parametrization of compactly supported orthonormal wavelets the parametrization of two channel reconstruction quadrature mirror filter banks is extended to obtain a single characterization of discrete orthonormal wavelets in particular it is shown that discrete orthonormal wavelets of support less than 2n 1 where n is an even integer are parametrized by n 1 real parameters each taking values in 0 2 pi a parametrization of discrete orthonormal wavelets with a number of vanishing moments greater than one is also given

multiresolution analysis generated by a seed function in this paper we use the equivalence result originally proved by the author which relates a multiresolution analysis mra of l2 r and an orthonormal set of single electron wave functions in the lowest landau level to build up a procedure which produces starting with a certain square integrable function a mra of l2 r

control of mobile manipulators in a task space this note addresses the problem of position control of mobile manipulators operating in the task space with state constraints a relatively simple class of task space regulators consisting of a generalized transpose jacobian controller with a nonlinear quasi velocity term an integral term including a function of manipulator coordinates and the task error plus the gradient of a kinematic criterion function is proposed the lyapunov stability theory is used to derive the control scheme through the use of the gradient of the criterion function an optimal solution to the mobile manipulator task is ensured the performance of the proposed control strategy is illustrated through computer simulations for a mobile manipulator operating in a three dimensional task space

localizations on complex networks we study the structural characteristics of complex networks using the representative eigenvectors of the adjacent matrix the probability distribution function of the components of the representative eigenvectors are proposed to describe the localization on networks where the euclidean distance is invalid several quantities are used to describe the localization properties of the representative states such as the participation ratio the structural entropy and the probability distribution function of the nearest neighbor level spacings for spectra of complex networks whole cell networks in the real world and the watts strogatz small world and barabasi albert scale free networks are considered the networks have nontrivial localization properties due to the nontrivial topological structures it is found that the ascending order ranked series of the occurrence probabilities at the nodes behave generally multifractally this characteristic can be used as a structural measure of complex networks

diffusion in deterministic fractals a model for polymer electrolytes abstract we present simulation results for random walks on a family of sierpinski carpets under a periodically varying bias the diffusivity obtained from these results shows a power law variation of the bias with frequency the exponent depends on details of the carpet generator we discuss applicability of these results to real materials with fractal structure such as polymer electrolytes with different salt concentrations

a wavelet or lifting scheme based imputation method summary the paper proposes a new approach to imputation using the expected sparse representation of a surface in a wavelet or lifting scheme basis our method incorporates a bayesian mixture prior for these wavelet coefficients into a gibbs sampler to generate a complete posterior distribution for the variable of interest intuitively the estimator operates by borrowing strength from those observed neighbouring values to impute at the unobserved sites we demonstrate the strong performance of our estimator in both one and two dimensional imputation problems where we also compare its application with the standard imputation techniques of kriging and thin plate splines

scaling exponents for random walks on sierpinski carpets and number of distinct sites visited a new algorithm for infinite fractal lattices the scaling exponent for the mean square distance covered in a random walk dw and the average number of distinct sites visited dn are determined for a family of sierpinski carpet patterns we suggest a new random walk algorithm to generate walks on an effectively infinite deterministic fractal lattice the algorithm is applied to several sierpinski carpet patterns with the same hausdorff dimension we show that the systems have a quite different scaling exponent dw and further that the generally accepted result dn ds does not hold for all of these where ds is the spectral dimension

exponential bases paley wiener spaces and applications abstract we investigate the connection between translation bases for paley wiener spaces and exponential fourier bases for a domain we apply these results to the characterization of vector valued time frequency translations of a paley wiener window signal

the pore structure of sierpinski carpets in this paper a new method is developed to investigate the pore structure of finitely and even infinitely ramified sierpinski carpets the holes in every iteration stage of the carpet are described by a hole counting polynomial this polynomial can be computed iteratively for all carpet stages and contains information about the distribution of holes with different areas and perimeters from which dimensions governing the scaling of these quantities can be determined whereas the hole area is known to be two dimensional the dimension of the hole perimeter may be related to the random walk dimension

