wave propagation characterization and design of two dimensional elastic chiral metacomposite in this work a chiral metacomposite is proposed by integrating two dimensional periodic chiral lattice with elastic metamaterial inclusions for low frequency wave applications the plane harmonic wave propagation in the proposed metacomposite is investigated through the finite element technique and bloch s theorem band diagrams are obtained to illustrate wave properties of the chiral metacomposite effective dynamic properties of the chiral metacomposite are numerically calculated to explain low frequency bandgap behavior in the chiral metacomposite interestingly doubly negative effective density and modulus of the chiral metacomposite are found in a specific frequency range where a pass band with negative group velocity is observed tuning of the resulting low frequency bandgaps is then discussed by adjusting microstructure parameters of the metamaterial inclusion and lattice geometry specifically design of a metacomposite beam structure for the broadband low frequency vibration suppression is demonstrated

maximum volume clustering a new discriminative clustering approach the large volume principle proposed by vladimir vapnik which advocates that hypotheses lying in an equivalence class with a larger volume are more preferable is a useful alternative to the large margin principle in this paper we introduce a new discriminative clustering model based on the large volume principle called maximum volume clustering mvc and then propose two approximation schemes to solve this mvc model a soft label mvc method using sequential quadratic programming and a hard label mvc method using semi definite programming respectively the proposed mvc is theoretically advantageous for three reasons the optimization involved in hard label mvc is convex and under mild conditions the optimization involved in soft label mvc is akin to a convex one in terms of the resulting clusters secondly the soft label mvc method possesses a clustering error bound thirdly mvc includes the optimization problems of a spectral clustering two relaxed k means clustering and an information maximization clustering as special limit cases when its regularization parameter goes to infinity experiments on several artificial and benchmark data sets demonstrate that the proposed mvc compares favorably with state of the art clustering methods

vibro acoustic response of orthogonally stiffened panels the effects of finite dimensions abstract this paper investigates the effects of finite dimensions on the vibro acoustic response of orthogonally stiffened panels three types of excitations are considered acoustical excitation point force excitation and random excitation by a turbulent boundary layer in each case a spatially windowed periodic model is compared with a rayleigh ritz model where the modes of the un stiffened panel are used as the basis functions the latter model accounts for the reflected wave field generated at the boundaries by assuming that the panel is simply supported on the contrary the windowed periodic model only accounts for finiteness on sound radiation the assumption of an infinite periodic structure is used to calculate the panel response numerical studies show that when the bending wavelength becomes comparable or smaller than the stiffener spacing the periodic model is able to reproduce the results obtained with the rayleigh ritz model to complement the study the developed models are compared with numerical simulations finite element method and with experimental results

statistical mechanics and phase transitions in clustering a new approach to clustering based on statistical physics is presented the problem is formulated as fuzzy clustering and the association probability distribution is obtained by maximizing the entropy at a given average variance the corresponding lagrange multiplier is related to the temperature and motivates a deterministic annealing process where the free energy is minimized at each temperature critical temperatures are derived for phase transitions when existing clusters split it is a hierarchical clustering estimating the most probable cluster parameters at various average variances

a clustering fuzzification algorithm based on alm abstract in this paper we propose a fuzzification method for clusters produced from a clustering process based on active learning method alm alm is a soft computing methodology which is based on a hypothesis claiming that human brain interprets information in pattern like images the proposed fuzzification method is applicable to all non fuzzy clustering algorithms as a post process the most outstanding advantage of this method is the ability to determine the membership degrees of each data to all clusters based on the density and shape of the clusters it is worth mentioning that for existing fuzzy clustering algorithms such as fcm the membership degree is usually determined as a function of distance to the center of the clusters in our proposed method all data points of a cluster will play a role in order to determine the membership degrees consequently the obtained membership degrees will depend on all of the data points of clusters the amount of data points and the density distribution of the clusters simulations prove the advantages of the proposed method

convergence of matrix continued fractions the aim of this work is to give some criteria on the convergence of matrix continued fractions we begin by presenting some new results which generalize the links between the convergent elements of real continued fractions secondly we give necessary and sufficient conditions for the convergence of continued fractions of matrix arguments this paper will be completed by illustrating the theoretical results with some examples

a high level programming language implementation of topology optimization applied to steady state navier stokes flow we present a versatile high level programming language implementation of non linear topology optimization our implementation is based on the commercial software package femlab and it allows a wide range of optimization objectives to be dealt with easily we exemplify our method by studies of steady state navier stokes flow problems thus extending the work by borrvall and petersson on topology optimization of fluids in stokes flow int j num meth fluids 2003 41 77 107 we analyse the physical aspects of the solutions and how they are affected by different parameters of the optimization algorithm a complete example of our implementation is included as femlab code in an appendix copyright 2005 john wiley sons ltd

k means type algorithms a generalized convergence theorem and characterization of local optimality the k means algorithm is a commonly used technique in cluster analysis in this paper several questions about the algorithm are addressed the clustering problem is first cast as a nonconvex mathematical program then a rigorous proof of the finite convergence of the k means type algorithm is given for any metric it is shown that under certain conditions the algorithm may fail to converge to a local minimum and that it converges under differentiability conditions to a kuhn tucker point finally a method for obtaining a local minimum solution is given

waves in lattices with imperfect junctions and localized defect modes a correspondence between continuum periodic structures and discrete lattices is well known in the theory of elasticity frequently lattice models are the result of the discretization of continuous mechanical problems in this paper we discuss the discretization of two dimensional square thin walled structures we consider the case when thin walled bridges have defects in the vicinity of junctions at these points the displacement satisfies an effective robin type boundary condition we study a defect vibration mode localized in the neighbourhood of the damaged junction we analyse dispersion diagrams that show the existence of standing waves in a structure with periodically distributed defects

