a radial basis function algorithm with automatic model order determination we present a new radial basis function rbf algorithm for constructing nonlinear models from data that may be sparsely scattered in high dimensions we propose a simplified method for identifying function locations that is based on an approximation to the autocorrelation function local regions are now defined based on zero crossings of the modified autocorrelation contribution the resulting local spatiotemporal data appear to capture increased structure as evidenced by the reduced number of basis functions required to achieve algorithm convergence and the fact that the resulting approximations have significantly improved accuracy we prove a zero crossing lemma and convergence of the algorithm in the norm for continuous functions over a compact domain further we show that several hypotheses tests can be used to detect this convergence the model parameters and the number of basis functions are determined automatically from the given data the only user parameter is the confidence level of the hypothe

effective distance between nested margulis tubes we give sharp effective bounds on the distance between tori of fixed injectivityradius inside a margulis tube in a hyperbolic 3 manifold

quantum hypothesis testing with group symmetry the asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system we consider various asymptotic error exponents in connection with the problems of the chernoff bound the hoeffding bound and stein s lemma and derive bounds on these quantities in terms of their corresponding statistical distance measures a special emphasis is put on the comparison of the performances of group invariant and unrestricted measurements

the proper formula for relative entropy and its asymptotics in quantum probability umegaki s relative entropys trd logd logd of states and with density operatorsd andd respectively is shown to be an asymptotic exponent considered from the quantum hypothesis testing viewpoint it is also proved that some other versions of the relative entropy give rise to the same asymptotics as umegaki s one as a byproduct the inequality tra logab tra loga logb is obtained for positive definite matricesa andb

cusp geometry of fibered 3 manifolds let f be a surface and suppose that varphi colon f to f is a pseudo anosov homeomorphism fixing a puncture p of f the mapping torus m m varphi is hyperbolic and contains a maximal cusp c about the puncture p we show that the area and height of the cusp torus partial c is equal to the stable translation distance of varphi acting on the arc complex scr a f p up to an explicitly bounded multiplicative error our proof relies on elementary facts about the hyperbolic geometry of pleated surfaces in particular the proof of this theorem does not use any deep results from teichm uller theory kleinian group theory or the coarse geometry of scr a f p a similar result holds for quasi fuchsian manifolds n cong f times bbb r in that setting we find a combinatorial estimate for the area and height of the cusp annulus in the convex core of n up to explicitly bounded multiplicative and additive error as an application we show that covers of punctured surfaces induce quasi isometric embeddings of arc complexes

sandwiched renyi divergence satisfies data processing inequality sandwiched quantum renyi divergence has been recently defined in the independent works of wilde et al strong converse for the classical capacity of entanglement breaking channels preprint arxiv 1306 1586 2013 and muller lennert et al on quantum renyi entropies a new definition some properties and several conjectures preprint arxiv 1306 3142v1 2013 this new quantum divergence has already found applications in quantum information theory here we further investigate properties of this new quantum divergence in particular we show that sandwiched renyi divergence satisfies the data processing inequality for all values of 1 moreover we prove that holevo information a variant of holevo information defined in terms of sandwiched renyi divergence is super additive our results are based on holder s inequality the riesz thorin theorem and ideas from the theory of complex interpolation we also employ sion s minimax theorem

general formulas for capacity of classical quantum channels the capacity of a classical quantum channel or in other words the classical capacity of a quantum channel is considered in the most general setting where no structural assumptions such as the stationary memoryless property are made on a channel a capacity formula as well as a characterization of the strong converse property is given just in parallel with the corresponding classical results of verdu han 1994 which are based on the so called information spectrum method the general results are applied to the stationary memoryless case with or without cost constraint on inputs whereby a deep relation between the channel coding theory and the hypothesis testing for two quantum states is elucidated

the coding theorem for a class of quantum channels with long term memory in this paper we consider the transmission of classical information through a class of quantum channels with long term memory which are convex combinations of memoryless channels hence the memory of such channels can be considered to be given by a markov chain which is aperiodic but not irreducible we prove the coding theorem and weak converse for this class of channels the main techniques that we employ are a quantum version of feinstein s fundamental lemma feinstein a 1954 ire trans pgit 4 2 22 khinchin a i 1957 mathematical foundations of information theory ii on the fundamental theorems of information theory new york dover chapter iv and a generalization of helstrom s theorem helstrom c w 1976 quantum detection and estimation theory mathematics in science and engineering vol 123 london academic

