pre dft processing using eigenanalysis for coded ofdm with multiple receive antennas in broadband wireless communications coded orthogonal frequency division multiplexing ofdm can be used with multiple receive antennas to achieve both frequency diversity and space diversity in this scenario the optimal approach is subcarrier based space combining however such an approach is quite complex because multiple discrete fourier transform dft blocks each per receive antenna are used we propose a pre dft processing scheme based upon eigenanalysis in the proposed scheme the received signals are weighted and combined both before and after the dft processing as a result the required number of dft blocks can be significantly reduced with perfect weighting coefficients the margin of the performance improvement decreases along with the increase of the number of dft blocks thus enabling effective performance and complexity tradeoff to achieve a maximum average pairwise codeword distance it will be shown that the maximum number of dft blocks required is equal to the minimum of the number of receive antennas and the number of distinct paths in the channel when the number of distinct paths is larger than the number of receive antennas and with a smaller number of dft blocks extensive simulation results will also show that near optimal performance can still be achieved for most channels finally in an ofdm system with differential modulation we use a signal covariance matrix to obtain the weighting coefficients before the dft processing in this case simulation results will demonstrate that the performance of the proposed scheme can be better than subcarrier based space combining but with much lower complexity

fast fe bem algorithms for orthotropic frictional contact summary this paper presents a new and efficient methodology for solving 3d frictional contact problems considering an orthotropic friction law the contact methodology is based on a proposed augmented lagrangian formulation for orthotropic frictional contact problems and a new discrete contact operator which allows to reduce the number of unknowns in a newton like algorithm that accelerates the attainment of the solution a fast uzawa scheme is also proposed on the basis of the steffensen s method both algorithms prove to be very robust and efficient to solve orthotropic frictional contact problems the proposed formalism has the advantage of being very compact and valid for both the fem and the bem numerical results are given to demonstrate the validity of the formulation and algorithms proposed copyright 2013 john wiley sons ltd

the nsbeti method an extension of the feti method to non symmetrical bem fem coupled problems summary the finite element tearing and interconnecting feti method is recognized as an effective domain decomposition tool to achieve scalability in the solution of partitioned second order elasticity problems in the boundary element tearing and interconnecting beti method a direct extension of the feti algorithm to the bem the symmetric galerkin bem formulation is used to obtain symmetric system matrices making possible to apply the same feti conjugate gradient solver in this work we propose a new beti variant labeled nsbeti that allows to couple substructures modeled with the fem and or non symmetrical bem formulations the method connects non matching bem and fem subdomains using localized lagrange multipliers and solves the associated non symmetrical flexibility equations with a bi cgstab iterative algorithm scalability issues of nsbeti in bem bem and combined bem fem coupled problems are also investigated copyright 2012 john wiley sons ltd

adaptive blind deconvolution of linear channels using renyi s entropy with parzen window estimation blind deconvolution of linear channels is a fundamental signal processing problem that has immediate extensions to multiple channel applications in this paper we investigate the suitability of a class of parzen window based entropy estimates namely renyi s entropy as a criterion for blind deconvolution of linear channels comparisons between maximum and minimum entropy approaches as well as the effect of entropy order equalizer length sample size and measurement noise on performance will be investigated through monte carlo simulations the results indicate that this nonparametric entropy estimation approach outperforms the standard bell sejnowski and normalized kurtosis algorithms in blind deconvolution in addition the solutions using shannon s entropy were not optimal either for super or sub gaussian source densities

a variational principle for the formulation of partitioned structural systems a continuum based variational principle is presented for the formulation of the discrete governing equations of partitioned structural systems this application includes coupled substructures as well as subdomains obtained by mesh decomposition the present variational principle is derived by a series of modifications of a hybrid functional originally proposed by atluri for finite element development the interface is treated by a displacement frame and a localized version of the method of lagrange multipliers interior displacements are decomposed into rigid body and deformational components to handle floating subdomains both static and dynamic versions are considered an important application of the present principle is the treatment of nonmatching meshes that arise from various sources such as separate discretization of substructures independent mesh refinement and global local analysis the present principle is compared with that of a globalized version of the multiplier method copyright 2000 john wiley sons ltd

adaptive modeling of damage growth using a coupled fem bem approach summary we propose a coupled boundary element method bem and a finite element method fem for modelling localized damage growth in structures bem offers the flexibility of modelling large domains efficiently while the non linear damage growth is accurately accounted by a local fem mesh an integral type nonlocal continuum damage mechanics with adapting fem mesh is used to model multiple damage zones and follow their propagation in the structure strong form coupling bem hosted is achieved using lagrange multipliers because the non linearity is isolated in the fem part of the system of equations the system size is reduced using schur complement approach then the solution is obtained by a monolithic newton method that is used to solve both domains simultaneously the coupled bem fem approach is verified by a set of convergence studies where the reference solution is obtained by a fine fem in addition the method is applied to multiple fractures growth benchmark problems and shows good agreement with the literature copyright 2015 john wiley sons ltd

a mortar segment to segment contact method for large deformation solid mechanics abstract contact modeling is still one of the most difficult aspects of non linear implicit structural analysis most 3d contact algorithms employed today use node on segment approaches for contacting dissimilar meshes two pass node on segment contact approaches have the well known deficiency of locking due to over constraint in this work we develop and demonstrate a segment to segment contact approach based on the mortar method by eliminating the over constraint this method appears to be much more robust than the node on segment approach furthermore node on segment approaches suffer when individual nodes slide out of contact at contact surface boundaries or when contacting nodes slide from facet to facet this causes jumps in the contact forces due to the discrete nature of the constraint enforcement and difficulties in convergence for implicit solution techniques these jumps in forces are avoided in the segment to segment approach since penetration is measured by the occluded weighted volume which varies smoothly with perturbations until now all mortar schemes have been developed for small deformation sliding and have mainly been applied on flat surfaces here we will present the integration scheme and the linearization approach used for handling the contact surface integrals in the event of large sliding the schemes are designed to conserve linear momentum and can be applied to arbitrarily curved 3d surfaces although expensive our numerical examples demonstrate that the approach is far more robust than even smoothed node on segment contact techniques that is problems previously not solvable with node on segment can now be solved with our segment to segment contact

