linear preservers of weak majorization on l1 i when i is an infinite set abstract the necessary and sufficient conditions that a bounded linear map on the banach space l 1 i may be considered as a linear preserver of weak majorization on l 1 i where i is an arbitrary infinite set are given also we prove that the set of all linear preservers of weak majorization is closed under the norm topology

new bounds on the lieb thirring constants improved estimates on the constants l d for 1 2 3 2 d n in the inequalities for the eigenvalue moments of schrodinger operators are established

on the extension of linear contractions some results of the hahn banach type resume let be a norm on rn and s a compact convex semigroup of linear contractions given two k tuples of n vectors x 1 x k and y 1 y k we seek conditions for the existence of a contraction s s that simultaneously takes x i to y i that is sx i y i for all i 1 k straightforward application of the separation theorem for convex sets provides a general but abstract result in the form of a system of inequalities specializing to the 1 norm and the norm respectively and s to comprise either all contractions or those contractions that preserve a particular linear form it is possible to evaluate the characteristic functionals arising from the separation theoem therby the abstract results can be rduced to a tractable form which turns out to be of the hahn banach type

a simple variant of the mizuno todd ye predictor corrector algorithm and its objective function free complexity in this paper we propose a simple variant of the mizuno todd ye predictor corrector algorithm for linear programming our variant employs a simple and a natural scaling invariant search directio

monomer dimer problem on random planar honeycomb lattice we consider the monomer dimer md problem on a random planar honeycomb lattice model namely the random multiple chain this is a lattice system with non periodic boundary condition whose generating process is inspired by the growth of single walled zigzag carbon nanotubes by applying algebraic and combinatorial techniques we establish a calculating expression of the md partition function for bipartite graphs which corresponds to the permanent of a matrix further by using the transfer matrix argument we show that the computing problem of the permanent of high order matrix can be converted into some lower order matrices for this family of lattices based on which we derive an explicit recurrence formula for evaluating the md partition function of multiple chains and random multiple chains finally we analyze the expectation of the number of monomer dimer arrangements on a random multiple chain and the asymptotic behavior of the annealed md entropy when the multiple chain becomes infinite in width and length respectively

on sub and superadditive vector valued maps with applications to group majorization in this paper motivated by results in s s dragomir quasilinearity of some functionals associated with monotonic convex functions rgmia res rep coll 14 2011 artcle 24 13 pp and m niezgoda cone orderings group majorizations and similarly separable sequences linear algebra appl 436 3 2012 pp 579 594 we investigate maps involving quotient p p with an 1 subadditive operator and a positive superadditive functional we pay special attention to vector valued operators we study the subadditivity of the map p p f p p with 1 increasing convex f next we give applications for group majorization preorders we establish some preorder preservation results for the map p p p with a group majorization g and a combination 1 2 of preorders 1 and 2 in consequence we show that the function p f p p is g increasing

a strongly polynomial algorithm to solve combinatorial linear programs khachiyan and recently karmarkar gave polynomial algorithms to solve the linear programming problem these algorithms have a small theoretical drawback namely the number of arithmetic steps depends on the size of the input numbers we present a polynomial linear programming algorithm whose number of arithmetic steps depends only on the size of the numbers in the constraint matrix but is independent of the size of the numbers in the right hand side and objective vectors in particular it gives a polynomial algorithm for the minimum cost flow and multicommodity flow problems in which the number of arithmetic steps is independent of the size of the costs and capacities the algorithm makes use of an existing polynomial linear programming algorithm the problem of whether any algorithm has a running time that is independent even of the size of the numbers in the constraint matrix remains open

log majorization related to renyi divergences abstract for z 0 with 1 motivated by comparison between different kinds of renyi divergences in quantum information we consider log majorization between the matrix functions p a b b 1 2 b 1 2 a b 1 2 b 1 2 q z a b b 1 2 z a z b 1 2 z z of two positive semi definite matrices a b we precisely determine the parameters z for which p a b log q z a b and q z a b log p a b hold respectively