operator log convex functions and operator means we study operator log convex functions on 0 and prove that a continuous nonnegative function on 0 is operator log convex if and only if it is operator monotone decreasing several equivalent conditions related to operator means are given for such functions operator log concave functions are also discussed

zero crossing rates of mixtures and products of gaussian processes formulas for the expected zero crossing rate of non gaussian mixtures and products of gaussian processes are obtained the approach we take is to first derive the expected zero crossing rate in discrete time and then obtain the rate in continuous time by an appropriate limiting argument the processes considered which are non gaussian but derived from gaussian processes serve to illustrate the variability of the zero crossing rate in terms of the normalized autocorrelation function p t of the process for gaussian processes rice s formula gives the expected zero crossing rate in continuous time as 1 spl pi spl radic spl rho 0 we show processes exist with expected zero crossing rates given by spl kappa spl pi spl radic spl rho 0 with either spl kappa spl gt 1 or spl kappa spl lt 1 consequently such processes can have an arbitrarily large or small zero crossing rate as compared to a gaussian process with the same autocorrelation function

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

monotone gain first order autocorrelation and zero crossing rate autocorrelation of a weakly stationary time series is discussed when the gain is monotone increasing the first order autocorrelation cannot increase otherwise when the gain is monotone decreasing the correlation cannot decrease further when the gain is strictly monotone the first order autocorrelation is unchanged if and only if the process is a pure sinusoid with probability 1 under the gaussian assumption the zero crossing rate moves oppositely from the first order autocorrelation 1 introduction in this paper it is shown that when a weakly stationary process is filtered with a time invariant linear filter possessing a monotone increasing decreasing gain the first order autocorrelation cannot increase decrease if in addition the gain is strictly monotone the first order autocorrelation is unchanged if and only if the process is a pure sinusoid with probability 1 when the relationship between the autocorrelation and the zero crossing rate is known this can be translated into statements concerning the zero crossing rate the gaussian case is the best example kedem 1984 let zt t o 1 2 1 be a real valued zero mean stationary process with autocorrelation pk and spectral distribution function fgo 0 cl wr let denote a time invariant linear filter with transfer function h g satisfying the conditions that hg h w and that the squared gain ihgo 12 is integrable with respect to the distribution function f let pk h be the kth order autocorrelation of the filtered process y z t t 0 1

sufficient subalgebras and the relative entropy of states of a von neumann algebra a subalgebram 0 of a von neumann algebram is called weakly sufficient with respect to a pair of states if the relative entropy of and coincides with the relative entropy of their restrictions tom 0 the main result says thatm 0 is weakly sufficient for if and only ifm 0 contains the radon nikodym cocycle d d t other conditions are formulated in terms of generalized conditional expectations and the relative hamiltonian

zero crossing rates of functions of gaussian processes formulas for the expected zero crossing rates of random processes that are monotone transformations of gaussian processes can be obtained by using two different techniques the first technique involves derivation of the expected zero crossing rate for discrete time processes and extends the result of the continuous time case by using an appropriate limiting argument the second is a direct method that makes successive use of r price s 1958 theorem the chain rule for derivatives and s o rice s 1954 formula for the expected zero crossing rate of a gaussian process a constant which depends on the variance of the transformed process and a second moment of its derivative is derived multiplying rice s original expression by this constant yields the zero crossing formula for the transformed process the two methods can be used for the general level crossing problem of random processes that are monotone functions of a gaussian process

on the quantum renyi relative entropies and related capacity formulas following csiszar s approach in classical information theory it is shown that the quantum relative entropies with parameter 0 1 can be represented as generalized cutoff rates and hence a direct operational interpretation of the quantum relative entropies are provided it is also shown that various generalizations of the holevo capacity defined in terms of the relative entropies coincide for the parameter range 0 2 and an upper bound on the one shot e capacity of a classical quantum channel in terms of these capacities is given

generalized relative entropies and the capacity of classical quantum channels we provide lower and upper bounds on the information transmission capacity of one single use of a classical quantum channel the lower bound is expressed in terms of the hoeffding capacity which we define similarly to the holevo capacity but replacing the relative entropy with the hoeffding distance similarly our upper bound is in terms of a quantity obtained by replacing the relative entropy with the recently introduced max relative entropy in the definition of the divergence radius of a channel