fuzzy relations and fuzzy groups abstract given a group s we consider fuzzy relations on s that is maps from s s into 0 1 of particular interest is to investigate conditions under which the fuzzy relation becomes a fuzzy subgroup on s s we prove that if is a fuzzy subset of s and is the strongest fuzzy relation on s that is a fuzzy relation on then is a fuzzy subgroup if and only if is a fuzzy subgroup a number of other results are obtained about the interrelationships between fuzzy relations on s including the weakest fuzzy relation and fuzzy subgroups on s s

sparse signal approximation via nonseparable regularization the calculation of a sparse approximate solution to a linear system of equations is often performed using either l1 norm regularization and convex optimization or nonconvex regularization and nonconvex optimization combining these principles this paper describes a type of nonconvex regularization that maintains the convexity of the objective function thereby allowing the calculation of a sparse approximate solution via convex optimization the preservation of convexity is viable in the proposed approach because it uses a regularizer that is nonseparable the proposed method is motivated and demonstrated by the calculation of sparse signal approximation using tight frames examples of denoising demonstrate improvement relative to l1 norm regularization

block sparsity induced adaptive filter for multi clustering system identification in order to improve the performance of least mean square lms based adaptive filtering for identifying block sparse systems a new adaptive algorithm called block sparse lms bs lms is proposed in this paper the basis of the proposed algorithm is to insert a penalty of block sparsity which is a mixed l2 0 norm of adaptive tap weights with equal group partition sizes into the cost function of traditional lms algorithm to describe a block sparse system response we first propose a markov gaussian model which can generate a kind of system responses of arbitrary average sparsity and arbitrary average block length using given parameters then we present theoretical expressions of the steady state misadjustment and transient convergence behavior of bs lms with an appropriate group partition size for white gaussian input data based on the above results we theoretically demonstrate that bs lms has much better convergence behavior than l0 lms with the same small level of misadjustment finally numerical experiments verify that all of the theoretical analysis agrees well with simulation results in a large range of parameters

affine matrix rank minimization problem via non convex fraction function penalty abstract affine matrix rank minimization problem is a fundamental problem in many important applications it is well known that this problem is combinatorial and np hard in general in this paper a continuous promoting low rank non convex fraction function is studied to replace the rank function in this np hard problem an iterative singular value thresholding algorithm is proposed to solve the regularization transformed affine matrix rank minimization problem with the change of the parameter in non convex fraction function we could get some much better results which is one of the advantages for the iterative singular value thresholding algorithm compared with some state of art methods some convergence results are established moreover we proved that the value of the regularization parameter 0 cannot be chosen too large indeed there exists 0 such that the optimal solution of the regularization transformed affine matrix rank minimization problem is equal to zero for any numerical experiments on matrix completion problems and image inpainting problems show that our method performs effective in finding a low rank matrix compared with some state of art methods

minimizing nonconvex functions for sparse vector reconstruction in this paper we develop a novel methodology for minimizing a class of nonconvex concave on the non negative orthant functions for solving an underdetermined linear system of equations as x when the solution vector s is known a priori to be sparse the proposed technique is based on locally replacing the original objective function by a quadratic convex function which is easily minimized the resulting algorithm is iterative and is absolutely converging to a fixed point of the original objective function for a certain selection of convex objective functions the class of algorithms called iterative reweighted least squares irls is shown to be a special case of the proposed methodology thus the proposed algorithms are a generalization and unification of the previous methods in addition we also propose a new class of algorithms with better convergence properties compared to the regular irls algorithms and hence can be considered as enhancements to these algorithms since the original objective functions are nonconvex the proposed algorithm is susceptible to convergence to a local minimum to alleviate this difficulty we propose a random perturbation technique that enhances the performance of the proposed algorithm the numerical results show that the proposed algorithms outperform some of the well known algorithms that are usually utilized for solving the same problem

entropy minimization for supervised digital communications channel equalization this paper investigates the application of error entropy minimization algorithms to digital communications channel equalization the pdf of the error between the training sequence and the output of the equalizer is estimated using the parzen windowing method with a gaussian kernel and then the renyi s quadratic entropy is minimized using a gradient descent algorithm by estimating renyi s entropy over a short sliding window an online training algorithm is also introduced moreover for a linear equalizer an orthogonality condition for the minimum entropy solution that leads to an alternative fixed point iterative minimization method is derived the performance of linear and nonlinear equalizers trained with entropy and mean square error mse is compared as expected the results of training a linear equalizer are very similar for both criteria since even if the input noise is non gaussian the output filtered noise tends to be gaussian on the other hand for nonlinear channels and using a multilayer perceptron mlp as the equalizer differences between both criteria appear specifically it is shown that the additional information used by the entropy criterion yields a faster convergence in comparison with the mse

coupling finite and boundary element methods for static and dynamic elastic problems with non conforming interfaces a coupling algorithm is presented which allows for the flexible use of finite and boundary element methods as local discretization methods on the subdomain level dirichlet to neumann maps are realized by means of each discretization method such maps are common for the treatment of static problems and are here transferred to dynamic problems this is realized based on the similarity of the structure of the systems of equations obtained after discretization in space and time the global set of equations is then established by incorporating the interface conditions in a weighted sense by means of lagrange multipliers therefore the interface continuity condition is relaxed and the interface meshes can be non conforming the field of application are problems from elastostatics and elastodynamics

mixing matrix estimation from sparse mixtures with unknown number of sources in blind source separation many methods have been proposed to estimate the mixing matrix by exploiting sparsity however they often need to know the source number a priori which is very inconvenient in practice in this paper a new method namely nonlinear projection and column masking npcm is proposed to estimate the mixing matrix a major advantage of npcm is that it does not need any knowledge of the source number in npcm the objective function is based on a nonlinear projection and its maxima just correspond to the columns of the mixing matrix thus a column can be estimated first by locating a maximum and then deflated by a masking operation this procedure is repeated until the evaluation of the objective function decreases to zero dramatically thus the mixing matrix and the number of sources are estimated simultaneously because the masking procedure may result in some small and useless local maxima particle swarm optimization pso is introduced to optimize the objective function feasibility and efficiency of pso are also discussed comparative experimental results show the efficiency of npcm especially in the cases where the number of sources is unknown and the sources are relatively less sparse

