ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

the postulations a la d alembert and a la cauchy for higher gradient continuum theories are equivalent a review of existing results in order to found continuum mechanics two different postulations have been used the first introduced by lagrange and piola starts by postulating how the work expended by internal interactions in a body depends on the virtual velocity field and its gradients then by using the divergence theorem a representation theorem is found for the volume and contact interactions which can be exerted at the boundary of the considered body this method assumes an a priori notion of internal work regards stress tensors as dual of virtual displacements and their gradients deduces the concept of contact interactions and produces their representation in terms of stresses using integration by parts the second method conceived by cauchy and based on the celebrated tetrahedron argument starts by postulating the type of contact interactions which can be exerted on the boundary of every suitably regular part of a body then it proceeds by proving the existence of stress tensors from a balance type postulate in this paper we review some relevant literature on the subject discussing how the two postulations can be reconciled in the case of higher gradient theories finally we underline the importance of the concept of contact surface edge and wedge s order forces

spectrum estimation by wavelet thresholding of multitaper estimators current methods for power spectrum estimation by wavelet thresholding use the empirical wavelet coefficients derived from the log periodogram unfortunately the periodogram is a very poor estimate when the true spectrum has a high dynamic range and or is rapidly varying in addition because the distribution of the log periodogram is markedly non gaussian special wavelet dependent thresholding schemes are needed these difficulties can be bypassed by starting with a multitaper spectrum estimator the logarithm of this estimator is close to gaussian distributed if a moderate number spl ges 5 of tapers are used in contrast to the log periodogram log multitaper estimates are not approximately pairwise uncorrelated at the fourier frequencies but the form of the correlation can be accurately and simply approximated for scale independent thresholding the correlation acts in accordance with the wavelet shrinkage paradigm to suppress small scale noise spikes while leaving informative coarse scale coefficients relatively unattenuated this simple approach to spectrum estimation is demonstrated to work very well in practice additionally the progression of the variance of wavelet coefficients with scale can be accurately calculated allowing the use of scale dependent thresholds this more involved approach also works well in practice but is not uniformly preferable to the scale independent approach

an isogeometric implicit g1 mixed finite element for kirchhoff space rods abstract in the paper we present a multi patch isogeometric mixed element with implicit geometric continuity at the ends for the analysis of non polar kirchhoff space rods rotations are introduced at the ends of the element analogously to the hermitian interpolation performing a change of basis for the configuration space a mixed method in which the internal forces are interpolated by means of an l 2 projection leading to a b formulation is used to cope with the membrane flexural locking that affects the solution the efficiency of the method in avoiding locking and instabilities is investigated the formulation adopted has the advantage with respect to other formulations that a non full global stiffness matrix is obtained this approach appears very appealing for efficient analyses of general assemblies of 3d non polar elements

embedded structural entities in nurbs based isogeometric analysis the core idea of this article is nested parametrization in the context of isogeometric analysis the method has been inspired by trimming procedures and can be applied to different applications like local modifications and enhancements of thin walled structures or coupling of two overlying elements by embedding one in the other a remodeling for an explicit representation of the boundaries is avoided which would be contradictory to the aim of isogeometric analysis of using the original cad model the nested entity is directly linked to the super element however its element formulation is independent of the super element formulation within this article the derivation implementation and application is shown in particular for one dimensional entities embedded into 2d domains consequently the definition of an embedded curve in the surface is required and realized by using nurbs curves in the parameter space of the corresponding surface this curve with its respective predefined base vectors serves as the basis for new element formulations or adaptation of already developed element formulations which are based on the geometric description of a curve in detail an adapted formulation of the recently developed nonlinear isogeometric spatial bernoulli beam by the authors is presented in this paper furthermore those embedded curves are used for line supports and loads as well as a mass manipulation the accuracy of the proposed element formulation is verified by several benchmark examples and the potential for future applications is briefly revealed

nonlinear isogeometric spatial bernoulli beam abstract a new element formulation of a geometrically nonlinear spatial curved beam assuming bernoulli theory including torsion without warping is proposed the element formulation is derived directly from the 3d continuum by means of nonlinear kinematics thus accounting for large displacements the geometric description of the proposed element is adapted from the spatial rod of greco and cuomo 2013 and extended to a nonlinear element formulation the proposed formulation can handle arbitrary orientations of the cross section along the beam in this publication nurbs are used as basis functions for discretization since they can easily provide the required c 1 continuity between elements the presented element formulation has four degrees of freedom three for displacements and one for the rotation around the center line in order to prove the accuracy of the developed spatial bernoulli beam several numerical examples are presented and compared to analytic solutions and other element formulations

wavelet threshold estimators for data with correlated noise wavelet threshold estimators for data with stationary correlated noise are constructed by applying a level dependent soft threshold to the coefficients in the wavelet transform a variety of threshold choices is proposed including one based on an unbiased estimate of mean squared error the practical performance of the method is demonstrated on examples including data from a neurophysiological context the theoretical properties of the estimators are investigated by comparing them with an ideal but unattainable bench mark that can be considered in the wavelet context as the risk obtained by ideal spatial adaptivity and more generally is obtained by the use of an oracle that provides information that is not actually available in the data it is shown that the level dependent threshold estimator performs well relative to the bench mark risk and that its minimax behaviour cannot be improved on in order of magnitude by any other estimator the wavelet domain structure of both short and long range dependent noise is considered and in both cases it is shown that the estimators have near optimal behaviour simultaneously in a wide range of function classes adapting automatically to the regularity properties of the underlying model the proofs of the main results are obtained by considering a more general multivariate normal decision theoretic problem