strong converse exponents for a quantum channel discrimination problem and quantum feedback assisted communication this paper studies the difficulty of discriminating between an arbitrary quantum channel and a replacer channel that discards its input and replaces it with a fixed state the results obtained here generalize those known in the theory of quantum hypothesis testing for binary state discrimination we show that in this particular setting the most general adaptive discrimination strategies provide no asymptotic advantage over non adaptive tensor power strategies this conclusion follows by proving a quantum stein s lemma for this channel discrimination setting showing that a constant bound on the type i error leads to the type ii error decreasing to zero exponentially quickly at a rate determined by the maximum relative entropy registered between the channels the strong converse part of the lemma states that any attempt to make the type ii error decay to zero at a rate faster than the channel relative entropy implies that the type i error necessarily converges to one we then refine this latter result by identifying the optimal strong converse exponent for this task as a consequence of these results we can establish a strong converse theorem for the quantum feedback assisted capacity of a channel sharpening a result due to bowen furthermore our channel discrimination result demonstrates the asymptotic optimality of a non adaptive tensor power strategy in the setting of quantum illumination as was used in prior work on the topic the sandwiched renyi relative entropy is a key tool in our analysis finally by combining our results with recent results of hayashi and tomamichel we find a novel operational interpretation of the mutual information of a quantum channel mathcal n as the optimal type ii error exponent when discriminating between a large number of independent instances of mathcal n and an arbitrary worst case replacer channel chosen from the set of all replacer channels

asymptotic error rates in quantum hypothesis testing we consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies and find a closed form expression for the asymptotic exponential rate at which the error probability tends to zero this leads to the identification of the quantum generalisation of the classical chernoff distance which is the corresponding quantity in classical symmetric hypothesis testing

a quantum version of sanov s theorem we present a quantum version of sanov s theorem focussing on a hypothesis testing aspect of the theorem there exists a sequence of typical subspaces for a given set of stationary quantum product states asymptotically separating them from another fixed stationary product state analogously to the classical case the separating rate on a logarithmic scale is equal to the infimum of the quantum relative entropy with respect to the quantum reference state over the set while in the classical case the separating subsets can be chosen universally in the sense that they depend only on the chosen set of i i d processes in the quantum case the choice of the separating subspaces depends additionally on the reference state

strong converse and stein s lemma in quantum hypothesis testing the hypothesis testing problem for two quantum states is treated we show a new inequality between the errors of the first kind and the second kind which complements the result of hiai and petz 1991 to establish the quantum version of stein s lemma the inequality is also used to show a bound on the probability of errors of the first kind when the power exponent for the probability of errors of the second kind exceeds the quantum relative entropy which yields the strong converse in quantum hypothesis testing finally we discuss the relation between the bound and the power exponent derived by han and kobayashi 1989 in classical hypothesis testing

a strong converse for classical channel coding using entangled inputs a fully general strong converse for channel coding states that when the rate of sending classical information exceeds the capacity of a quantum channel the probability of correctly decoding goes to zero exponentially in the number of channel uses even when we allow code states which are entangled across several uses of the channel such a statement was previously only known for classical channels and the quantum identity channel by relating the problem to the additivity of minimum output entropies we show that a strong converse holds for a large class of channels including all unital qubit channels the d dimensional depolarizing channel and the werner holevo channel this further justifies the interpretation of the classical capacity as a sharp threshold for information transmission

dehn filling volume and the jones polynomial given a hyperbolic 3 manifold with torus boundary we bound the change in volume under a dehn filling where all slopes have length at least 2 this result is applied to give explicit diagrammatic bounds on the volumes of many knots and links as well as their dehn fillings and branched covers finally we use this result to bound the volumes of knots in terms of the coefficients of their jones polynomials

quasiconformal homeomorphisms and the convex hull boundary we investigate the relationship between an open simply connected region s 2 and the boundary y of the hyperbolic convex hull in h 3 of s 2 a counterexample is given to thurston s conjecture that these spaces are related by a 2 quasiconformal homeomorphism which extends to the identity map on their common boundary in the case when the homeomorphism is required to respect any group of mobius transformations which preserves we show that the best possible universal lipschitz constant for the nearest point retraction r y is 2 we find explicit universal constants 0 c 2 c 1 such that no pleating map which bends more than c 1 in some interval of unit length is an embedding and such that any pleating map which bends less than c 2 in each interval of unit length is embedded we show that every k quasiconformal homeomorphism d 2 d 2 is a k k quasi isometry where k is an explicitly computed function the multiplicative constant is best possible and the additive constant k is best possible for some values of k

on certain properties of the relative entropy of states of operator algebras the aim of the present paper is to establish certain properties of the relative entropy functional in the general context of c algebras most of these properties have been observed under more restrictive conditions in earlier papers the celebrated strong subadditivity of the entropy gives such an example the general approach is applied to prove the existence of the mean relative entropy for a noncommutative stationary markov chain with conditional expectations