on maximal eigenfrequency separation in two material structures the 1d and 2d scalar cases abstract we present a method to maximize the separation of two adjacent eigenfrequencies in structures with two material components the method is based on finite element analysis and topology optimization in which an iterative algorithm is used to find the optimal distribution of the materials results are presented for eigenvalue problems based on the 1d and 2d scalar wave equations two different objectives are used in the optimization the difference between two adjacent eigenfrequencies and the ratio between the squared eigenfrequencies in the 1d case we use simple interpolation of material parameters but in the 2d case the use of a more involved interpolation is needed and results obtained with a new interpolation function are shown in the 2d case the objective is reformulated into a double bound formulation due to the complication from multiple eigenfrequencies it is shown that some general conclusions can be drawn that relate the material parameters to the obtainable objective values and the optimized designs

the response of two dimensional periodic structures to impulsive point loading abstract this work is concerned with the response of an infinite two dimensional periodic structure to an impulsive point load or equivalently the response of a finite system at times before the disturbance reaches the system boundaries initially a model approach is employed to yield an expression for the response of a finite system under born von karman boundary conditions by allowing the system size to become large the modal response summation is converted to an integral and the method of stationary phase is employed with de allowance being made for the occurrence of caustics with this approach the response is expressed in terms of the properties of the phase constant surfaces which arise in the analysis of plane wave motion through the system the method is applied to an example lumped mass system and a comparison is made with results yield by direct numerical simulation the method is found to be efficient and accurate and a number of observations are made regarding the physical nature of the system response

linear time maximum margin clustering maximum margin clustering mmc is a newly proposed clustering method which has shown promising performance in recent studies it extends the computational techniques of support vector machine svm to the unsupervised scenario traditionally mmc is formulated as a nonconvex integer programming problem which makes it difficult to solve several methods have been proposed in the literature to solve the mmc problem based on either semidefinite programming sdp or alternating optimization however these methods are still time demanding when handling large scale data sets which limits its application in real world problems in this paper we propose a cutting plane maximum margin clustering cpmmc algorithm it first decomposes the nonconvex mmc problem into a series of convex subproblems by making use of the constrained concave convex procedure cccp then for each subproblem our algorithm adopts the cutting plane algorithm to solve it moreover we show that the cpmmc algorithm takes o sn time to converge with guaranteed accuracy where n is the number of samples in the data set and s is the sparsity of the data set i e the average number of nonzero features of the data samples we also derive the multiclass version of our cpmmc algorithm experimental evaluations on several real world data sets show that cpmmc performs better than existing mmc methods both in efficiency and accuracy

constrained clustering as an optimization method a deterministic annealing approach to clustering is derived on the basis of the principle of maximum entropy this approach is independent of the initial state and produces natural hierarchical clustering solutions by going through a sequence of phase transitions it is modified for a larger class of optimization problems by adding constraints to the free energy the concept of constrained clustering is explained and three examples are are given in which it is used to introduce deterministic annealing the previous clustering method is improved by adding cluster mass variables and a total mass constraint the traveling salesman problem is reformulated as constrained clustering yielding the elastic net en approach to the problem more insight is gained by identifying a second lagrange multiplier that is related to the tour length and can also be used to control the annealing process the open path constraint formulation is shown to relate to dimensionality reduction by self organization in unsupervised learning a similar annealing procedure is applicable in this case as well

a double expansion method for the frequency response of finite length beams with periodic parameters abstract a double expansion method for the frequency response of finite length beams with periodic distribution parameters is proposed the vibration response of the beam with spatial periodic parameters under harmonic excitations is studied the frequency response of the periodic beam is the function of parametric period and then can be expressed by the series with the product of periodic and non periodic functions the procedure of the double expansion method includes the following two main steps first the frequency response function and periodic parameters are expanded by using identical periodic functions based on the extension of the floquet bloch theorem and the period parametric differential equation for the frequency response is converted into a series of linear differential equations with constant coefficients second the solutions to the linear differential equations are expanded by using modal functions which satisfy the boundary conditions and the linear differential equations are converted into algebraic equations according to the galerkin method the expansion coefficients are obtained by solving the algebraic equations and then the frequency response function is finally determined the proposed double expansion method can uncouple the effects of the periodic expansion and modal expansion so that the expansion terms are determined respectively the modal number considered in the second expansion can be reduced remarkably in comparison with the direct expansion method the proposed double expansion method can be extended and applied to the other structures with periodic distribution parameters for dynamics analysis numerical results on the frequency response of the finite length periodic beam with various parametric wave numbers and wave amplitude ratios are given to illustrate the effective application of the proposed method and the new frequency response characteristics including the parameter excited modal resonance doubling peak frequency response and remarkable reduction of the maximum frequency response for certain parametric wave number and wave amplitude the results have the potential application to structural vibration control

generalised nonlocal image smoothing we propose a discrete variational approach for image smoothing consisting of nonlocal data and smoothness constraints that penalise general dissimilarity measures defined on image patches one of such dissimilarity measures is the weighted l 2 distance between patches in such a case we derive an iterative neighbourhood filter that induces a new similarity measure in the photometric domain it can be regarded as an extended patch similarity measure that evaluates not only the patch similarity of two chosen pixels but also the similarity of their corresponding neighbours this leads to a more robust smoothing process since the pixels selected for averaging are more coherent with the local image structure by slightly modifying the way the similarities are computed we obtain two related filters the nl means filter of buades et al siam multiscale model simul 4 2 490 530 2005b and the nds filter of mrazek et al geometric properties for incomplete data computational imaging and vision vol 31 pp 335 352 springer dordrecht 2006 in fact the proposed approach can be considered as a generalisation of the latter filter to the space of patches we also provide novel insights into relations of the nds filter with diffusion regularisation methods as well as with some recently proposed graph regularisation techniques we evaluate our method for the task of denoising greyscale and colour images degraded with gaussian and salt and pepper noise demonstrating that it compares very well to other more sophisticated approaches

optimal by accuracy and optimal by order cubature formulae in interpolational classes in this paper the problem of optimal integration for fast oscillatory functions of two variables is solved constructively in the case where a priori information is limited the connection of this problem with the problem of optimal recovery of a function from interpolational classes is analysed using properties of majorants and minorants for these functional classes

learning spectral clustering with application to speech separation spectral clustering refers to a class of techniques which rely on the eigenstructure of a similarity matrix to partition points into disjoint clusters with points in the same cluster having high similarity and points in different clusters having low similarity in this paper we derive new cost functions for spectral clustering based on measures of error between a given partition and a solution of the spectral relaxation of a minimum normalized cut problem minimizing these cost functions with respect to the partition leads to new spectral clustering algorithms minimizing with respect to the similarity matrix leads to algorithms for learning the similarity matrix from fully labelled data sets we apply our learning algorithm to the blind one microphone speech separation problem casting the problem as one of segmentation of the spectrogram

