obtained by transforming a wavelet system, namely Daubechies, using some stereographic operators. We prove that our estimator achieves an optimal rate of convergence on some Besov type class of functions by adapting to unknown smoothness....
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Estimation of a smoothness parameter by spline wavelets
PublicationWe consider the smoothness parameter s*(f) of a function f∈L2(R) in terms of Besov spaces. The existing results on estimation of smoothness [K. Dziedziul, M. Kucharska and B. Wolnik, J. Nonparametric Statist. 23 (2011)] employ the Haar basis and are limited to the case 0
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Smooth Orthogonal Projections on Riemannian Manifold
PublicationWe construct a decomposition of the identity operator on a Riemannian manifold M as a sum of smooth orthogonal projections subordinate to an open cover of M. This extends a decomposition on the real line by smooth orthogonal projection due to Coifman and Meyer (C. R. Acad. Sci. Paris, S´er. I Math., 312(3), 259–261 1991) and Auscher, Weiss, Wickerhauser (1992), and a similar decomposition when M is the sphere by Bownik and Dziedziul (Const....
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Density smoothness estimation problem using a wavelet approach
PublicationIn this paper we consider a smoothness parameter estimation problem for a density function. The smoothness parameter of a function is defined in terms of Besov spaces. This paper is an extension of recent results (K. Dziedziul, M. Kucharska, B. Wolnik, Estimation of the smoothness parameter ). The construction of the estimator is based on wavelets coefficients. Although we believe that the effective estimation of the smoothness...
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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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Estimating the parameter of inequality aversion on the basis of a parametric distribution of incomes
PublicationResearch background: In applied welfare economics, the constant relative inequality aversion function is routinely used as the model of a social decisionmaker’s or a society’s preferences over income distributions. This function is entirely determined by the parameter, ε, of inequality aversion. However, there is no authoritative answer to the question of what the range of ε an analyst should select for empirical work. Purpose...
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The asymptotic formula for the error in orthogonal projection
PublicationW pracy podano formułę asymptotyczną błędu aproksymacji dla rzutów ortogonalnych w normie L^p.
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Parametrized Local Reduced-Order Models With Compressed Projection Basis for Fast Parameter-Dependent Finite-Element Analysis
PublicationThis paper proposes an automated parametric local model-order reduction scheme for the expedited design of microwave devices using the full-wave finite-element method (FEM). The approach proposed here results in parameterized reduced-order models (ROMs) that account for the geometry and material variation in the selected subregion of the structure. In each subregion, a parameter-dependent projection basis is generated by concatenating...
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Comparison of the fracture toughness of pine wood determined on the basis of orthogonal linear cutting and frame sawing
PublicationIn this paper, the values of the fracture toughness of Scots pine determined by cutting tests are presented. The cutting tests were carried out using the samples of Scotch pine (Pinus sylvestris L.) from Pomeranian Region, Poland. These experiments were carried out on two research stands: orthogonal linear cutting tests were conducted using the microtome instrument and the frame saw PRW-15M was used for sawing tests. The values...
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Fast Algorithms for Identification of Time-Varying Systems with Both Smooth and Discontinuous Parameter Changes
PublicationThe problem of noncausal identification of a time-varying linear system subject to both smooth and occasional jump-type changes is considered and solved using the preestimation technique combined with the basis function approach to modeling the variability of system parameters. The proposed estimation algorithms yield very good parameter tracking results and are computationally attractive.
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ESTIMATING AVERSION TO RANK INEQUALITY UNDERLYING SELECTED ITALIAN INDICES OF INCOME INEQUALITY
PublicationIn this paper, we estimate aversion to rank inequality (ATRI) underlying selected Italian income inequality indices, I, notably the Pietra index, the Bonferroni index and the “new” Zenga index. We measure ATRI by the parameter v of the generalised Gini index G(v). ATRI is distinct from aversion to income inequality, as measured by parameter ε of Atkinson’s index A(ε). We propose eliciting v from the equation I = GE(v). As, in general,...
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Cost-efficient multi-objective design optimization of antennas in highly-dimensional parameter spaces
PublicationMulti-objective optimization of antenna structures in highly-dimensional parameter spaces is investigated. For expedited design, variable-fidelity EM simulations and domain patching algorithm are utilized. The results obtained for a monopole antenna with 13 geometry parameters are compared with surrogate-assisted optimization involving response surface approximation modeling.
