the application of the enhanced hoshen kopelman algorithm for processing unbounded images the enhanced hoshen kopelman ehk algorithm for the analysis of connected components in images that are unbounded in one of their dimensions is introduced the algorithm characterizes in a single pass the shapes of all the connected components in a multiple class image by computing the spatial moments the area the boundary and the bounding boxes of the connected components the algorithm is applied to a real time surface defect simulation and to a landsat image analysis the algorithm s performance is compared to the performances of related algorithms

blind spectral unmixing based on sparse nonnegative matrix factorization nonnegative matrix factorization nmf is a widely used method for blind spectral unmixing su which aims at obtaining the endmembers and corresponding fractional abundances knowing only the collected mixing spectral data it is noted that the abundance may be sparse i e the endmembers may be with sparse distributions and sparse nmf tends to lead to a unique result so it is intuitive and meaningful to constrain nmf with sparseness for solving su however due to the abundance sum to one constraint in su the traditional sparseness measured by l0 l1 norm is not an effective constraint any more a novel measure termed as s measure of sparseness using higher order norms of the signal vector is proposed in this paper it features the physical significance by using the s measure constraint smc a gradient based sparse nmf algorithm termed as nmf smc is proposed for solving the su problem where the learning rate is adaptively selected and the endmembers and abundances are simultaneously estimated in the proposed nmf smc there is no pure index assumption and no need to know the exact sparseness degree of the abundance in prior yet it does not require the preprocessing of dimension reduction in which some useful information may be lost experiments based on synthetic mixtures and real world images collected by aviris and hydice sensors are performed to evaluate the validity of the proposed method

inversion error condition number and approximate inverses of uncertain matrices abstract the classical condition number is a very rough measure of the effect of perturbations on the inverse of a square matrix first it assumes that the perturbation is infinitesimally small second it does not take into account the perturbation structure e g vandermonde similarly the classical notion of the inverse of a matrix neglects the possibility of large structured perturbations we define a new quantity the structured maximal inversion error that takes into account both structure and non necessarily small perturbation size when the perturbation is infinitesimal we obtain a structured condition number we introduce the notion of approximate inverse as a matrix that best approximates the inverse of a matrix with structured perturbations when the perturbation varies in a given range for a wide class of perturbation structures we show how to use convex semidefinite programming to compute bounds on the structured maximal inversion error and structured condition number and compute an approximate inverse the results are exact when the perturbation is unstructured we then obtain an analytic expression for the approximate inverse when the perturbation is unstructured and additive we recover the classical condition number the approximate inverse is the operator related to the total least squares orthogonal regression problem

on the non negative garrotte estimator summary we study the non negative garrotte estimator from three different aspects consistency computation and flexibility we argue that the non negative garrotte is a general procedure that can be used in combination with estimators other than the original least squares estimator as in its original form in particular we consider using the lasso the elastic net and ridge regression along with ordinary least squares as the initial estimate in the non negative garrotte we prove that the non negative garrotte has the nice property that with probability tending to 1 the solution path contains an estimate that correctly identifies the set of important variables and is consistent for the coefficients of the important variables whereas such a property may not be valid for the initial estimators in general we show that the non negative garrotte can turn a consistent estimate into an estimate that is not only consistent in terms of estimation but also in terms of variable selection we also show that the non negative garrotte has a piecewise linear solution path using this fact we propose an efficient algorithm for computing the whole solution path for the non negative garrotte simulations and a real example demonstrate that the non negative garrotte is very effective in improving on the initial estimator in terms of variable selection and estimation accuracy

