generalizing the hough transform to detect arbitrary shapes abstract the hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve the initial work showed how to detect both analytic curves 1 2 and non analytic curves 3 but these methods were restricted to binary edge images this work was generalized to the detection of some analytic curves in grey level images specifically lines 4 circles 5 and parabolas 6 the line detection case is the best known of these and has been ingeniously exploited in several applications 7 8 9 we show how the boundaries of an arbitrary non analytic shape can be used to construct a mapping between image space and hough transform space such a mapping can be exploited to detect instances of that particular shape in an image furthermore variations in the shape such as rotations scale changes or figure ground reversals correspond to straightforward transformations of this mapping however the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes this makes the generalized hough transform a kind of universal transform which can be used to find arbitrarily complex shapes

efficient parallel algorithms for string editing and related problems the string editing problem for input strings x and y consists of transforming x into y by performing a series of weighted edit operations on x of overall minimum cost an edit operation on x can be the deletion of a symbol from x the insertion of a symbol in x or the substitution of a symbol of x with another symbol this problem has a well known o x y time sequential solution efficient pram parallel algorithms for the string editing problem are given if m min x y and n max x y then the crew bound is o log m log n time with o mn log m processors the crow bound is o log n log log m 2 time with o mn log log m processors in all algorithms space is o mn

optimal correspondence of string subsequences the definition of optimal correspondent subsequence ocs which extends the finite alphabet editing error minimization matching to infinite alphabet penalty minimization matching is given the authors prove that the string distance derived from ocs is a metric an algorithm to compute the string to string ocs is given the computational complexity of ocs is analyzed ocs is more efficient than relaxation and elastic matching for 1d problems an algorithm combining syntactic information in template matching is given to show the ease of integrating regular grammar into the ocs technique since in different applications different penalty functions may be required two of them are discussed one pointwise and the other piecewise the pointwise application consists of a stereo epipolar line matching problem solved by using string to string ocs the feasibility of applying ocs to upc bar code recognition is investigated showing the elegance of string to regular expression ocs compared to the relaxation and elastic matching techniques

reduced commutativity of moduli of operators abstract in this paper we investigate the question of when the equations a s a s a a s s s where s is a finite set of positive integers imply the quasinormality or normality of a in particular it is proved that if s p m m p n n p where p 1 and 2 m n then a is quasinormal moreover if a is invertible and s m n n m with m n then a is normal the case when s m m n and a n a n a a n is also discussed

monotone matrix functions of two variables abstract monotone operator functions were studied by koranyi who generalised lowner s theorem on monotone matrix functions of arbitrary high order n to two variables an alternate proof of koranyi s representation of monotone operator functions is provided

operator means of probability measures abstract let p be the complete metric space consisting of positive invertible operators on an infinite dimensional hilbert space with the thompson metric we introduce the notion of operator means of probability measures on p in parallel with kubo and ando s definition of two variable operator means and show that every operator mean is contractive for the wasserstein distance by means of a fixed point method we consider deformation of such operator means and show that the deformation of any operator mean becomes again an operator mean in our sense based on this deformation procedure we prove a number of properties and inequalities for operator means of probability measures

spherical and hyperbolic embeddings of data many computer vision and pattern recognition problems may be posed as the analysis of a set of dissimilarities between objects for many types of data these dissimilarities are not euclidean i e they do not represent the distances between points in a euclidean space and therefore cannot be isometrically embedded in a euclidean space examples include shape dissimilarities graph distances and mesh geodesic distances in this paper we provide a means of embedding such non euclidean data onto surfaces of constant curvature we aim to embed the data on a space whose radius of curvature is determined by the dissimilarity data the space can be either of positive curvature spherical or of negative curvature hyperbolic we give an efficient method for solving the spherical and hyperbolic embedding problems on symmetric dissimilarity data our approach gives the radius of curvature and a method for approximating the objects as points on a hyperspherical manifold without optimisation for objects which do not reside exactly on the manifold we develop a optimisation based procedure for approximate embedding on a hyperspherical manifold we use the exponential map between the manifold and its local tangent space to solve the optimisation problem locally in the euclidean tangent space this process is efficient enough to allow us to embed data sets of several thousand objects we apply our method to a variety of data including time warping functions shape similarities graph similarity and gesture similarity data in each case the embedding maintains the local structure of the data while placing the points in a metric space