isogeometric collocation methods for cosserat rods and rod structures abstract we present a novel method for the mechanical simulation of slender elastic spatial rods and rod structures subject to large deformation and rotation we develop an isogeometric collocation method for the geometrically exact nonlinear cosserat rod theory the rod centerlines are represented as spatial nurbs curves and cross section orientations are parameterized in terms of unit quaternions as 4 dimensional nurbs curves within the isogeometric framework the strong forms of the equilibrium equations of forces and moments of the discretized cosserat model are collocated leading to an efficient method for higher order discretizations for rod structures consisting of multiple connected rods we introduce a formulation with rigid quasi g 1 coupling it is based on the strong enforcement of continuity of displacement and change of cross section orientation at interfaces we also develop a mixed isogeometric formulation which is based on an independent discretization of internal forces and moments and alleviates shear locking for thin rods the novel rod simulation methods are verified by numerical convergence studies further computational examples include realistic applications with large deformations and rotations as well as a large scale rod structure with several hundreds of coupled rods and complex buckling behavior

a consistent co rotational formulation for non linear three dimensional beam elements abstract this paper describes a co rotational formulation for three dimensional beams in which both the internal force vector and tangent stiffness matrix are consistently derived from the adopted strain measures the latter relate to standard beam theory but are embedded in a continuously rotating frame a set of numerical examples show that the element provides an excellent numerical performance

an implicit multi patch b spline interpolation for kirchhoff love space rod abstract the paper presents a novel formulation for the isogeometric analysis of assemblies of kirchhoff love space rod elements introducing a multi patch implicit g 1 formulation so that an automatic non singular stiffness operator is obtained without the need of adding continuity conditions the goal is achieved using a polar decomposition of the deformation of the first and last segments of the control polygon that allows to introduce directly the end rotations as degrees of freedom both parametric and geometric continuity can be obtained in this way we use bezier and b spline interpolations and we show that they are able to attain very good accuracy for developing a 3d exact curve element with geometric torsion pre twisted rod in the paper the performance of the multi patch elements is examined comparing the rates of convergence of the l 2 error norm for the multi patch and single patch formulations it is shown that the rate of convergence remains the same although in certain cases the accuracy is lower for the multi patch solutions

singularity detection and processing with wavelets the mathematical characterization of singularities with lipschitz exponents is reviewed theorems that estimate local lipschitz exponents of functions from the evolution across scales of their wavelet transform are reviewed it is then proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their lipschitz exponents the wavelet transform of singularities with fast oscillations has a particular behavior that is studied separately the local frequency of such oscillations is measured from the wavelet transform modulus maxima it has been shown numerically that one and two dimensional signals can be reconstructed with a good approximation from the local maxima of their wavelet transform modulus as an application an algorithm is developed that removes white noises from signals by analyzing the evolution of the wavelet transform maxima across scales in two dimensions the wavelet transform maxima indicate the location of edges in images

lagrangian aspects of the kirchhoff elastic rod the relation between euler s planar elastic curves and vortex filaments evolving by the localized induction equation lie of hydrodynamics was discovered by hasimoto in 1971 basic facts about an integrable case of kirchhoff elastic rods are described here which amplify the connection between the variational problem for rods and the soliton equation lie in particular it is shown that the centerline of the kirchhoff rod is an equilibrium for a linear combination of the first three conserved hamiltonians in the lie hierarchy

glauber dynamics on trees and hyperbolic graphs we study continuous time glauber dynamics for random configurations with local constraints e g proper coloring ising and potts models on finite graphs with n vertices and of bounded degree we show that the relaxation time defined as the reciprocal of the spectral gap 1 2 for the dynamics on trees and on planar hyperbolic graphs is polynomial in n for these hyperbolic graphs this yields a general polynomial sampling algorithm for random configurations we then show that for general graphs if the relaxation time 2 satisfies 2 o 1 then the correlation coefficient and the mutual information between any local function which depends only on the configuration in a fixed window and the boundary conditions decays exponentially in the distance between the window and the boundary for the ising model on a regular tree this condition is sharp

minimax adaptive spectral estimation from an ensemble of signals we develop a statistical method for estimating the spectrum from a data set that consists of several signals all of which are realizations of a common random process we first find estimates of the common spectrum using each signal then we construct m partial aggregates each partial aggregate is a linear combination of m 1 of the spectral estimates the weights are obtained from the data via a least squares criterion the final spectral estimate is the average of these m partial aggregates we show that our final estimator is minimax rate adaptive if at least two of the estimators per signal attain the optimal rate n 2alpha 2alpha 1 for spectra belonging to a generalized lipschitz ball with smoothness index alpha our simulation study strongly suggests that our procedure works well in practice and in a large variety of situations is preferable to the simple averaging of the m spectral estimates

wavelet thresholding techniques for power spectrum estimation estimation of the power spectrum s f of a stationary random process can be viewed as a nonparametric statistical estimation problem we introduce a nonparametric approach based on a wavelet representation for the logarithm of the unknown s f this approach offers the ability to capture statistically significant components of ln s f at different resolution levels and guarantees nonnegativity of the spectrum estimator the spectrum estimation problem is set up as a problem of inference on the wavelet coefficients of a signal corrupted by additive non gaussian noise we propose a wavelet thresholding technique to solve this problem under specified noise resolution tradeoffs and show that the wavelet coefficients of the additive noise may be treated as independent random variables the thresholds are computed using a saddle point approximation to the distribution of the noise coefficients

