computationally efficient sine wave synthesis for acoustic waveform processing methods and apparatus for reducing discontinuities between frames of sinusoidally modeled acoustic waveforms such as speech which occur when sampling at low frame rates a fast fourier transform based overlap add technique is applied to amplitude frequency and phase components of sinusoidal waves after frame to frame sine wave matching has been performed matched sine wave amplitudes and frequencies are linearly interpolated and mid point phase is estimated such that the mid frame sine wave is best fit to the most recent half frame segments of the lagging and leading sine waves synthetic mid frame sine waves are generated using the interpolated amplitude and frequency and estimated phase values synthesized acoustic waveforms of high quality from original source waveforms can be produced in sinusoidal analysis synthesis operations at coding frame rates of 50 hz and lower the methods and devices disclosed herein are particularly useful for computationally efficient coding and synthesis of speech waveforms

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

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

encoding and synthesis of tonal audio signals using dominant sinusoids and a vector quantized residual tonal signal tonal audio signals can be modeled as a sum of sinusoids with time varying frequencies amplitudes and phases an efficient encoder and synthesizer of tonal audio signals is disclosed the encoder determines time varying frequencies amplitudes and optionally phases for a restricted number of dominant sinusoid components of the tonal audio signal to form a dominant sinusoid parameter sequence these components are removed from the tonal audio signal to form a residual tonal signal the residual tonal signal is encoded using a residual tonal signal encoder rtse in one embodiment the rtse generates a vector quantization codebook vqc and residual codebook sequence rcs the vqc may contain time domain residual waveforms selected from the residual tonal signal synthetic time domain residual waveforms with magnitude spectra related to the residual tonal signal magnitude spectrum encoding vectors or a combination of time domain waveforms and magnitude spectrum encoding vectors the tonal audio signal synthesizer uses a sinusoidal oscillator bank to synthesize a set of dominant sinusoid components from the dominant sinusoid parameter sequence generated during encoding in one embodiment a residual tonal signal is synthesized using a vqc and rcs generated by the rtse during encoding if the vqc includes time domain waveforms an interpolating residual waveform oscillator may be used to synthesize the residual tonal signal the synthesized dominant sinusoids and synthesized residual tonal signal are summed to form the synthesized tonal audio signal

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

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

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

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

musical synthesizer combining deterministic and stochastic waveforms a musical sound analyzer and synthesizer uses a model that considers a sound to be composed of two types of elements a deterministic component plus a stochastic component the deterministic component is represented as a series of sinusoids with an amplitude and a frequency function for each sinusoid the stochastic component is represented as a series of magnitude spectral envelopes from this representation sounds can be synthesized that in the absence of modifications can behave as perceptual identities that is they are perceptually equal to the original sound in addition stored representations of sounds can be easily modified in a musical synthesizer to create a wide variety of new sounds

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

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

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

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

extremal binary self dual codes in this correspondence we investigate binary extremal self dual codes numerous extremal self dual codes and interesting self dual codes with minimum weight d 14 and 16 are constructed in particular the first extremal type i 86 43 16 code and new extremal self dual codes with weight enumerators which were not previously known to exist for lengths 40 50 52 and 54 are constructed we also determine the possible weight enumerators for extremal type i codes of lengths 66 100

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

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

a method for constructing self dual codes with an automorphism of order 2 in this paper we investigate binary self dual codes with an automorphism of order 2 with c cycles and f fixed points a method for constructing such codes using self orthogonal codes of length c and self dual codes of length f is presented we apply this method to construct extremal self dual codes of lengths 40 42 44 52 54 and 58 some of them have weight enumerators for which self dual codes were previously not known to exist we prove that there do not exist self dual 50 25 10 and 96 48 20 codes with an automorphism of order 2 with f fixed points for f 0 in their automorphism groups