quantum correlations and distinguishability of quantum states a survey of various concepts in quantum information is given with a main emphasis on the distinguishability of quantum states and quantum correlations covered topics include generalized and least square measurements state discrimination quantum relative entropies the bures distance on the set of quantum states the quantum fisher information the quantum chernoff bound bipartite entanglement the quantum discord and geometrical measures of quantum correlations the article is intended both for physicists interested not only by collections of results but also by the mathematical methods justifying them and for mathematicians looking for an up to date introductory course on these subjects which are mainly developed in the physics literature

dynamic programming alignment of sequences representing cyclic patterns string alignment by dynamic programming is generalized to include cyclic shift and corresponding optimal alignment cost for strings representing cyclic patterns a guided search algorithm uses bounds on alignment costs to find all optimal cyclic shifts the bounds are derived from submatrices of an initial dynamic programming matrix algorithmic complexity is analyzed for major stages in the search the applicability of the method is illustrated with satellite dna sequences and circularly permuted protein sequences

phase only filtering for the masses of dna data a new approach to sequence alignment alignment of dna segments containing repetitive nucleotide base patterns is an important task in several genomics applications including dna sequencing dna fingerprinting pathogen detection and gene finding one of the most efficient procedures used for this task is the cross correlation method the main computations of the procedure are the discrete fourier transform dft and a pointwise multiplication of two complex fourier transform sequences in this paper the standard magnitude and phase cross correlation technique is compared with the lesser known but closely related phase only cross correlation method it is shown that for a periodic dna sequence the standard approach leads to significant sidelobes in the cross correlation the magnitude of which increases with sequence length while the phase only approach yields a perfect cross correlation with zero sidelobes for a dna sequence that contains both irregularly distributed symbols and periodic patterns the difference in performance is less pronounced but still significant numerical experiments on synthesized and real data demonstrate that the phase only approach is robust to isolated symbol insertions and deletions and that it is capable of identifying positions of matching segments in the sequence

a matrix convexity approach to some celebrated quantum inequalities abstract some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the hansen pedersen jensen inequalities a general argument is given using matrix perspectives of operator convex functions a matrix analogue of marechal s extended perspectives provides additional inequalities including a p q 1 result of lieb

algorithms for approximate string matching the edit distance between strings a 1 a m and b 1 b n is the minimum cost s of a sequence of editing steps insertions deletions changes that convert one string into the other a well known tabulating method computes s as well as the corresponding editing sequence in time and in space o mn in space o min m n if the editing sequence is not required starting from this method we develop an improved algorithm that works in time and in space o s min m n another improvement with time o s min m n and space o s min s m n is given for the special case where all editing steps have the same cost independently of the characters involved if the editing sequence that gives cost s is not required our algorithms can be implemented in space o min s m n since s o max m n the new methods are always asymptotically as good as the original tabulating method as a by product algorithms are obtained that given a threshold value t test in time o t min m n and in space o min t m n whether s t finally different generalized edit distances are analyzed and conditions are given under which our algorithms can be used in conjunction with extended edit operation sets including for example transposition of adjacent characters

operator monotone functions jacobi operators and orthogonal polynomials abstract we reveal a connection between operator monotone functions and orthogonal polynomials especially we express an operator monotone function with a jacobi operator and show that it is a limit of rational operator monotone functions further we prove that the principal inverse of an orthogonal polynomial is operator monotone and hence it has a holomorphic extension to the open upper half plane namely a pick function or nevanlinna function

the ando hiai inequalities for the solution of the generalized karcher equation and related results abstract in this paper we shall give a concrete relation between the generalized karcher equation and operator means as its solution next we shall show two types of the ando hiai inequalities for the solution of the generalized karcher equation in this discussion we also give a property of relative operator entropy

matrix convexity of functions of two variables abstract let i j be intervals such that 0 i j let mm be the algebra of all m m complex matrices and let mm i be the set of all hermitian members of mm whose spectrum is contained in i let m be the set of all hermitian projections in mm we give a complete characterization of the set of functions f i j r which satisfy the inequality p q f pap qbq p q p q f a b p q for all a m m i b mn j p m q n we also generalize some results on matrix convexity of functions of one variable to the case of functions of two variables

higher adeles and non abelian riemann roch abstract we show a riemann roch theorem for group ring bundles over an arithmetic surface this is expressed using the higher adeles of beilinson parshin and the tame symbol via a theory of adelic equivariant chow groups and chern classes the theorem is obtained by combining a group ring coefficient version of the local riemann roch formula as in kapranov vasserot with results on k groups of group rings and an explicit description of group ring bundles over p 1 our set up provides an extension of several aspects of the classical frohlich theory of the galois module structure of rings of integers of number fields to arithmetic surfaces