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

the response of two dimensional periodic structures to harmonic point loading a theoretical and experimental study of a beam grillage abstract this work is concerned with the response of a beam grillage system to a harmonic point load this system serves as a particular example of a two dimensional periodic structure and the aim of the work is to validate a number of recent results regarding the general nature of the response of such structures to a localized excitation source the grillage is analyzed by using the hierarchical finite element method to model a single period and then employing periodic structure theory to yield the phase constant surfaces which are needed for the forced response analysis the theoretical work is complemented by an experimental study of a grillage system a relatively high level of damping treatment is employed to produce a non reverberant system that behaves in a similar manner to an infinitely extended system both the theoretical and experimental results show that the response can exhibit highly directional beaming the spatial pattern of which is strongly dependent on the excitation frequency and this finding is fully consistent with the findings of the aforementioned general study

efficient visual tracking using particle filter with incremental likelihood calculation in this paper we propose a particle filter that determines the weight of each particle employing the incremental likelihood calculation since there is usually a large overlap region between the two particles that are sequentially generated determining the weight of the particle has only a small time cost therefore the real time performance of the proposed tracker can be dramatically improved extensive experimental results for single object and multiple object tracking scenarios are presented to demonstrate the efficiency of the proposed approach finally an interesting color based active vision system is developed for a free floating space robot testbed to facilitate teleoperation

bayesian k means as a maximization expectation algorithm we introduce a new class of maximization expectation me algorithms where we maximize over hidden variables but marginalize over random parameters this reverses the roles of expectation and maximization in the classical expectation maximization algorithm in the context of clustering we argue that these hard assignments open the door to very fast implementations based on data structures such as kd trees and conga lines the marginalization over parameters ensures that we retain the ability to infer model structure i e number of clusters as an important example we discuss a top down bayesian k means algorithm and a bottom up agglomerative clustering algorithm in experiments we compare these algorithms against a number of alternative algorithms that have recently appeared in the literature

the nested dirichlet process in multicenter studies subjects in different centers may have different outcome distributions this article is motivated by the problem of nonparametric modeling of these distributions borrowing information across centers while also allowing centers to be clustered starting with a stick breaking representation of the dirichlet process dp we replace the random atoms with random probability measures drawn from a dp this results in a nested dp prior which can be placed on the collection of distributions for the different centers with centers drawn from the same dp component automatically clustered together theoretical properties are discussed and an efficient markov chain monte carlo algorithm is developed for computation the methods are illustrated using a simulation study and an application to quality of care in u s hospitals

shape optimization of phononic band gap structures incorporating inertial amplification mechanisms abstract the aim of this study is to obtain a wide and deep phononic gap at low frequencies in a two dimensional periodic solid structure with embedded inertial amplification mechanisms size and shape optimizations are performed on the building block mechanism of the periodic structure to maximize phononic gap stop band width and depth it is shown that shape optimization offers a wider and deeper gap when both size and shape optimized mechanisms have the same mass and stiffness values analysis of the shape optimized mechanism is carried out using two different finite element models one using beam elements and the other using shell elements both models produced similar results for the stop band width and depth a two dimensional periodic structure is constructed with the shape optimized building block mechanisms moreover experimental and numerical frequency response results of this periodic structure are obtained the matching frequency response results indicate that the two dimensional periodic structure has a wide and deep phononic gap for in plane excitations furthermore due to proper selection of the out of plane thickness of the periodic structure out of plane vibration modes do not occur within the phononic gap

analytical approach for the floquet theory of delay differential equations we present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states to this end we start with approximately determining such reference states by extending the poincare lindstedt and the shohat expansions which were originally developed for ordinary differential equations then we systematically elaborate a linear stability analysis around a time periodic reference state this allows us to approximately calculate the floquet eigenvalues and their corresponding eigensolutions by using matrix valued continued fractions

mercer kernel based clustering in feature space the article presents a method for both the unsupervised partitioning of a sample of data and the estimation of the possible number of inherent clusters which generate the data this work exploits the notion that performing a nonlinear data transformation into some high dimensional feature space increases the probability of the linear separability of the patterns within the transformed space and therefore simplifies the associated data structure it is shown that the eigenvectors of a kernel matrix which defines the implicit mapping provides a means to estimate the number of clusters inherent within the data and a computationally simple iterative procedure is presented for the subsequent feature space partitioning of the data

dispersive elastodynamics of 1d banded materials and structures analysis abstract the elastodynamics of 1d periodic materials and finite structures comprising these materials are studied with particular emphasis on correlating their frequency dependent characteristics and on elucidating their pass band and stop band behaviors dispersion relations are derived for periodic materials and are employed in a novel manner for computing both pass band and stop band complex mode shapes through simulations of harmonically induced wave motion within a finite number of unit cells conformity of the frequency band structure between infinite and finite periodic systems is shown in particular only one or two unit cells of a periodic material could be sufficient for frequency bandedness to carry over from the infinite periodic case and only three to four unit cells are necessary for the decay in normalized transmission within a stop band to practically saturate with an increase in the number of cells dominant speeds in the scattered wave field within the same finite set of unit cells are observed to match those of phase and group velocities of the infinite periodic material within the most active pass band dynamic response due to impulse excitation also is shown to capture the infinite periodic material dynamical characteristics finally steady state vibration analyses are conducted on a finite fully periodic structure revealing a conformity in the natural frequency spread to the frequency band layout of the infinite periodic material the steady state forced response is observed to exhibit mode localization patterns that resemble those of the infinite periodic medium and it is shown that the maximum localized response under stop band conditions could be significantly less than in an equivalent homogenous structure and the converse is true for pass band conditions