some majorization inequalities induced by schur products in euclidean jordan algebras abstract in a euclidean jordan algebra v of rank n an element x is said to be majorized by an element y symbolically x y if the corresponding eigenvalue vector x is majorized by y in r n in this article we describe pointwise majorization inequalities of the form t x s x where t and s are linear transformations induced by schur products specializing we recover analogs of majorization inequalities of schur hadamard and oppenheimer stated in the setting of euclidean jordan algebras as well as majorization inequalities connecting quadratic and lyapunov transformations on v we also show how schur products induced by certain scalar means such as arithmetic geometric harmonic and logarithmic means naturally lead to majorization inequalities

free point processes and free extreme values we continue here the study of free extreme values begun in ben arous and voiculescu ann probab 34 2037 2059 2006 we study the convergence of the free point processes associated with free extreme values to a free poisson random measure voiculescu in lecture notes in mathematics springer heidelberg pp 279 349 1998 barndorff nielsen and thorbjornsen in probab theory relat fields 131 197 228 2005 we relate this convergence to the free extremal laws introduced in ben arous and voiculescu ann probab 34 2037 2059 2006 and give the limit laws for free order statistics

numerical solution of inverse scattering problems with multi experimental limited aperture data in this paper a regularized homotopy continuation method is presented for numerical solution of nonlinear ill posedness inverse problems two major difficulties for solving these inverse problems by an optimization method are the ill posedness and the presence of many local minima classic iterative methods such as gauss newton or levenberg marquardt algorithms offer fast local convergence but might not be able to compute the global minimum based on a natural concept of multi experimental data a regularized homotopy continuation method is constructed to compute the global minimum as the experimental index t increases continuously the global minimizer can be computed continuously by using local optimization methods by discretizing the continuous homotopy method various recursive linearization algorithms are developed these algorithms are applied to numerical solution of an inverse medium scattering problem which reconstructs the refractive index of an inhomogeneous medium from limited aperture measurements of the far field pattern of the scattered fields it is assumed that the data is measured at multiple frequencies the inverse scattering problem with limited aperture is challenging since without full aperture measurements the ill posedness and nonlinearity of the inverse problem become more severe an efficient regularized iterative linearization method recursive linearization with respect to the wave number is developed for solving the inverse problem the convergence of the iterative method is examined by numerical examples

linear maps preserving group majorization abstract a necessary and sufficient condition for a linear map to preserve group majorizations is given the condition is applied to prove some preservation results

comparison of homotopy perturbation method and homotopy analysis method comparison of homotopy perturbation method hpm and homotopy analysis method is made revealing that the former is more powerful than the later furthermore the hpm is further developed in this paper by applying the modern perturbation methods

a wavelet multilevel method for ill posed problems stabilized by tikhonov regularization an additive schwarz iteration is described for the fast resolution of linear ill posed problems which are stabilized by tikhonov regularization the algorithm and its analysis are presented in a general framework which applies to integral equations of the first kind discretized either by spline functions or daubechies wavelets numerical experiments are reported on to illustrate the theoretical results and to compare both discretization schemes

global convergence property of the affine scaling methods for primal degenerate linear programming problems in this paper we investigate the global convergence property of the affine scaling method under the assumption of dual nondegeneracy the behavior of the method near degenerate vertices is analyzed in detail on the basis of the equivalence between the affine scaling methods for homogeneous lp problems and karmarkar s method it is shown that the step size 1 8 where the displacement vector is normalized with respect to the distance in the scaled space is sufficient to guarantee the global convergence for dual nondegenerate lp problems the result can be regarded as a counterpart to dikin s global convergence result on the affine scaling method assuming primal nondegeneracy

fast seismic ray tracing new methods for the fast accurate and efficient calculation of large classes of seismic rays joining two points x s and x r in very general two dimensional configurations are presented the medium is piecewise homogeneous with arbitrary interfaces separating regions of different elastic properties i e differing wave speeds c p and c s in general there are 2 n 1 rays joining x s to x r while making contact with n interfaces our methods find essentially all such rays for a given n by using continuation or homotopy methods on the wave speeds to solve the ray equations determined by snell s law in addition travel times ray amplitudes and caustic locations are obtained when several receiver positions x j r are to be included as in a gather our techniques easily yield all the rays for the entire gather by employing continuation in the receiver location the applications mainly to geophysical inverse problems are reported elsewhere