monge properties of sequence alignment alignment is an important sequence comparison measure algorithms that compute alignments have a wide range of applications namely in bioinformatic tools alignments can be computed as maximum scoring paths in alignment dags in this paper we study the properties of matrices that contain alignment scores between a string and all the sub strings of another string we focus on the fact that these matrices have the monge property and are sparse in some sense related studies were recently presented for hsm and dist matrices leading to o nlogn procedure for multiplying those matrices where o n bounds the sizes of the strings our results strictly generalize previous solutions we measure the sparseness of the matrices with variable d and present an algorithm for matrix multiplication in o email protected log 3 email protected time which we improve to o email protected log 2 email protected within the same space we discuss applications of this algorithm namely fully incremental alignment and alignment update we study experimentally the performance of the methods we propose

the convex concave characteristics of gaussian channel capacity functions in this correspondence we give several inherent properties of the capacity function of a gaussian channel with and without feedback by using some operator inequalities and matrix analysis we give a new proof method which is different from the method appearing in k yanagi and h w chen operator inequality and its application to information theory taiwanese j math vol 4 no 3 pp 407 416 sep 2000 we obtain the following results c sub n z p and c sub n fb z p are both concave functions of p c sub n z p is a convex function of the noise covariance matrix and c sub n fb z p is a convex like function of the noise covariance matrix this new proof method is very elementary and the results shall help study the capacity of gaussian channel finally we state a conjecture concerning the convexity of c sub n fb spl middot p

inverse functions of polynomials and orthogonal polynomials as operator monotone functions we study the operator monotonicity of the inverse of every polynomial with a positive leading coefficient let p n n o be a sequence of orthonormal polynomials and p n the restriction of p n to a n where a n is the maximum zero of p n then p 1 n and the composite p n 1 o p 1 n are operator monotone on 0 furthermore for every polynomial p with a positive leading coefficient there is a real number a so that the inverse function of p t a p a defined on 0 oo is semi operator monotone that is for matrices a b 0 p a a p a 2 p b a p a 2 implies a 2 b 2

concavity of some operator functions and frechet differential mappings abstract by using operator perspectives of regular operator mappings we obtain some operator concave convex functions and derive the concavity convexity of some trace functions associated with the frechet differential mapping of certain power functions especially we explore the concavity of the frechet differential mapping x d g x d f x 1 in positive definite invertible operators with f t t p for 0 p 1 and g t t q for p q p 1 and also with f t log t and g t t q for 0 q 1

quantum f divergences in von neumann algebras ii maximal f divergences as a continuation of the study by hiai j math phys 59 102202 2018 on standard f divergences we make a systematic study of maximal f divergences in general von neumann algebras for maximal f divergences apart from their definition based on haagerup s l1 space we present the general integral expression and the variational expression in terms of reverse tests from these expressions as well as the definition we prove important properties of maximal f divergences for instance the monotonicity inequality the joint convexity the lower semicontinuity and the martingale convergence the inequality between the standard and the maximal f divergences is also given as a continuation of the study by hiai j math phys 59 102202 2018 on standard f divergences we make a systematic study of maximal f divergences in general von neumann algebras for maximal f divergences apart from their definition based on haagerup s l1 space we present the general integral expression and the variational expression in terms of reverse tests from these expressions as well as the definition we prove important properties of maximal f divergences for instance the monotonicity inequality the joint convexity the lower semicontinuity and the martingale convergence the inequality between the standard and the maximal f divergences is also given

modulus of convexity for operator convex functions given an operator convex function f x we obtain an operator valued lower bound for cf x 1 c f y f cx 1 c y c 0 1 the lower bound is expressed in terms of the matrix bregman divergence a similar inequality is shown to be false for functions that are convex but not operator convex

an order inequality characterizing invariant barycenters on symmetric cones abstract this paper is concerned with invariant and contractive barycenters on the wasserstein space of probability measures on metric spaces of non positive curvature where the center of gravity also called the cartan barycenter is the canonical barycenter on hadamard spaces we establish an order inequality of probability measures on partially ordered symmetric spaces of non compact type namely symmetric cones self dual homogeneous cones characterizing the cartan barycenter among other invariant and contractive barycenters the derived inequality and partially ordered structures on the probability measure space lead also to significant results on norm inequalities including the ando hiai inequality for probability measures on symmetric cones

k1 of a p adic group ring i the determinantal image abstract we study the k group k 1 of the group ring for a finite group over a coefficient ring which is p adically complete and admits a lift of frobenius in this paper we consider the image of k 1 under the determinant map the central tool is the group logarithm which we can define using the frobenius lift using this we prove a fixed point theorem for the determinantal image of k 1