entropy based uncertainty measures for l sup 2 spl ropf sup n spl lscr sup 2 spl zopf and spl lscr sup 2 spl zopf n spl zopf with a hirschman optimal transform for spl lscr sup 2 spl zopf n spl zopf the traditional heisenberg weyl measure quantifies the joint localization uncertainty or concentration of a signal in the phase plane based on a product of energies expressed as signal variances in time and in frequency in the image processing literature the term compactness also has been used to refer to this same notion of joint localization in the sense of a signal representation that is efficient simultaneously in time or space and frequency in this paper we consider hirschman uncertainty principles based not on energies and variances directly but rather on entropies computed with respect to normalized energy densities in time and frequency unlike the heisenberg weyl measure this entropic hirschman notion of joint uncertainty extends naturally from the case of infinitely supported continuous time signals to the cases of both finitely and infinitely supported discrete time signals for the first time we consider these three cases together and study them relative to one another in the case of infinitely supported continuous time signals we find that consistent with the energy based heisenberg principle the optimal time frequency concentration with respect to the hirschman uncertainty principle is realized by translated and modulated gaussian functions in the two discrete cases however the entropy based measure yields optimizers that may be generated by applying compositions of operators to the kronecker delta study of the discrete cases yields two interesting results first in the finitely supported case the hirschman optimal functions coincide with the so called picket fence functions that are also optimal with respect to the joint time frequency counting measure of donoho and stark second the hirschman optimal functions in the infinitely supported case can be reconciled with continuous time gaussians through a certain limiting process while a different limiting process can be used to reconcile the finitely and infinitely supported discrete cases there does not appear to be a straightforward limiting process that unifies all three cases the optimizers from the finitely supported discrete case are decidedly non gaussian we perform a very simple experiment that indicates that the hirschman optimal transform hot is superior to the discrete fourier transform dft and discrete cosine transform dct in terms of its ability to separate or resolve two limiting cases of localization in frequency viz pure tones and additive white noise we believe that these differences arise from the use of entropy rather than energy as an optimality criterion and are intimately related to the apparent incongruence between the infinitely supported continuous time case and the finitely supported discrete time case

single variable formulations and isogeometric discretizations for shear deformable beams abstract we present numerical formulations of timoshenko beams with only one unknown the bending displacement and it is shown that all variables of the beam problem can be expressed in terms of it and its derivatives we develop strong and weak forms of the problem the strong form of the problem involves the fourth derivative of the bending displacement whereas the symmetric weak form involves somewhat surprisingly third and second derivatives based on these we develop isogeometric collocation and galerkin formulations that are completely locking free and involve only half the degrees of freedom compared to standard timoshenko beam formulations several numerical tests are presented to demonstrate the performance of the proposed formulations

narrowband acoustic doppler volume backscattering signal ii spectral centroid estimation for pt i see ibid vol 50 p 2644 2655 2002 this paper proposes a novel algorithm to estimate the time varying spectral centroid of the narrowband doppler volume backscattering signal it is constructed in a semi parametric way that is modeling parametrically the local narrowband evolutionary spectrum using an ar 2 and nonparametrically adapting its time varying coefficients using the wavelet shrinkage the improved performance is gained by the underlying linear prediction function of the ar 2 and the minimax optimality of the unknown smoothness adaptation of the wavelet shrinkage procedure

b spline interpolation of kirchhoff love space rods the paper deals with the isogeometric analysis via b splines of space rods under kirchhoff love hypotheses the approach was used by gontier and vollmer 12 for developing a plane curve element within the framework of the timoshenko rod model but they adopted only one patch to represent entirely the geometry of the rod furthermore the authors developed their theory only for plane elements in this work we develop an isogeometric approach for the numerical analysis of the 3d kirchhoff love rod theory we use b splines and bezier interpolations and we show that they are able to attain very good accuracy for rod structures particularly for developing a 3d exact curve element with geometric torsion the paper presents an original parametrization of the geometric torsion that proves to be very effective the use of b splines allows to avoid discontinuities on the geometrical quantities and particularly on the normal fields so that even relatively low order interpolation functions are able to yield accurate results

isogeometric analysis for nonlinear planar kirchhoff rods weighted residual formulation and collocation of the strong form abstract high order shape functions used in isogeometric analysis allow the direct solution not only to the weighted residual formulation of the strong form opening the door to new integration schemes e g reduced gauss lobatto quadrature integration at superconvergent sites but also to collocation approaches e g using greville or superconvergent collocation points the goal of the present work is to compare these different methods through the application to the planar kirchhoff rod a fourth order rotation free formulation used to model slender beams under large deformations robustness of the geometrically nonlinear solution is improved using the mixed integration point mip newton a method that combines the advantages of displacement and mixed formulations based on the observations of the convergence plots convergence order estimates are provided for each discretization method advantages and weaknesses in terms of robustness and computation cost are also discussed for a set of benchmarks

spectral density estimation using sharpened periodograms this correspondence introduces the use of sharpened periodograms for spectral density estimation it is shown analytically that spectrum estimates obtained from smoothing the sharpened periodograms enjoy higher order bias reduction when compared with the ordinary smoothed periodogram estimates the promising numerical performances of using sharpened periodograms for spectral density estimation are illustrated via numerical experiments

an isogeometric collocation method for frictionless contact of cosserat rods abstract a frictionless contact formulation for spatial rods is developed within the framework of isogeometric collocation the structural mechanics is described by the cosserat theory of geometrically nonlinear spatial rods the numerical discretization is based on an isogeometric collocation method where the geometry and solution fields are represented as nurbs curves and the strong forms of the equilibrium equations are collocated at greville points in this framework a frictionless rod to rod contact formulation is proposed contact points are detected by a coarse level and a refined search for close centerline points and reaction forces are computed by the actual penetration of rod surface points so that the enforcement of the contact constraints is performed with the penalty method an important aspect is the application of contact penalty forces as point loads within the collocation scheme and methods for this purpose are proposed and evaluated the overall contact algorithm is validated by and applied to several numerical examples