solving diffusion equation using wavelet method a wavelet based numerical method based on wavelets of hermite cubic splines is presented for computing singularly perturbed convection dominated diffusion equation the advantages of the method are explained to improve the accuracy of singular areas wavelets are configured hierarchically for solving algebraic equations numerical examples show that the proposed method has good efficiency and precision

a modified layered step interior point algorithm for linear programming the layered step interior point algorithm was introduced by vavasis and ye the algorithm accelerates the path following interior point algorithm and its arithmetic complexity depends only on the coefficient matrixa the main drawback of the algorithm is the use of an unknown big constant bar chi a in computing the search direction and to initiate the algorithm we propose a modified layered step interior point algorithm which does not use the big constant in computing the search direction the constant is required only for initialization when a well centered feasible solution is not available and it is not required if an upper bound on the norm of a primal dual optimal solution is known in advance the complexity of the simplified algorithm is the same as that of vavasis and ye 1998 the mathematical programming society inc published by elsevier science b v

classical and quantum probability we follow the development of probability theory from the beginning of the last century emphasizing that quantum theory is really a generalization of this theory the great achievements of probability theory such as the theory of processes generalized random fields estimation theory and information geometry are reviewed their quantum versions are then described

inequalities for monotonic arrangements of eigenvalues abstract this article corrects clarifies and extends results in 5 on inequalities for sequence rearrangements and for eigenvalues the prototypes for these results are the inequalities of hardy littlewood and polya about monotonic rearrangements we examine some analogous results for eigenvalues of matrices and of their products

multiresolution parameterization for geophysical inverse problems a model parameterization based on a multiresolution wavelet representation is proposed for geophysical inverse problems in this study the matrix equation for the wavelet representation of the model is constructed by dual wavelet transforms of a readily built matrix based on the pixel parameterization we demonstrate the merits of the proposed parameterization using the simple examples of geophysical data gridding and 3d seismic tomography and comparing the results with those obtained by the conventional pixel parameterization it is shown that for the conventional damped least squares solutions of pixel parameterized models regularization by norm damping deteriorates the underlying model correlation due to sparse and heterogeneous sampling whereas roughness damping schemes impose a priori arbitrary correlation length irrespective of the heterogeneous sampling the scale hierarchy embedded in the proposed multiresolution parameterization facilitates the compromise between the dual spatial and scale resolution depending on the local richness of the data constraints across different scales at a site model variation of various scale spectra can be robustly resolved through the scale hierarchy there is thus no need to invoke additional smoothness regularization

free extreme values free probability analogues of the basics of extreme value theory are obtained based on ando s spectral order this includes clas sification of freely max stable laws and their domains of attraction using free extremal convolutions on the distributions these laws coincide with the limit laws in the classical peaks over threshold approach a free extremal projection valued process over a measure space is constructed which is related to the free poisson point process

majorization doubly stochastic matrices and comparison of eigenvalues abstract 1 basic properties of majorization 2 isotone maps and algebraic operations 3 double sub and superstochasticity 4 doubly stochastic matrices 5 doubly stochastic matrices with minimum permanent 6 comparison of eigenvalues 7 doubly stochastic maps

a strong bound on the integral of the central path curvature and its relationship with the iteration complexity of primal dual path following lp algorithms the main goals of this paper are to i relate two iteration complexity bounds derived for the mizuno todd ye predictor corrector mty p c algorithm for linear programming lp and ii study the geometrical structure of the lp central path the first iteration complexity bound for the mty p c algorithm considered in this paper is expressed in terms of the integral of a certain curvature function over the traversed portion of the central path the second iteration complexity bound derived recently by the authors using the notion of crossover events introduced by vavasis and ye is expressed in terms of a scale invariant condition number associated with m n constraint matrix of the lp in this paper we establish a relationship between these bounds by showing that the first one can be majorized by the second one we also establish a geometric result about the central path which gives a rigorous justification based on the curvature of the central path of a claim made by vavasis and ye in view of the behavior of their layered least squares path following lp method that the central path consists of mathcal o n 2 long but straight continuous parts while the remaining curved part is relatively short

