co rotational beam elements with warping effects in instability problems the present paper investigates the formulation of 3d co rotational beam elements for the buckling and post buckling analysis of frame structures following pacoste and eriksson comput methods app

finite elements with increased freedom in choosing shape functions starting with a mathematical statement of the convergence requirements for an element stiffness matrix the paper discusses displacement shape functions that may be used in connection with the potential energy principle in short these functions must be force orthogonal and energy orthogonal but they need not be conforming satisfy interelement compatibility it is shown that the requirements to the displacement functions may be greatly relaxed through slight modifications of the coupling stiffness between fundamental and higher order displacement modes several alternative formulations are examined in particular a new free formulation is suggested using this form which is very simple the only requirement to the displacement patterns used is that they should contain the fundamental deformation modes and be linearly independent applications of the theory to triangular and rectangular plate bending elements are shown the simple stiffness matrix for the latter is given explicitly the numerical results compare favourably with other types of finite elements

estimation and statistical bounds for three dimensional polar shapes in diffuse optical tomography voxel based reconstructions in diffuse optical tomography dot using a quadratic regularization functional tend to produce very smooth images due to the attenuation of high spatial frequencies this then causes difficulty in estimating the spatial extent and contrast of anomalous regions such as tumors given an assumption that the target image is piecewise constant we can employ a parametric model to estimate the boundaries and contrast of an inhomogeneity directly in this paper we describe a method to directly reconstruct such a shape boundary from diffuse optical measurements we parameterized the object boundary using a spherical harmonic basis and derived a method to compute sensitivities of measurements with respect to shape parameters we introduced a centroid constraint to ensure uniqueness of the combined shape center parameter estimate and a projected newton method was utilized to optimize the object center position and shape parameters simultaneously using the shape jacobian we also computed the cramer rao lower bound on the theoretical estimator accuracy given a particular measurement configuration object shape and level of measurement noise knowledge of the shape sensitivity matrix and of the measurement noise variance allows us to visualize the shape uncertainty region in three dimensions giving a confidence region for our shape estimate we have implemented our shape reconstruction method using a finite difference based forward model to compute the forward and adjoint fields reconstruction results are shown for a number of simulated target shapes and we investigate the problem of model order selection using realistic levels of measurement noise assuming a signal to noise ratio in the amplitude measurements of 40 db and a standard deviation in the phase measurements of 0 1deg we are able to estimate an object represented with an eighth order spherical harmonic model having an absorption contrast of 0 15 cm 1 and a volume of 4 82 cm3 with errors of less than 10 in object volume and absorption contrast we also investigate the robustness of our shape based reconstruction approach to a violation of the assumption that the medium is purely piecewise constant

flexible skew symmetric shape model for shape representation classification and sampling skewness of shape data often arises in applications e g medical image analysis and is usually overlooked in statistical shape models in such cases a gaussian assumption is unrealistic and a formulation of a general shape model which accounts for skewness is in order in this paper we present a novel statistical method for shape modeling which we refer to as the flexible skew symmetric shape model fssm the model is sufficiently flexible to accommodate a departure from gaussianity of the data and is fairly general to learn a mean shape template with a potential for classification and random generation of new realizations of a given shape robustness to skewness results from deriving the fssm from an extended class of flexible skew symmetric distributions in addition we demonstrate that the model allows us to extract principal curves in a point cloud the idea is to view a shape as a realization of a spatial random process and to subsequently learn a shape distribution which captures the inherent variability of realizations provided they remain with high probability within a certain neighborhood range around a mean specifically given shape realizations fssm is formulated as a joint bimodal distribution of angle and distance from the centroid of an aggregate of random points mean shape is recovered from the modes of the distribution while the maximum likelihood criterion is employed for classification