isogeometric collocation using analysis suitable t splines of arbitrary degree abstract this paper deals with the use of analysis suitable t splines of arbitrary degree in combination with isogeometric collocation methods for the solution of second and fourth order boundary value problems in fact analysis suitable t splines appear to be a particularly efficient locally refinable basis for isogeometric collocation able to conserve the cost of only one point evaluation per degree of freedom typical of standard nurbs based isogeometric collocation furthermore t splines allow to easily create highly non uniform meshes without introducing elements with high aspect ratios this makes it possible to avoid the numerical instabilities that may arise in the case of problems characterized by reduced regularity when neumann boundary conditions are imposed in strong form and elements with high aspect ratio are used the local refinement properties of t splines can be also successfully exploited to approximate problems where point loads are applied finally several numerical tests are herein presented in order to confirm all the above mentioned features as well as the good overall convergence properties of the combination of isogeometric collocation and analysis suitable t splines

invariant hermitian finite elements for thin kirchhoff rods ii the linear three dimensional case abstract this paper considers the formulation of finite elements for thin kirchhoff rods in the three dimensional case extending our work on plane rods presented in 5 the new issue to be addressed besides the basic consideration of the three dimensional geometry is the approximation of the rod s torsion still in the geometrically linear setting of infinitesimal strains in particular it is the goal of this paper to identify approximations that preserve the basic invariance properties of the underlying structural theory in the sense that the fundamental rigid body modes of translations and infinitesimal rotations are represented exactly without straining accounting fully for the rod s curvature and associated kirchhoff s kinematics in contrast to common straight framework element approximations based on the simplified euler bernoulli beam kinematics to this purpose different basic and new interpolations of the angle of twist rotation as well as interpolations of directors increments in the setting provided by a cosserat treatment of the rod s kinematics are explored and studied in detail including rigorous analytical characterizations of the aforementioned rigid body modes these different interpolations are combined with the new c 1 continuous hermitian interpolation developed in that reference for the axis displacements extended to general three dimensionally curved rods as well as with an assumed strain mixed treatment to improve the overall performance of the finite elements several representative numerical simulations are presented to illustrate the properties and the numerical performance of the different new finite elements

opinion formation games with dynamic social influences abstract we investigate opinion formation games with dynamic social influences where opinion formation and social relationships co evolve in a cross influencing manner we show that these games always admit an ordinal potential and so pure nash equilibria and we design a polynomial time algorithm for computing the set of all pure nash equilibria and the set of all social optima of a given game we also derive non tight upper and lower bounds on the price of anarchy and stability which only depend on the players stubbornness that is on the scaling factor used to counterbalance the cost that a player incurs for disagreeing with the society and the cost she incurs for breaking away from her innate beliefs

a binary wavelet decomposition of binary images we construct a theory of binary wavelet decompositions of finite binary images the new binary wavelet transform uses simple module 2 operations it shares many of the important characteristics of the real wavelet transform in particular it yields an output similar to the thresholded output of a real wavelet transform operating on the underlying binary image we begin by introducing a new binary field transform to use as an alternative to the discrete fourier transform over gf 2 the corresponding concept of sequence spectra over gf 2 is defined using this transform a theory of binary wavelets is developed in terms of two band perfect reconstruction filter banks in gf 2 by generalizing the corresponding real field constraints of bandwidth vanishing moments and spectral content in the filters we construct a perfect reconstruction wavelet decomposition we also demonstrate the potential use of the binary wavelet decomposition in lossless image coding

a locking free finite element formulation and reduced models for geometrically exact kirchhoff rods in this work we suggest a locking free geometrically exact finite element formulation incorporating the modes of axial tension torsion and bending of thin kirchhoff beams with arbitrary initial curvatures and cross section shapes the proposed formulation has been designed in order to represent general load cases and three dimensional problem settings in the geometrically nonlinear regime of large deformations from this comprehensive theory we not only derive a general beam model but also several reduced formulations which deliver accurate solutions for special problem classes concerning the beam geometry and the external loads the advantages of these reduced models arise for example in terms of simplified finite element formulations less degrees of freedom per element and consequently a higher computational efficiency of the corresponding numerical models a second core topic of this publication is the treatment of membrane locking which is a locking phenomenon predominantly occurring in highly slender curved structures thus exactly in the prime field of application for kirchhoff theories in order to address the membrane locking effect we will propose a new interpolation strategy for the axial strain field and compare this method with common approaches such as assumed natural strains ans or reduced integration the effectiveness of this method as well as the consistency and accuracy of the general finite element formulation and the reduced beam models will be illustrated with selected numerical examples

wavelet thresholding via mdl for natural images we study the application of rissanen s 1989 principle of minimum description length mdl to the problem of wavelet denoising and compression for natural images after making a connection between thresholding and model selection we derive an mdl criterion based on a laplacian model for noiseless wavelet coefficients we find that this approach leads to an adaptive thresholding rule while achieving mean squared error performance comparable with other popular thresholding schemes the mdl procedure tends to keep far fewer coefficients from this property we demonstrate that our method is an excellent tool for simultaneous denoising and compression we make this claim precise by analyzing mdl thresholding in two optimality frameworks one in which we measure rate and distortion based on quantized coefficients and one in which we do not quantize but instead record rate simply as the number of nonzero coefficients

tree structured wavelet estimation in a mixed effects model for spectra of replicated time series this article develops a method for estimating the spectrum of a stationary process using time series traces recorded from experimental designs our procedure estimates the common log spectrum and the variability over the traces or subjects using a mixed effects model we combine spatially adaptive smoothing methods with recursive dyadic partitioning to construct a model for predicting subject specific effects the method is easy to implement and can handle large datasets because it uses the discrete wavelet transform which is computationally efficient numerical studies confirm that the proposed method performs very well despite its simplicity the method is also applied to a multisubject electroencephalogram dataset