biorthogonal spline type wavelets let f be an orthonormal scaling function with approximation degree p 1 and let b nbe the b spline of order n then spline type scaling functions defined by n b n n 1 2 possess higher approximation order p n 1 and compact support the corresponding biorthogonal wavelet functions are also constructed this technique is extended to the case of biorthogonal scaling function system as an application of the method supplied in this paper one can easily construct a sequence of pairs of biorthogonal spline type scaling functions from one pair of biorthogonal scaling functions or an orthonormal scaling function in particular if both the method and the lifting scheme of sweldens see 1 are applied then all pairs of biorthogonal spline type scaling functions shown in references 2 and 3 can be constructed from the haar scaling function

wavelets generated by using discrete singular convolution kernels this paper explores the connection between wavelet methods and an efficient computational algorithm the discrete singular convolution dsc many new dsc kernels are constructed and they are identified as wavelet scaling functions two approaches are proposed to generate wavelets from dsc kernels two well known examples the canny filter and the mexican hat wavelet are found to be special cases of the present dsc kernel generated wavelets a family of wavelet generators proposed in this paper are found to form an infinite dimensional lie group which has an invariant subgroup of translation and dilation if dsc kernels form an orthogonal system they are found to span a wavelet subspace in a multiresolution analysis

an adaptive regulator of robotic manipulators in the task space this note addresses the problem of position control of robotic manipulators both nonredundant and redundant in the task space a computationally simple class of task space regulators consisting of a transpose adaptive jacobian controller plus an adaptive term estimating generalized gravity forces is proposed the lyapunov stability theory is used to derive the control scheme the conditions on controller gains ensuring asymptotic stability are obtained herein in a form of simple inequalities including some information extracted from both robot kinematic and dynamic equations the performance of the proposed control strategy is illustrated through computer simulations for a direct drive arm of a scara type redundant manipulator with the three revolute kinematic pairs operating in a two dimensional task space

nonuniform multiresolution analyses and spectral pairs abstract a generalization of the notion of multiresolution analysis based on the theory of spectral pairs is considered in contrast to the standard setting the associated subspacev0ofl2 r has as an orthonormal basis a collection of translates of the scaling function of the form x where 0 r n 2z n 1 is an integer andris an odd integer with 1 r 2n 1 such thatrandnare relatively prime andzis the set of all integers furthermore the corresponding dilation factor is 2n the case wheren 1 corresponding to the usual definition of a multiresolution analysis with dilation factor 2 a necessary and sufficient condition for the existence of associated wavelets which is always satisfied whenn 1 or 2 is obtained and is shown to always hold if the fourier transform of is a constant multiple of the characteristic function of a set

information theoretic wavelet noise removal for inverse elastic wave scattering theory a discussion of noise removal in ultrasound elastic wave scattering for nondestructive evaluation is given the methods used in this paper include a useful suboptimal wiener filter information theory and orthonormal wavelets the multiresolution analysis mra due to mallat is the key wavelet feature used here whereas fourier transforms have a translational symmetry wavelets have a dilation or affine symmetry which consists of the semi direct product of a translation with a change of scale of the variable the mra describes the scale change features of orthonormal wavelet families first an empirical method of noise removal from scattered elastic waves using wavelets is shown to markedly improve the l 1 and l 2 error norms this suggests that the wavelet scale can act as dial to tune out noise maximization of the kullback liebler information is also shown to provide a scale dependent noise removal technique that supports but does not prove the intuition that certain small energy coefficients that are retained contain large information content the wavelet mra thereby locates islands of information in the phase space of the signal it is conjectured that this method holds more generally

families of biorthogonal wavelets several families of biorthogonal wavelet bases are constructed with various properties in particular for a given filter fn of finite length 2n 1 a parametric family of dual filters fvn of length 2n 1 is constructed the parametric nature of the dual filters makes it possible to design the optimum dual filter fv0n corresponding to a fixed filter fn