periodicity effects of axial waves in elastic compound rods abstract floquet analysis is applied to the bernoulli euler model for axial waves in a periodic rod explicit asymptotic formulae for the stop band borders are given and the topology of the stop band pattern is explained eigenfrequencies of the symmetric unit cell are determined by the phase closure principle and their correspondence with stop band formation is shown steady state and transient dynamics of a periodic rod of finite length are analysed numerically and the difference in structural response when excitation is done in either stop or pass bands is demonstrated a physical interpretation of the underlying mechanisms of stop bands is proposed

fourier or bessel transformations of highly oscillatory functions an algorithm for integral transformation of highly oscillatory functions is presented it is a generalization of the standard gaussian quadrature method but has the virtue that the usual tedious tests of convergence of the numerical results is not necessary the effectiveness and accuracy of the algorithm is tested for both large arguments and higher orders of the bessel function

color image segmentation using adaptive mean shift and statistical model based methods in this paper we propose an unsupervised segmentation algorithm for color images based on gaussian mixture models gmms the number of mixture components is determined automatically by adaptive mean shift in which local clusters are estimated by repeatedly searching for higher density points in feature vector space for the estimation of parameters of gmms the mean field annealing expectation maximization em is employed the mean field annealing em provides a global optimal solution to overcome the local maxima problem in a mixture model by combining the adaptive mean shift and the mean field annealing em natural color images are segmented automatically without over segmentation or isolated regions the experiments show that the proposed algorithm can produce satisfactory segmentation without any a priori information

clustering via geometric median shift over riemannian manifolds the mean shift algorithms have been successfully applied to many areas such as data clustering feature analysis and image segmentation however they still have two limitations one is that they are ineffective in clustering data with low dimensional manifolds because of the use of the euclidean distance for calculating distances the other is that they sometimes produce poor results for data clustering and image segmentation this is because a mean may not be a point in a data set in order to overcome the two limitations we propose a novel approach for the median shift over riemannian manifolds that uses the geometric median and geodesic distances unlike the mean the geometric median of a data set is one of points in the set compared to the euclidean distance the geodesic distances can better describe data points distributed on riemannian manifolds based on these two facts we first present a novel density function that characterizes points on a manifold with the geodesic distance the shift of the geometric median over the riemannian manifold is derived from maximizing this density function after this we present an algorithm for geometric median shift over riemannian manifolds together with theoretical proofs of its correctness extensive experiments have demonstrated that our method outperforms the state of the art algorithms in data clustering image segmentation and noise filtering on both synthetic data sets and real image databases

phononic band gaps and vibrations in one and two dimensional mass spring structures the vibrational response of finite periodic lattice structures subjected to periodic loading is investigated special attention is devoted to the response in frequency ranges with gaps in the band structure for the corresponding infinite periodic lattice the effects of boundaries viscous damping and imperfections are studied by analyzing two examples a 1 d filter and a 2 d wave guide in 1 d the structural response in the band gap is shown to be insensitive to damping and small imperfections in 2 d the similar effect of damping is noted for one type of periodic structure whereas for another type the band gap effect is nearly eliminated by damping in both 1 d and 2 d it is demonstrated how the free structural boundaries affect the response in the band gap due to local resonances finally 2 d wave guides are considered by replacing the periodic structure with a homogeneous structure in a straight and a 90 bent path and it is shown how the vibrational response is confined to the paths in the band gap frequency ranges

resonant frequency primitive waveforms and star waves in lattices for square and triangular lattices we have found a new line localized primitive waveform lpw existing at a resonant frequency in two dimensional 2d case the lpw represents a line of oscillating particles while the lattice outside this line remains at rest we show that a a single lpw does not conduct energy however a band consisting of two or more neighboring lpws is a conductor with the phase shift dependent energy flux velocity b any canonical sinusoidal wave consists of lpws in turn the lpw can be represented by a superposition of the sinusoidal waves these two types of waves are connected by the discrete fourier transform c there are two three lpw orientations for the square triangular lattice and this is why the sinusoidal wave group velocity orientation is piecewise constant at this frequency it coincides with the nearest lpw orientation d lpw can also exist at a lower frequency being localized at the lattice halfplane boundary further for 3d lattices plane localized waveforms are found to exist in a frequency region finally for the point harmonic excitation of 2d lattices we show that starlike waves develop with the rays in the lpw directions

wave propagation in continuous periodic structures research contributions from southampton 1964 1995 abstract after brief reference to some early studies by other investigators this paper focuses mainly on methods developed at the university of southampton since 1964 to analyze and predict the free and forced wave motion in continuous periodic engineering structures beginning with receptance methods which have been applied to periodic beams and rib skin structures it continues with a method of direct solution of the wave equation this uses floquet s principle and has been applied to beams and quasi one dimensional periodic plates and cylindrical shells sample curves of the propagation and attenuation constants pertaining to these structures are presented a limited discussion of the transfer matrix then follows after which the method of space harmonics is introduced as the method best suited to the prediction of sound radiated from a vibrating periodic structure reviewed next are some theorems and variational principles relating to periodic structures which have been developed at southampton and which form a basis for finding natural frequencies of finite structures or for computing free and forced wave notion by energy methods this has led to the finite element method in its standard and hierarchical forms being used to study wave motion in genuine two dimensional and three dimensional structures examples of this work are shown the method of phased array receptance functions is then introduced as possibly the easiest way of setting up exact equations for the propagation constants of uniform quasi one dimensional periodic structures a summary is finally presented of the limited and early work performed at southampton on simple disordered periodic structures

stochastic global optimization methods part 1 clustering methods in this stochastic approach to global optimization clustering techniques are applied to identify local minima of a real valued objective function that are potentially global three different methods of this type are described their accuracy and efficiency are analyzed in detail

quantization based clustering algorithm in this paper a quantization based clustering algorithm qbca is proposed to cluster a large number of data points efficiently unlike previous clustering algorithms qbca places more emphasis on the computation time of the algorithm specifically qbca first assigns the data points to a set of histogram bins by a quantization function then it determines the initial centers of the clusters according to this point distribution finally qbca performs clustering at the histogram bin level rather than the data point level we also propose two approaches to improve the performance of qbca further i a shrinking process is performed on the histogram bins to reduce the number of distance computations and ii a hierarchical structure is constructed to perform efficient indexing on the histogram bins finally we analyze the performance of qbca theoretically and experimentally and show that the approach 1 can be easily implemented 2 identifies the clusters effectively and 3 outperforms most of the current state of the art clustering approaches in terms of efficiency