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Expedited EM-driven multi-objective antenna design in highly-dimensional parameter spaces
PublicationA technique for low-cost multi-objective optimization of antennas in highly-dimensional parameter spaces is presented. The optimization procedure is expedited by exploiting fast surrogate models, including coarse-discretization EM antenna simulations and response surface approximations (RSA). The latter is utilized to yield an initial set of Pareto non-dominated designs which are further refined using response correction methods....
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New Approach to Noncasual Identification of Nonstationary Stochastic FIR Systems Subject to Both Smooth and Abrupt Parameter Changes
PublicationIn this technical note, we consider the problem of finite-interval parameter smoothing for a class of nonstationary linear stochastic systems subject to both smooth and abrupt parameter changes. The proposed parallel estimation scheme combines the estimates yielded by several exponentially weighted basis function algorithms. The resulting smoother automatically adjusts its smoothing bandwidth to the type and rate of nonstationarity...
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Estimation of the minimal number of periodic points for smooth self-maps of odd dimensional real projective spaces
PublicationLet f be a smooth self-map of a closed connected manifold of dimension m⩾3. The authors introduced in [G. Graff, J. Jezierski, Minimizing the number of periodic points for smooth maps. Non-simply connected case, Topology Appl. 158 (3) (2011) 276-290] the topological invariant NJD_r[f], where r is a fixed natural number, which is equal to the minimal number of r-periodic points in the smooth homotopy class of f. In this paper smooth...
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An improved frequency estimator for an adaptive active noise control scheme
PublicationAn improved frequency tracker is proposed for the recently introduced self optimizing narrowband interference canceller (SONIC). The scheme is designed for disturbances with quasi-linear frequency modulation and, under second-order Gaussian random-walk assumption, can be shown to be statistically efficient. One real-world experiment and several simulations show that a considerable improvement in disturbance rejection may be achieved...
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2022/2023_ZIMA Adaptive Control
e-Learning CoursesAdaptive control lecture materials
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Parameter selection of an adaptive PI state observer for an induction motor
PublicationThe paper discusses problems connected with the parameters selection of the proportional-integral observer, designed for recon- struction of magnetic fluxes and angular speed of an induction motor. The selection is performed in several stages that are focused on different criteria. The first stage consists in selecting observer’s gains and provides desired dynamical properties, taking into consideration immunity to disturbances and...
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The atlas of inequality aversion: theory and empirical evidence on 55 countries from the Luxembourg Income Study database
PublicationResearch background: In the distributive analysis, the constant relative inequality aversion utility function is a standard tool for ethical judgements of income distributions. The sole parameter ε of this function expresses a society’s aversion to inequality. However, the profession has not committed to the range of ε. When assessing inequality and other welfare characteristics, analysts assume an arbitrary level of ε, common...
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On Decision-Making Strategies for Improved-Reliability Size Reduction of Microwave Passives: Intermittent Correction of Equality Constraints and Adaptive Handling of Inequality Constraints
PublicationDesign optimization of passive microwave components is an intricate process, especially if the primary objective is a reduction of the physical size of the structure. The latter has become an important design consideration for a growing number of modern applications (mobile communications, wearable/implantable devices, internet of things), where miniaturization is imperative due to a limited space allocated for the electronic circuitry....
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Periodic points of latitudinal maps of the $m$-dimensional sphere
PublicationLet f be a smooth self-map of the m-dimensional sphere Sm. Under the assumption that f preserves latitudinal foliations with the fibres S1, we estimate from below the number of fixed points of the iterates of f. The paper generalizes the results obtained by Pugh and Shub and by Misiurewicz.
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Note on the multidimensional Gebelein inequality
PublicationWe generalize the Gebelein inequality for Gaussian random vectors in R^d.
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Compressed Projection Bases for Model-Order Reduction of Multiport Microwave Components Using FEM
PublicationThis paper presents a projection basis compression technique for generating compact reduced-order models (ROM) in the FE analysis of microwave devices. In this approach redundancy is removed from the projection basis by means of the proper orthogonal decomposition technique applied to the projected system of linear equations. Compression allows for keeping the size of a reduced-order model as small as possible without compromising...
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Reasoning with Projection in Multimodular Description Logics Knowledge Bases
PublicationWe present an approach to reasoning with projection, i.e. reasoning in which it is possible to focus on a selected part of knowledge (by neglecting some non-interesting fragments). Projection is most useful for modular knowledge bases in which only parts of knowledge have to be exchanged or imported to other modules. In this paper we present an optimized method of reasoning over results of projection. The tests indicate that the...