higher order extension of lowner s theory operator k tone functions the new notion of operator matrix k tone functions is introduced which is a higher order extension of operator matrix monotone and convex functions differential properties of matrix k tone functions are shown characterizations properties and examples of operator k tone functions are presented in particular integral representations of operator k tone functions are given generalizing familiar representations of operator monotone and convex functions

fast object recognition using dynamic programming from combination of salient line groups this paper presents a new method of grouping and matching line segments to recognize objects we propose a dynamic programming based formulation extracting salient line patterns by defining a robust and stable geometric representation that is based on perceptual organizations as the endpoint proximity we detect several junctions from image lines we then search for junction groups by using the collinear constraint between the junctions junction groups similar to the model are searched in the scene based on a local comparison a dp based search algorithm reduces the time complexity for the search of the model lines in the scene the system is able to find reasonable line groups in a short time

longest common subsequence problem for unoriented and cyclic strings given a finite set of strings x the longest common subsequence problem lcs consists in finding a subsequence common to all strings in x that is of maximal length lcs is a central problem in stringology and finds broad applications in text compression conception of error detecting codes or biological sequence comparison however in numerous contexts words represent cyclic or unoriented sequences of symbols and lcs must be generalized to consider both orientations and or all cyclic shifts of the strings involved this occurs especially in computational biology when genetic material is sequenced from circular dna or rna molecules in this work we define three variants of lcs when the input words are unoriented and or cyclic we show that these problems are np hard and w 1 hard if parameterized in the number of input strings these results still hold even if the three lcs variants are restricted to input languages over a binary alphabet we also settle the parameterized complexity of our problems for most relevant parameters moreover we study the approximability of these problems we discuss the existence of approximation bounds depending on the cardinality of the alphabet on the length of the shortest sequence and on the number of input sequences for this we prove that maximum independent set in r uniform hypergraphs is w 1 hard if parameterized in the cardinality of the sought independent set and at least as hard to approximate as maximum independent set in graphs

a unified approach to operator monotone functions abstract the notion of operator monotonicity dates back to a work by lowner in 1934 a map f s n s m is called operator monotone if a b implies f a f b here s n is the space of symmetric matrices with the semidefinite partial order often the function f is defined in terms of an underlying simpler function f of main interest is to find the properties of f that characterize operator monotonicity of f in that case it is said that f is also operator monotone classical examples are the lowner operators and the spectral scalar valued isotropic functions operator monotonicity for these two classes of functions is characterized in seemingly very different ways this work extends the notion of operator monotonicity to symmetric functions f on k arguments the latter is used to define generated k isotropic maps f s n s n k for any n k necessary and sufficient conditions are given for f to generate an operator monotone k isotropic map f when k 1 the k isotropic map becomes a lowner operator and when k n it becomes a spectral function this allows us to reconcile and explain the differences between the conditions for monotonicity for the lowner operators and the spectral functions

on a correspondence between regular and non regular operator monotone functions abstract we prove the existence of a bijection between the regular and the non regular operator monotone functions satisfying a certain functional equation as an application we give a new proof of the operator monotonicity of certain functions related to the wigner yanase dyson skew information

some results on matrix monotone functions abstract let a and b be hermitian matrices we say that a b if a b is nonnegative definite a function 0 r is said to be matrix monotone m m if a b 0 implies that a b matrix convex and concave functions can be similarly defined in this paper several known results some in sharper forms are given alternative proofs these include the following a a positive function t is m m iff t t is m m b if t is m m then both t t and t t are matrix convex and are almost always strictly convex on the other hand t is always concave and almost always strictly concave the concavity of m m functions and an inequality of hansen are consequences of a more general inequality on m m functions some complementary inequalities are also established we then prove an extension of lyapunov s theorem let a and p be positive definite matrices and either or 1 be a m m function then the unique matrix solution x of the matrix equation ax xa a p p a is positive definite a similar result holds for a related equation most of the results are obtained by exploiting the integral representation of m m functions

an extension of inequalities by ando abstract we give variations on ando s result comparing f b f a and f b a with respect to unitarily invariant norms on matrices

polygonal shape recognition using string matching techniques in this paper we study several aspects of the use of string matching techniques as an approach to the problem of recognizing and classifying polygons several authors have already proposed methods for polygon recognition that are based on string matching in many cases however linear strings are used to represent polygons which makes it difficult to handle different orientations of an object efficiently we can however easily extend the linear string matching techniques to cyclic strings at some small computational cost we will propose a method to represent polygons as cyclic strings and we will show how cyclic string matching techniques can be used for rotation translation and scale independent polygonal shape recognition we will however also point out the limitations of such an approach