evaluation of fourier transforms by gauss laguerre quadratures numerical schemes for the evaluation of fourier transforms with gauss laguerre quadratures are presented these schemes which incorporate functional values at complex arguments are tested for efficacy and accuracy the authors illustrate their effectiveness on a simple model system by computing the form factor and its laplacian for the neon atom

exact analysis of localized modes in two dimensional bi periodic mass spring systems with a single disorder abstract the frequency equation and localized modes in two dimensional bi periodic mass spring systems with one disordered subsystem are exactly analyzed by means of double u transformation at first a plane distributed mass spring system with 2 n 1 2 n 2 subsystems and cyclic periodicity in x and y directions is considered then by adopting a limiting process with n 1 n 2 approaching to infinity the limiting solution is applicable for the plane distributed bi periodic mass spring systems with boundary at infinity the explicit frequency equation and localized modes are derived some specific systems are taken as examples to demonstrate how to apply the formulas and equations obtained in the present paper in order to find the localized modes and corresponding frequencies

free vibrations of finite periodic structures in pass and stop bands of the counterpart infinite waveguides abstract the existence of frequency stop bands in which transmission of the vibro acoustic energy is impossible suggests that the periodic structures may be used for vibro isolation in any technical application however only a finite segment of such a structure can be used this paper is concerned with comparison of the eigenfrequency spectra of finite periodic structures with location of stop bands for their infinite counterparts a hierarchy of four mathematical models is considered in each case special attention is paid to eigenfrequencies and eigenmodes of a single periodicity cell with appropriate boundary conditions the influence of the amount of periodicity cells in a finite compound structure on its eigenfrequency spectrum is analyzed several features common for the considered models are found and discussed in the context of the existing knowledge on the subject

topology optimization of continuum structures subjected to filtered white noise stochastic excitations abstract this work addresses the challenge of topology optimization for continuum structures subjected to non white noise stochastic excitations the objective is to manipulate the variance of the stochastic dynamic response of a linear continuum structure through design the excitation is modeled as filtered white noise and the solution and sensitivities are obtained using the augmented state space formulation in the frequency domain to reduce the computational cost and maintain high accuracy closed form solutions are utilized for evaluating the response variance and modal truncation is adopted to reduce dimension the effect of which is investigated the solid isotropic material with penalization method is used together with the heaviside projection method to achieve a clear distinction between solid and void regions in the structure and the gradient based optimizer method of moving asymptotes informed by sensitivities of the real and complex eigenvectors is used to evolve the design the algorithm is demonstrated on design problems of minimizing the variance of stochastic response under a volume constraint and several numerical examples are provided to show the effectiveness of the method solutions are compared to conventional maximum stiffness solutions and as to be expected show markedly improved response under the considered stochastic dynamic excitation

band gap green s functions and localized oscillations we consider some typical continuous and discrete models of structures possessing band gaps and analyse the localized oscillation modes general considerations show that such modes can exist at any

asymptotics of eigenfrequencies in the dynamic response of elongated multi structures the paper addresses a mathematical model describing the dynamic response of an elongated bridge supported by elastic pillars the elastic system is considered as a multi structure involving subdomains of different limit dimensions connected via junction regions analytical formulae have been derived to estimate eigenfrequencies in the low frequency range the analytical findings for bloch floquet waves in an infinite periodic structure are compared with the finite element numerical computations for an actual bridge structure of finite length the asymptotic estimates obtained here have also been used as a design tool in problems of asymptotic optimization

eigenvalue problems for doubly periodic elastic structures and phononic band gaps we consider the problem of elastic waves propagating in a two dimensional array of circular cavities taking rigorous account of coupling between shear and dilational waves a technique originally due to rayleigh is derived that involves an elegant identity between the singular and non singular components of the stress fields in the array this leads to an infinite linear system which can be truncated and solved in order to determine the complete structure of the propagating modes of particular interest is the possibility of exhibiting phononic band gaps i e domains of frequency for which all propagating vibration in the material is suppressed

hierarchical dirichlet processes we consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups we assume that the number of mixture components is unknown a priori and is to be inferred from the data in this setting it is natural to consider sets of dirichlet processes one for each group where the well known clustering property of the dirichlet process provides a nonparametric prior for the number of mixture components within each group given our desire to tie the mixture models in the various groups we consider a hierarchical model specifically one in which the base measure for the child dirichlet processes is itself distributed according to a dirichlet process such a base measure being discrete the child dirichlet processes necessarily share atoms thus as desired the mixture models in the different groups necessarily share mixture components we discuss representations of hierarchical dirichlet processes

maximum margin clustering made practical motivated by the success of large margin methods in supervised learning maximum margin clustering mmc is a recent approach that aims at extending large margin methods to unsupervised learning however its optimization problem is nonconvex and existing mmc methods all rely on reformulating and relaxing the nonconvex optimization problem as semidefinite programs sdp though sdp is convex and standard solvers are available they are computationally very expensive and only small data sets can be handled to make mmc more practical we avoid sdp relaxations and propose in this paper an efficient approach that performs alternating optimization directly on the original nonconvex problem a key step to avoid premature convergence in the resultant iterative procedure is to change the loss function from the hinge loss to the laplacian square loss so that overconfident predictions are penalized experiments on a number of synthetic and real world data sets demonstrate that the proposed approach is more accurate much faster hundreds to tens of thousands of times faster and can handle data sets that are hundreds of times larger than the largest data set reported in the mmc literature

an edge based algorithm for discontinuity adaptive color image smoothing abstract we present a new scheme to increase the performance of edge preserving image smoothing algorithm from the parameter tuning of a markov random field mrf function this method is based on an automatic control of the image smoothing strength in the mrf function in which the parameter control of the function depends on edge magnitude resulted from discontinuities of image intensity without any binary decision for the edge magnitude direct use of full edge magnitude could improve the performance of discontinuity preserving image smoothing technique