asymptotic global confidence regions for 3 d parametric shape estimation in inverse problems this paper derives fundamental performance bounds for statistical estimation of parametric surfaces embedded in ropf3 unlike conventional pixel based image reconstruction approaches our problem is reconstruction of the shape of binary or homogeneous objects the fundamental uncertainty of such estimation problems can be represented by global confidence regions which facilitate geometric inference and optimization of the imaging system compared to our previous work on global confidence region analysis for curves two dimensional 2 d shapes computation of the probability that the entire surface estimate lies within the confidence region is more challenging because a surface estimate is an inhomogeneous random field continuously indexed by a 2 d variable we derive an asymptotic lower bound to this probability by relating it to the exceedence probability of a higher dimensional gaussian random field which can in turn be evaluated using the tube formula due to sun simulation results demonstrate the tightness of the resulting bound and the usefulness of the three dimensional global confidence region approach

energy conserving algorithms for a corotational formulation standard nonlinear schemes for the the simulation of elastodynamic problems have several shortcomings when considering high speed rotations to tackle these problems we use a corotational framework and a corresponding specific linearization to design new energy conserving numerical schemes in the two dimensional case an algorithm preserving also angular momentum is presented the existence of a solution for the fully discrete setting of this algorithm is established numerical results illustrate the flexibility and efficiency of the proposed algorithms

an outer bound on the storage bandwidth tradeoff of exact repair cooperative regenerating codes cooperative regenerating codes are a kind of erasure codes which are optimal in terms of minimizing the repair bandwidth an n k d r cooperative regenerating code has n storage nodes where k arbitrary nodes are enough to reconstruct original data and r failed nodes can be repaired cooperatively with the help of d arbitrary surviving nodes in the regenerating code framework there exists a tradeoff between the storage capacity of each node alpha and the repair bandwidth gamma but the problem of specifying the optimal storage bandwidth tradeoff of the exact repair cooperative regenerating codes remains open a key contribution of this paper is that an outer bound on the storage bandwidth tradeoff of exact repair linear cooperative regenerating codes is proposed this result can be regarded as a generalization of the outer bound proposed by prakash et al which specifies the optimal tradeoff of exact repair regenerating codes for the case of d k n 1 the proposed outer bound suggests the alpha gamma pairs that no exact repair codes can achieve but only functional repair codes can by observing the size of the set of such alpha gamma pairs the performance of the proposed outer bound is evaluated under various parameter settings

nirs spm statistical parametric mapping for near infrared spectroscopy near infrared spectroscopy nirs is a non invasive method to measure brain activity via changes in the degree of hemoglobin oxygenation through the intact skull as optically measured hemoglobin signals strongly correlate with bold signals simultaneous measurement using nirs and fmri promises a significant mutual enhancement of temporal and spatial resolutions although there exists a powerful statistical parametric mapping tool in fmri current public domain statistical tools for nirs have several limitations related to the quantitative analysis of simultaneous recording studies with fmri in this paper a new public domain statistical toolbox known as nirs spm is described it enables the quantitative analysis of nirs signal more specifically nirs data are statistically analyzed based on the general linear model glm and sun s tube formula the p values are calculated as the excursion probability of an inhomogeneous random field on a representation manifold that is dependent on the structure of the error covariance matrix and the interpolating kernels nirs spm not only enables the calculation of activation maps of oxy deoxy hemoglobin and total hemoglobin but also allows for the super resolution localization which is not possible using conventional analysis tools extensive experimental results using finger tapping and memory tasks confirm the viability of the proposed method

energy consistent corotational schemes for frictional contact problems in this paper we consider the unilateral frictional contact problem of a hyperelastic body in the case of large displacements and small strains in order to retain the linear elasticity framework we decompose the deformation into a large global rotation and a small elastic displacement this corotational approach is combined with a primal dual active set strategy to tackle the contact problem the resulting algorithm preserves both energy and angular momentum