wavelet methods for pdes some recent developments abstract this paper is concerned with recent developments of wavelet schemes for the numerical treatment of operator equations with special emphasis on two issues adaptive solution concepts and nontrivial domain geometries after describing a general multiresolution framework the key features of wavelet bases are highlighted namely locality norm equivalences and cancellation properties assuming first that wavelet bases with these properties are available on the relevant problem domains the relevance of these features for a wide class of stationary problems is explained in subsequent sections the main issues are preconditioning and the efficient adaptive application of wavelet representations of the involved operators we indicate then how these ingredients combined with concepts from nonlinear or best n term approximation culminate in an adaptive wavelet scheme for elliptic selfadjoint problems covering boundary value problems as well as boundary integral equations these schemes can be shown to exhibit convergence rates that are in a certain sense asymptotically optimal we conclude this section with some brief remarks on data structures and implementation interrelations with regularity in a certain scale of besov spaces and strategies of extending such schemes to unsymmetric or indefinite problems we address then the adaptive evaluation of nonlinear functionals of wavelet expansions as a central task arising in connection with nonlinear problems wavelet bases on nontrivial domains are discussed next the main issues are the development of fourier free construction principles and criteria for the validity of norm equivalences finally we indicate possible combinations of wavelet concepts with conventional discretizations such as finite element or finite volume schemes in connection with convection dominated and hyperbolic problems

the wavelet transform of stochastic processes with stationary increments and its application to fractional brownian motion the wavelet transform of random processes with wide sense stationary increments is shown to be a wide sense stationary process whose correlation function and spectral distribution are determined the second order properties of the coefficients in the wavelet orthonormal series expansion of such processes is obtained applications to the spectral analysis and to the synthesis of fractional brownian motion are given

multi resolution analysis and fractional quantum hall effect more results in a previous paper we have proved that any multi resolution analysis of 2 produces for even values of the inverse filling factor and for a square lattice a single electron wavefunction of the lowest landau level lll which together with its magnetic translate gives rise to an orthonormal set in the lll we have also discussed the inverse construction in this paper we simplify the procedure clarifying the role of the kq representation moreover we extend our previous results to the more physically relevant case of a triangular lattice and to odd values of the inverse filling factor we also comment on other possible shapes of the lattice as well as on the extension to other landau levels finally just as a first application of our technique we compute an approximation of the coulomb energy for the haar wavefunction for a filling 1 3

joint similarities and parameterizations for naimark complementary frames abstract it is known that the naimark complementary frames for a given frame are not necessarily unique up to the similarity in this paper we introduce the concept of joint complementary frame pairs for a given dual frame pair and prove that they are unique up to the joint similarity as an application we give a necessary and sufficient condition under which two naimark complementary frames are similar for different pairs of dual frames we present an operator parameterization for their joint complementary frame pairs

multiresolution expansion approximation order and quasiasymptotic behavior of tempered distributions abstract multiresolution analysis of tempered distributions is studied through multiresolution analysis on the corresponding test function spaces s r r r n 0 for a function h which is smooth enough and of appropriate decay it is shown that the derivatives of its projections to the corresponding spaces v j j z in a regular multiresolution analysis of l 2 r denoted by h j multiplied by a polynomial weight converge in sup norm i e h j h in s r r as j analogous result for tempered distributions is obtained by duality arguments the analysis of the approximation order of the projection operator within the framework of the theory of shift invariant spaces gives a further refinement of the results the order of approximation is measured with respect to the corresponding space of test functions as an application we give abelian and tauberian type theorems concerning the quasiasymptotic behavior of a tempered distribution at infinity

a maximum likelihood digital receiver using coordinate ascent and the discrete wavelet transform in this paper a maximum likelihood ml method is presented for joint estimation of amplitude phase time delay and data symbols in a single user direct sequence spread spectrum communication system since maximization of the likelihood function is analytically intractable a novel coordinate ascent algorithm is used to obtain sequential updates of the data symbols and all unknown nuisance parameters the novelty of the algorithm is due to the use of a multiresolution expansion of the received signal and the use of polynomial rooting in the complex plane in place of a line search over the signal delay parameter the multiresolution structure of the algorithm is exploited to reduce sensitivity to impulsive noise via wavelet thresholding computer simulations of the single user system show that the algorithm has fast convergence and comparison with theoretical lower bounds establishes that the algorithm achieves nearly optimal error performance