continuity and relative hamiltonians let n n 1 be a norm convergent sequence of normal states on a von neumann algebraa with n let kn n 1 be a strongly convergent sequence of self adjoint elements ofa withkn k it is shown that the sequence omega n k n n geqq 1 of perturbed states converges in norm to a related result holds forc algebras a counter example is provided to show that it is not sufficient to assume weak convergence of n n 1 even whenkn k for alln however conditions are given which together with weak convergence are sufficient relative entropy methods are used and a relative entropy inequality is proved

strong converse to the quantum channel coding theorem a lower bound on the probability of decoding error for a quantum communication channel is presented from which the strong converse to the quantum channel coding theorem is immediately shown the results and their derivations are mostly straightforward extensions of the classical counterparts which were established by arimoto 1973 except that more careful treatment is necessary here due to the noncommutativity of operators

on the relative entropy fora any subset of the bounded operators on a hilbert space containing the unit and and restrictions of states on toa ent a the entropy of relative to given the information ina is defined and given an axiomatic characterisation it is compared with ent the relative entropy introduced by umegaki and generalised by various authors which is defined only fora an algebra it is proved that ent and ent s agree on pairs of normal states on an injective von neumann algebra it is also proved that ent always has all the most important properties known for ent s monotonicity concavity w upper semicontinuity etc

classical capacities of compound and averaged quantum channels we determine the capacity of compound classical quantum channels as a consequence we obtain the capacity formula for the averaged classical quantum channels the capacity result for compound channels demonstrates as in the classical setting the existence of reliable universal classical quantum codes in scenarios where the only a priori information about the channel used for the transmission of information is that it belongs to a given set of memoryless classical quantum channels our approach is based on a universal classical approximation of the quantum relative entropy which in turn relies on a universal hypothesis testing result

asymptotic distinguishability measures for shift invariant quasifree states of fermionic lattice systems we apply the recent results of hiai et al j math phys 49 032112 2008 to the asymptotic hypothesis testing problem of locally faithful shift invariant quasifree states on a car algebra we use a multivariate extension of szeg s theorem to show the existence of the mean chernoff and hoeffding bounds and the mean relative entropy and show that these quantities arise as the optimal error exponents in suitable settings

the capacity of the quantum channel with general signal states it is shown that the capacity of a classical quantum channel with arbitrary possibly mixed states equals the maximum of the entropy bound with respect to all a priori distributions this completes the recent result of hausladen jozsa schumacher westmoreland and wootters 1996 who proved the equality for the pure state channel

asymptotics of quantum relative entropy from a representation theoretical viewpoint in this paper it is proved that the quantum relative entropy d can be asymptotically attained by the relative entropy of probabilities given by a certain sequence of positive operator valued measures povms the sequence of povms depends on but is independent of the choice of

the level crossing and inverse statistic analysis of german stock market index dax and daily oil price time series a b s t r a c t the level crossing and inverse statistics analysis of dax and oil price time series are given we determine the average frequency of positive slope crossings where t 1 is the average waiting time for observing the level again we estimate the probability p k which provides us the probability of observing k times of the level with positive slope in time scale t for analyzed time series we found that maximum k is about 6 we show that by using the level crossing analysis one can estimate how the dax and oil time series will develop we carry out the same analysis for the increments of dax and oil price log returns which is known as inverse statistics and provide the distribution of waiting times to observe some level for the increments 2011 elsevier b v all rights reserved stochastic processes occur in many natural and man made phenomena ranging from various indicators of economic activities in the stock market velocity fluctuations in turbulent flows and heartbeat dynamics etc 1 the level crossing analysis of stochastic processes has been introduced by rice 1944 1945 2 26 and used to describe the turbulence 16 rough surfaces 27 stock markets 28 burgers turbulence and kardar parisi zhang equation 29 30 the level crossing analysis of the data set has the advantage that it gives important global properties of the time series and do not need the scaling feature the almost of the methods in time series analysis are using the scaling features of time series and their applications are restricted to the time series with scaling properties our goal with the level crossing analysis is to characterize the statistical properties of the data set with the hope to better understand the underlying stochastic dynamics and provide a possible tool to estimate its dynamics the level crossing and inverse statistics analysis can be viewed as the complementary method to the other well known methods such as detrended fluctuation analysis dfa 31 detrended moving average dma 32 wavelet transform modulus maxima wtmm 33 rescaled range analysis r s 34 scaled windowed variance swv 35 langevin dynamics 36 detrended cross correlation analysis 37 multifactor analysis of