hybrid cluster identification i present a hybrid method for the labelling of clusters in two dimensional lattices which combines the recursive approach with iterative scanning to reduce the stack size required by the pure recursive technique while keeping its benefits single pass and straightforward cluster characterization and percolation detection parallel to the labelling while the capacity to hold the entire lattice in memory is usually regarded as the major constraint for the applicability of the recursive technique the required stack size is the real limiting factor resorting to recursion only for the transverse direction greatly reduces the recursion depth and therefore the required stack it also enhances the overall performance of the recursive technique as is shown by results on a set of uniform random binary lattices and on a set of samples of the ising model i also show how this technique may replace the recursive technique in wolff s cluster algorithm decreasing the risk of stack overflow and increasing its speed and the hoshen kopelman algorithm in the swendsen wang cluster algorithm allowing effortless characterization during generation of the samples and increasing its speed

a general model reduction with primal assembly in structural dynamics abstract a new formulation of general model reduction in structural dynamics is presented the proposed method consists of four attributes a hybrid method combining dynamic condensation and component mode synthesis that are arguably the most popular model reduction techniques a precise model reduction taking the inertia effect into consideration primal assembly at the boundary interface of substructures and general formulations of model reduction with primal assembly comparisons of the proposed model reduction method with the conventional methods are provided as well as an efficient model reduction procedure of the proposed method in particular its advantages and performance of the proposed method are thoroughly investigated with various numerical examples

a comparison of model reduction techniques from structural dynamics numerical mathematics and systems and control in this paper popular model reduction techniques from the fields of structural dynamics numerical mathematics and systems and control are reviewed and compared the motivation for such a comparison stems from the fact that the model reduction techniques in these fields have been developed fairly independently in addition the insight obtained by the comparison allows for making a motivated choice for a particular model reduction technique on the basis of the desired objectives and properties of the model reduction problem in particular a detailed review is given on mode displacement techniques moment matching methods and balanced truncation whereas important extensions are outlined briefly in addition a qualitative comparison of these methods is presented hereby focusing both on theoretical and computational aspects finally the differences are illustrated on a quantitative level by means of application of the model reduction techniques to a common example

extension of hoshen kopelman algorithm to non lattice environments abstract we extend the hoshen kopelman hk algorithm for cluster labeling to non lattice environments where sites are placed at random at non lattice points this extension is useful for continuum systems and disordered networks our extension of the hk algorithm relies on several data structures that describe network connectivity regardless of its dimensionality just as for the classic hk algorithm on lattices our extension is completed in a single pass through the sites of the network and cluster relabeling operates on a vector whose size is much smaller than the size of the network our extension of the hk algorithm works for any environment lattice or non lattice of any dimensionality type sites bonds or both and with arbitrary connectivity between the sites the proposed extension is illustrated through a simple network consisting of 16 sites and 24 bonds and applied to a complex network extracted from a 3d micro focused x ray ct image of bentheimer sandstone consisting of 3677 sites and 8952 bonds

considering the higher order effect of residual modes in the craig bampton method in this paper the accuracy of the craig bampton method one of the most widely used component mode synthesis methods is improved considering the higher order effect of residual modes that are si

percolation and cluster structure parameters the radius of gyration the squared radius of gyration of percolation clusters are determined in terms of the clusters second spatial moments using the enhanced hoshen kopelman algorithm for square and triangular lattices containing sites correlation length exponents and related exponents as well as their corresponding amplitudes are calculated in terms of the squared radius of gyration above and below the percolation threshold a coefficient for cluster compactness that is based on the squared radius of gyration of a cluster is introduced that coefficient is compared with a similar coefficient of compactness that is based on the cluster cyclomatic number

a dynamic condensation method using algebraic substructuring summary in this paper we develop a robust reduced order modeling method named algebraic dynamic condensation which is based on the improved reduced system irs method using algebraic substructuring the global mass and stiffness matrices are divided into many small submatrices without considering the physical domain and substructures and interface boundary are defined in the algebraic perspective the reduced model is then constructed using three additional procedures substructural stiffness condensation interface boundary reduction and substructural inertial effect condensation the formulation of the reduced model is simply expressed at a submatrix level without using a transformation matrix that induces huge computational cost through various numerical examples the performance of the proposed method is demonstrated in terms of accuracy and computational cost