a load identification method based on wavelet multi resolution analysis abstract load identification as a kind of indirect identification method uses system characteristic and responses to calculate loads a method based on wavelet multi resolution analysis is proposed in this paper by wavelet decomposition and transform at certain resolutions the proposed method transforms the convolution relation between responses and loads in time domain into the linear multiplicative relation between system responses and wavelet responses in the wavelet domain loads can be identified as long as the linear multiplicative relation is solved qualitative and quantitative rules are proposed for selecting parameters that affect the accuracy of the proposed method and are illustrated via numerical investigations the method is illustrated by a multi input multi output numerical simulation a multi input multi output laboratory experiment is performed to compare the proposed method with the frequency method on the identification ability

spline prewavelets for non uniform knots in this paper we develop a framework suitable for performing a multiresolution analysis using univariate spline spaces of arbitrary degree and with non uniform knot sequences to this end we show among other things the existence of compactly supported prewavelets and of prewavelets that are globally supported but decay exponentially in each case we obtain a decomposition of a fine spline space as a sum of a coarse spline space plus a spline space spanned by prewavelets

the coastline and lake shores on a fractal island we compute the fractal dimensions of the hulls or external boundary and the boundaries of the internal cavities in several deterministic as well as random fractal structures our conclusion is that the two fractal dimensions are in fact identical the deterministic fractals we study are sierpinski carpets sc in a two dimensional space and the random fractals are percolation clusters at criticality as an intermediate case we present results on some randomized sc in the random structures statistics of the area and perimeters of all internal cavities or holes are taken and the fractal dimension of the hull borderline is computed two different definitions of the borderline are used considering nearest neighbours as well as nearest and second nearest neighbours as connected the conclusion is valid for both cases

minimax estimation via wavelet shrinkage we attempt to recover an unknown function from noisy sampled data using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coefficients the shrinkage can be tuned to be nearly minimax over any member of a wide range of triebel and besov type smoothness constraints and asymptotically minimax over besov bodies with p q linear estimates cannot achieve even the minimax rates over triebel and besov classes with p 2 so the method can significantly outperform every linear method e g kernel smoothing spline sieve in a minimax sense variants of our method based on simple threshold nonlinear estimators are nearly minimax our method possesses the interpretation of spatial adaptivity it reconstructs using a kernel which may vary in shape and bandwidth from point to point depending on the data least favorable distributions for certain of the triebel and besov scales generate objects with sparse wavelet transforms many real objects have similarly sparse transforms which suggests that these minimax results are relevant for practical problems sequels to this paper which was first drafted in november 1990 discuss practical implementation spatial adaptation properties universal near minimaxity and applications to inverse problems

finite time control of robotic manipulators this work offers the solution at the control feed back level of the accurate trajectory tracking subject to finite time convergence dynamic equations of a rigid robotic manipulator are assumed to be uncertain moreover globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory based on the suitably defined non singular terminal sliding vector variable and the lyapunov stability theory we propose a class of absolutely continuous robust controllers which seem to be effective in counteracting both uncertain dynamics and unbounded disturbances the numerical simulation results carried out for a robotic manipulator consisting of two revolute kinematic pairs operating in a two dimensional joint space illustrate performance of the proposed controllers

quantum field theory in ninety minutes on presente divers aspects de la theorie quantique des champs la theorie p 2 a 2 dimensions la theorie 3 4 a 3 dimensions la theorie de yang mills a 4 dimensions