cramer rao bounds for parametric shape estimation in inverse problems we address the problem of computing fundamental performance bounds for estimation of object boundaries from noisy measurements in inverse problems when the boundaries are parameterized by a finite number of unknown variables our model applies to multiple unknown objects each with its own unknown gray level or color and boundary parameterization on an arbitrary known background while such fundamental bounds on the performance of shape estimation algorithms can in principle be derived from the cramer rao lower bounds very few results have been reported due to the difficulty of computing the derivatives of a functional with respect to shape deformation we provide a general formula for computing cramer rao lower bounds in inverse problems where the observations are related to the object by a general linear transform followed by a possibly nonlinear and noisy measurement system as an illustration we derive explicit formulas for computed tomography fourier imaging and deconvolution problems the bounds reveal that highly accurate parametric reconstructions are possible in these examples using severely limited and noisy data

a unified formulation of small strain corotational finite elements i theory this paper presents a unified theoretical framework for the corotational cr formulation of finite elements in geometrically nonlinear structural analysis the key assumptions behind cr are i strains from a corotated configuration are small while ii the magnitude of rotations from a base configuration is not restricted following a historical outline the basic steps of the element independent cr formulation are presented the element internal force and consistent tangent stiffness matrix are derived by taking variations of the internal energy with respect to nodal freedoms it is shown that this framework permits the derivation of a set of cr variants through selective simplifications this set includes some previously used by other investigators the different variants are compared with respect to a set of desirable qualities including self equilibrium in the deformed configuration tangent stiffness consistency invariance symmetrizability and element independence we discuss the main benefits of the cr formulation as well as its modeling limitations

a tight rate bound and matching construction for locally recoverable codes with sequential recovery from any number of multiple erasures this paper considers the natural extension of locally recoverable codes lrc to the case of t 1 erased symbols while several approaches have been proposed for the handling of multiple erasures in the approach considered here the t erased symbols are recovered in succession each time contacting at most r other symbols for assistance under the local recovery constraint this sequential approach is the most general and hence offers the maximum possible code rate we characterize the rate of an lrc with sequential recovery for any r geq 3 and any t by first deriving an upper bound on the code rate and then constructing a binary code achieving this optimal rate the upper bound derived here proves an earlier conjecture our approach permits us to deduce the structure of the parity check matrix of a rate optimal lrc with sequential recovery the derived structure of parity check matrix leads to a graphical description of the code used in code construction a subclass of binary codes that are both rate and block length optimal are shown to correspond to certain regular graphs known as moore graphs that have the smallest number of vertices for a given girth a connection with tornado codes is also made

the detection of local shape changes via the geometry of hotelling s t 2 fields this paper is motivated by the problem of detecting local changes or differences in shape between two samples of objects via the nonlinear deformations required to map each object to an atlas standard local shape changes are then detected by high values of the random field of hotelling s t 2 statistics for detecting a change in mean of the vector deformations at each point in the object to control the null probability of detecting a local shape change we use the recent result of adler that the probability that a random field crosses a high threshold is very accurately approximated by the expected euler characteristic ec of the excursion set of the random field above the threshold we give an exact expression for the expected ec of a hotelling s t 2 field and we study the behavior of the field near local extrema this extends previous results for gaussian random fields by adler and x 2 t and f fields by worsley and cao for illustration these results are applied to the detection of differences in brain shape between a sample of 29 males and 23 females

statistical bias of conic fitting and renormalization introducing a statistical model of noise in terms of the covariance matrix of the n vector we point out that the least squares conic fitting is statistically biased we present a new fitting scheme called renormalization for computing an unbiased estimate by automatically adjusting to noise relationships to existing methods are discussed and our method is tested using real and synthetic data