jensen and minkowski inequalities for operator means and anti norms abstract jensen inequalities for positive linear maps of choi and hansen pedersen type are established for a large class of operator matrix means such as some p means and some kubo ando means these results are also extensions of the minkowski determinantal inequality to this end we develop the study of anti norms a notion parallel to the symmetric norms in matrix analysis including functionals like schatten q norms for a parameter q 1 and the minkowski functional det 1 n a

operator inequalities from a general theorem to concrete inequalities abstract the aim of this paper is to give a method to extract concrete inequalities from a general theorem which is established by making use of majorization relation between functions by this method we can get a lot of inequalities among others we extend furuta inequality as follows let f i g j be positive operator monotone functions on 0 and put k t t r 0 f 1 t r 1 f m t r m h t t p 0 g 1 t p 1 g n t p n where p 0 1 and r i 0 p j 0 then 0 a c b implies for 0 1 r 0 p r 0 with p p 0 p n k c 1 2 h a k c 1 2 k c 1 2 h c k c 1 2 k c 1 2 h b k c 1 2 moreover we show log c 1 2 e a c 1 2 log c 1 2 e c c 1 2 log c 1 2 e b c 1 2 provided c is invertible we also refer to operator geometric mean

an improved algorithm for solving the banded cyclic string to string correction problem the banded cyclic string to string correction bcssc problem is a generalized version of the cyclic string to string correction cssc problem and has some applications in stereo matching and speech recognition this note presents an improved algorithm for solving the bcssc problem and the time complexity required ranges from o nm to o nm log b where n and m are the lengths of the two strings and b is the allowable bandwidth the result of this paper generalizes the result of gregor and thomason 1996 for solving the cssc problem since the special version of the bcssc problem can be transformed into the cssc problem when setting b m

superadditivity and derivative of operator functions abstract we will show that if i j a i a j 0 for bounded operators a i 0 i 1 2 n then g i a i i g a i for every operator convex function g t on 0 with g 0 0 in particular i a i log i a i i a i log a i if each a i is invertible let a b 0 and a be invertible then we will observe that the frechet derivative d g s a b is increasing on 0 s for every operator convex function g t on 0 if and only if a b b a 0

attributed string matching with merging for shape recognition a new structural approach to shape recognition using attributed string matching with merging is proposed after illustrating the disadvantages of conventional symbolic string matching using changes deletions and insertions attributed strings are suggested for matching each attributed string is an ordered sequence of shape boundary primitives each representing a basic boundary structural unit line segment with two types of numerical attributes length and direction a new type of primitive edit operation called merge is then introduced which can be used to combine and then match any number of consecutive boundary primitives in one shape with those in another the resulting attributed string matching with merging approach is shown useful for recognizing distorted shapes experimental results prove the feasibility of the proposed approach for general shape recognition some possible extensions of the approach are also included

monotone metrics on matrix spaces abstract the study of monotone inner products under stochastic mappings on the space of matrices was initiated by morozova and chentsov motivated by information geometry they did not show a monotone metric but proposed several candidates the main result of the present paper is to provide an abundance of monotone metrics by means of operator monotone functions and to characterize them it turns out that there is a correspondence between monotone metrics and operator means in the sense of kubo and ando it follows that all proposals of morozova and chentsov are indeed monotone metrics

localizing overlapping parts by searching the interpretation tree this paper discusses how local measurements of positions and surface normals may be used to identify and locate overlapping objects the objects are modeled as polyhedra or polygons having up to six degrees of positional freedom relative to the sensors the approach operates by examining all hypotheses about pairings between sensed data and object surfaces and efficiently discarding inconsistent ones by using local constraints on distances between faces angles between face normals and angles relative to the surface normals of vectors between sensed points the method described here is an extension of a method for recognition and localization of nonoverlapping parts previously described in 18 and 15

efficient dynamic programming alignment of cyclic strings by shift elimination abstract optimal alignment of two strings of length m and n is computed in time o mn by dynamic programming when the strings represent cyclic patterns the alignment computation must consider all possible shifts and the computation complexity increases accordingly we present an algorithm for efficient dynamic programming alignment of cyclic strings which uses a previously established channeling technique to reduce the complexity of each alignment and a new shift elimination technique to reduce the number of alignments carried out the result is a data dependent time complexity that varies between o 2 mn and o mn log 2 n an experimental evaluation is provided using randomly generated sequences