large deformations of planar extensible beams and pantographic lattices heuristic homogenization experimental and numerical examples of equilibrium the aim of this paper is to find a computationally efficient and predictive model for the class of systems that we call pantographic structures the interest in these materials was increased by the possibilities opened by the diffusion of technology of three dimensional printing they can be regarded once choosing a suitable length scale as families of beams also called fibres interconnected to each other by pivots and undergoing large displacements and large deformations there are however relatively few ready to use results in the literature of nonlinear beam theory in this paper we consider a discrete spring model for extensible beams and propose a heuristic homogenization technique of the kind first used by piola to formulate a continuum fully nonlinear beam model the homogenized energy which we obtain has some peculiar and interesting features which we start to describe by solving numerically some exemplary deformation problems furthermore we consider pantographic structures find the corresponding homogenized second gradient deformation energies and study some planar problems numerical solutions for these two dimensional problems are obtained via minimization of energy and are compared with some experimental measurements in which elongation phenomena cannot be neglected

studies of refinement and continuity in isogeometric structural analysis we investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework we consider two simple one dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate nurbs solids we also develop a local refinement strategy that we utilize in one of the shell analyses we find that increased smoothness that is the k method leads to a significant increase in accuracy for the problems of structural vibrations over the classical c0c0 continuous p method whereas a judicious insertion of c0c0 continuous surfaces about singularities in a mesh otherwise generated by the k method usually outperforms a mesh in which all basis functions attain their maximum level of smoothness we conclude that the potential for the k method is high but smoothness is an issue that is not well understood due to the historical dominance of c0c0 continuous finite elements and therefore further studies are warranted

an efficient blended mixed b spline formulation for removing membrane locking in plane curved kirchhoff rods abstract mixed formulations of the b type when applied to b spline representations bear significant computational cost and lead to a full stiffness matrix in this work we present an efficient mixed formulation for avoiding membrane locking of curved non polar plane rods in the context of isogeometric analysis an efficient spline reconstruction of the assumed axial strains obtained by means of a local projection at the element level is performed using the method proposed by thomas et al 2015 for the reconstruction of the geometry in this way a much smaller bandwidth of the stiffness matrix is obtained with respect to the non local b formulation with significant reduction of the computational cost the blended mixed formulation splits in two steps in the first step the local b operators are defined at the element level via projection of the strain measure both l 2 projection and discrete collocation approaches are considered successively by means of the spline reconstruction algorithm the global projection of the strain measures at the patch level is defined numerical experiments show that the proposed method in addition to completely remove membrane locking yields the same accuracy and rate of convergence as the non local b method

a reconstructed local b formulation for isogeometric kirchhoff love shells abstract an efficient assumed strain formulation for avoiding the membrane locking of non polar shells is developed in the context of b spline interpolation assumed membrane strains are introduced locally in each element with a local l 2 projection and then a spline reconstruction algorithm developed by thomas et al 2015 is employed for reconstructing the membrane strain at the global patch level in this way a banded stiffness matrix is obtained that strongly reduces the computational cost with respect to the standard b formulation for isogeometric analysis the main advantages of the proposed method are the reproduction of regular membrane strain fields an accurate membrane locking free solution and an high computational efficiency with respect to standard b formulation the method can be applied for any polynomial degree of the b spline interpolation the effectiveness of the proposed method is demonstrated analyzing some bending and membrane dominated problem commonly employed as benchmark in the shell literature

isogeometric shape optimization of shells using semi analytical sensitivity analysis and sensitivity weighting abstract we present isogeometric shape optimization for shell structures applying sensitivity weighting and semi analytical analysis we use a rotation free shell formulation and all involved geometry models i e initial design analysis model optimization model and final design use the same geometric basis in particular nurbs a sensitivity weighting scheme is presented which eliminates certain effects of the chosen discretization on the design update a multilevel design approach is applied such that the design space can be chosen independently from the analysis space the use of semi analytical sensitivities allows having different polynomial degrees for design and analysis model different numerical examples are performed which confirm the applicability of the proposed method furthermore a shape optimization example with an exact solution is presented which can serve as general benchmark for shape optimization methods

bloch theorem for isogeometric analysis of periodic problems governed by high order partial differential equations abstract with the emergence of isogeometric analysis iga numerical rotation free solutions to high order partial differential equations pdes are facilitated indeed iga allows the use of high order continuous basis functions through the domain for periodic systems the bloch theorem is useful for analyzing wave propagation restricting the analysis to a single unit cell and applying periodic boundary conditions however in the literature boundary conditions are only accounting for c 0 continuity and we propose in the present paper to enforce the g 1 continuity as well or to maintain the angle in case of unit cells meeting at kinks while g 1 continuity is enforced by maintaining the collinearity between adjacent control points in the presence of kinks variations of the field derived with respect to opposite in plane edge normals are linked by the rodrigues rotation matrix this method applied at collocation points belonging to the unit cell edges can be viewed as a novel approach of coupling multi patch geometries with kinks avoiding the use of nonlinear multipliers or additional bending strip elements both transfer matrix and indirect methods of the bloch theorem are investigated for respectively quasi one and quasi two dimensional wave propagation in periodic structures discretized by nurbs based iga dispersion curves of a set of numerical problems treating isogeometric rotation free extensible elastica beams and kirchhoff love shells are then analyzed

a simple span selector for periodogram smoothing summary one approach to estimating the spectral density of a stationary time series is to smooth the periodogram and one important component of this approach is the choice of the span for smoothing this note proposes a new span selector which is based on unbiased risk estimation the proposed span selector is simple and does not impose strong conditions on the unknown spectrum for example it does not require the unknown spectrum to possess a second derivative which is a typical requirement of most plug in type or spline based methods the finite sample performance of the proposed span selector is illustrated via a small simulation