on quantum renyi entropies a new generalization and some properties the renyi entropies constitute a family of information measures that generalizes the well known shannon entropy inheriting many of its properties they appear in the form of unconditional and conditional entropies relative entropies or mutual information and have found many applications in information theory and beyond various generalizations of renyi entropies to the quantum setting have been proposed most prominently petz s quasi entropies and renner s conditional min max and collision entropy however these quantum extensions are incompatible and thus unsatisfactory we propose a new quantum generalization of the family of renyi entropies that contains the von neumann entropy min entropy collision entropy and the max entropy as special cases thus encompassing most quantum entropies in use today we show several natural properties for this definition including data processing inequalities a duality relation and an entropic uncertainty relation

asymptotics of varadhan type and the gibbs variational principle for a large class of quantum models of mean field type the thermodynamic limit of the free energy density is proved to be given by the gibbs variational principle the latter is shown to be equivalent to a non commutative version of varadhan s asymptotic formula

strong converse exponent for classical quantum channel coding we determine the exact strong converse exponent of classical quantum channel coding for every rate above the holevo capacity our form of the exponent is an exact analogue of arimoto s given as a transform of the renyi capacities with parameters alpha 1 it is important to note that unlike in the classical case there are many inequivalent ways to define the renyi divergence of states and hence the renyi capacities of channels our exponent is in terms of the renyi capacities corresponding to a version of the renyi divergences that has been introduced recently in muller lennert et al j math phys 54 12 122203 2013 arxiv 1306 3142 and wilde et al commun math phys 331 2 593 622 2014 arxiv 1306 1586 our result adds to the growing body of evidence that this new version is the natural definition for the purposes of strong converse problems

the weil petersson metric and volumes of 3 dimensional hyperbolic convex cores we present a coarse interpretation of the weil petersson distance dwp x y between two finite area hyperbolic riemann surfaces x and y using a graph of pants decompositions introduced by hatcher and thurston the combinatorics of the pants graph reveal a connection between riemann surfaces and hyperbolic 3 manifolds conjectured by thurston the volume of the convex core of the quasi fuchsian manifold q x y with x and y in its conformal boundary is comparable to the weil petersson distance dwp x y in applications we relate the weil petersson distance to the hausdorff dimen sion of the limit set and the lowest eigenvalue of the laplacian for q x y and give a new finiteness criterion for geometric limits mathematics department university of chicago 5734 s university ave chicago il 60637 e mail address brock math uchicago edu

typical support and sanov large deviations of correlated states discrete stationary classical processes as well as quantum lattice states are asymptotically confined to their respective typical support the exponential growth rate of which is given by the maximal ergodic entropy in the iid case the distinguishability of typical supports can be asymptotically specified by means of the relative entropy according to sanov s theorem we give an extension to the correlated case referring to the newly introduced class of hp states

a study of locc detection of a maximally entangled state using hypothesis testing we study how well we can answer the question is the given quantum state equal to a certain maximally entangled state using locc in the context of hypothesis testing under several locality and invariance conditions optimal tests will be derived for several special cases by using basic theory of group representations some optimal tests are realized by performing quantum teleportation and checking whether the state is teleported we will also give a finite process for realizing some optimal tests the performance of the tests will be numerically compared

entropy and quantum kolmogorov complexity a quantum brudno s theorem in classical information theory entropy rate and algorithmic complexity per symbol are related by a theorem of brudno in this paper we prove a quantum version of this theorem connecting the von neumann entropy rate and two notions of quantum kolmogorov complexity both based on the shortest qubit descriptions of qubit strings that run by a universal quantum turing machine reproduce them as outputs

coding theorems for compound problems via quantum renyi divergences recently a new notion of quantum renyi divergences has been introduced by muller lennert dupuis szehr fehr and tomamichel and wilde winter and yang which found a number of applications in strong converse theorems here we show that these new renyi divergences are also useful tools to obtain coding theorems in the direct domain of various problems we demonstrate this by giving new and considerably simplified proofs for the achievability parts of stein s lemma with composite null hypothesis universal state compression and the classical capacity of compound classical quantum channels based on single shot error bounds already available in the literature and simple properties of the quantum renyi divergences the novelty of our proofs is that the composite compound coding theorems can be almost directly obtained from the single shot error bounds essentially with the same effort as for the case of simple null hypothesis single source single channel