uncertainty principle and quantum fisher information ii heisenberg and schrodinger uncertainty principles give lower bounds for the product of variances var a var b if the observables a b are not compatible namely if the commutator a b is not zero in this paper we prove an uncertainty principle in schrodinger form where the bound for the product of variances var a var b depends on the area spanned by the commutators i a and i b with respect to an arbitrary quantum version of the fisher information

the fast track to lowner s theorem abstract the operator monotone functions defined in the positive half line are of particular importance we give a version of the theory in which integral representations for these functions can be established directly without invoking lowner s detailed analysis of matrix monotone functions of a fixed order or the theory of analytic functions we found a canonical relationship between positive and arbitrary operator monotone functions defined in the positive half line and this result effectively reduces the theory to the case of positive functions

robust symbolic representation for shape recognition and retrieval a new method for shape recognition and retrieval is proposed here the suggested algorithm is based on several steps the algorithm analyzes the contour of pairs of shapes their contours are recovered and represented by a pair of n points obtained by linear interpolation given two points p i and q j from the two shapes the cost of their matching is evaluated by using the shape context and by using dynamic programming the best matching between the point sets is obtained dynamic programming not only recovers the best matching but also identifies occlusions i e points in the two shapes which cannot be properly matched given the correspondence between the two point sets the two contours are aligned using procrustes analysis after alignment each contour is transformed into a string of symbols and a modified version of edit distance is used to compute the similarity between strings of symbols finally recognition and retrieval are obtained by a simple nearest neighbor procedure the algorithm has been tested on a large set of shape databases kimia mpeg 7 natural silhouette database gesture database marine database swedish leaf database diatom database eth 80 3d object database providing performances for both in recognition and in retrieval superior to most of previously proposed approaches

a characterization of extended monotone metrics abstract classical information geometry has emerged from the study of geometrical aspect of the statistical estimation cencov characterized the fisher metric as a canonical metric on probability simplexes s n 1 x 1 x n r n x i 1 from a statistical point of view and campbell extended the characterization of the fisher metric from probability simplexes to positive cone r n in quantum information geometry quantum states which are represented by positive hermitian matrices with trace one are regarded as an extension of probability distributions a quantum version of the fisher metric is introduced and is called a monotone metric petz characterized the monotone metrics on the space of all quantum states in terms of operator monotone functions a purpose of the present paper is to extend a characterization of monotone metrics from the space of all states to the space of all positive hermitian matrices on finite dimensional hilbert space this characterization corresponds quantum modification of campbell s work

finite blocklength and moderate deviation analysis of hypothesis testing of correlated quantum states and application to classical quantum channels with memory martingale concentration inequalities constitute a powerful mathematical tool in the analysis of problems in a wide variety of fields ranging from probability and statistics to information theory and machine learning here we apply techniques borrowed from this field to quantum hypothesis testing which is the problem of discriminating quantum states belonging to two different sequences rho n n and sigma n n we obtain achievability bounds on the finite blocklength type ii stein and hoeffding errors which for i i d states are in general tighter than the corresponding bounds obtained by audenaert mosonyi and verstraete we also derive finite blocklength bounds and moderate deviation results for pairs of sequences of correlated states satisfying a non homogeneous factorization property examples of such sequences include gibbs states of spin chains with translation invariant finite range interaction as well as finitely correlated quantum states we apply our results to find bounds on the capacity of a certain class of classical quantum channels with memory which satisfy a so called channel factorization property both in the finite blocklength and moderate deviation regimes

trace functions with applications in quantum physics we consider both known and not previously studied trace functions with applications in quantum physics by using perspectives we obtain convexity statements for different notions of residual entropy including the entropy gain of a quantum channel studied by holevo and others

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

inequalities for the wasserstein mean of positive definite matrices abstract we prove majorization inequalities for different means of positive definite matrices these include the cartan mean the karcher mean the log euclidean mean the wasserstein mean and the power mean

on generalized powers stormer s inequality abstract a generalization of powers stormer s inequality for operator monotone functions on 0 and for positive linear functional on general c algebras will be proved it also will be shown that the generalized powers stormer inequality characterizes the tracial functionals on c algebras