algebra of multidimensional periodic operators with defects the procedure for calculating the spectrum of discrete periodic operators perturbed by periodic operators of smaller dimensions is obtained some properties of the corresponding algebra of operators with defects are considered these results yield explicit expressions for propagative guided and other localized spectra of different physical operators on periodic structures coupled with various defects as shown in the example of the schrodinger operator on 2d lattice with linear and point defects the explicit formula for the localized spectrum can be helpful to solve inverse problems such as a recovery of point defects

floquet green function formalism for harmonically driven hamiltonians a method is proposed for the calculation of the floquet green function of a general hamiltonian with harmonic time dependence we use matrix continued fractions to derive an expression for the dynamical effective potential that can be used to calculate the floquet green function of the system we demonstrate the formalism for the simple case of a space periodic in the tight binding approximation hamiltonian with a defect whose on site energy changes harmonically with time we study the local density of states for this system and the behaviour of the localized states as a function of the different parameters that characterize the system

information maximization clustering based on squared loss mutual information information maximization clustering learns a probabilistic classifier in an unsupervised manner so that mutual information between feature vectors and cluster assignments is maximized a notable advantage of this approach is that it involves only continuous optimization of model parameters which is substantially simpler than discrete optimization of cluster assignments however existing methods still involve nonconvex optimization problems and therefore finding a good local optimal solution is not straightforward in practice in this letter we propose an alternative information maximization clustering method based on a squared loss variant of mutual information this novel approach gives a clustering solution analytically in a computationally efficient way via kernel eigenvalue decomposition furthermore we provide a practical model selection procedure that allows us to objectively optimize tuning parameters included in the kernel function through experiments we demonstrate the usefulness of the pr

optimum design of band gap beam structures abstract the design of band gap structures receives increasing attention for many applications in mitigation of undesirable vibration and noise emission levels a band gap structure usually consists of a periodic distribution of elastic materials or segments where the propagation of waves is impeded or significantly suppressed for a range of external excitation frequencies maximization of the band gap is therefore an obvious objective for optimum design this problem is sometimes formulated by optimizing a parameterized design model which assumes multiple periodicity in the design however it is shown in the present paper that such an a priori assumption is not necessary since in general just the maximization of the gap between two consecutive natural frequencies leads to significant design periodicity the aim of this paper is to maximize frequency gaps by shape optimization of transversely vibrating bernoulli euler beams subjected to free standing wave vibration or forced time harmonic wave propagation and to study the associated creation of periodicity of the optimized beam designs the beams are assumed to have variable cross sectional area given total volume and length and to be made of a single linearly elastic material without damping numerical results are presented for different combinations of classical boundary conditions prescribed orders of the upper and lower natural frequencies of maximized natural frequency gaps and a given minimum constraint value for the beam cross sectional area to study the band gap for travelling waves a repeated inner segment of the optimized beams is analyzed using floquet theory and the waveguide finite element wfe method finally the frequency response is computed for the optimized beams when these are subjected to an external time harmonic loading with different excitation frequencies in order to investigate the attenuation levels in prescribed frequency band gaps the results demonstrate that there is almost perfect correlation between the band gap size location of the emerging band structure and the size location of the corresponding natural frequency gap in the finite structure

the response of two dimensional periodic structures to point harmonic forcing abstract this analysis is concerned with the response of an infinite two dimensional periodic structure to point harmonic loading initially a damped finite system is considered and the system size is then allowed to tend to infinity it is shown that the response in the far field can be expressed in terms of the properties of the phase constant surfaces which arise in the analysis of plane wave motion through the system within a pass band it is found that the physical nature of the response is strongly affected by the presence or otherwise of a caustic in the absence of a caustic the response amplitude has a relatively smooth spatial distribution if a caustic is present then the response amplitude has a complex spatial pattern and a dead region of very low response occurs the theory is applied to a two dimensional mass spring periodic system and a comparison is made with an exact calculation for the response of a large finite system excellent agreement is obtained between the two sets of results the work has application to all types of two dimensional periodic structures including orthogonally stiffened plates and shells and it raises the possibility of designing a periodic structure to act as a spatial filter to isolate sensitive equipment from a localized excitation source

dimensionality reduction of multimodal labeled data by local fisher discriminant analysis reducing the dimensionality of data without losing intrinsic information is an important preprocessing step in high dimensional data analysis fisher discriminant analysis fda is a traditional technique for supervised dimensionality reduction but it tends to give undesired results if samples in a class are multimodal an unsupervised dimensionality reduction method called locality preserving projection lpp can work well with multimodal data due to its locality preserving property however since lpp does not take the label information into account it is not necessarily useful in supervised learning scenarios in this paper we propose a new linear supervised dimensionality reduction method called local fisher discriminant analysis lfda which effectively combines the ideas of fda and lpp lfda has an analytic form of the embedding transformation and the solution can be easily computed just by solving a generalized eigenvalue problem we demonstrate the practical usefulness and high scalability of the lfda method in data visualization and classification tasks through extensive simulation studies we also show that lfda can be extended to non linear dimensionality reduction scenarios by applying the kernel trick

plane wave propagation and frequency band gaps in periodic plates and cylindrical shells with and without heavy fluid loading free plane wave propagation in infinitely long periodic elastic structures with and without heavy fluid loading is considered the structures comprise continuous elements of two different types connected in an alternating sequence in the absence of fluid loading an exact solution which describes wave motion in each unboundedly extended element is obtained analytically as a superposition of all propagating and evanescent waves continuity conditions at the interfaces between elements are formulated and standard floquet theory is applied to set up a characteristic determinant an efficient algorithm to compute bloch parameters propagation constants as a function of the excitation frequency is suggested and the location of band gaps is studied as a function of non dimensional parameters of the structure s composition in the case of heavy fluid loading an infinitely large number of propagating or evanescent waves exist in each unboundedly extended elasto acoustic element of a periodic structure wave motion in each element is then presented in the form of a modal decomposition with a finite number of terms retained in these expansions and the accuracy of such an approximation is assessed a generalized algorithm is used to compute bloch parameters for a periodic structure with heavy fluid loading as a function of the excitation frequency and similarly to the previous case the location of band gaps is studied