decentralized dynamics for finite opinion games game theory studies situations in which strategic players can modify the state of a given system in the absence of a central authority solution concepts such as nash equilibrium have been defined in order to predict the outcome of such situations in multi player settings it has been pointed out that to be realistic a solution concept should be obtainable via processes that are decentralized and reasonably simple accordingly we look at the computation of solution concepts by means of decentralized dynamics these are algorithms in which players move in turns to decrease their own cost and the hope is that the system reaches an equilibrium quickly we study these dynamics for the class of opinion games recently introduced by bindel et al 10 these are games important in economics and sociology that model the formation of an opinion in a social network we study best response dynamics and show upper and lower bounds on the convergence to nash equilibria we also study a noisy version of best response dynamics called logit dynamics and prove a host of results about its convergence rate as the noise in the system varies to get these results we use a variety of techniques developed to bound the mixing time of markov chains including coupling spectral characterizations and bottleneck ratio

numerical efficiency locking and unlocking of nurbs finite elements abstract the strategy of using finite elements with nurbs shape functions for approximation of both geometry and displacements isogeometric approach is investigated from the point of view of finite element technology convergence rates are compared to those of classical finite element approaches utilizing standard lagrange shape functions moreover typical locking phenomena are examined it is found that higher order inter element continuity within the nurbs approach results in identical convergence rates but smaller absolute errors compared to c 0 continuous approaches however nurbs finite elements suffer from the same locking problems as finite elements using lagrange shape functions the discrete shear gap dsg method a general framework for formulation of locking free elements is applied to develop a new class of nurbs finite elements the resulting nurbs dsg elements are absolutely free from locking and preserve the property of improved accuracy compared with standard locking free finite elements the method is exemplified for the timoshenko beam model but may be applied to more general cases

approximating the permanent a randomised approximation scheme for the permanent of a 0 1s presented the task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph the latter is accomplished by simulating a markov chain whose states are the matchings in the graph for a wide class of 0 1 matrices the approximation scheme is fully polynomial i e runs in time polynomial in the size of the matrix and a parameter that controls the accuracy of the output this class includes all dense matrices those that contain sufficiently many 1 s and almost all sparse matrices in some reasonable probabilistic model for 0 1 matrices of given density for the approach sketched above to be computationally efficient the markov chain must be rapidly mixing informally it must converge in a short time to its stationary distribution a major portion of the paper is devoted to demonstrating that the matchings chain is rapidly mixing apparently the first such result for a markov chain with genuinely c

a method of sieves for multiresolution spectrum estimation and radar imaging a method of sieves using splines is proposed for regularizing maximum likelihood estimates of power spectra this method has several important properties including the flexibility to be used at multiple resolution levels the resolution level is defined in terms of the support of the polynomial b splines used an expression for the optimal rate of growth of the sieve is derived using a discrepancy measure derived from the kullback leibler divergence of parameterized density functions while the sieves may be defined on nonuniform grids in the case of uniform grids the optimal sieve size corresponds to an optimal resolution iterative algorithms for obtaining the maximum likelihood sieve estimates are derived applications to spectrum estimation and radar imaging are proposed

time invariant orthonormal wavelet representations a simple construction of an orthonormal basis starting with a so called mother wavelet together with an efficient implementation gained the wavelet decomposition easy acceptance and generated a great research interest in its applications an orthonormal basis may not however always be a suitable representation of a signal particularly when time or space invariance is a required property the conventional way around this problem is to use a redundant decomposition we address the time invariance problem for orthonormal wavelet transforms and propose an extension to wavelet packet decompositions we show that it is possible to achieve time invariance and preserve the orthonormality we subsequently propose an efficient approach to obtain such a decomposition we demonstrate the importance of our method by considering some application examples in signal reconstruction and time delay estimation

invariant isogeometric formulations for three dimensional kirchhoff rods abstract in the isogeometric formulation for three dimensional kirchhoff rods the invariance is required such that rigid body modes associated with translations and infinitesimal rotations can be exactly represented by enforcing the invariance in the isogeometric formulation of the rod the equilibrium of forces and moments at fixed ends is preserved and the performance is improved considerably for elements of finite sizes we recognize that not all existing isogeometric formulations are invariant for general geometry of rods though an alternative formulation based on the frenet serret frame and rotation angle representation was shown to be invariant it does not work for rods with vanishing curvature while its accuracy is affected by the low continuity of the angle of twist used motivated by this two new invariant isogeometric formulations are developed through different interpolations for the angle of twist one uses the derivatives of the nurbs functions as the basis for the angle of twist interpolation and the other uses a mixed interpolation incorporating both the lagrange and nurbs functions several representative numerical examples were prepared to verify the accuracy and robustness of the two new formulations particularly for rods of variable curvatures simulated by elements of finite or large sizes the proposed formulations are demonstrated to outperform the two existing ones mentioned in predicting the displacements end reactions and stress resultants

a haar fisz technique for locally stationary volatility estimation summary we consider a locally stationary model for financial log returns whereby the returns are independent and the volatility is a piecewise constant function with jumps of an unknown number and locations defined on a compact interval to enable a meaningful estimation theory we demonstrate that the model explains well the common characteristics of log returns we propose a new wavelet thresholding algorithm for volatility estimation in this model in which haar wavelets are combined with the variance stabilising fisz transform the resulting volatility estimator is mean square consistent with a near parametric rate does not require any pre estimates is rapidly computable and is easily implemented we also discuss important variations on the choice of estimation parameters we show that our approach both gives a very good fit to selected currency exchange datasets and achieves accurate long and short term volatility forecasts in comparison to the garch 1 1 and moving window techniques