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Shub’s conjecture for smooth longitudinal maps of S^m
PublicationLet f be a smooth map of the m-dimensional sphere Sm to itself, preserving the longitudinal foliation. We estimate from below the number of fixed points of the iterates of f , reduce Shub’s conjecture for longitudinal maps to a lower dimensional classical version, and prove the conjecture in case m = 2 and in a weak form for m = 3.
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Capon-like DoA estimator for rotating arrays
PublicationWe propose a nonparametric superresolution DoA estimator that is suitable for use with rotating arrays. The proposed method can be regarded as an extension of the Capon approach. We investigate its properties using computer simulations and present results obtained by processing of real world data.
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Estimation of the smoothness of density
PublicationZdefiniowano parametr gładkości w klasach Biesowa. Skonstruowano estymator gładkości.
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Estimating inequality aversion from subjective assessments of the just noticeable differences in welfare
PublicationResearch background: In Economics, the concept of inequality aversion corresponds with the concept of risk aversion in the literature on making decision under uncertainty. The risk aversion is estimated on the basis of subjective reactions of people to various lottery prospects. In Economics, however, an efficient method of estimating inequality aversion has not been developed yet. Purpose of the article: The main aim of this paper...
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Image projection in Immersive 3D Visualization Laboratory
PublicationIn recent years, many centers in the world attempted to build a virtual reality laboratory. The main idea of such laboratory is to allow the user to “immerse” into and move in a computer-generated virtual world. In the paper, the underlying principles of the system of virtual reality (VR) are described. The selected implementations constructed by the research centers of the world are also presented. The cave automatic virtual environment...
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Pareto Ranking Bisection Algorithm for EM-Driven Multi-Objective Design of Antennas in Highly-Dimensional Parameter Spaces
PublicationA deterministic technique for fast surrogate-assisted multi-objective design optimization of antennas in highly-dimensional parameters spaces has been discussed. In this two-stage approach, the initial approximation of the Pareto set representing the best compromise between conflicting objectives is obtained using a bisection algorithm which finds new Pareto-optimal designs by dividing the line segments interconnecting previously...
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Constructive entanglement test from triangle inequality
PublicationWe derive a simple lower bound on the geometric measure of entanglement for mixed quantum states in the case of a general multipartite system. The main ingredient of the presented derivation is the triangle inequality applied to the root infidelity distance in the space of density matrices. The obtained bound leads to entanglement criteria with a straightforward interpretation. The proposed criteria provide an experimentally accessible,...
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Pluralist View on Inequality from Luxemburg Income Study (LIS)
PublicationThe authors start by reviewing the history of the Luxembourg Income Study (LIS), originating from an interdisciplinary project involving economists, sociologists, and political scientists, centered on the cross-country perspective in inequality analysis. They then conduct a meta-analysis of the papers produced by scholars who have taken advantage of the data availability, showing how the theme of income/wealth inequality has been...
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Global and regional economic inequality: Methods of measurement and evidences
PublicationThe lack of countries’ statistical income data, comparable across countries and years, seems to be the main reason of controversial conjectures concerning global inequality and its evolution over time. In the databases, which purport to collect income data on a worldwide scale, only some summary statistics (quantile income shares, means, Gini indices) are presented. Therefore, the development of efficient methods of extracting...
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A Goal-Oriented Error Estimator for Reduced Basis Method Modeling of Microwave Devices
PublicationThis letter proposes a novel a-posteriori error estimator suitable for the reduced order modeling of microwave circuits. Unlike the existing error estimators based on impedance function residuals, the new one exploits the residual error associated with the computation of the scattering matrix. The estimator can be effectively used in the Reduced Basis Method (RBM) to automatically generate reduced-order models. The results of numerical...
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Reliable Multi-Stage Optimization of Antennas for Multiple Performance Figures in Highly-Dimensional Parameter Spaces
PublicationDesign of modern antenna structures needs to account for multiple performance figures and geometrical constraints. Fulfillment of these calls for the development of complex topologies described by a large number of parameters. EM-driven tuning of such designs is mandatory yet immensely challenging. In this letter, a new framework for multi-stage design optimization of multi-dimensional antennas with respect to several performance...