a formulation based on localized lagrange multipliers for bem fem coupling in contact problems this paper presents a unified formulation for the combination of the finite element method fem and the boundary element method bem in 3d frictional contact problems that is based on the use of localized lagrange multipliers llms resolution methods for the contact problem between non matching meshes have traditionally been based on a direct coupling of the contacting solids using classical lagrange multipliers these methods tend to generate strongly coupled systems that require a deep knowledge of the discretization characteristics on each side of the contact zone complicating the process of mixing different numerical techniques in this work a displacement contact frame is inserted between the fe and be interface meshes discretized and finally connected to the contacting substructures using llms collocated at the mesh interface nodes this methodology will provide a partitioned formulation which preserves software modularity and facilitates the connection of non matching fe and be meshes

multiwavelet prestack kirchhoff migration the problems of stretching and aliasing usually occur in prestack kirchhoff migration a multiwavelet based approach is proposed to provide an alternative approach to resolve these problems two steps are involved in the multiwavelet based algorithm the first step is the decomposition of the seismic traces with a series of wavelets of different dominant frequencies this step is based on the principle of basis pursuit and is enhanced for more accurate and sparse decomposition by adding an adaptive subdictionary that is associated with the minima and maxima of a seismic trace the second step is wavelet migration based on the kirchhoff formulation using a novel approach the outer iteration is the wavelets of the input seismic traces which ensures that an input wavelet is only used once in the entire migration process this enables output of multiple migrated images of different wavelets of dominant frequency ranges elimination of noisy images and composition of images for specific interpretation and reservoir characterization purposes with very little extra computational cost the stretching and aliasing problems are naturally resolved because interpolation on the seismic trace is not required in the migration we tested the algorithm using a synthetic model with a dipping layer and a 2d real seismic section we compared our results with results obtained by conventional kirchhoff migration

sparse signal estimation by maximally sparse convex optimization this paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing e g sparse deconvolution this paper aims to induce sparsity more strongly than l1 norm regularization while avoiding non convex optimization for this purpose this paper describes the design and use of non convex penalty functions regularizers constrained so as to ensure the convexity of the total cost function f to be minimized the method is based on parametric penalty functions the parameters of which are constrained to ensure convexity of f it is shown that optimal parameters can be obtained by semidefinite programming sdp this maximally sparse convex msc approach yields maximally non convex sparsity inducing penalty functions constrained such that the total cost function f is convex it is demonstrated that iterative msc imsc can yield solutions substantially more sparse than the standard convex sparsity inducing approach i e l1 norm minimization

why simple shrinkage is still relevant for redundant representations shrinkage is a well known and appealing denoising technique introduced originally by donoho and johnstone in 1994 the use of shrinkage for denoising is known to be optimal for gaussian white noise provided that the sparsity on the signal s representation is enforced using a unitary transform still shrinkage is also practiced with nonunitary and even redundant representations typically leading to very satisfactory results in this correspondence we shed some light on this behavior the main argument in this work is that such simple shrinkage could be interpreted as the first iteration of an algorithm that solves the basis pursuit denoising bpdn problem while the desired solution of bpdn is hard to obtain in general we develop a simple iterative procedure for the bpdn minimization that amounts to stepwise shrinkage we demonstrate how the simple shrinkage emerges as the first iteration of this novel algorithm furthermore we show how shrinkage can be iterated turning into an effective algorithm that minimizes the bpdn via simple shrinkage steps in order to further strengthen the denoising effect

super exponential methods for blind deconvolution a class of iterative methods for solving the blind deconvolution problem i e for recovering the input of an unknown possibly nonminimum phase linear system by observation of its output is presented these methods are universal do not require prior knowledge of the input distribution are computationally efficient and statistically stable and converge to the desired solution regardless of initialization at a very fast rate the effects of finite length of the data finite length of the equalizer and additive noise in the system on the attainable performance intersymbol interference are analyzed it is shown that in many cases of practical interest the performance of the proposed methods is far superior to linear prediction methods even for minimum phase systems recursive and sequential algorithms are also developed which allow real time implementation and adaptive equalization of time varying systems

non gaussian reflectivity entropy and deconvolution standard deconvolution techniques assume that the wavelet is minimum phase but generally make no assumptions about the amplitude distribution of the primary reflection coefficient sequence for a white reflection sequence the assumption of a gaussian distribution means that recovery of the true phase of the wavelet is impossible however a non gaussian distribution in theory allows recovery of the phase it is generally recognized that primary reflection coefficients typically have a non gaussian amplitude distribution deconvolution techniques that assume whiteness but seek to exploit the non gaussianity include wiggins minimum entropy deconvolution med claerbout s parsimonious deconvolution and gray s variable norm deconvolution these methods do not assume minimum phase the deconvolution filter is defined by the maximization of a function called the objective i examine these and other med type deconvolution techniques maximizing the objective by setting derivatives to zero results in most case

iterative concave rank approximation for recovering low rank matrices in this paper we propose a new algorithm for recovery of low rank matrices from compressed linear measurements the underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values and then minimize the resulting approximation subject to the linear constraints the accuracy of the approximation is controlled via a scaling parameter where a smaller corresponds to a more accurate fitting the consequent optimization problem for any finite is nonconvex therefore to decrease the risk of ending up in local minima a series of optimizations is performed starting with optimizing a rough approximation a large and followed by successively optimizing finer approximations of the rank with smaller s to solve the optimization problem for any 0 it is converted to a new program in which the cost is a function of two auxiliary positive semidefinite variables the paper shows that this new program is concave and applies a majorize minimize technique to solve it which in turn leads to a few convex optimization iterations this optimization scheme is also equivalent to a reweighted nuclear norm minimization nnm for any 0 we derive a necessary and sufficient condition for the exact recovery which are weaker than those corresponding to nnm on the numerical side the proposed algorithm is compared to nnm and a reweighted nnm in solving affine rank minimization and matrix completion problems showing its considerable and consistent superiority in terms of success rate