prototype selection for dissimilarity based classifiers a conventional way to discriminate between objects represented by dissimilarities is the nearest neighbor method a more efficient and sometimes a more accurate solution is offered by other dissimilarity based classifiers they construct a decision rule based on the entire training set but they need just a small set of prototypes the so called representation set as a reference for classifying new objects such alternative approaches may be especially advantageous for non euclidean or even non metric dissimilarities the choice of a proper representation set for dissimilarity based classifiers is not yet fully investigated it appears that a random selection may work well in this paper a number of experiments has been conducted on various metric and non metric dissimilarity representations and prototype selection methods several procedures like traditional feature selection methods here effectively searching for prototypes mode seeking and linear programming are compared to the random selection in general we find out that systematic approaches lead to better results than the random selection especially for a small number of prototypes although there is no single winner as it depends on data characteristics the k centres works well in general for two class problems an important observation is that our dissimilarity based discrimination functions relying on significantly reduced prototype sets 3 10 of the training objects offer a similar or much better classification accuracy than the best k nn rule on the entire training set this may be reached for multi class data as well however such problems are more difficult

free vibration analysis of continuous rectangular plates vibration characteristics of rectangular plates continuous over full range line supports or partial line supports have been studied by using a discrete method concentrated loads with heaviside unit functions and dirac delta functions are used to simulate the line supports the fundamental differential equations are established for the bending problem of the continuous plate by transforming these differential equations into integral equations and using the trapezoidal rule of the approximate numerical integration the solution of these equations is obtained green function which is the solution of deflection of the bending problem of plate is used to obtain the characteristic equation of the free vibration the effects of the line support the variable thickness and aspect ratio on the frequencies and mode shapes are considered by comparing the numerical results obtained by the present method with those previously published the efficiency and accuracy of the present method are investigated

kernel dimension reduction in regression we present a new methodology for sufficient dimension reduction sdr our methodology derives directly from the formulation of sdr in terms of the conditional independence of the covariate x from the response y given the projection of x on the central subspace cf j amer statist assoc 86 1991 316 342 and regression graphics 1998 wiley we show that this conditional independence assertion can be characterized in terms of conditional covariance operators on reproducing kernel hilbert spaces and we show how this characterization leads to an m estimator for the central subspace the resulting estimator is shown to be consistent under weak conditions in particular we do not have to impose linearity or ellipticity conditions of the kinds that are generally invoked for sdr methods we also present empirical results showing that the new methodology is competitive in practice

application of matrix valued integral continued fractions to spectral problems on periodic graphs with defects we show that spectral problems for periodic operators on lattices with embedded defects of lower dimensions can be solved with the help of matrix valued integral continued fractions while these continued fractions are usual in the approximation theory they are less known in the context of spectral problems we show that the spectral points can be expressed as zeros of determinants of the continued fractions they are also useful in the analysis of inverse problems one to one correspondence between spectral data and defects finally the explicit formula for the resolvent in terms of the continued fractions is provided we apply some of the results to the schrodinger operator acting on graphene with line and point defects

the mean shift algorithm and its relation to kernel regression we investigate the connection between the asymptotic bias of the well known nadaraya watson kernel regression and the mean shift ms vector with the gaussian kernel we first show that the asymptotic bias for the univariate nadaraya watson kernel regression can be estimated using the ms scalar then we investigate the general d dimensional case d 1 and derive a formula for the asymptotic bias as a function of the ms vector we show that when the regression function is a linear function of its entries then the asymptotic bias can be represented as a linear function of the ms vector the ms algorithm for the univariate and the linear cases can be used to find points where the nadaraya watson kernel regression gives an unbiased estimate furthermore this connection suggests that exploiting the theoretical properties of the asymptotic bias of the nadaraya watson kernel regression may be helpful to show the convergence of the ms algorithm through the simulations we show that how the given theoretical results can be used to estimate the bias of the estimated clean signal by just observing the noisy signal having access to the bias of the estimator enables us to evaluate the accuracy of the estimated clean data which later will be used to design a quantizer

the convergence rate of continued fractions representing solutions of a riccati equation the aim of this note is to generalize and apply results on matrix continued fractions representing the solution of discrete matrix riccati equations assuming uniform bounds for the norm of the matrix coefficients of the continued fraction the minimal and maximal solutions of the corresponding algebraic riccati equation can be accurately enclosed

regularized multitask learning for multidimensional log density gradient estimation log density gradient estimation is a fundamental statistical problem and possesses various practical applications such as clustering and measuring nongaussianity a naive two step approach of first estimating the density and then taking its log gradient is unreliable because an accurate density estimate does not necessarily lead to an accurate log density gradient estimate to cope with this problem a method to directly estimate the log density gradient without density estimation has been explored and demonstrated to work much better than the two step method the objective of this letter is to improve the performance of this direct method in multidimensional cases our idea is to regard the problem of log density gradient estimation in each dimension as a task and apply regularized multitask learning to the direct log density gradient estimator we experimentally demonstrate the usefulness of the proposed multitask method in log density gradient estimation and mode seeking clustering

the harmonic response of rectangular sandwich plates with multiple stiffening a flexural wave analysis abstract an exact analytical method is presented for the vibration response of a finite three layered rectangular sandwich plate with a visco elastic core subjected to a harmonic line force which varies sinusoidally across the plate uniform parallel stiffeners which may all be different span the plate between one pair of simply supported edges the other pair of edges may have any degree or type of uniform constraint in the analysis the known flexural wave motion in an infinite parallel unstiffened plate subjected to a single harmonic line force or moment is utilized a matrix equation is set up for the reactions imposed on the plate by the stiffeners and for the amplitudes of wave motion reflected from the ends of a finite plate the sandwich core may have large or small amounts of damping results computed from the theory are presented and are shown to compare well with experimental data the influence of the stiffener and core properties on the plate harmonic response is readily determined

matrix representations of multidimensional integral and ergodic operators abstract we provide a representation of the c algebra generated by multidimensional integral operators with piecewise constant kernels and discrete ergodic operators this representation allows us to find the spectrum and to construct the explicit functional calculus on this algebra the method can be useful in various applications since many discrete approximations of integral and differential operators belong to this algebra some examples are also presented 1 we construct an explicit functional calculus for extended fredholm integral operators with piecewise constant kernels 2 we find a wave function and spectral estimates for 3d discrete schrodinger equation with planar guided local potential defects and point sources the accuracy of approximation of continuous multi kernel integral operators by the operators with piecewise constant kernels is also discussed