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New Algorithms for Adaptive Notch Smoothing
PublicationThe problem of extraction/elimination of a nonstationary complex sinusoidal signal buried in noise is considered. This problem is usually solved using adaptive notch filtering (ANF)algorithms. It is shown that accuracy of signal estimation can be increased if the results obtained from ANF are further processed using a cascade of appropriately designed filters. The resulting adaptive notch smoothing (ANS) algorithms can be employed...
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Classical to Path-Integral Adaptive Resolution in Molecular Simulation: Towards a Smooth Quantum-Classical Coupling
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Periodic Points for Sphere Maps Preserving MonopoleFoliations
PublicationLet S^2 be a two-dimensional sphere. We consider two types of its foliations with one singularity and maps f:S^2→S^2 preserving these foliations, more and less regular. We prove that in both cases f has at least |deg(f)| fixed points, where deg(f) is a topological degree of f. In particular, the lower growth rate of the number of fixed points of the iterations of f is at least log|deg(f)|. This confirms the Shub’s conjecture in...
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Public Spaces - Coexistence and Participation
PublicationThe paper is an attempt to answer two questions: (1) how to develop positive social relations and citizenship among residents of cities in Poland and (2) howsuitable shaping of public space affects the activation and integration of local residents.The specificity of the post-war process of urbanization in Poland - a country traditionally agricultural - was its political dimension (forced 'nationalisation' of agriculture and industrialization...
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Bound on Bell inequalities by fraction of determinism and reverse triangle inequality
PublicationIt is an established fact that entanglement is a resource. Sharing an entangled state leads to nonlocal correlations and to violations of Bell inequalities. Such nonlocal correlations illustrate the advantage of quantum resources over classical resources. In this paper, we quantitatively study Bell inequalities with 2 × n inputs. As found in Gisin et al. [Int. J. Quantum. Inform. 05, 525 (2007)], quantum mechanical correlations...
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Buckling of frame braced by linear elastic springs
PublicationIn the design codes and specifications, simplifed formulae or diagrams are given for determining the buckling lengths of frame columns based on the ruling criterion of considering frames as sway or non sway. Due to the fact that, the code formulae utilize onlylocal stifness distributions, these formulae may yield in certain cases rather erroneous results. In most code formulas a case of weakly braced frames is usually not considered.In...
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Specialization and inequality along the development path: an interindustry analysis.
PublicationCelem niniejszej rozprawy doktorskiej jest przeprowadzenie empirycznej analizy procesów zwišzanych ze zmianami w strukturze specjalizacyjnej państw w procesie rozwoju ekonpmicznego oraz zwišzanych z nimi efektami dystrybucyjnymi dotyczšcymi rozkładu płac i dochodu. Rozprawa składa się z czterech częci: I. Employment and export specialization patterns versus GDP per capita performance - unifying approach; II.Determinants of export...
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Determining the leakage current resistive component by the orthogonal vector method
PublicationThe measurement of the metal – oxide surge arresters (MOSA) leakage current and the analysis of its components is a key diagnostic criterion according to technical standards. During on site MOSA condition assessment, the easy way is based on the measurement only leakage current, without the inconvenient live working measurements of supply voltage. Orthogonal vectors method of determination the resistive leakage current is presented....
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On-line measurement of wood surface smoothness
PublicationThe latest progress in the field of optics and microelectronics resulted in development of new generation vision systems capable of scanning surface topography with very high sampling frequencies. The blue color of illuminating light as well as novel systems for controlling ultra-thin laser line thickness allows measurement of the porous surface of wood with a triangulation method. Three alternative sensors were tested here in...
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Generalized adaptive notch smoothing revisited
PublicationThe problem of identification of quasi-periodically varying dynamic systems is considered. This problem can be solved using generalized adaptive notch filtering (GANF) algorithms. It is shown that the accuracy of parameter estimates can be significantly increased if the results obtained from GANF are further processed using a cascade of appropriately designed filters. The resulting generalized adaptive notch smoothing (GANS) algorithm...
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Quantum communication complexity advantage implies violation of a Bell inequality
PublicationWe obtain a general connection between a quantum advantage in communication complexity and non-locality. We show that given any protocol offering a (sufficiently large) quantum advantage in communication complexity, there exists a way of obtaining measurement statistics which violate some Bell inequality. Our main tool is port-based teleportation. If the gap between quantum and classical communication complexity can grow arbitrarily...