a new dual mortar method for curved interfaces 2d elasticity dual mortar method formulations have shown to be a very effective and efficient way for interfacing e g tying contacting dissimilar meshes on the other hand we have recently found that they can sometimes perform quite poorly when applied to curved surfaces in some solid mechanics applications a new modified two dimensional dual mortar method for piecewise linear finite elements is developed that overcomes this deficiency and is demonstrated on a model problem furthermore mathematical analysis is provided to demonstrate the optimal convergence and stability of the new method copyright 2005 john wiley sons ltd

an algorithm to solve coupled 2d rolling contact problems this work presents a new approach to the steady state rolling contact problem for two dimensional elastic bodies with and without force transmission the problem solution is achieved by minimizing a general function representing the equilibrium equation and the contact restrictions the boundary element method is used to compute the elastic influence coefficients of the surface points involved in the contact equilibrium equations while the contact conditions are represented with the help of variational inequalities and projection functions finally the minimization problem is solved by the generalized newton s method with line search four classic rolling problems are also solved and commented on copyright 2000 john wiley sons ltd

an iterative bayesian algorithm for sparse component analysis in presence of noise we present a bayesian approach for sparse component analysis sca in the noisy case the algorithm is essentially a method for obtaining sufficiently sparse solutions of underdetermined systems of linear equations with additive gaussian noise in general an underdetermined system of linear equations has infinitely many solutions however it has been shown that sufficiently sparse solutions can be uniquely identified our main objective is to find this unique solution our method is based on a novel estimation of source parameters and maximum a posteriori map estimation of sources to tackle the great complexity of the map algorithm when the number of sources and mixtures become large we propose an iterative bayesian algorithm iba this iba algorithm is based on the map estimation of sources too but optimized with a steepest ascent method the convergence analysis of the iba algorithm and its convergence to true global maximum are also proved simulation results show that the performance achieved by the iba algorithm is among the best while its complexity is rather high in comparison to other algorithms simulation results also show the low sensitivity of the iba algorithm to its simulation parameters

numerical implementation of two nonconforming finite element methods for unilateral contact we consider the finite element approximation of the unilateral contact problem between elastic bodies we are interested in a practical problem which often occurs in finite element computations concerning two independently discretized bodies in unilateral contact it follows that the nodes of both bodies located on the contact surface do not fit together we present two different approaches in order to define unilateral contact on nonmatching meshes the first is an extension of the mortar finite element method to variational inequalities that defines the contact in a global way on the contrary the second one expresses local node on segment contact conditions in both cases the theoretical approximation properties are given then we implement and compare the two methods

on the error of estimating the sparsest solution of underdetermined linear systems let a be an n m matrix with m n and suppose that the underdetermined linear system as x admits a sparse solution s0 for which s0 0 1 2 spark a such a sparse solution is unique due to a well known uniqueness theorem suppose now that we have somehow a solution s as an estimation of s0 and suppose that s is only approximately sparse that is many of its components are very small and nearly zero but not mathematically equal to zero is such a solution necessarily close to the true sparsest solution more generally is it possible to construct an upper bound on the estimation error s s0 2 without knowing s0 the answer is positive and in this paper we construct such a bound based on minimal singular values of submatrices of a we will also state a tight bound which is more complicated but besides being tight enables us to study the case of random dictionaries and obtain probabilistic upper bounds we will also study the noisy case that is where x as n moreover we will see that where s0 0 grows to obtain a predetermined guaranty on the maximum of s s0 2 s is needed to be sparse with a better approximation this can be seen as an explanation to the fact that the estimation quality of sparse recovery algorithms degrades where s0 0 grows

kernel risk sensitive loss definition properties and application to robust adaptive filtering nonlinear similarity measures defined in kernel space such as correntropy can extract higher order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non gaussian signal processing and machine learning in this paper we propose a new similarity measure in kernel space called the kernel risk sensitive loss krsl and provide some important properties we apply the krsl to adaptive filtering and investigate the robustness and then develop the mkrsl algorithm and analyze the mean square convergence performance compared with correntropy the krsl can offer a more efficient performance surface thereby enabling a gradient based method to achieve faster convergence speed and higher accuracy while still maintaining the robustness to outliers theoretical analysis results and superior performance of the new algorithm are confirmed by simulation

on the adaptive finite element method of steady state rolling contact for hyperelasticity in finite deformations in this paper we present an adaptive finite element method for steady state rolling contact in finite deformations along with a residual based a posteriori error estimator for rolling contact problem with coulomb friction a general formulation of rolling contact geometry is derived from the point of view of differential geometry solvability conditions for the rolling contact problems are discussed we use newton s method to solve variational equations derived from a penalty regularization of the finite element approximation of the rolling contact problem we provide a numerical example to illustrate the method

invariancy of sparse recovery algorithms in this paper a property for sparse recovery algorithms called invariancy is introduced the significance of invariancy is that the performance of the algorithms with this property is less affected when the sensing i e the dictionary is ill conditioned this is because for this kind of algorithms there exists implicitly an equivalent well conditioned problem which is being solved some examples of sparse recovery algorithms will also be considered and it will be shown that some of them such as sl0 basis pursuit using interior point lp solver focuss and hard thresholding algorithms are invariant and some others like matching pursuit and spgl1 are not then as an application example of the invariancy property a sparse decomposition based method for direction of arrival estimation is reviewed and it is shown that if an invariant algorithm is utilized for solving the corresponding sparse recovery problem the spatial characteristics of the sensors will have essentially no effect on the final estimation provided that the number of sensors is large enough

estimating the entropy of a signal with applications we present a new estimator of the entropy of continuous signals we model the unknown probability density of data in the form of an ar spectrum density and use regularized long ar models to identify the ar parameters we then derive both an analytical expression and a practical procedure for estimating the entropy from sample data we indicate how to incorporate recursive and adaptive features in the procedure we evaluate and compare the new estimator with other estimators based on histograms kernel density models and order statistics finally we give several examples of applications an adaptive version of our entropy estimator is applied to detection of law changes blind deconvolution and source separation