optimal locally repairable codes of distance 3 and 4 via cyclic codes like classical block codes a locally repairable code also obeys the singleton type bound we call a locally repairable code optimal if it achieves the singleton type bound in the breakthrough work of tamo and barg several classes of optimal locally repairable codes were constructed via subcodes of reed solomon codes thus the lengths of the codes given by tamo and barg are upper bounded by the code alphabet size q recently it was proved through the extension of construction by tamo and barg that the length of q ary optimal locally repairable codes can be q 1 by jin et al surprisingly barg et al presented a few examples of q ary optimal locally repairable codes of small distance and locality with code length achieving roughly q 2 very recently it was further shown in the work of li et al that there exist q ary optimal locally repairable codes with the length bigger than q 1 and the distance proportional to n thus it becomes an interesting and challenging problem to construct new families of q ary optimal locally repairable codes of length bigger than q 1 in this paper we construct a class of optimal locally repairable codes of distances 3 and 4 with unbounded length i e length of the codes is independent of the code alphabet size our technique is through cyclic codes with particular generator and parity check polynomials that are carefully chosen

the stability of nonlinear least squares problems and the cramer rao bound a number of problems of interest in signal processing can be reduced to nonlinear parameter estimation problems the traditional approach to studying the stability of these estimation problems is to demonstrate finiteness of the cramer rao bound crb for a given noise distribution we review an alternate deterministic notion of stability for the associated nonlinear least squares nls problem from the realm of nonlinear programming i e that the global minimizer of the least squares problem exists and varies smoothly with the noise furthermore we show that under mild conditions identifiability of the parameters along with a finite crb for the case of gaussian noise is equivalent to the deterministic stability of the nls problem finally we demonstrate the application of our result which is general to the problems of multichannel blind deconvolution and sinusoid retrieval to generate new stability results for these problems with little additional effort

pliable fractional repetition codes for distributed storage systems design and analysis a distributed storage system dss is one of the most vital components of a cloud computing system used for storing and sharing big data among authorized users a typical dss consists of n storage nodes each with a storage capacity of alpha units of data such that the entire file stored on the dss can be recovered by accessing any k nodes the objective of this paper is to construct fractional repetition fr codes with applications in dsss fr codes are the key to constructing a class of distributed storage codes with exact repair by transfer i e upon failure a failed storage node is exactly regenerated through simple downloading a major drawback of existing fr codes is that they are insufficiently flexible to adapt adequately to system changes in dsss to address this problem this paper introduces a new type of fr codes called pliable fr codes in which both the per node storage alpha and repetition degree rho can easily and simultaneously be adjusted in addition this paper presents several constructions of pliable fr codes and provides a relatively comprehensive analysis of the constructed pliable fr codes which reveals the following versatile properties of the codes 1 the transposed codes of the constructed codes are also pliable fr codes 2 the constructed codes attain a tight upper bound on the file size with equality at least for 1 le k where k is the smallest value of k such that k alpha k 1 frac n 1 rho 1 3 the constructed codes also meet a singleton like bound on the minimum distance at least for 1 le k which demonstrates their optimality 4 the computational complexity necessary for determining the file size or the minimum distance of the constructed codes can be greatly reduced when it is hard to exactly determine them and 5 the constructed codes can be used as fractional repetition batch codes to provide load balancing in dsss for which the batch size i e the number of symbols that can be read in parallel can be exactly determined

cramer rao bounds for 2 d target shape estimation in nonlinear inverse scattering problems with application to passive radar we present new methods for computing fundamental performance limits for two dimensional 2 d parametric shape estimation in nonlinear inverse scattering problems with an application to passive radar imaging we evaluate cramer rao lower bounds crb on shape estimation accuracy using the domain derivative technique from nonlinear inverse scattering theory the crb provides an unbeatable performance limit for any unbiased estimator and under fairly mild regularity conditions is asymptotically achieved by the maximum likelihood estimator mle the resultant crbs are used to define an asymptotic global confidence region centered around the true boundary in which the boundary estimate lies with a prescribed probability these global confidence regions conveniently display the uncertainty in various geometric parameters such as shape size orientation and position of the estimated target and facilitate geometric inferences numerical simulations are performed using the layer approach and the nystrom method for computation of domain derivatives and using fourier descriptors for target shape parameterization this analysis demonstrates the accuracy and generality of the proposed methods