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

multitaper power spectrum estimation and thresholding wavelet packets versus wavelets it was suggested that spectrum estimation can be accomplished by applying wavelet denoising methodology to wavelet packet coefficients derived from the logarithm of a spectrum estimate the particular algorithm we consider consists of computing the logarithm of the multitaper spectrum estimator applying an orthonormal transform derived from a wavelet packet tree to the log multitaper spectrum ordinates thresholding the empirical wavelet packet coefficients and then inverting the transform for a small number of tapers suitable transforms partitions for the logarithm of the multitaper spectrum estimator are derived using a method matched to statistical thresholding properties the partitions thus derived starting from different stationary time series are all similar and easily derived and any differences between the wavelet packet and discrete wavelet transform dwt approaches are minimal for a larger number of tapers where the chosen parameters satisfy the conditions of a proven theorem the simple dwt again emerges as appropriate hence using our approach to thresholding and the method of partitioning we conclude that the dwt approach is a very adequate wavelet based approach and that the use of wavelet packets is unnecessary

continuum and discrete models for structures including quasi inextensible elasticae with a view to the design and modeling of composite reinforcements abstract inspired by some composite fiber reinforcements used in aeronautical engineering and by the need of conceiving new metamaterials some discrete models including quasi inextensible elasticae are considered a class of continuum models approximately describing the macroscopic mechanical behavior of introduced structures is then heuristically proposed some of these continuum models can be regarded as a special kind of second gradient elastic media in which the higher gradient elasticity is conferred by the flexural stiffnesses of elasticae constituting the microscopic lattice the discrete models are studied by means of suitably tailored numerical codes designed to avoid numerical instabilities and locking and a comparison of discrete versus continuum models is attempted the obtained results show that the theory of generalized continua may be useful in some engineering applications and it plays a relevant role in the mechanics of woven composites the introduced discrete and continuum models are used to describe the so called bias extension test on woven fabrics and it is shown that a good choice to correctly reproduce the targeted phenomenology is to use a second gradient continuum theory however as discussed throughout the paper in the context of rigorous micro macro identification procedures there still remain many open problems to be solved especially when dealing with systems subjected to particular constraints such as inextensibility

modeling and estimation of multiresolution stochastic processes an overview is provided of the several components of a research effort aimed at the development of a theory of multiresolution stochastic modeling and associated techniques for optimal multiscale statistical signal and image processing a natural framework for developing such a theory is the study of stochastic processes indexed by nodes on lattices or trees in which different depths in the tree or lattice correspond to different spatial scales in representing a signal or image in particular it is shown how the wavelet transform directly suggests such a modeling paradigm this perspective then leads directly to the investigation of several classes of dynamic models and related notions of multiscale stationarity in which scale plays the role of a time like variable the investigation of models on homogeneous trees is emphasized the framework examined here allows for consideration in a very natural way of the fusion of data from sensors with differing resolutions also thanks to the fact that wavelet transforms do an excellent job of compressing large classes of covariance kernels it is seen that these modeling paradigms appear to have promise in a far broader context than one might expect

isogeometric collocation for three dimensional geometrically exact shear deformable beams abstract we extend the isogeometric collocation method to the geometrically nonlinear beams an exact kinematic formulation able to represent three dimensional displacements and rotations without any restriction in magnitude is presented without the introduction of the moving frame concept a displacement based formulation is adopted full linearization of the strong form of the governing equations is derived consistently with the underlying geometric structure of the configuration manifold incremental rotations are parametrized through eulerian rotation vectors and configuration updates are performed by means of the exponential map numerical tests demonstrate that the proposed combination of isogeometric collocation method with the chosen rotations parametrization results in an efficient computational scheme able to model complex problems with high accuracy

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

locking free isogeometric collocation formulation for three dimensional geometrically exact shear deformable beams with arbitrary initial curvature abstract this paper presents a displacement based and a mixed isogeometric collocation formulations for three dimensional geometrically exact shear deformable beams with arbitrarily curved initial geometry strong forms of both formulations are consistently linearized with respect to the underlying configuration manifold high efficiency is achieved by using a geometrically consistent kinematic model in which incremental rotations are parametrized through the spatial rotation vector several numerical tests demonstrate that the proposed mixed formulation is totally locking free for any choice of approximation degree mixed formulation also exhibits higher robustness in the incremental iterative algorithm elimination of shear locking and low computational cost assured by the combination of isogeometric collocation with a consistent kinematic model result in a very efficient accurate and geometrically powerful method able to handle geometrically complex beam problems

effects of parameterization and knot placement techniques on primal and mixed isogeometric collocation formulations of spatial shear deformable beams with varying curvature and torsion abstract we present a displacement based and a mixed isogeometric collocation iga c formulation for free form three dimensional shear deformable beams with high and rapidly varying curvature and torsion when such complex shapes are concerned the approach used to build the iga geometric model becomes relevant although iga c has been so far successfully applied to a wide range of problems the effects that different parameterization and knot placement techniques may have on the accuracy of collocation based formulations is still an unexplored field to fill this gap primal and mixed formulations are used combining two parameterization methods chord length and equally spaced with two knot placement techniques uniformly spaced and de boor with respect to the space varying frenet local frame we derive the strong form of the governing equations in a compact form through the definition of two matrix operators conveniently used to perform first and second order derivatives of the vector fields involved in the formulations this approach is very efficient and easy to implement within a collocation based scheme several challenging numerical experiments allow to test the different considered parameterizations and knot placement techniques revealing in particular that with the primal formulation an equally spaced parameterization is definitively the most recommended choice and it should always be used with an approximation degree of at least p 6 although some caution must be adopted when very high jacobians and small curvatures occur the same holds for the mixed formulation with the difference that p 4 is enough to yield accurate results