sparse regularization via convex analysis sparse approximate solutions to linear equations are classically obtained via l1 norm regularized least squares but this method often underestimates the true solution as an alternative to the l1 norm this paper proposes a class of nonconvex penalty functions that maintain the convexity of the least squares cost function to be minimized and avoids the systematic underestimation characteristic of l1 norm regularization the proposed penalty function is a multivariate generalization of the minimax concave penalty it is defined in terms of a new multivariate generalization of the huber function which in turn is defined via infimal convolution the proposed sparse regularized least squares cost function can be minimized by proximal algorithms comprising simple computations

fuzzy sets fuzzy relations and fuzzy groups some interrelations abstract we define closure operator on the set of fuzzy relations on s and show that the closed hull of a fuzzy relation s is given by s s we define strong fuzzy relation and derive some results to investigate the relationship between closed strong and symmetric fuzzy relations we give a counterexample to show that the composition of two closed fuzzy relations need not be a closed fuzzy relation we also give a much simpler proof of theorem 4 2 of bhattacharya and mukherjee and provide counterexamples to show that their lemma 3 4 and theorem 3 1 of das do not always remain true

formulation and comparison of algorithms for frictional contact problems this paper presents two algorithms for solving the discrete quasi static small displacement linear elastic contact problem with coulomb friction the algorithms are adoptions of a newton method for solving b differentiable equations and an interior point method for solving smooth constrained equations for the application of the former method the contact problem is formulated as a system of b differentiable equations involving the projection operator onto sets with simple structure for the application of the latter method the contact problem is formulated as a system of smooth equations involving complementarity conditions and with the non negativity of variables treated as constraints the two algorithms are numerically tested for two dimensional problems containing up to 100 contact nodes and up to 100 time increments results show that at the present stage of development the newton method is superior both in robustness and speed additional comparison is made with a commercial finite element code

analysis of sparse representation and blind source separation in this letter we analyze a two stage cluster then l1 optimization approach for sparse representation of a data matrix which is also a promising approach for blind source separation bss in which fewer sensors than sources are present first sparse representation factorization of a data matrix is discussed for a given overcomplete basis matrix the corresponding sparse solution coefficient matrix with minimum l1 norm is unique with probability one which can be obtained using a standard linear programming algorithm the equivalence of the l1 norm solution and the l0 norm solution is also analyzed according to a probabilistic framework if the obtained l1 norm solution is sufficiently sparse then it is equal to the l0 norm solution with a high probability furthermore the l1 norm solution is robust to noise but the l0 norm solution is not showing that the l1 norm is a good sparsity measure these results can be used as a recoverability analysis of bss as discussed the basis matrix in this article is estimated using a clustering algorithm followed by normalization in which the matrix columns are the cluster centers of normalized data column vectors zibulevsky pearlmutter boll and kisilev 2000 used this kind of two stage approach in underdetermined bss our recoverability analysis shows that this approach can deal with the situation in which the sources are overlapped to some degree in the analyzed domain and with the case in which the source number is unknown it is also robust to additive noise and estimation error in the mixing matrix finally four simulation examples and an eeg data analysis example are presented to illustrate the algorithm s utility and demonstrate its performance

l0 norm based structural sparse least square regression for feature selection this paper presents a novel approach for feature selection with regard to the problem of structural sparse least square regression sslsr rather than employing the l1 norm regularization to control the sparsity we directly work with sparse solutions via l0 norm regularization in particular we develop an effective greedy algorithm where the forward and backward steps are combined adaptively to resolve the sslsr problem with the intractable l r 0 norm on the one hand features with the strongest correlation to classes are selected in the forward steps on the other hand redundant features which contribute little to the improvement of the objective function are removed in the backward steps furthermore we provide solid theoretical analysis to prove the effectiveness of the proposed method experimental results on synthetic and real world data sets from different domains also demonstrate the superiority of the proposed method over the state of the arts highlightswe impose l0 norm inequality constraint to build the structural sparse lsr problem we develop an adaptive algorithm to ensure the structural sparsity accurately theoretical results on the efficiency and effectiveness of our method are provided experimental results prove the superiority of our method over the state of the arts

a contact formulation based on localized lagrange multipliers formulation and application to two dimensional problems the non penetration condition in contact problems is traditionally based on the classical lagrange multiplier method this method makes extensive use of modelling details of the contacting bodies for contact enforcement as the contact surface meshes are in general non matching to deal with this problem we introduce a novel element in the lagrange multiplier approach of contact modelling namely a contact frame placed in between contacting bodies it acts as a medium through which contact forces are transferred without violating equilibrium in the contact domain for discrete contact models only nodal information of the contacting bodies is required which makes the proposed contact enforcement generic the contact frame has its own independent freedoms which allows the formulation to pass contact patch tests by design copyright 2002 john wiley sons ltd

iterative sparsification projection fast and robust sparse signal approximation in this paper we address recovery of sparse signals from compressed measurements and sparse signal approximation which have received considerable attention over the last decade first we revisit smoothed l0 sl0 a well known sparse recovery algorithm and give some insights into it that have not been noticed previously specifically we re derive the sl0 algorithm based on proximal methods and using recent results in solving nonconvex problems by proximal algorithms we provide a convergence guarantee for it in addition inspired by this derivation we propose a general family of algorithms which we call iterative sparsification projection isp having sl0 as a special member our algorithmic framework starts with an initial guess for the unknown sparse vector and then iteratively sparsifies it using a fixed threshold followed by projecting the result onto the admissible solution set the threshold is then decreased and the same process is repeated the algorithm terminates when the threshold becomes sufficiently small or another stopping criterion is satisfied we also propose a robust projection to handle the situations with observation noise or model uncertainties our extensive simulations confirm the promising performance of the isp algorithms compared with some well known algorithms