lower bounds for parametric estimation with constraints a chapman robbins form of the barankin bound is used to derive a multiparameter cramer rao cr type lower bound on estimator error covariance when the parameter theta in r sup n is constrained to lie in a subset of the parameter space a simple form for the constrained cr bound is obtained when the constraint set theta sub c can be expressed as a smooth functional inequality constraint it is shown that the constrained cr bound is identical to the unconstrained cr bound at the regular points of theta sub c i e where no equality constraints are active on the other hand at those points theta in theta sub c where pure equality constraints are active the full rank fisher information matrix in the unconstrained cr bound must be replaced by a rank reduced fisher information matrix obtained as a projection of the full rank fisher matrix onto the tangent hyperplane of the full rank fisher matrix onto the tangent hyperplane of the constraint set at theta a necessary and sufficient condition involving the forms of the constraint and the likelihood function is given for the bound to be achievable and examples for which the bound is achieved are presented in addition to providing a useful generalization of the cr bound the results permit analysis of the gain in achievable mse performance due to the imposition of particular constraints on the parameter space without the need for a global reparameterization

low complexity array codes for random and clustered 4 erasures a new family of low complexity array codes is proposed for correcting 4 column erasures the new codes are tailored for the new error model of clustered column erasures that captures the properties of high order failure combinations in storage arrays the model of clustered column erasures considers the number of erased columns together with the number of clusters into which they fall without pre defining the sizes of the clusters this model addresses the problem of correlated device failures in storage arrays whereby each failure event may affect multiple devices in a single cluster the new codes correct essentially all combinations of clustered 4 erasures i e those combinations that fall into three or less clusters the new codes are significantly more efficient in all relevant complexity measures than the best known 4 erasure correcting codes these measures include encoding complexity decoding complexity and update complexity

recovering convex edges of an image from noisy tomographic data we consider the problem of recovering edges of an image from noisy tomographic data the original image is assumed to have a discontinuity jump edge along the boundary of a compact convex set the radon transform of the image is observed with noise and the problem is to estimate the edge we develop an estimation procedure which is based on recovering the support function of the edge it is shown that the proposed estimator is nearly optimal in order in a minimax sense numerical examples illustrate reasonable practical behavior of the estimation procedure

security in locally repairable storage in this paper we extend the notion of locally repairable codes to secret sharing schemes the main problem that we consider is to find optimal ways to distribute the shares of a secret among a set of storage nodes participants such that the content of each node share can be recovered by using the contents of only few other nodes and at the same time the secret can be reconstructed by only some allowable subsets of nodes as a special case an eavesdropper observing some set of specific nodes such as less than certain number of nodes does not get any information in other words we propose to study a locally repairable distributed storage system that is secure against a passive eavesdropper that can observe some subsets of nodes we provide a number of results related to such systems including upper bounds and achievability results on the number of bits that can be securely stored with these constraints in particular we provide conditions under which a locally repairable code can be turned into a secret sharing scheme and extend the results of secure repairable storage to cooperative repair and storage on networks in addition we consider perfect secret sharing schemes over general access structures under locality constraints and give an example of a perfect secret sharing scheme that can have small locality finally we provide a lower bound on the size of a share compared with the size of the secret that shows how locality affects the sizes of shares in a perfect scheme

on the locality of codeword symbols consider a linear n k d q code c we say that the ith coordinate of c has locality r if the value at this coordinate can be recovered from accessing some other r coordinates of c data storage applications require codes with small redundancy low locality for information coordinates large distance and low locality for parity coordinates in this paper we carry out an in depth study of the relations between these parameters we establish a tight bound for the redundancy n k in terms of the message length the distance and the locality of information coordinates we refer to codes attaining the bound as optimal we prove some structure theorems about optimal codes which are particularly strong for small distances this gives a fairly complete picture of the tradeoffs between codewords length worst case distance and locality of information symbols we then consider the locality of parity check symbols and erasure correction beyond worst case distance for optimal codes using our structure theorem we obtain a tight bound for the locality of parity symbols possible in such codes for a broad class of parameter settings we prove that there is a tradeoff between having good locality and the ability to correct erasures beyond the minimum distance