exponential error rates in multiple state discrimination on a quantum spin chain we consider decision problems on finite sets of hypotheses represented by pairwise different shift invariant states on a quantum spin chain the decision in favor of one of the hypotheses is based on outcomes of generalized measurements performed on local states on blocks of finite size we assume the existence of the mean quantum chernoff distances of any pair of states from the given set and refer to the minimum of them as the mean generalized quantum chernoff distance we establish that this minimum specifies an asymptotic bound on the exponential rate of decay of the averaged probability of rejecting the true state in increasing block size if the mean quantum chernoff distance of any pair of the hypothetic states is achievable as an asymptotic error exponent in the corresponding binary problem this assumption is in particular fulfilled by shift invariant product states independent and identically distributed states further we provide a constructive proof for the existence of a sequence of quan

comments on zero crossing rates of functions of gaussian processes with reply an observation is made concerning the average zero crossing rate for some stationary random processes considered by barnett and kedem see ibid vol 37 no 4 p 1188 94 1991

two approaches to obtain the strong converse exponent of quantum hypothesis testing for general sequences of quantum states we present two general approaches to obtain the strong converse exponent of simple quantum hypothesis testing for correlated quantum states one approach requires that the states satisfy a certain factorization property typical examples of such states are the temperature states of translation invariant finite range interactions on a spin chain the other approach requires the differentiability of a regularized renyi alpha divergence in the parameter alpha typical examples of such states include temperature states of non interacting fermionic lattice systems and classical irreducible markov chains in all cases we get that the strong converse exponent is equal to the hoeffding anti divergence which in turn is obtained from the regularized renyi divergences of the two states

generalized framework for the level crossing analysis of ordered random processes this paper investigates the following general problem relating to ordered random processes given n independent but not necessarily identical random processes how frequently on average does any given process become one of the pth p 1 2 n 1 largest processes this is a fundamental problem arising in the design and analysis of contemporary multidimensional wireless communication systems e g multiantenna multiuser employing opportunistic selection we formulate this problem as one involving the level crossing rate lcr of a carefully defined ordered random process across the zero threshold which we solve by developing a new mathematical framework based on the theory of permanents for the case where the processes correspond to time varying rayleigh fading channels we present exact closed form formulas for the lcr simplified tight upper bounds as well as asymptotic results for n and p approaching infinity but with fixed ratio these results reveal interesting fundamental limits for the lcr and are shown to given meaningful insight even for small values of n and p we further use our mathematical framework to characterize the required per branch and overall switching rate of a generalized selection combining diversity receiver allowing for different average powers for each branch with the aid of majorization theory we demonstrate that the overall switching rate is maximized when the power delay profile is uniform

comments on new criteria for blind deconvolution of nonminimum phase systems channels with reply it is pointed out that certain criteria proposed in the paper by shalvi and weinstein see ibid vol 36 no 2 p 312 21 1990 have been proposed before in the context of real valued signals furthermore it is noted that the assertion made in the paper that all local maxima of the proposed criteria correspond to the desired equalizer solution holds true strictly speaking only for infinite length equalizers there exist counterexamples which show existence of false local maxima when finite length equalizers are used finally it is also noted that in the presence of additive gaussian noise of unknown power spectral density at the input to the equalizer equivalently at the channel output it is not clear if the methods proposed in the paper will yield the desired response up to a constant gain

a limit of the quantum renyi divergence recently an interesting quantity called the quantum renyi divergence or sandwiched renyi relative entropy was defined for pairs of positive semi definite operators and it depends on a parameter and acts as a parent quantity for other relative entropies which have important operational significance in quantum information theory the quantum relative entropy and the min and max relative entropies there is however another relative entropy called the 0 relative renyi entropy which plays a key role in the analysis of various quantum information processing tasks in the one shot setting we prove that the 0 relative renyi entropy is obtainable from the quantum renyi divergence only if and have equal supports this along with existing results in the literature suggests that it suffices to consider two essential parent quantities from which operationally relevant entropic quantities can be derived the quantum renyi divergence with parameter 1 2 and the relative renyi entropy with 0 1

hypothesis testing for gaussian states on bosonic lattices the asymptotic state discrimination problem with simple hypotheses is considered for a cubic lattice of bosons a complete solution is provided for the problems of the chernoff and the hoeffding bounds and stein s lemma in the case when both hypotheses are gaussian states with gauge and translation invariant quasifree parts