two new three dimensional contact algorithms for staggered lagrangian hydrodynamics abstract this paper presents two new three dimensional contact algorithms for staggered lagrangian hydrodynamics named discrete accurate matching method and discrete lagrangian multiplier method these new contact algorithms utilize the unified contact algorithm for contact searching contact segments from all potential contact surfaces are treated as a single set the basic idea of these new methods is to partition all contact segments into triangular facets firstly then for each pair of two triangular facets which correspond to a hitting node and a target node respectively these two triangular facets are projected to one plane and their intersection area is calculated the nodal masses and nodal forces of the hitting node and the target node are distributed to the intersection portions of these two triangular facets respectively according to the proportion of the intersection area to corresponding nodal area in the discrete accurate matching method the masses and forces of the intersection portions of these two triangular facets are added to corresponding contact nodes of each other and then the accelerations and velocities of the contact nodes are updated while in the discrete lagrangian multiplier method the intersection portions of these two triangular facets are considered as a 1d contact pair in the normal direction for which the contact force is explicitly calculated by the lagrangian multiplier method for a 1d contact pair of one hitting point and one target point then the contact force being added to corresponding contact nodes these new contact algorithms are assessed through several numerical tests performed on three dimensional structured and unstructured meshes the results of these tests show the accuracy and robustness of these new methods

a new method to introduce constraints in cell centered lagrangian schemes we describe a new method to introduce constraints in cell centered lagrangian schemes in the framework of compressible hydrodynamics in this paper we apply it to the modeling of contact and sliding on solid wall boundaries we illustrate our method which is based on the minimization of a specific objective function by several basic problems

solving 2d transient rolling contact problems using the bem and mathematical programming techniques this work presents a new approach to the transient rolling contact of two dimensional elastic bodies a solution will be obtained by minimizing a general b differentiable function representing the equilibrium equations and the contact conditions at each time step inertial effects are not taken into account and the boundary element method is used to compute the elastic influence coefficients of the surface points involved in contact equilibrium equations the contact conditions are represented with the help of variational inequalities and projection functions finally the minimization problem is solved using the generalized newton s method with line search the results are compared with some example problems and the influence of discretization and integration time step on the results is discussed copyright 2001 john wiley sons ltd

a fast approach for overcomplete sparse decomposition based on smoothed ell 0 norm in this paper a fast algorithm for overcomplete sparse decomposition called sl0 is proposed the algorithm is essentially a method for obtaining sparse solutions of underdetermined systems of linear equations and its applications include underdetermined sparse component analysis sca atomic decomposition on overcomplete dictionaries compressed sensing and decoding real field codes contrary to previous methods which usually solve this problem by minimizing the l 1 norm using linear programming lp techniques our algorithm tries to directly minimize the l 1 norm it is experimentally shown that the proposed algorithm is about two to three orders of magnitude faster than the state of the art interior point lp solvers while providing the same or better accuracy

enhanced sparsity by non separable regularization this paper develops a convex approach for sparse one dimensional deconvolution that improves upon l1 norm regularization the standard convex approach we propose a sparsity inducing non separable non convex bivariate penalty function for this purpose it is designed to enable the convex formulation of ill conditioned linear inverse problems with quadratic data fidelity terms the new penalty overcomes limitations of separable regularization we show how the penalty parameters should be set to ensure that the objective function is convex and provide an explicit condition to verify the optimality of a prospective solution we present an algorithm an instance of forward backward splitting for sparse deconvolution using the new penalty

a perturbed lagrangian formulation for the finite element solution of contact problems making use of a perturbed lagrangian formulation a finite element procedure for contact problems is developed for the general case in which node to node contact no longer holds the proposed procedure leads naturally to a discretization of the contact interface into contact segments within the context of a bilinear interpolation for the displacement field a mixed finite element approximation is introduced by assuming discont naous contact pressure constant on the contact segment because of this piece wise constant approximation the gap function enters into the formulation in an average sense instead of through a point wise definition numerical examples are presented that illustrate the performance of the proposed procedure current finite element formulations for contact problems based on either the classical lagrange parameter procedure l 3 12 203 or the penalty function method 4 6 11 are characterized by a point wise enforcement of the contact constraint condition in the sense that penetration of the bodies is established on a nodal basis moreover in this methods the recovery of the contact pressure over the element from the contact nodal forces generally requires an additional procedure within the framework of classical lagrange multiplier methods the contact condition is exactly satisfied by transforming the constrained problem into an unconstrained one with the introduction of additional variables lagrange multipliers these extra variables add computational effort to the solution process which often requires special procedures to handle the presence of zero diagonal terms penalty methods on the other hand enable one to transform the constrained problem into an unconstrained one without introducing additional variables the constraint condition is now satisfied only approximately for finite values of the penalty parameter the main difhculty associated with these methods however lies in the poor conditioning of the problem as the penalty is increased to more accurately enforce the constraint condition this is a well understood phenomenon particularly in the context of the incompressible and nearly incompressible problem in solid and fluid mechanics e g see l 22 25 for a review recently augmented lagrangian procedures have been proposed as a promising way to partially overcome these difficulties and regularize the penalty formulation e g see the survey in 7 8 within the framework of zinearited e u c it is possible to restrict the finite element formulation of contact problems by assuming that node to node contact occurs this is in fact the case often considered in the literature l 2 4 6 12 20 211 in the general context of fully

a mortar finite element method using dual spaces for the lagrange multiplier the mortar finite element method allows the coupling of different discretization schemes and triangulations across subregion boundaries in the original mortar approach the matching at the interface is realized by enforcing an orthogonality relation between the jump and a modified trace space which serves as a space of lagrange multipliers in this paper this lagrange multiplier space is replaced by a dual space without losing the optimality of the method the advantage of this new approach is that the matching condition is much easier to realize in particular all the basis functions of the new method are supported in a few elements the mortar map can be represented by a diagonal matrix in the standard mortar method a linear system of equations must be solved the problem is considered in a positive definite nonconforming variational as well as an equivalent saddle point formulation

blind source separation by sparse decomposition in a signal dictionary the blind source separation problem is to extract the underlying source signals from a set of linear mixtures where the mixing matrix is unknown this situation is common in acoustics radio medical signal and image processing hyperspectral imaging and other areas we suggest a two stage separation process a priori selection of a possibly overcomplete signal dictionary for instance a wavelet frame or a learned dictionary in which the sources are assumed to be sparsely representable followed by unmixing the sources by exploiting the their sparse representability we consider the general case of more sources than mixtures but also derive a more efficient algorithm in the case of a nonovercomplete dictionary and an equal numbers of sources and mixtures experiments with artificial signals and musical sounds demonstrate significantly better separation than other known techniques