towards 3 query locally decodable codes of subexponential length a q query locally decodable code ldc encodes an n bit message x as an n bit codeword c x such that one can probabilistically recover any bit xi of the message by querying only q bits of the codeword c x even after some constant fraction of codeword bits has been corrupted we give new constructions of three query ldcs of vastly shorter length than that of previous constructions specifically given any mersenne prime p e 2t 1 we design three query ldcs of length n e exp o n1 t for every n based on the largest known mersenne prime this translates to a length of less than exp o n10 7 compared to exp o n1 2 in the previous constructions it has often been conjectured that there are infinitely many mersenne primes under this conjecture our constructions yield three query locally decodable codes of length n e exp no 1 log log n for infinitely many n we also obtain analogous improvements for private information retrieval pir schemes we give 3 server pir schemes with communication complexity of o n10 7 to access an n bit database compared to the previous best scheme with complexity o n1 5 25 assuming again that there are infinitely many mersenne primes we get 3 server pir schemes of communication complexity no 1 log logn for infinitely many n previous families of ldcs and pir schemes were based on the properties of low degree multivariate polynomials over finite fields our constructions are completely different and are obtained by constructing a large number of vectors in a small dimensional vector space whose inner products are restricted to lie in an algebraically nice set

the second generation feti methods and their application to the parallel solution of large scale linear and geometrically non linear structural analysis problems the feti algorithms are a family of numerically scalable domain decomposition methods they have been designed in the early 1990s for solving iteratively and on parallel machines large scale systems of equations arising from the finite element discretization of solid mechanics structural engineering structural dynamics and acoustic scattering problems and for analyzing complex structures obtained from the assembly of substructures with incompatible discrete interfaces in this paper we present the second generation of these methods that operate more efficiently on large numbers of subdomains offer greater robustness better performance and more flexibility for implementation on a wider variety of computational platforms we also report on the application and performance of these methods for the solution of geometrically non linear structural analysis problems we discuss key aspects of their implementation on shared and distributed memory parallel processors benchmark them against optimized direct sparse solvers and highlight their potential with the solution of large scale structural mechanics problems with several million degrees of freedom

on sequential locally repairable codes we consider the locally repairable codes lrcs aiming at sequentially recovering multiple erasures in particular we propose and study the so called n k r t sequential lrcs slrc as an n k linear code where any t leq t erasures can be sequentially recovered each by r 2 leq r other code symbols here sequential recovering means that the erased symbols are recovered one by one and an already recovered symbol can be used to recover the remaining erased symbols this important recovering method in contrast with the extensively studied parallel recovering is currently far from being thoroughly understood more specifically there are to date no codes constructed for arbitrary t geq 3 erasures and bounds to evaluate the performance of such codes we first derive a tight upper bound on the code rate of the n k r t slrc for t 3 and r geq 2 we then propose two constructions of binary n k r t slrcs for general r t geq 2 existing constructions only deal with t leq 7 erasures the first construction generalizes the method of direct product construction the second construction is based on the resolvable configurations and yields slrcs for any r geq 2 and odd t geq 3 for both constructions the rates are optimal for t in 2 3 and are higher than most of the existing lrc families for arbitrary t geq 4