dynamic multiscale spatiotemporal models for gaussian areal data summary we introduce a new class of dynamic multiscale models for spatiotemporal processes arising from gaussian areal data specifically we use nested geographical structures to decompose the original process into multiscale coefficients which evolve through time following state space equations our approach naturally accommodates data that are observed on irregular grids as well as heteroscedasticity moreover we propose a multiscale spatiotemporal clustering algorithm that facilitates estimation of the nested geographical multiscale structure in addition we present a singular forward filter backward sampler for efficient bayesian estimation our multiscale spatiotemporal methodology decomposes large data analysis problems into many smaller components and thus leads to scalable and highly efficient computational procedures finally we illustrate the utility and flexibility of our dynamic multiscale framework through two spatiotemporal applications the first example considers mortality ratios in the state of missouri whereas the second example examines agricultural production in espirito santo state brazil

fractional splines and wavelets we extend schoenberg s family of polynomial splines with uniform knots to all fractional degrees alpha 1 these splines which involve linear combinations of the one sided power functions x alpha max 0 x alpha are alpha holder continuous for alpha 0 we construct the corresponding b splines by taking fractional finite differences and provide an explicit characterization in both time and frequency domains we show that these functions satisfy most of the properties of the traditional b splines including the convolution property and a generalized fractional differentiation rule that involves finite differences only we characterize the decay of the b splines that are not compactly supported for nonintegral alpha s their most astonishing feature in reference to the strang fix theory is that they have a fractional order of approximation alpha 1 while they reproduce the polynomials of degree lceil alpha rceil for alpha frac 1 2 they satisfy all the requirements for a multiresolution analysis of ll 2 riesz bounds two scale relation and may therefore be used to build new families of wavelet bases with a continuously varying order parameter our construction also yields symmetrized fractional b splines which provide the connection with duchon s general theory of radial m s splines including thin plate splines in particular we show that the symmetric version of our splines can be obtained as the solution of a variational problem involving the norm of a fractional derivative

multi resolution analysis and fractional quantum hall effect an equivalence result in this article we prove that any multi resolution analysis of l2 r produces for some values of the filling factor a single electron wave function of the lowest landau level lll which together with its magnetic translation gives rise to an orthonormal set in the lll we also discuss the inverse construction moreover we extend this procedure to the higher landau levels and we discuss the analogies and the differences between this procedure and the one previously proposed by j p antoine and the author

a block spin construction of ondelettes part i lemarie functions using block spin assignments we construct anl2 orthonormal basis consisting of dyadic scalings and translates of just a finite number of functions these functions have exponential localization and for even values of a construction parameterm one can make them classcm 1 with vanishing moments up to orderm inclusive such a basis has an important application to phase cell cluster expansions in quantum field theory

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

refinement of operator valued reproducing kernels this paper studies the construction of a refinement kernel for a given operator valued reproducing kernel such that the vector valued reproducing kernel hilbert space of the refinement kernel contains that of the given kernel as a subspace the study is motivated from the need of updating the current operator valued reproducing kernel in multi task learning when underfitting or overfitting occurs numerical simulations confirm that the established refinement kernel method is able to meet this need various characterizations are provided based on feature maps and vector valued integral representations of operator valued reproducing kernels concrete examples of refining translation invariant and finite hilbert schmidt operator valued reproducing kernels are provided other examples include refinement of hessian of scalar valued translation invariant kernels and transformation kernels existence and properties of operator valued reproducing kernels preserved during the refinement process are also investigated

task space adaptive control of robotic manipulators with uncertainties in gravity regressor matrix and kinematics thus far most research in adaptive control of robotic manipulators has assumed that models of regressor matrix and kinematics are known exactly to overcome these drawbacks we propose in this paper a task space adaptive law for setpoint control of robots with uncertainties in gravity regressor matrix and kinematics in addition we investigate the stability problem when an estimated task space velocity is used in the feedback loop sufficient conditions for choosing the feedback gains gravity regressor and jacobian matrix are presented to guarantee the stability

wavelets of multiplicity r a multiresolution approximation km m z of l2 r is of multi plicity r 0 if there are r functions x r whose translates form a riesz basis for v in the general theory we derive necessary and sufficient conditions for the translates of x r y x y r to form a riesz basis for v the resulting reconstruction and decomposition sequences lead to the construction of dual bases for v0 and its orthogonal complement w0 in vx the general theory is applied in the construction of spline wavelets with mul tiple knots algorithms for the construction of these wavelets for some special cases are given