the homotopy perturbation method for nonlinear oscillators with discontinuities in the paper the homotopy perturbation method is applied to the nonlinear oscillators with discontinuities only one iteration leads to high accuracy of the solutions

some eigenvalue inequalities for positive semidefinite matrix power products abstract we study the eigenvalues of positive semidefinite matrix power products and obtain some inequalities most of which are in terms of majorization in particular for a b 0 0 we prove log 1 a b log 1 a b the result is a generalization of some work of marcus lieb thirring le couteur bushell and trustrum

a wavelet multiscale method for the inverse problem of a nonlinear convection diffusion equation abstract this paper is concerned with the problem of identifying the diffusion parameters in a nonlinear convection diffusion equation which arises as the saturation equation in the fractional flow formulation of the two phase porous media flow equations the forward problem is discretized using finite difference methods and the inverse problem is formulated as a minimization problem with regularization terms in order to overcome disturbance of local minimum a wavelet multiscale method is applied to solve this parameter identification inverse problem this method works by decomposing the inverse problem into multiple scales with wavelet transform so that the original inverse problem is reformulated to a set of sub inverse problems relying on scale variables and successively solving these sub inverse problems according to the size of scale from the smallest to the largest the stable and fast regularized gauss newton method is applied to each scale numerical simulations show that the proposed algorithm is widely convergent computationally efficient and has the anti noise and de noising abilities

a wavelet multiscale homotopy method for the inverse problem of two dimensional acoustic wave equation abstract by introducing the wavelet multiscale method and the homotopy method to the inversion process for the velocity estimation problem of two dimensional acoustic wave equation in seismic prospecting a joint inversion method wavelet multiscale homotopy method is designed which is stable globally convergent and has the ability of noise suppression the results of numerical simulations and noise suppression tests indicate our method s effectiveness

a widely convergent generalized pulse spectrum technique for the coefficient inverse problem of differential equations abstract a new algorithm of the generalized pulse spectrum technique gpst is constructed for the solution of coefficient inverse problems of differential equations and a skill of saving computational cost is designed in choosing regularizing parameters to overcome the defect of the local convergence of the gpst a widely convergent gpst is illustrated numerical simulations are carried out for solving the inverse problem of 1 d seismic prospection to test the feasibility without real measurement data the computational results show the method s effectiveness

reconstruction of a permeability field with the wavelet multiscale homotopy method for a nonlinear convection diffusion equation this paper deals with the reconstruction of a piecewise constant permeability field for a nonlinear convection diffusion equation which arises as the saturation equation in the fractional flow formulation of the two phase porous media flow equations this permeability identification problem is solved through the minimization of a cost functional which depends on the discrepancy in a least square sense between some measurements and associated predictions in order to cope with the local convergence property of the optimizer the presence of numerous local minima in the cost functional and the large computational cost a wavelet multiscale homotopy is developed implemented and validated this method combines the wavelet multiscale inversion idea with the homotopy method numerical results illustrate the global convergence computational efficiency anti noise ability of the proposed method

majorization and singular values iii abstract we obtain a majorization inequality which relates the singular values of a complex square matrix a and those of t a where t is a linear map the inequality takes a particularly simple form if t is positive the results generalize several known majorization inequalities for eigenvalues and singular values

a note on the lyapunov equation some results on the sensitivity of the solution of the stable lyapunov equation are shown to follow easily from well known theorems of functional analysis

permutation invariant proper polyhedral cones and their lyapunov rank abstract the lyapunov rank of a proper cone k in a finite dimensional real hilbert space is defined as the dimension of the space of all lyapunov like transformations on k or equivalently the dimension of the lie algebra of the automorphism group of k this rank measures the number of linearly independent bilinear relations needed to express a complementarity system on k that arises for example from a linear program or a complementarity problem on the cone motivated by the problem of describing spectral proper cones where the complementarity system can be expressed as a square system that is where the lyapunov rank is greater than equal to the dimension of the ambient space we consider proper polyhedral cones in r n that are permutation invariant for such cones we show that the lyapunov rank is either 1 in which case the cone is irreducible or n in which case the cone is isomorphic to r n in the latter case we show that the corresponding spectral cone is isomorphic to a symmetric cone