a fully quantum asymptotic equipartition property the classical asymptotic equipartition property is the statement that in the limit of a large number of identical repetitions of a random experiment the output sequence is virtually certain to come from the typical set each member of which is almost equally likely in this paper a fully quantum generalization of this property is shown where both the output of the experiment and side information are quantum an explicit bound on the convergence is given which is independent of the dimensionality of the side information this naturally leads to a family of reacutenyi like quantum conditional entropies for which the von neumann entropy emerges as a special case

the classification of kleinian surface groups i models and bounds we give the first part of a proof of thurston s ending lamination conjecture in this part we show how to construct from the end invariants of a kleinian surface group a lipschitz model for the thick part of the corresponding hyperbolic manifold this enables us to describe the topological structure of the thick part and to give a priori geometric bounds

coding theorem and strong converse for quantum channels we present a new proof of holevo s 1973 1977 coding theorem for transmitting classical information through quantum channels and its strong converse the technique is largely inspired by wolfwitz s 1964 combinatorial approach using types of sequences as a byproduct of our approach which is independent of previous ones both in the coding theorem and the converse we can give a new proof of holevo s information bound

monotonicity of a relative renyi entropy we show that a recent definition of relative renyi entropy is monotone under completely positive trace preserving maps this proves a recent conjecture of muller lennert et al on quantum renyi entropies a new definition some properties j math phys 54 122203 2013 e print arxiv 1306 3142v1 see also e print arxiv 1306 3142

mixed 3 manifolds are virtually special letm be a compact oriented irreducible 3 manifold which is neither a graph manifold nor a hyperbolic manifold we prove that 1m is virtually special

classical capacity of quantum channels with general markovian correlated noise the classical capacity of a quantum channel with arbitrary markovian correlated noise is evaluated for the general case of a channel with long term memory which corresponds to a markov chain which does not converge to equilibrium the capacity is expressed in terms of the communicating classes of the markov chain for an irreducible and aperiodic markov chain the channel is forgetful and one retrieves the known expression kretschmann and werner in phys rev a 72 062323 2005 for the capacity

on the level crossing duration distributions of nakagami processes the problem related to the fade and non fade duration distributions fdd and nfdd of randomly distributed signals has been studied for more than forty years however for non gaussian processes closed form general solutions for these distributions are still unknown in this paper we use an orthogonal series expansion to analyze the fdd and nfdd also known as downcrossing and upcrossing duration distributions respectively for the rather general case of nakagami distributed random processes our results show that for asymptotic and non asymptotic threshold levels the crossing duration distributions can be approximated in a simple closed form way using the gamma distribution we back up this approximation with some goodness of fit metrics and show how the parameters of such distribution can be computed a priori analytically

the classification of kleinian surface groups ii the ending lamination conjecture thurston s ending lamination conjecture states that a hyperbolic 3manifold n with nitely generated fundamental group is uniquely determined by its topological type and its end invariants in this paper we prove this conjecture for kleinian surface groups the general case when n has incompressible ends relative to its cusps follows readily the main ingredient is a uniformly bilipschitz model for the quotient of h 3 by a kleinian surface group

bandwidth estimation from multiple level crossings of stochastic signals motivated by a broad range of potential applications in event driven signal processing inference we examine a class of spectral moments estimators derived from multiple level crossings of a stationary gaussian stochastic signal as well as non gaussian signals being monotone transformations of the gaussian signal the established spectral moments estimators are used to obtain estimates of the stochastic signal bandwidth both the mean squared bandwidth and the absolute bandwidth are taken into account also the notion of the power bandwidth is introduced and its estimation is examined we prove that the proposed estimates are consistent as the length of the observed time interval is increasing the accuracy of the proposed bandwidth estimation methods from multiple level crossings is assessed in simulation studies

quantum state discrimination bounds for finite sample size in the problem of quantum state discrimination one has to determine by measurements the state of a quantum system based on the a priori side information that the true state is one of the two given and completely known states or in general it is not possible to decide the identity of the true state with certainty and the optimal measurement strategy depends on whether the two possible errors mistaking for or the other way around are treated as of equal importance or not results on the quantum chernoff and hoeffding bounds and the quantum stein s lemma show that if several copies of the system are available then the optimal error probabilities decay exponentially in the number of copies and the decay rate is given by a certain statistical distance between and the chernoff distance the hoeffding distances and the relative entropy respectively while these results provide a complete solution to the asymptotic problem they are not completely satisfying from a practical point of vi