codes with locality for two erasures codes with locality are a class of codes introduced by gopalan et al to efficiently repair a failed node by minimizing the number of nodes contacted during repair an n k systematic code is said to have information locality r if each message symbol can be recovered by accessing leq r other symbols an n k code is said to have all symbol locality r if each code symbol can be recovered by accessing leq r other symbols in this paper we consider a generalization of codes with all symbol locality to the case of handling two erasures we study codes with locality that can recover from two erasures via a sequence of two local parity check computations we refer to these codes as sequential recovery locally repairable codes denoted by 2 seq lr codes earlier approaches to handling multiple erasures considered recovery in parallel the sequential approach allows us to potentially construct codes with improved minimum distance we derive an upper bound on the rate of 2 seq lr codes we provide constructions based on regular graphs which are rate optimal with respect to the derived bound we also characterize the structure of any rate optimal code by studying the generalized hamming weights of the dual code we derive a recursive upper bound on the minimum distance of 2 seq lr codes we also provide constructions of a family of codes based on turan graphs that are optimal with respect to this bound we also present explicit distance optimal turan graph based constructions of 2 seq lr codes for certain parameters our approach also leads to a new bound on the minimum distance of codes with all symbol locality for the single erasure case

an excursion into large rotations the present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in 1 it is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix t appertaining to a rotation about an arbitrary axis also analysed is the case of multiple rotations about fixed or follower axes particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations this theme is discussed in some detail for a number of cases semitangential rotations for which commutativity holds first proposed in 2 3 are also considered furthermore an elementary geometrical analysis of large rotations is also given finally we deduce in an appendix using a judicious reformulation of quarternions the compound pseudovector representing the combined effect of n rotations in the author s opinion the present approach appears preferable to a pure vectorial scheme and even more so to an indicial formulation and is computationally more convenient

a co rotational element time integration strategy for non linear dynamics new procedures are proposed for implicit dynamic analysis using the finite element method the main aim is to give stable solutions with significant rigid body motions in particular rotations in contrast to most conventional approaches the time integration strategy is closely linked to the element technologies with the latter involving a form of co rotational procedure for the undamped situation one of the solution procedures leads to an algorithm that exactly conserves energy when constant external forces are applied i e with gravity loading

constructions and properties of linear locally repairable codes in this paper locally repairable codes with all symbol locality are studied methods to modify already existing codes are presented it is also shown that with high probability a random matrix with a few extra columns guaranteeing the locality property is a generator matrix for a locally repairable code with a good minimum distance the proof of the result provides a constructive method to find locally repairable codes finally constructions of three infinite classes of optimal vector linear locally repairable codes over a small alphabet independent of the code size are given

a study of optimal membrane triangles with drilling freedoms abstract this article compares derivation methods for constructing optimal membrane triangles with corner drilling freedoms the term optimal is used in the sense of exact inplane pure bending response of rectangular mesh units of arbitrary aspect ratio following a comparative summary of element formulation approaches the construction of an optimal three node triangle using the andes formulation is presented the construction is based upon techniques developed by 1991 in student term projects but taking advantage of the more general framework of templates developed since the optimal element that fits the andes template is shown to be unique if energy orthogonality constraints are enforced two other formulations are examined and compared with the optimal model retrofitting the conventional linear strain triangle element by midpoint migrating and congruential transformations is shown unable to produce an optimal element while rank deficiency is inevitable use of the quadratic strain field of the 1988 allman triangle or linear filtered versions thereof is also unable to reproduce the optimal element moreover these elements exhibit serious aspect ratio lock these predictions are verified on benchmark examples

cooperative regenerating codes one of the design objectives in distributed storage system is the minimization of the data traffic during the repair of failed storage nodes by repairing multiple failures simultaneously and cooperatively rather than successively and independently further reduction of repair traffic is made possible a closed form expression of the optimal tradeoff between the repair traffic and the amount of storage in each node for cooperative repair is given we show that the points on the tradeoff curve can be achieved by linear cooperative regenerating codes with an explicit bound on the required finite field size the proof relies on a max flow min cut type theorem from combinatorial optimization for submodular flows two families of explicit constructions are given