a multiresolution method for distributed parameter estimation a multiresolution method for distributed parameter estimation or inverse problems is studied numerically the identification of the coefficient of an elliptic equation in one dimension is considered as our model problem first multiscale bases are used to analyze the degree of ill posedness of the inverse problem second based on some numerical results it is shown that the method of scale by scale multiresolution yields robust and fast convergence finally it is shown how the method gives a natural regularization approach which is complementary to tikhonov s regularization

a homotopy method for nonlinear inverse problems we develop a homotopy method for nonlinear inverse problems where the forward problems are governed by some forms of differential equations a tikhonov style regularization approach yields an optimization problem ordinary iterative methods may fail to solve this problem due to their locally convergent properties then the fixed point homotopy method is introduced to solving the normal equation of the optimization problem and a new and globally convergent algorithm is constructed which is highly effective in the aspects of speed of computation ability of noise suppression and wide region of convergence as a practical application the method is used to solve the inverse problem of 2 d acoustic wave equation we demonstrate the merits and effectiveness of our algorithm on two realistic model problems

on the complexity of following the central path of linear programs by linear extrapolation ii a class of algorithms is proposed for solving linear programming problems withm inequality constraints by following the central path using linear extrapolation with a special adaptive choice of steplengths the latter is based on explicit results concerning the convergence behaviour of newton s method to compute points on the central pathx r r 0 and this allows to estimate the complexity i e the total numbern n r of steps needed to go from an initial pointx r to a final pointx r 0 by an integral of the local weighted curvature of the primal dual path here the central curve is parametrized with the logarithmic penalty parameterr 0 it is shown that for large classes of problems the complexity integral i e the number of stepsn is not greater than constm log r where 1 2 e g 1 4 or 3 8 note that 1 2 gives the complexity of zero order methods we also provide a lower bound for the complexity showing that for some problems the above estimation can hold only for 1 3 as a byproduct many analytical and structural properties of the primal dual central path are obtained there are for instance close relations between the weighted curvature and the logarithmic derivatives of the slack variables the dependence of these quantities on the parameterr is described also related results hold for a family of weighted trajectories into which the central path can be embedded

majorizations and inequalities in matrix theory abstract in matrix theory majorization plays a significant role for instance majorization relations among eigenvalues and singular values of matrices produce a lot of norm inequalities and even matrix inequalities this survey article is intended as a review of recent results in matrix theory related to majorization

a note on properties of condition numbers abstract the condition numbers described by stewart todd and others for a matrix a are given by the suprema of the norms of all the oblique projection operators respectively on the image space of a t and the null space of a this paper shows that these two numbers coincide

a wavelet multi scale method for the inverse problem of diffuse optical tomography this paper deals with the estimation of optical property distributions of participating media from a set of light sources and sensors located on the boundaries of the medium this is the so called diffuse optical tomography problem such a non linear ill posed inverse problem is solved through the minimization of a cost function which depends on the discrepancy in a least square sense between some measurements and associated predictions in the present case predictions are based on the diffuse approximation model in the frequency domain while the optimization problem is solved by the l bfgs algorithm to cope with the local convergence property of the optimizer and the presence of numerous local minima in the cost function a wavelet multi scale method associated with the l bfgs method is developed implemented and validated this method relies on a reformulation of the original inverse problem into a sequence of sub inverse problems of different scales using wavelet transform from the largest scale to the smallest one numerical results show that the proposed method brings more stability with respect to the ordinary l bfgs method and enhances the reconstructed images for most of initial guesses of optical properties

a dantzig wolfe like variant of karmarkar s interior point linear programming algorithm we show that a variant of karmarkar s projective algorithm for linear programming can be viewed as following the approach of dantzig wolfe decomposition at each iteration the current primal feasible solution generates prices which are used to form a simple subproblem the solution to the subproblem is then incorporated into the current feasible solution with a suitable choice of stepsize a constant reduction in potential function is achieved at each iteration we also use our analysis to motivate a new primal simplex pivot rule that is closely related to rules used by e klotz and l schrage