complex valued filtering based on the minimization of complex error entropy in this paper we consider the training of complex valued filter based on the information theoretic method we first generalize the error entropy criterion to complex domain to present the complex error entropy criterion ceec due to the difficulty in estimating the entropy of complex valued error directly the entropy bound minimization ebm method is used to compute the upper bounds of the entropy of the complex valued error and the tightest bound selected by the ebm algorithm is used as the estimator of the complex error entropy then based on the minimization of complex error entropy mcee and the complex gradient descent approach complex valued learning algorithms for both the linear transverse filter and the nonlinear neural network are derived the algorithms are applied to complex valued linear filtering and complex valued nonlinear channel equalization to demonstrate their effectiveness and advantages

fuzzy subgroups some characterizations the notion of a fuzzy set was first introduced in 1965 by zadeh 12 since then the theory of fuzzy sets has gone through remarkably rapid strides with well over 4000 papers by now see for example the bibliography 3 several textbooks for example 2 and 6 and an international journal solely devoted to it s the theory has found wideranging applications in such diverse fields as automata control theory decision theory and social behavior pattern studies to name just a few for an interesting expository account see rosenfeld lo and also the book review 7 in 9 rosenfeld introduced the notion of a fuzzy group and showed that many concepts of group theory can be extended in an elementary manner to develop the theory of fuzzy groups in particular he characterized all the fuzzy subgroups of cyclic groups of prime order 9 proposition 5 101 fuzzy groups were further investigated by das in 1 where he characterized all the fuzzy subgroups of finite cyclic groups l theorem 4 21 in this connection he introduced the notion of level subgroups of a fuzzy subgroup which is based on the notion of a level subset introduced earlier by zadeh for a finite group das showed that these level subgroups of a fuzzy subgroup form a chain 1 corollary 3 11 and also constructed a fuzzy subgroup whose chain of level subgroups is maximal in the following special cases when the group is i a direct product of cyclic groups of prime orders ii abelian l theorem 3 41 we analyze the level subgroups of a fuzzy subgroup in more detail and investigate whether the family of level subgroups of a fuzzy subgroup deter

a scaled boundary finite element method for modelling crack face contact problems abstract in the case of arbitrary traction on the side faces of an object a polynomial function of the radial coordinate can be employed to describe the side face loads using the scaled boundary finite element method sbfem a sbfem shape function considering the side face loads is presented together with the corresponding stiffness matrix and equivalent node load the lagrange multiplier method is used to establish the contact model between the crack faces the elements corresponding to the crack faces are divided into non crack tip elements and crack tip elements for the former the crack is designated the boundary of the polygonal sbfem element the contact tractions on the boundary are assigned to the nodes where the lagrange multiplier is applied for the point constraints for the latter the lagrange multiplier is assumed to be linear on the side faces for the segment constraints numerical examples demonstrate the validity of the proposed sbfem in addressing the crack face contact problem

inverse mass matrix via the method of localized lagrange multipliers summary an efficient method for generating the mass matrix inverse of structural dynamic problems is presented which can be tailored to improve the accuracy of target frequency ranges and or wave contents the present method bypasses the use of biorthogonal construction of a kernel inverse mass matrix that requires special procedures for boundary conditions and free edges or surfaces and constructs the free free inverse mass matrix employing the standard fem procedure the various boundary conditions are realized by the the method of localized lagrange multipliers in particular the present paper constructs the kernel inverse matrix by employing the standard fem elemental mass matrices it is shown that the accuracy of the present inverse mass matrix is almost identical to that of a conventional consistent mass matrix or a combination of lumped and consistent mass matrices numerical experiments with the proposed inverse mass matrix are carried out to validate its effectiveness when applied to vibration analysis of bars beams and plain stress problems this article is protected by copyright all rights reserved

a general criterion for analog tx rx beamforming under ofdm transmissions in this paper we study beamforming schemes for a novel mimo transceiver which performs adaptive signal combining in the radio frequency rf domain assuming perfect channel knowledge at the receiver side we consider the problem of designing the transmit and receive rf beamformers under orthogonal frequency division multiplexing ofdm transmissions in particular a general beamforming criterion is proposed which depends on a single parameter this parameter establishes a tradeoff between the energy of the equivalent siso channel after tx rx beamforming and its spectral flatness the proposed cost function embraces most reasonable criteria for designing analog tx rx beamformers hence for particular values of the proposed criterion reduces to the minimization of the mean square error mse the maximization of the system capacity or the maximization of the received signal to noise ratio snr in general the proposed criterion results in a nonconvex optimization problem however we show that the problem can be rewritten as a convex cost function subject to a couple of rank one constraints and hence it can be approximately solved by semidefinite relaxation sdr techniques since the computational cost of sdr for this problem is rather high and building on the observation that the minima of the original problem must be solutions of a pair of coupled eigenvalue problems we propose yet another simple and efficient gradient search algorithm which in practice provides satisfactory solutions with a moderate computational cost finally several numerical examples show the good performance of the proposed technique for both uncoded and 802 11a coded transmissions

underdetermined blind modal identification of structures by earthquake and ambient vibration measurements via sparse component analysis abstract sparse component analysis sca approach was adopted to handle underdetermined blind modal identification of structures where the number of sensors is less than the number of active modes to exploit the sparsity of structural responses in time frequency domain short time fourier transform stft was used in this study the proposed sca based approach has two main stages modal matrix estimation and modal displacement estimation in the first stage hierarchical clustering algorithm was used to estimate the modal matrix the clustering algorithm was preceded by a preprocessing step to select the points in time frequency domain that only one mode makes contribution in the responses these points were fed to the clustering algorithm as an input performing this analysis enhanced the modal matrix estimation accuracy and reduced the computational cost while conducting clustering analysis having estimated mixing matrix the complex valued modal responses in the transformed domain were recovered via smoothed zero norm sl 0 algorithm in a broad sense using the sl 0 algorithm permits researchers to use any kind of transform in seeking sparsity regardless of obtaining real valued or complex valued signals in transformed domain natural frequencies and damping ratios were extracted from the recovered modal responses performance of the proposed method was investigated using a synthetic example and a benchmark structure with earthquake and ambient excitation respectively