novel modal methods for transient analysis with a reduced order model based on enhanced craig bampton formulation abstract for transient analysis of structural dynamics with reduced order model rom data recovery procedures that use modal methods such as the classical mode acceleration ma and modal displacement md methods are an important step in order to increase the convergence and accuracy of the solution in this work we propose novel ma and md methods for highly accurate transient analysis with a reduced order model based on enhanced craig bampton ecb formulation which is an extension of the classical craig bampton cb method that is a way to reduce the size of a finite element fe model the performance of the proposed data recovery approach is demonstrated with two numerical examples we also investigate the relation between the proposed and classical ma and md methods

a component mode selection method based on a consistent perturbation expansion of interface displacement abstract a mode selection method is presented for the reduced order modeling rom of structural systems in conjunction with the craig bampton component mode synthesis technique the proposed method is derived by using a consistent expansion of the interface displacement in terms of a frequency dependent small parameter as applied to a craig bampton like rom formulation it is found that this procedure yields a coupling mechanism of the modes of the full model to those of substructures the present mode selection method employs this coupling mechanism as an indicator labeled as the cms method for the substructural modal contributions to the full model the performance of the proposed method is demonstrated by various numerical examples and compared favorably with existing method such as the cms method

nonlinear hyperspectral unmixing with robust nonnegative matrix factorization we introduce a robust mixing model to describe hyperspectral data resulting from the mixture of several pure spectral signatures the new model extends the commonly used linear mixing model by introducing an additional term accounting for possible nonlinear effects that are treated as sparsely distributed additive outliers with the standard nonnegativity and sum to one constraints inherent to spectral unmixing our model leads to a new form of robust nonnegative matrix factorization with a group sparse outlier term the factorization is posed as an optimization problem which is addressed with a block coordinate descent algorithm involving majorization minimization updates simulation results obtained on synthetic and real data show that the proposed strategy competes with the state of the art linear and nonlinear unmixing methods

a family of craig bampton methods considering residual mode compensation abstract in this paper we investigate the formulation of a family of craig bampton cb methods considering residual modes by o callahan s approximation and adding generalized coordinate vectors containing unknown eigenvalues in addition we propose an nth order higher order cb hcbn method for compensating the n 1 th residual flexibility in the nth order hcb hcbn method by o callahan s approach therefore various cb methods with improved performance such as the enhanced craig bampton ecb method which uses o callahan s approximation and the higher order craig bampton hcb method which adds generalized coordinate vectors and hcb are employed for the comparison of performance with the aid of multiprecision computing through three benchmark examples it is revealed that the hcb1 method a modified version of the first order hcb method hcb1 with the aid of o callahan s approximation proposed shows better performance than hcb1 with the same number of retained modes however hcb2 and hcb3 modified versions of the second and third order hcb method respectively cannot be improved further from the results we concluded that this was due to the limitation of o callahan s approach which many researchers have fundamentally questioned

an algebraic substructuring method for large scale eigenvalue calculation this paper is concerned with solving large scale eigenvalue problems by algebraic substructuring algebraic substructuring refers to the process of applying matrix reordering and partitioning algorithms to divide a large sparse matrix into smaller submatrices from which a subset of spectral components are extracted and combined to form approximate solutions to the original problem through an algebraic analysis we identify critical conditions under which a simple version of algebraic substructuring works well this particular version of substructuring is identical to the component mode synthesis cms method see r r craig and m c c bampton em coupling of substructures for dynamic analysis aiaa j 6 1968 pp 1313 1319 and w c hurty em vibrations of structure systems by component mode synthesis j engrg mech 86 1960 pp 51 69 when the matrix reordering is based on a geometric partitioning of the computational domain we observe an interesting connection between the accuracy of an approximate eigenpair obtained through substructuring and the distribution of the components of eigenvectors of a canonical matrix pencil congruent to the original problem a priori error bounds for the smallest eigenpair approximation are developed this development leads to a simple heuristic for choosing spectral components modes from each substructure the effectiveness of such a heuristic is demonstrated with numerical examples we show that algebraic substructuring can be effectively used to solve a generalized eigenvalue problem arising from the finite element analysis of an accelerator structure