characterizations bounds and probabilistic analysis of two complexity measures for linear programming problems this note studies a a condition number used in the linear programming algorithm of vavasis and ye 14 whose running time depends only on the constraint matrix a m n and a a variant of another condition number due to ye 17 that also arises in complexity analyses of linear programming problems we provide a new characterization of a and relate a and a furthermore we show that if a is a standard gaussian matrix then e ln a o min mlnn n thus the expected running time of the vavasis ye algorithm for linear programming problems is bounded by a polynomial in m and n for any right hand side and objective coefficient vectors when a is randomly generated in this way as a corollary of the close relation between a and a we show that the same bound holds for e ln a

extremal majorizing and anti majorizing matrices in this note we study the convex set of all real n x n matrices which either increase or decrease mi xednlnrss when applied to any monotonously ordered probability n vector and we compute a complete list of its extremals in both cases 0 i998 published by

the solution of van der waerden s problem for permanents in this paper a solution to van der waerden s problem is presented it is hoped that the solution of this problem will stimulate new and vigorous interest in the theory of permanents and related topics permanents are ideal objects of study having both practical applications and abstract mathematical problems problems involving permanents tend to be easily stated but only solvable using deep methods the theory of permanents as an independent branch of mathematics which has developed parallel to the theory of determinants is far from exhausted many difficult questions must still be resolved in particular the problem of calculation and estimation of permanents for specific classes of matrices is of prime importance the solution of van der waerden s problem makes use of the penetrating force of the method of mixed volumes from combinatorial analysis even hilbert noted that there were connections to be uncovered between the theory of mixed volumes and other areas of mathematics the method of mixed volumes is ideally suited to solving extremal problems and problems of uniqueness and obtaining deep new inequalities it is reasonable to assume that in the future the method of mixed volumes will stand with that of generating functions as one of the basic analytic tools of computational combinatorial analysis

a widely convergent method for determining the distributed parameters of an elliptical equation a new widely convergent method for the problem of determining the distributed parameters of a differential equation is illustrated numerical simulations are carried out to test the feasibility and to study the general characteristics of this method without the real measurement data the computation results show that the method is feasible and efficient

hadamard products and golden thompson type inequalities abstract by using hadamard products we give some reasonable upper and lower bounds of golden thompson type for e h 1 h m where h i i 1 2 m are arbitrary hermitian matrices and is an arbitrary unitarily invariant norm

on scaled projections and pseudoinverses abstract let x be a matrix of full column rank and let d be a diagonal matrix with positive diagonal elements the weighted pseudoinverse defined by x d x t dx 1 x t d and the associated oblique projection p d xx d arise in many applications in this paper we show that the norms of both matrices are bounded by numbers that are independent of d

a new iteration complexity bound for the mty predictor corrector algorithm in this paper we present a new iteration complexity bound for the mizuno todd ye predictor corrector mty p c primal dual interior point algorithm for linear programming the analysis of the paper is based on the important notion of crossover events introduced by vavasis and ye for a standard form linear program min ctx ax b x ge 0 with decision variable x in re n e show that the mty p c algorithm started from a well centered interior feasible solution with duality gap n mu 0 finds an interior feasible solution with duality gap less than n eta in cal o t mu 0 eta n 3 5 log bar chi a iterations where t t equiv min n 2 log log t log t for all t 0 and bar chi a is a scaling invariant condition number associated with the matrix a more specifically bar chi a is the infimum of all the conditions numbers bar chi ad where d varies over the set of positive diagonal matrices under the setting of the turing machine model our analysis yields an cal o n 3 5 l a min n 2 log l l iteration complexity bound for the mty p c algorithm to find a primal dual optimal solution where la and l are the input sizes of the matrix a and the data a b c respectively this contrasts well with the classical iteration complexity bound for the mty p c algorithm which depends linearly on l instead of log l