estimating the number of peaks in a random field using the hadwiger characteristic of excursion sets with applications to medical images excursion sets has been studied by adler who defined the ig integral geometry characteristic of excursion sets as a multidimensional analogue of the number of upcrossings of the threshold by a unidimensional process the ig characteristic equals the euler characteristic of an excursion set provided that the set does not touch the boundary of the volume and adler found the expected ig characteristic for a stationary random field inside a fixed volume worsley evans marrett and neelin used the ig characteristic as an estimator of the number of regions of activation of positron emission tomography pet images of blood flow in the brain unfortunately the ig characteristic is only defined on intervals it is not invariant under rotations and it can fail to count connected regions that touch the boundary this is important since activation often occurs in the cortical regions near the boundary of the brain in this paper we study the hadwiger characteristic which is defined on arbitrary sets is invariant under rotations and does count connected regions whether they touch the boundary or not our main result is a simple expression for the expected hadwiger characteristic for an isotropic stationary random field in two and three dimensions and on a smooth surface embedded in three dimensions results are applied to pet studies of pain perception and word recognition

asymptotic global confidence regions in parametric shape estimation problems we introduce confidence region techniques for analyzing and visualizing the performance of two dimensional parametric shape estimators assuming an asymptotically normal and efficient estimator for a finite parameterization of the object boundary cramer rao bounds are used to define an asymptotic confidence region centered around the true boundary computation of the probability that an entire boundary estimate lies within the confidence region is a challenging problem because the estimate is a two dimensional nonstationary random process we derive lower bounds on this probability using level crossing statistics the same bounds also apply to asymptotic confidence regions formed around the estimated boundaries lower bounding the probability that the entire true boundary lies within the confidence region the results make it possible to generate asymptotic confidence regions for arbitrary prescribed probabilities these asymptotic global confidence regions conveniently display the uncertainty in various geometric parameters such as shape size orientation and position of the estimated object and facilitate geometric inferences numerical simulations suggest that the new bounds are quite tight

on secrecy capacity of minimum storage regenerating codes in this paper we revisit the problem of characterizing the secrecy capacity of minimum storage regenerating msr codes under the passive l 1 l 2 eavesdropper model where the eavesdropper has access to data stored on l 1 nodes and the repair data for an additional l 2 nodes we study it from the information theoretic perspective first some general properties of msr codes as well as a simple and generally applicable upper bound on secrecy capacity are given second a new concept of stable msr codes is introduced where the stable property is shown to be closely linked with secrecy capacity finally a comprehensive and explicit result on secrecy capacity in the linear msr scenario is present which generalizes all related works in the literature and also predicts certain results for some unexplored linear msr codes

co rotational flat facet triangular elements for shell instability analyses abstract this paper investigates the formulation of co rotational flat facet triangular elements for the numerical analysis of instability phenomena in shell structures the elements have three nodes with six degrees of freedom at each node the term co rotational relates here to the provision of a local system that continuously rotates and translates with the element following mainly nour omid and rankin b nour omid and c c rankin finite rotation analysis and consistent linearization using projectors comput methods appl mech engrg 93 1991 353 384 the definition of an element resorts to a change of variables from the local frame to the global one this is done through the use of a projector matrix which relates the variations of the local displacements to the variations of the global ones by extracting the rigid body modes from the latter the main difference from the original formulation lies in the parameterization of 3d finite rotations in contrast to the paper by nour omid and rankin a parameterization based on the rotational vector is here adopted and thus an additional change of variables has to be performed as a result the rotational variables become additive and the necessity of a special updating procedure is avoided the main feature of the adopted formulation is its independence of the local assumptions used to derive the internal forces and tangent stiffness in local coordinates for a certain class of elements i e elements with the same number of nodes and degrees of freedom the main co rotational framework is the same using this property three types of local formulations are considered a set of carefully chosen test problems is used in order to assess the performances of the three element types

variational formulation in the geometrically nonlinear thin elastic shell theory abstract the variational formulation for thin elastic shells undergoing large deflections is discussed no restrictions are imposed on the magnitude of the rotational part of the deformation gradient yet it is assumed that the strains remain small everywhere in the shell ten functional and associated variational principles are derived including the hu washizu the hellinger reissner the generalized complementary energy and the stationary potential energy principles the total lagrangian description tld is exclusively used