algorithms for designing wavelets to match a specified signal algorithms for designing a mother wavelet spl psi x such that it matches a signal of interest and such that the family of wavelets 2 sup j 2 spl psi 2 sup j x k forms an orthonormal riesz basis of l sup 2 spl rscr are developed the algorithms are based on a closed form solution for finding the scaling function spectrum from the wavelet spectrum many applications require wavelets that are matched to a signal of interest most current design techniques however do not design the wavelet directly they either build a composite wavelet from a library of previously designed wavelets modify the bases in an existing multiresolution analysis or design a scaling function that generates a multiresolution analysis with some desired properties in this paper two sets of equations are developed that allow us to design the wavelet directly from the signal of interest both sets impose bandlimitedness resulting in closed form solutions the first set derives expressions for continuous matched wavelet spectrum amplitudes the second set of equations provides a direct discrete algorithm for calculating close approximations to the optimal complex wavelet spectrum the discrete solution for the matched wavelet spectrum amplitude is identical to that of the continuous solution at the sampled frequencies an interesting byproduct of this work is the result that meyer s spectrum amplitude construction for an orthonormal bandlimited wavelet is not only sufficient but necessary specific examples are given which demonstrate the performance of the wavelet matching algorithms for both known orthonormal wavelets and arbitrary signals

relations between multiresolution analysis and quantum mechanics we discuss a procedure to construct multiresolution analyses mra of l2 r starting from a given seed function h s which should satisfy some conditions our method originally related to the quantum mechanical hamiltonian of the fractional quantum hall effect is shown to be model independent the role of a canonical map between certain canonically conjugate operators is discussed this clarifies our previous procedure and makes much easier most of the original formulas producing a convenient framework to produce examples of mra

anomalous diffusion on random fractal composites stochastic fractals generated from combinations of deterministic fractals have the advantage of being tractable to some extent but also being closer to real materials since they are partially disordered in the present work we focus our attention on the remarkable nonlinear mixing behavior exhibited by fractals generated as random combinations of two different sierpinski carpet generators when patterns with different anomalous diffusion exponents and the same or different fractal dimensions are combined together the effective diffusion exponent cannot in general be expressed as a linear weighted average of the diffusion exponents of the constituents the effective exponent may show a maximum or minimum for certain compositions an explanation of this interesting phenomenon is offered on the basis of details of the carpet generator particularly on the number and position of connection points which determine the connectivity of the fractal composite

modelling porous structures by repeated sierpinski carpets abstract porous materials such as sedimentary rocks often show a fractal character at certain length scales deterministic fractal generators iterated upto several stages and then repeated periodically provide a realistic model for such systems on the fractal diffusion is anomalous and obeys the law r 2 t 2 d w where r 2 is the mean square distance covered in time t and d w 2 is the random walk dimension the question is how is the macroscopic diffusivity related to the characteristics of the small scale fractal structure which is hidden in the large scale homogeneous material in particular do structures with same d w necessarily lead to the same diffusion coefficient at the same iteration stage the present paper tries to shed some light on these questions

wavelet transform based adaptive filters analysis and new results in this paper the wavelet transform is used in an adaptive filtering structure the coefficients of the adaptive filter are updated by the help of the least mean square lms algorithm first the wavelet transform based adaptive filter wtaf is described and it is analyzed for its wiener optimal solution then the performance of the wtaf is studied by the help of learning curves for three different convergence factors 1 constant convergence factor 2 time varying convergence factor and 3 exponentially weighted convergence factor the exponentially weighted convergence factor is proposed to introduce scale based variation to the weight update equation it is shown for two different sets of data that the rate of convergence increases significantly for all three wtaf structures as compared to that of time domain lms the high convergence rates of the wtaf give us reason to expect that it will perform well in tracking rapid changes in a signal