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

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

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

inverse transform narrow band broad band sound synthesis an additive sound synthesis process for generating complex realistic sounds is realized in a computationally efficient manner in accordance with one aspect of the invention polyphony is efficiently achieved by dosing the energy of a given partial between separate transform sums corresponding to different channels in accordance with another aspect of the invention noise 87 is injected by randomly perturbing the phase of the sound either on a per partial basis or on a transform sum basis in the latter instance the phase is perturbed in different regions of the spectrum to a degree determined by the amount of energy present in the respective regions of the spectrum in accordance with yet another aspect of the invention a transform sum 83 representing a sound is processed in the transform domain to achieve with great economy effects achievable only at much greater expense outside the transform domain other transforms besides the fourier transform may be used to advantage for example use of the hartley transform produces comparable results but allows transforms to be computed at approximately twice the speed as the fourier transform

processing of acoustic waveforms a sinusoidal model for acoustic waveforms is applied to develop a new analysis synthesis technique which characterizes a waveform by the amplitudes frequencies and phases of component sine waves these parameters are estimated from a short time fourier transform rapid changes in the highly resolved spectral components are tracked using the concept of birth and death of the underlying sine waves the component values are interpolated from one frame to the next to yield a representation that is applied to a sine wave generator the resulting synthetic waveform preserves the general waveform shape and is perceptually indistinguishable from the original furthermore in the presence of noise the perceptual characteristics of the waveform as well as the noise are maintained the method and devices disclosed herein are particularly useful in speech coding time scale modification frequency scale modification and pitch modification

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

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

new extremal self dual codes of lengths 42 and 44 all extremal binary self dual codes of lengths 42 and 44 which have an automorphism of order 5 with eight independent cycles are obtained up to equivalence there are 109 inequivalent 42 21 8 codes with such an automorphism all 44 22 8 codes that are obtained have 29 different weight enumerators

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

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

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

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

shadow bounds for self dual codes conway and sloane 1990 have previously given an upper bound on the minimum distance of a singly even self dual binary code using the concept of the shadow of a self dual code we improve their bound finding that the minimum distance of a self dual binary code of length n is at most 4 n 24 4 except when n mod 24 22 when the bound is 4 n 24 6 we also show that a code of length a multiple of 24 meeting the bound cannot be singly even the same technique gives similar results for additive codes over gf 4 relevant to quantum coding theory

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

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

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

methods for generating the voiced portion of speech signals the pitch estimation method is improved sub integer resolution pitch values are estimated in making the initial pitch estimate the sub integer pitch values are preferably estimated by interpolating intermediate variables between integer values pitch regions are used to reduce the amount of computation required in making the initial pitch estimate pitch dependent resolution is used in making the initial pitch estimate with higher resolution being used for smaller values of pitch the accuracy of the voiced unvoiced decision is improved by making the decision dependent on the energy of the current segment relative to the energy of recent prior segments if the relative energy is low the current segment favors an unvoiced decision if high it favors a voiced decision voiced harmonics are generated using a hybrid approach some voiced harmonics are generated in the time domain whereas the remaining harmonics are generated in the frequency domain this preserves much of the computational savings of the frequency domain approach while at the same time improving speech quality voiced harmonics generated in the frequency domain are generated with higher frequency accuracy the harmonics are frequency scaled transformed into the time domain with a discrete fourier transform interpolated and then time scaled

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

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

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

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

some new extremal self dual codes with lengths 44 50 54 and 58 we construct extremal self dual codes with lengths 44 50 54 and 58 they have weight enumerators for which extremal codes were previously not known to exist two methods are used for constructing the codes using self dual codes of same or smaller length to obtain the codes we use a combinatorial optimization search

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

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

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

new extremal binary 44 22 8 codes one of the problems in coding theory is constructing self dual codes whose weight enumerators are not yet known to exist we use the concept of neighbors and construct extremal binary self dual 44 22 8 codes whose weight enumerators are not yet known to exist

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

a new upper bound on the minimal distance of self dual codes it is shown that the minimal distance d of a binary self dual code of length n or 74 is at most 2 n 6 10 this bound is a consequence of some new conditions on the weight enumerator of a self dual code obtained by considering a particular translate of the code called its shadow these conditions also enable one to find the highest possible minimal distance of a self dual code for all n or 60 to show that self dual codes with d or 22 with d or 8 exist precisely for n 24 32 and n or 26 and with d or 10 exist precisely for n or 46 and to show that there are exactly eight self dual codes of length 32 with d 8 several of the self dual codes of length 34 have trivial group this appears to be the smallest length where this can happen