target detection based on a dynamic subspace for hyperspectral target detection it is usually the case that only part of the targets pixels can be used as target signatures so can we use them to construct the most proper background subspace for detecting all the probable targets in this paper a dynamic subspace detection dsd method which establishes a multiple detection framework is proposed in each detection procedure blocks of pixels are calculated by the random selection and the succeeding detection performance distribution analysis manifold analysis is further used to eliminate the probable anomalous pixels and purify the subspace datasets and the remaining pixels construct the subspace for each detection procedure the final detection results are then enhanced by the fusion of target occurrence frequencies in all the detection procedures experiments with both synthetic and real hyperspectral images hsi evaluate the validation of our proposed dsd method by using several different state of the art methods as the basic detectors with several other single detectors and multiple detection methods as comparable methods improved receiver operating characteristic curves and better separability between targets and backgrounds by the dsd methods are illustrated the dsd methods also perform well with the covariance based detectors showing their efficiency in selecting covariance information for detection the dynamic subspace detection theory is a useful background statistics estimation our method can find the most suitable pixels to construct detectors targets can be further distinguished by a fusion of all the detection procedures

matched shrunken cone detector mscd bayesian derivations and case studies for hyperspectral target detection hyperspectral images hsis possess non negative properties for both hyperspectral signatures and abundance coefficients which can be naturally modeled using cone based representation however in hyperspectral target detection cone based methods are barely studied in this paper we propose a new regularized cone based representation approach to hyperspectral target detection as well as its two working models by incorporating into the cone representation l 2 norm and l 1 norm regularizations respectively we call the new approach the matched shrunken cone detector mscd also important we provide principled derivations of the proposed mscd from the bayesian perspective we show that mscd can be derived by assuming a multivariate half gaussian distribution or a multivariate half laplace distribution as the prior distribution of the coefficients of the models in the experimental studies we compare the proposed mscd with the subspace methods and the sparse representation based methods for hsi target detection two real hyperspectral data sets are used for evaluating the detection performances on sub pixel targets and full pixel targets respectively results show that the proposed mscd can outperform other methods in both cases demonstrating the competitiveness of the regularized cone based representation

cluster diversity and entropy on the percolation model the lattice animal identification algorithm we present an algorithm to identify and count different lattice animals la s in the site percolation model this algorithm allows a definition of clusters based on the distinction of cluster shapes in contrast with the well known hoshen kopelman algorithm in which the clusters are differentiated by their sizes it consists in coding each unit cell of a cluster according to the nearest neighbors nn and ordering the codes in a proper sequence in this manner a la is represented by a specific code sequence in addition with some modification the algorithm is capable of differentiating between fixed and free la s the enhanced hoshen kopelman algorithm j hoshen m w berry and k s minser phys rev e 56 1455 1997 is used to compose the set of nn code sequences of each cluster using monte carlo simulations on planar square lattices up to 2000x2000 we apply this algorithm to the percolation model we calculate the cluster diversity and cluster entropy of the system which leads to the determination of probabilities associated with the maximum of these functions we show that these critical probabilities are associated with the percolation transition and with the complexity of the system

monte carlo and series study of corrections to scaling in two dimensional percolation corrections to scaling for percolation cluster numbers in two dimensions are studied by monte carlo simulations of very large systems up to 17 109 lattice sites and by series analysis both series and monte carlo work suggests that the value of the correction to scaling exponent is slightly lower at the percolation threshold than away from it moreover the corrections to scaling observed at pc omega equivalent to 0 64 might be due to the mixing of scaling fields rather than to the irrelevant scaling fields the monte carlo results are compatible with finite size scaling and finite size scaling corrections are estimated technical problems associated with monte carlo simulation of very large systems are discussed in an appendix