rism single modal image registration via rank induced similarity measure similarity measure is an important block in image registration most traditional intensity based similarity measures e g sum of squared difference correlation coefficient and mutual information assume a stationary image and pixel by pixel independence these similarity measures ignore the correlation between pixel intensities hence perfect image registration cannot be achieved especially in the presence of spatially varying intensity distortions here we assume that spatially varying intensity distortion such as bias field is a low rank matrix based on this assumption we formulate the image registration problem as a nonlinear and low rank matrix decomposition nllrmd therefore image registration and correction of spatially varying intensity distortion are simultaneously achieved we illustrate the uniqueness of nllrmd and therefore we propose the rank of difference image as a robust similarity in the presence of spatially varying intensity distortion finally by incorporating the gaussian noise we introduce rank induced similarity measure based on the singular values of the difference image this measure produces clinically acceptable registration results on both simulated and real world problems examined in this paper and outperforms other state of the art measures such as the residual complexity approach

mimo radar 3d imaging based on combined amplitude and total variation cost function with sequential order one negative exponential form in inverse synthetic aperture radar isar imaging a target is usually regarded as consist of a few strong specular scatterers and the distribution of these strong scatterers is sparse in the imaging volume in this paper we propose to incorporate the sparse signal recovery method in 3d multiple input multiple output radar imaging algorithm sequential order one negative exponential soone function which forms homotopy between ell 1 and ell 0 norms is proposed to measure the sparsity gradient projection is used to solve a constrained nonconvex soone function minimization problem and recover the sparse signal however while the gradient projection method is computationally simple it is not robust when a matrix in the algorithm is ill conditioned we thus further propose using diagonal loading and singular value decomposition methods to improve the robustness of the algorithm in order to handle targets with large flat surfaces a combined amplitude and total variation objective function is also proposed to regularize the shapes of the flat surfaces simulation results show that the proposed gradient projection of soone function method is better than orthogonal matching pursuit cosamp ell 1 magic bayesian method with laplace prior smoothed ell 0 method and ell 1 ell s in high snr cases for recovery of pm 1 random spikes sparse signal the quality of the simulated 3d images and real data isar images obtained using the new method is better than that of the conventional correlation method and minimum ell 2 norm method and competitive to the aforementioned sparse signal recovery algorithms

a simple algorithm for localized construction of non matching structural interfaces a simple and effective algorithm for the modular construction of non matched interfaces is presented for the partitioned solution of large scale structural problems the formulation is based on a recently developed four field variational principle which introduces a connection frame between the interfaced partitions a key result of the present study is a frame nodal placement criterion that uniquely determines the frame discretization into piecewise linear elements so that the interface patch test condition is satisfied a priori the method is demonstrated with several 2d and 3d example problems

sgbem with lagrange multipliers applied to elastic domain decomposition problems with curved interfaces using non matching meshes an original approach to the solution of linear elastic domain decomposition problems by the symmetric galerkin boundary element method is developed the approach is based on searching for the saddle point of a new potential energy functional with lagrange multipliers the interfaces can be either straight or curved open or closed the two coupling conditions equilibrium and compatibility along an interface are fulfilled in a weak sense by means of lagrange multipliers interface displacements and tractions which enables non matching meshes to be used at both sides of interfaces between subdomains the accuracy and robustness of the method is tested by several numerical examples where the numerical results are compared with the analytical solution of the solved problems and the convergence rates of two error norms are evaluated for h refinements of matching and non matching boundary element meshes copyright 2010 john wiley sons ltd

recovery of low rank matrices under affine constraints via a smoothed rank function in this paper the problem of matrix rank minimization under affine constraints is addressed the state of the art algorithms can recover matrices with a rank much less than what is sufficient for the uniqueness of the solution of this optimization problem we propose an algorithm based on a smooth approximation of the rank function which practically improves recovery limits on the rank of the solution this approximation leads to a non convex program thus to avoid getting trapped in local solutions we use the following scheme initially a rough approximation of the rank function subject to the affine constraints is optimized as the algorithm proceeds finer approximations of the rank are optimized and the solver is initialized with the solution of the previous approximation until reaching the desired accuracy on the theoretical side benefiting from the spherical section property we will show that the sequence of the solutions of the approximating programs converges to the minimum rank solution on the experimental side it will be shown that the proposed algorithm termed srf standing for smoothed rank function can recover matrices which are unique solutions of the rank minimization problem and yet not recoverable by nuclear norm minimization furthermore it will be demonstrated that in completing partially observed matrices the accuracy of srf is considerably and consistently better than some famous algorithms when the number of revealed entries is close to the minimum number of parameters that uniquely represent a low rank matrix

fem and bem coupling in elastostatics using localized lagrange multipliers the equations produced by the finite and boundary element methods in structural mechanics are expressed in different variables and cannot be linked without modifications conventional coupling methods of these numerical techniques have traditionally been based on the use of classical lagrange multipliers making a direct connection of the two solids through their common interfaces using matching meshes and altering the formulation of one of the methods to make it compatible with the other in this work a discrete surface called frame is interposed between the connected subdomains to approximate their common interface displacements it is treated using a finite element discretization and connected to each substructure using localized lagrange multipliers collocated at the interface nodes this methodology facilitates the connection of non matching finite and boundary element meshes avoiding modifications to the numerical methods used and providing a partitioned formulation which preserves software modularity

on the average uncertainty for systems with nonlinear coupling abstract the increased uncertainty and complexity of nonlinear systems have motivated investigators to consider generalized approaches to defining an entropy function new insights are achieved by defining the average uncertainty in the probability domain as a transformation of entropy functions the shannon entropy when transformed to the probability domain is the weighted geometric mean of the probabilities for the exponential and gaussian distributions we show that the weighted geometric mean of the distribution is equal to the density of the distribution at the location plus the scale i e at the width of the distribution the average uncertainty is generalized via the weighted generalized mean in which the moment is a function of the nonlinear source both the renyi and tsallis entropies transform to this definition of the generalized average uncertainty in the probability domain for the generalized pareto and student s t distributions which are the maximum entropy distributions for these generalized entropies the appropriate weighted generalized mean also equals the density of the distribution at the location plus scale a coupled entropy function is proposed which is equal to the normalized tsallis entropy divided by one plus the coupling