a unified design method for adaptive visual tracking control of robots with eye in hand fixed camera configuration a unified design method is proposed in this paper to handle adaptive visual tracking control problem of robots in the proposed scheme the robot dynamic parameters camera intrinsic and extrinsic parameters and position parameters of feature points are assumed to be uncertain a unified kinematics model is presented to simultaneously cope with kinematics modeling problem of robots with the eye in hand or fixed camera configuration based on the unified kinematics a unified design method is proposed to solve the visual tracking control problem of robots with the eye in hand or fixed camera configuration by using the depth independent interaction matrix framework adaptive laws are derived to handle the unknown parameters lyapunov stability analysis is provided to show asymptotical convergence of image position and velocity tracking errors to show the effectiveness of the proposed unified design method experimental results for both camera configurations are also given

multi resolution multi scale topology optimization a new paradigm abstract the purpose of this work is to present a new concept multi resolution multi scale topology optimization the key idea of the present strategy is that design optimization should be performed progressively from low to high resolution not at a single resolution level to achieve the multi resolution strategy design optimization is formulated in a wavelet based variable space not in a direct density variable space the major advantages of the multi resolution design optimization include 1 topologically simple and close to the global optimum structures may be obtained without any explicit constraint and 2 the convergence is not sensitive to mathematical programming methods for the efficient numerical implementation of the multi resolution approach the side constraints imposed on the direct density variables are removed by mapping the density variables into intermediate variables these intermediate variables are then wavelet transformed to new design variables it is addressed that the present multi resolution topology optimization can resolve major numerical instability problems such as mesh dependencies and local minima the usefulness of the multi scale nature of the wavelets in the present multi resolution multi scale optimization formulation is also discussed

adaptive learning for event modeling and characterization adaptive learning of specific patterns or events of interest has been an area of significant research for various applications in the last two decades in developing diagnostic evaluation and safety monitoring applications of a propulsion system it is critical to detect characterize and model events of interest it is a challenging task since the detection system should allow adaptive characterization of potential events of interest and correlate them to learn new models for future detection for online health monitoring and diagnostic evaluation in this paper a novel framework is established using a hierarchical adaptive clustering approach with fuzzy membership functions to characterize specific events of interest from the measured and processed features raw engine measurement data is first analyzed using the wavelet transform to provide features for localization of frequency information for use in the classification system a method combining hierarchical and fuzzy k means clustering is then applied to a set of selected measurements and computed features to determine the events of interest during engine operations experimental results have shown that the proposed approach is effective and computationally efficient to detect characterize and model new events of interest from data collected through continuous operations

fractals their transfer matrices and their eigen dimensional sequences this paper defines and studies a general algorithm for constructing new families of fractals in euclidean space this algorithm involves a sequence of linear interscale transformations that proceed from large to small scales the authors find that the fractals obtained in this fashion decompose in intrinsic fashion into linear combinations of a variable number of addend fractals the addends relative weights and fractal dimensionalities are obtained explicitly through an interscale matrix which they call the transfer matrix of the fractal tmf the authors first demonstrate by a series of examples then prove rigorously that the eigenvalues of our tmfs are real and positive and that the fractal dimensions of the addend fractals are the logarithms of the eigenvalues of their tmf they say that these dimensions form the overall fractal s eigendimensional sequence the eigenvalues of their tmf are integers in the non random variants of the construction but are non integer in the random variants a geometrical interpretation of the eigenvalues and the eigenvectors is given their tmf have other striking and very special properties that deserve additional attention

multiscale autoregressive processes i schur levinson parametrizations in many applications it is of interest to analyze and recognize phenomena occurring at different scales the recently introduced wavelet transforms provide a time and scale decomposition of signals that offers the possibility of such analysis a corresponding statistical framework to support the development of optimal multiscale statistical signal processing algorithms is described the theory of multiscale signal representation leads naturally to models of signals on trees and this provides the framework for investigation in particular the class of isotropic processes on homogeneous trees is described and a theory of autoregressive models is developed in this context this leads to generalizations of schur and levinson recursions associated properties of the resulting reflection coefficients and the initial pieces in a system theory for multiscale modeling