notes on egoritsjev s proof of the van der waerden conjecture abstract a solution to the van der waerden conjecture on the minimum of the permanent of doubly stochastic matrices has recently been found by g p ergoritsjev in russian because of the wide interest in this conjecture it seems useful to make the solution more accessible professor van lint has kindly consented to have his notes including a direct proof of an inequality available in the literature only in a more general form published in this journal ed r a b

directional quasi convexity asymmetric schur convexity and optimality of consecutive partitions the current paper has the following distinct goals 1 to generalize standard quasi convexity to obtain a weaker property of functions that suffices for optimality of extreme points specifically it is required that intersections of the level sets of the function with line segments having direction in a prescribed set are convex 2 to characterize schur convexity for symmetric functions through the above generalization of quasi convexity thereby obtaining a previously unknown relationship of schur convexity and standard convexity the new characterization is used to extend the definition of schur convexity to functions which are not symmetric 3 to obtain new sufficient conditions for the optimality of consecutive partitions by using the new definition of schur convexity for functions that are not necessarily symmetric the conclusion that schur convexity is an instance of a convexity property that implies the optimality of extreme points unifies two approaches that were used in the literature to prove optimality of subsets of the domain of real valued functions the two tools quasi convexity and schur convexity were previously considered as distinct techniques

approximating the permanent via importance sampling with application to the dimer covering problem we estimate the asymptotic growth rate of the number of dimer covers of a cubic lattice our estimate 3 0 4466 0 0006 is consistent with the lower bounds obtained by hammersley and later schrijver and the more recent improved upper bound obtained by ciucu obtaining this estimate is an important step toward approximating the partition function of the cubic monomer dimer system from the partition function all of the standard thermodynamic quantities can be evaluated it is well known that computing 3 is equivalent to computing the permanent of a certain 0 1 matrix we describe an extremely efficient monte carlo algorithm for approximating the permanent previous work on monte carlo approaches includes the pioneering results of jerrum and sinclair who use a rapidly mixing random walk our method is inspired by results of soules on convergence of sinkhorn balancing to obtain a maximum entropy doubly stochastic matrix we use the sinkhorn balanced matrix to generate an importance function that allows us to do direct random sampling rather than a random walk that converges to a limiting distribution

a variant of the vavasis ye layered step interior point algorithm for linear programming in this paper we present a variant of vavasis and ye s layered step path following primal dual interior point algorithm for linear programming our algorithm is a predictor corrector type algorithm which uses from time to time the layered least squares lls direction in place of the affine scaling as direction it has the same iteration complexity bound of vavasis and ye s algorithm namely cal o n 3 5 log bar chi a n where n is the number of nonnegative variables and bar chi a is a certain condition number associated with the constraint matrix a vavasis and ye s algorithm requires explicit knowledge of bar chi a which is very hard to compute or even estimate in order to compute the layers for the lls direction in contrast our algorithm uses the as direction at the current iterate to determine the layers for the lls direction and hence does not require the knowledge of bar chi a a variant with similar properties and with the same complexity has been developed by megiddo mizuno and tsuchiya math programming 82 1998 pp 339 355 however their algorithm needs to compute n lls directions on every iteration while ours computes at most one lls direction on any given iteration

g majorization inequalities for linear maps abstract we give a unified approach to majorization inequalities for linear maps via g majorization preorderings a particular attention is paid to positive linear maps some classical and recently obtained inequalities are derived from the results

on the monotonicity of scalar curvature in classical and quantum information geometry we study the monotonicity under mixing of the scalar curvature for the geometries on the simplex of probability vectors from the results obtained and from numerical data we are led to some conjectures about quantum geometries and wigner yanase dyson information finally we show that this last conjecture implies the truth of the petz conjecture about the monotonicity of the scalar curvature of the bogoliubov kubo mori monotone metric

linear preservers of majorization on lp i abstract in this paper we use doubly stochastic operators to extend the notion of majorization on l p where i is assumed to be an infinite set and p 1 and then characterize the structure of all bounded linear maps on this space which preserve majorization we will see that the two cases p 1 and p 1 lead to different structures