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

some convex and monotone matrix functions we prove some matrix monotonicity and matrix convexity properties for functions derived from operator connections as a consequence we prove that a certain product of matrix monotone functions is a matrix monotone function similar results are proved for matrix convex functions these results include some known results for matrix monotone and matrix convex functions

some results on strongly operator convex functions and operator monotone functions abstract this paper concerns three classes of real valued functions on intervals operator monotone functions operator convex functions and strongly operator convex functions strongly operator convex functions were previously treated in 3 and 4 where operator algebraic semicontinuity theory or operator theory were substantially used in this paper we provide an alternate treatment that uses only operator inequalities or even just matrix inequalities we show also that if t 0 is a point in the domain of a continuous function f then f is operator monotone if and only if f t f t 0 t t 0 is strongly operator convex using this and previously known results we provide some methods for constructing new functions in one of the three classes from old ones we also include some discussion of completely monotone functions in this context and some results on the operator convexity or strong operator convexity of f when f is operator convex or strongly operator convex

loewner s theorem in several variables abstract in this paper we establish a multivariable non commutative generalization of loewner s theorem characterizing operator monotone functions as real functions admitting analytic continuation mapping the upper complex half plane into itself the non commutative several variable theorem proved here represents several variable operator monotone functions of positive operator tuples not a priori assumed to be analytic or continuous as a schur complement of a positive linear matrix pencil to achieve this we establish the abstract integral formula for these functions using only matrix convexity and lmis that represents operator monotone and operator concave free functions as a conditional expectation of a schur complement of a linear matrix pencil on a tensor product operator algebra the results can be applied to any of the various multivariable operator means that have been constructed in the last decades or so including the karcher mean to obtain an explicit closed formula for these operator means

flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes curve matching is one instance of the fundamental correspondence problem our flexible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations a syntactic representation is constructed for both curves and an edit transformation which maps one curve to the other is found using dynamic programming we present extensive experiments where we apply the algorithm to silhouette matching in these experiments we examine partial occlusion viewpoint variation articulation and class matching where silhouettes of similar objects are matched based on the qualitative syntactic matching we define a dissimilarity measure and we compute it for every pair of images in a database of 121 images we use this experiment to objectively evaluate our algorithm first we compare our results to those reported by others second we use the dissimilarity values in order to organize the image database into shape categories the veridical hierarchical organization stands as evidence to the quality of our matching and similarity estimation

equilateral polygon approximation of closed contours numerous algorithms have been suggested for computing polygonal approximations of closed contours we present an algorithm which as a unique feature creates polygons which are equilateral that is whose edges are all of the same length this allows one dimensional shape descriptions to be derived using the interior polygon angles conceptually the algorithm is an optimization framework for finding the minimum energy configuration of a mechanical system of particles and springs that represent the contour points the polygon vertices and their interaction in practice the dominant points are detected on the gaussian smoothed contour and used to seed an initial polygon nonlinear programming is then used to minimize the system energy subject to the constraint that adjacent vertices must be equidistant the objective function is the sum of a curvature weighted distance between each vertex and a set of contour points associated therewith experimental results are given for closed contours obtained from grey scale images

sk 1 of finite abelian groups i g which can be used both for specific computations and to prove general theo rems for certain classes of groups d st2 in collaboration with oliver we have greatly extended the power of our computational methods the results of all computations as well as the ad ditional methods leading to them will appear in the sequel a d o s to this paper in a future issue of inventiones there we derive a very efficient algo rithm for computing

on matrix inequalities between the power means counterexamples abstract we prove that the known sufficient conditions on the real parameters p q for which the matrix power mean inequality a p b p 2 1 p a q b q 2 1 q holds for every pair of matrices a b 0 are indeed best possible the proof proceeds by constructing 2 2 counterexamples the best possible conditions on p q for which a p 1 p a q 1 q holds for every unital positive linear map and a 0 are also clarified

dynamic programming for detecting tracking and matching deformable contours the problem of segmenting an image into separate regions and tracking them over time is one of the most significant problems in vision terzopoulos et al 1987 proposed an approach to detect the contour regions of complex shapes assuming a user selected initial contour not very far from the desired solution we propose to further explore the information provided by the user s selected points and apply an optimal method to detect contours which allows a segmentation of the image the method is based on dynamic programming dp and applies to a wide variety of shapes it is exact and not iterative we also consider a multiscale approach capable of speeding up the algorithm by a factor of 20 although at the expense of losing the guaranteed optimality characteristic the problem of tracking and matching these contours is addressed for tracking the final contour obtained at one frame is sampled and used as initial points for the next frame then the same dp process is applied for matching a novel strategy is proposed where the solution is a smooth displacement field in which unmatched regions are allowed while cross vectors are not the algorithm is again based on dp and the optimal solution is guaranteed we have demonstrated the algorithms on natural objects in a large spectrum of applications including interactive segmentation and automatic tracking of the regions of interest in medical images