winding clusters in percolation on the torus and the mobius strip using a simulation technique introduced recently we study winding clusters in percolation on the torus and the mobius strip for different aspect ratios the asynchronous parallelization of the simulation makes very large system and sample sizes possible our high accuracy results are fully consistent with predictions from conformal field theory the numerical results for the mobius strip and the number distribution of winding clusters on the torus await theoretical explanation to our knowledge this study is the first of its kind

matched subspace detectors we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise we derive the generalized likelihood ratio glr for each problem in the class we then establish the invariances for the glr and argue that these are the natural invariances for the problem in each case the glr is a maximal invariant statistic and the distribution of the maximal invariant statistic is monotone this means that the glr test glrt is the uniformly most powerful invariant detector we illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise in each case we give the distribution for the detector and compute performance curves

a dual craig bampton method for dynamic substructuring a novel component mode synthesis method for dynamic analysis of structures is presented it is based on free interface vibration modes and residual flexibility components although the ingredients are the same as in previously published procedures e g macneal or rubin our method is fundamentally different in that it assembles the substructures using interface forces dual assembly and enforces only weak interface compatibility the new formulation is based on a fully consistent reduction approach and the reduced matrices so obtained are exactly dual to the craig bampton reduced matrices the new free interface substructuring method proposed here is thus more natural then classical free interface synthesis procedures and leads to simpler reduced matrices we illustrate the efficiency of the dual craig bampton approach for reducing the dynamical representation on a three dimensional frame

cluster number scaling in two dimensional percolation the cluster distribution for site percolation on the triangular lattice is studied at and close to pc using monte carlo techniques lattice sizes range as high as 2 56 1010 sites and periodic boundary conditions are imposed instead of the customary free boundaries in order to reduce residual finite size effects the results support scaling to leading order both at and near pc corrections to scaling are also examined but through a value for the associated exponent is obtained the results suggest that a description based on a single exponent may not be adequate

monte carlo experiments on percolation the influence of boundary conditions the slow convergence of the cluster size distribution observed in recent monte carlo simulations of two dimensional site percolation is shown to be due to the use of free boundary conditions when periodic boundaries are employed the convergence is improved considerably to the extent that the integrated size distribution for large typically 1010 site lattices is essentially flat over a range of cluster sizes spanning three orders of magnitude the existence of this plateau originally predicted by scaling theory leads to an improved estimate of the critical probability for the square lattice the observed correction to scaling is not readily characterised by a single additive term a fact which helps one to understand the wide range of published exponent estimates

percolation and cluster structure parameters the enhanced hoshen kopelman algorithm an enhanced hoshen kopelman ehk algorithm for calculating cluster structure parameters is presented for the site percolation problem the ehk algorithm enables efficient calculation of cluster spatial moments perimeters and bounding boxes for very large monte carlo simulated lattices the algorithm is used to compute the squared radius of gyration and internal perimeters of clusters in 3000 ifmmode times else texttimes fi 3000 square simulated lattices the squared radius of gyration was used to calculate the value of the correlation length exponent

distribution of averages in a correlated gaussian medium as a tool for estimation of the cluster size distribution calculation of the distribution of the average value of a gaussian random field in a finite domain is carried out for different cases the results of the calculation demonstrate a strong dependence of the width of the distribution on the spatial correlations of the field comparison to the simulation results for the distribution of the size of the cluster indicates that the distribution of an average field could serve as a useful tool for the estimation of the asymptotic behavior of the distribution of the size of the clusters for deep clusters where value of the field on each site is much greater than the rms disorder

cluster size distribution at criticality monte carlo studies of the cluster size distribution for the site percolation problem on the triangular lattice are extended to lattices with up to 4 1011 sites agreement with the predictions of scaling theory at pc is excellent over a range of cluster sizes spanning five orders of magnitude