letter to the editor on quadrature of bessel transformations a method for integral transformations of highly oscillatory functions bessel functions is presented it is based on the filon type method and the decay of the error can be increased as increases the effectiveness and accuracy of the quadrature is tested for both large arguments and higher orders of bessel functions in the case where the orders are nonnegative integers

density estimation with confidence sets exemplified by superclusters and voids in the galaxies abstract a method is presented for forming both a point estimate and a confidence set of semiparametric densities the final product is a three dimensional figure that displays a selection of density estimates for a plausible range of smoothing parameters the boundaries of the smoothing parameter are determined by a nonparametric goodness of fit test that is based on the sample spacings for each value of the smoothing parameter our estimator is selected by choosing the normal mixture that maximizes a function of the sample spacings a point estimate is selected from this confidence set by using the method of cross validation an algorithm to find the mixing distribution that maximizes the spacings functional is presented these methods are illustrated with a data set from the astronomy literature the measurements are velocities at which galaxies in the corona borealis region are moving away from our galaxy if the galaxies are clustered the velocity density will be multimodal with clusters correspond

mean shift mode seeking and clustering mean shift a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed in the paper this generalization makes some k means like clustering algorithms its special cases it is shown that mean shift is a mode seeking process on the surface constructed with a shadow kernal for gaussian kernels mean shift is a gradient mapping convergence is studied for mean shift iterations cluster analysis if treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data applications in clustering and hough transform are demonstrated mean shift is also considered as an evolutionary strategy that performs multistart global optimization

optimal by order quadrature formulae for fast oscillatory functions with inaccurately given a priori information abstract in this article the authors construct optimal by order quadrature formulae for integration of fast oscillatory functions in interpolational classes c 1 l n 1 and c 1 l n e 1 the construction of efficient formulae for numerical integration of fast oscillatory functions is based on the application of the residual method and the method of quasi solutions both cases weak and strong oscillations are considered results of numerical examples are presented

fourier transforms of slowly converging functions exemplified by electromagnetic wave propagation in evanescent structures fourier type integrals often balk at numerical evaluation with simple quadrature algorithms a suitable strategy to cope with slowly decaying oscillating integrands over unbounded integration intervals is to subdivide the interval and extrapolate the sequence of partial sums this paper supported by numerical examples presents guidelines for the choice of the partition points it will be shown that the first subdivision point must be selected with particular care in order to obtain reliable extrapolation results as a practical example we explore the propagation of an electromagnetic wavefront in a dispersive evanescent medium which should despite recent speculations on superluminal signal transmission travel with exactly the speed of light it appears that the partition extrapolation strategy correctly computes the behaviour of the wave whereas other methods fail to give satisfying answers what is particularly appealing about the proposed method is that it requires only moderate analysis of the integrand and can be composed from standard numerical algorithms

frequency analysis of a heterogeneous perforated panel using a super element formulation abstract heterogeneous perforated panels represent a wide class of structural elements with holes where perforations and matrix are of dissimilar materials e g metallic member of a perforated hybrid joint with resin fillings there is a variety of objectives for introducing holes e g weight saving or mechanical interlock where there is a regular pattern to the arrangement of holes the perforated element can be assimilated to a lattice in the present study numerical analysis has been conducted on investigating the shock frequency filtering phenomenon encountered in two dimensional 2d lattice structures a super element of the primitive cell unit cell of the lattice has been formulated and applied in conjunction with the floquet bloch s principle to study the shock response characteristics plane wave propagation is investigated by constructing the first brillouin zone of the primitive cell in associated fourier space k space the frequency characteristics are presented in the band structure diagram the study emphasizes the existence of frequency pass and stop bands and the extent of this phenomenon the frequency filtering effects of the heterogeneous perforated 2d lattice has shown its potential value to improve the structural performance of perforated hybrid joints subjected to dynamic loads

gaussian mean shift is an em algorithm the mean shift algorithm based on ideas proposed by fukunaga and hosteller is a hill climbing algorithm on the density defined by a finite mixture or a kernel density estimate mean shift can be used as a nonparametric clustering method and has attracted recent attention in computer vision applications such as image segmentation or tracking we show that when the kernel is gaussian mean shift is an expectation maximization em algorithm and when the kernel is non gaussian mean shift is a generalized em algorithm this implies that mean shift converges from almost any starting point and that in general its convergence is of linear order for gaussian mean shift we show 1 the rate of linear convergence approaches 0 superlinear convergence for very narrow or very wide kernels but is often close to 1 thus extremely slow for intermediate widths and exactly 1 sublinear convergence for widths at which modes merge 2 the iterates approach the mode along the local principal component of the data points from the inside of the convex hull of the data points and 3 the convergence domains are nonconvex and can be disconnected and show fractal behavior we suggest ways of accelerating mean shift based on the em interpretation

the forced vibration of one dimensional multi coupled periodic structures an application to finite element analysis abstract a general theory for the forced vibration of multi coupled one dimensional periodic structures is presented as a sequel to a much earlier general theory for free vibration starting from the dynamic stiffness matrix of a single multi coupled periodic element it derives matrix equations for the magnitudes of the characteristic free waves excited in the whole structure by prescribed harmonic forces and or displacements acting at a single periodic junction the semi infinite periodic system excited at its end is first analysed to provide the basis for analysing doubly infinite and finite periodic systems in each case total responses are found by considering just one periodic element an already known method of reducing the size of the computational problem is reexamined expanded and extended in detail involving reduction of the dynamic stiffness matrix of the periodic element through a wave coordinate transformation use of the theory is illustrated in a combined periodic structure finite element analysis of the forced harmonic in plane motion of a uniform flat plate excellent agreement between the computed low frequency responses and those predicted by simple engineering theories validates the detailed formulations of the paper the primary purpose of the paper is not towards a specific application but to present a systematic and coherent forced vibration theory carefully linked with the existing free wave theory