applications of approximate string matching to 2d shape recognition abstract a new method for the recognition of arbitrary two dimensional 2d shapes is described it is based on string edit distance computation the recognition method is invariant under translation rotation scaling and partial occlusion a set of experiments are described demonstrating the robustness and reliability of the proposed approach

a generalization of araki s log majorization abstract we generalize araki s log majorization to the log convexity theorem for the eigenvalues of a p 1 2 b p a p 1 2 as a function of p 0 where a b are positive semidefinite matrices and are positive linear maps between matrix algebras similar generalizations of the log majorization of ando hiai type for the weighted geometric mean a b are also given including a lemma on general operator means a e of a and a projection e

on a reverse heinz kato furuta inequality abstract in the set up of minkowski spaces the schwarz inequality holds with the reverse inequality sign as a consequence the same occurs with the triangle inequality in this note extensions of this indefinite version of the schwarz inequality are presented namely a reverse heinz kato furuta inequality valid for timelike vectors is included and related inequalities that also hold with the reverse sign are investigated

operator means and positivity of block operators the aim of this paper is to find some sufficient conditions for positivity of block matrices of positive operators it is shown that for positive operators a b c and for every non negative operator monotone function f on 0 infty the block matrix begin aligned left begin array cc f a f c f c f b end array right end aligned is positive if and only if c le a b in particular if c le a b then begin aligned left begin array cc a c c b end array right end aligned is positive

mixed matrix operator inequalities we will show that if 0 a b c and s s t t 1 then a s bs t ct implies that ar 2 s bss t cst ar 2 ar 2 s bts t ctt ar 2 s r t r fort 1 t s 0 r 0 and a1 r ar 2 s bts t ctt ar 2 1 r t r fort 1 r 0 these are the extensions of inequalities shown by t furuta proc amer math soc 101 1987 85 111 1991 511 moreover we will give an inequality say mixed inequality which includes the above inequalities and the inequality due to hansen pedersen math ann 258 1982 229

an operator monotone function tlogt t 1log2t and strictly chaotic order we consider the function f t defined by f t tlogt t 1log2t firstly we shall show direct and simplified proofs of operator monotonicity of f t and its dual function f t tlog2ttlogt t 1 without appealing of lowner theorem then we shall show the following loga logb thereexists 0 1 suchthatf a f b holds forall 0 by using the result we summarize the following interesting contrast between a b 0 and a b 0 a b 0 thereexists 0 1 suchthatf a f b holds i forall 0 ii a b 0 f a f b forall 0 1 finally we cite a counterexample related to as follows thereexiststritlypositiveoperatorsaandbsuchthatloga logb c butf a f b doesnotholdforany 0

the hasegawa petz mean properties and inequalities abstract we study a family of means introduced by h hasegawa and d petz 1996 13 properties with respect to the parameter such as monotonicity and logarithmic concavity further monotonicity and concavity in the mean variables are shown besides the comparison between the hasegawa petz mean and the geometric mean is completely solved the connection to earlier results on operator monotonicity and some applications are also discussed

strong converse for identification via quantum channels we present a simple proof of the strong converse for identification via discrete memoryless quantum channels based on a novel covering lemma the new method is a generalization to quantum communication channels of ahlswede s 1979 1992 approach to classical channels it involves a development of explicit large deviation estimates to the case of random variables taking values in self adjoint operators on a hilbert space this theory is presented separately in an appendix and we illustrate it by showing its application to quantum generalizations of classical hypergraph covering problems

perspectives of matrix convex functions in this paper we generalize the main results of effros eg 2009 proc natl acad sci usa 106 1006 1008 namely we provide the necessary and sufficient conditions for jointly convexity of perspective functions and generalized perspective functions

edit distance based kernel functions for structural pattern classification a common approach in structural pattern classification is to define a dissimilarity measure on patterns and apply a distance based nearest neighbor classifier in this paper we introduce an alternative method for classification using kernel functions based on edit distance the proposed approach is applicable to both string and graph representations of patterns by means of the kernel functions introduced in this paper string and graph classification can be performed in an implicit vector space using powerful statistical algorithms the validity of the kernel method cannot be established for edit distance in general however by evaluating theoretical criteria we show that the kernel functions are nevertheless suitable for classification and experiments on various string and graph datasets clearly demonstrate that nearest neighbor classifiers can be outperformed by support vector machines using the proposed kernel functions

quantum data processing we prove a data processing inequality for quantum communication channels which states that processing a received quantum state may never increase the mutual information between input and output states