rotation free isogeometric analysis of an arbitrarily curved plane bernoulli euler beam abstract the present study elucidates linear static analysis for plane beam structures using the isogeometric approach a novel methodology for rotation free analysis of an arbitrarily curved bernoulli euler beam in the convective frame of reference is derived in detail the full degeneration of a 3d continuum beam to a 1d line has been presented and a fully applicable isogeometric finite element has been obtained the driving force behind developing the present research has been the derivation of the nurbs based isogeometric analysis which will enable an elegant formulation of the plane bernoulli euler beams being a function only of the global rectangular cartesian coordinates the verification and accuracy of the research are obtained via a thorough comparison between theory finite element analyses and relevant examples from literature an excellent agreement of results is achieved and usefulness for academic and practical purposes alike are proved the effects of the hpk refinements are illuminated and it is observed that the convergences for the most variables and refinement techniques are not monotonic a special attention is paid to the influence of the product of maximum curvature and thickness of beam on the accuracy of the solution the limits of applicability of the present approach are defined for a few specific types of analyses the derived formulation is geometrically exact and appropriate for the analysis of strongly curved bernoulli euler beams

efficient quadrature for nurbs based isogeometric analysis abstract we initiate the study of efficient quadrature rules for nurbs based isogeometric analysis a rule of thumb emerges the half point rule indicating that optimal rules involve a number of points roughly equal to half the number of degrees of freedom or equivalently half the number of basis functions of the space under consideration the half point rule is independent of the polynomial order of the basis efficient rules require taking into account the precise smoothness of basis functions across element boundaries several rules of practical interest are obtained and a numerical procedure for determining efficient rules is presented we compare the cost of quadrature for typical situations arising in structural mechanics and fluid dynamics the new rules represent improvements over those used previously in isogeometric analysis

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

conditional spectral analysis of replicated multiple time series with application to nocturnal physiology abstractthis article considers the problem of analyzing associations between power spectra of multiple time series and cross sectional outcomes when data are observed from multiple subjects the motivating application comes from sleep medicine where researchers are able to noninvasively record physiological time series signals during sleep the frequency patterns of these signals which can be quantified through the power spectrum contain interpretable information about biological processes an important problem in sleep research is drawing connections between power spectra of time series signals and clinical characteristics these connections are key to understanding biological pathways through which sleep affects and can be treated to improve health such analyses are challenging as they must overcome the complicated structure of a power spectrum from multiple time series as a complex positive definite matrix valued function this article proposes a new approach to such analyses based on a tensor pr

haar fisz estimation of evolutionary wavelet spectra summary we propose a new haar fisz technique for estimating the time varying piecewise constant local variance of a locally stationary gaussian time series we apply our technique to the estimation of the spectral structure in the locally stationary wavelet model our method combines haar wavelets and the variance stabilizing fisz transform the resulting estimator is mean square consistent rapidly computable and easy to implement and performs well in practice we also introduce the haar fisz transform a device for stabilizing the variance of scaled x2 data and bringing their distribution close to gaussianity

a wavelet based spectral procedure for steady state simulation analysis abstract we develop wassp a wavelet based spectral method for steady state simulation analysis first wassp determines a batch size and a warm up period beyond which the computed batch means form an approximately stationary gaussian process next wassp computes the discrete wavelet transform of the bias corrected log smoothed periodogram of the batch means using a soft thresholding scheme to denoise the estimated wavelet coefficients then taking the inverse discrete wavelet transform of the thresholded wavelet coefficients wassp computes estimators of the batch means log spectrum and the steady state variance parameter i e the sum of covariances at all lags for the original unbatched process finally by combining the latter estimator with the batch means grand average wassp provides a sequential procedure for constructing a confidence interval on the steady state mean that satisfies user specified requirements concerning absolute or relative precision as well as coverage probability an experimental performance evaluation demonstrates wassp s effectiveness compared with other simulation analysis methods

plane bias extension test for a continuum with two inextensible families of fibers a variational treatment with lagrange multipliers and a perturbation solution in the present paper a system constituted by two families of nearly inextensible fibers is studied the interest towards this kind of structures which can be suitably modeled by 2d continua with inextensible curves comes form both theoretical and applicative motivations indeed the advantageous weight strength ratio and the particularly safe behavior in fractures make them attractive in many engineering fields while the mechanical properties displayed by them are theoretically interesting and still not well understood in full generality we focused on dead loading traction boundary value problems assuming particular forms for the deformation energy associated to every node of the structure the main result of the paper consists in the determination of the nonlinear integral equations describing fibers directions for a specific class of deformation energies a perturbative analysis of a particular solution is also performed and some physical justification for one of the considered forms for the energy density are provided in the appendix

a simple algorithm for obtaining nearly optimal quadrature rules for nurbs based isogeometric analysis we develop new quadrature rules for isogeometric analysis based on the solution of a local nonlinear problem a simple and robust algorithm is developed to determine the rules which are exact for important b spline spaces of uniform and geometrically stretched knot spacings we consider both periodic and open knot vector configurations and illustrate the efficiency of the rules on selected boundary value problems we find that the rules are almost optimally efficient but much easier to obtain than optimal rules which require the solution of global nonlinear problems that are often ill posed

isogeometric collocation for kirchhoff love plates and shells abstract with the emergence of isogeometric analysis iga the galerkin rotation free discretization of kirchhoff love shells is facilitated enabling more efficient thin shell structural analysis high order shape functions used in iga also allow the collocation of partial differential equations avoiding the time consuming numerical integration of the galerkin technique the goal of the present work is to apply this method to nurbs based isogeometric kirchhoff love plates and shells under the assumption of small deformations since kirchhoff love plate theory yields a fourth order formulation two boundary conditions are required at each location on the contour generating some conflicts at the corners where there are more equations than needed to remedy this overdetermination we provide priority and averaging rules that cover all the possible combinations of adjacent edge boundary conditions i e the clamped simply supported symmetric and free supports greville and alternative superconvergent points are used for nurbs basis of even and odd degrees respectively for square circular and annular flat plates convergence orders are found to be in agreement with a priori error estimates the proposed isogeometric collocation method is then validated and benchmarked against a galerkin implementation by studying a set of problems involving kirchhoff love shells