on converse bounds for classical communication over quantum channels we explore several new converse bounds for classical communication over quantum channels in both the one shot and asymptotic regimes first we show that the matthews wehner meta converse bound for entanglement assisted classical communication can be achieved by activated no signaling assisted codes suitably generalizing a result for classical channels second we derive a new efficiently computable meta converse on the amount of classical information unassisted codes can transmit over a single use of a quantum channel as applications we provide a finite resource analysis of classical communication over quantum erasure channels including the second order and moderate deviation asymptotics third we explore the asymptotic analogue of our new meta converse the upsilon information of the channel we show that its regularization is an upper bound on the classical capacity which is generally tighter than the entanglement assisted capacity and other known efficiently computable strong converse bounds for covariant channels we show that the upsilon information is a strong converse bound

concavity of certain matrix trace and norm functions ii abstract we refine epstein s method to prove joint concavity convexity of matrix trace functions of lieb type tr f a p 1 2 b q a p 1 2 and symmetric anti norm functions of the form f a p b q where and are positive linear maps is an operator mean and f x with a certain power is an operator monotone function on 0 moreover the variational method of carlen frank and lieb is extended to general non decreasing convex concave functions on 0 so that we prove joint concavity convexity of more trace functions of lieb type

hypothesis testing on invariant subspaces of the symmetric group part i quantum sanov s theorem and arbitrarily varying sources we report a proof of the quantum sanov theorem by the elementary application of basic facts about representations of the symmetric group together with a complete characterization of the optimal error exponent in a situation where the null hypothesis is given by an arbitrarily varying quantum source instead our approach differs from previous ones in two ways first it supports a reasoning inspired by the method of types second the measurement scheme we propose to distinguish the two alternatives not only does that job asymptotically perfectly but also yields additional information about the null hypothesis an example of that is given the measurement is composed of projections onto permutation invariant subspaces thus providing a direct link between one of the most basic tasks in quantum information on the one hand and fundamental objects in representation theory on the other we additionally connect to the representation theory by proving a relation between kostka numbers and quantum states and to state estimation via a generalization of a well known spectral estimation theorem to non i i d sequences

clustering properties in turbulent signals we consider the telegraph approximation ta of turbulent signals by ignoring their amplitude variability and retaining only their zero crossing information we establish a unique relationship between the spectral exponent of a signal and that of its ta whenever the signal possesses a gaussian pdf and a spectral shape in which the high frequency cut off is sufficiently sharp the velocity signals in most turbulent flows away from the wall satisfy these conditions adequately so that the kolmogorov spectral exponent of 5 3 for the turbulent velocity spectrum corresponds to a 4 3 spectral exponent for its ta by introducing a new scaling exponent to characterize the tendency of small scale fluctuations to cluster we show that the velocity and passive scalar signals display a finite tendency to cluster even in the limit of re rightarrow infty we advance the notion on the basis of the properties of the ta that turbulent processes belong to one of two classes either the white noise type or the markov lorentzian type

min and max relative entropies and a new entanglement monotone two new relative entropy quantities called the min and max relative entropies are introduced and their properties are investigated the well known min and max entropies introduced by renner are obtained from these we define a new entanglement monotone which we refer to as the max relative entropy of entanglement and which is an upper bound to the relative entropy of entanglement we also generalize the min and max relative entropies to obtain smooth min and max relative entropies these act as parent quantities for the smooth renyi entropies eth zurich ph d dissertation 2005 and allow us to define the analogues of the mutual information in the smooth renyi entropy framework further the spectral divergence rates of the information spectrum approach are shown to be obtained from the smooth min and max relative entropies in the asymptotic limit

three dimensional manifolds kleinian groups and hyperbolic geometry 1 a conjectural picture of 3 manifolds a major thrust of mathematics in the late 19th century in which poincare had a large role was the uniformization theory for riemann surfaces that every conformai structure on a closed oriented surface is represented by a riemannian metric of constant curvature for the typical case of negative euler characteristic genus greater than 1 such a metric gives a hyperbolic structure any small neighborhood in the surface is isometric to a neighborhood in the hyperbolic plane and the surface itself is the quotient of the hyperbolic plane by a discrete group of motions the exceptional cases the sphere and the torus have spherical and euclidean structures three manifolds are greatly more complicated than surfaces and i think it is fair to say that until recently there was little reason to expect any analogous theory for manifolds of dimension 3 or more except perhaps for the fact that so many 3 manifolds are beautiful the situation has changed so that i feel fairly confident in proposing the

error exponents in hypothesis testing for correlated states on a spin chain we study various error exponents in a binary hypothesis testing problem and extend recent results on the quantum chernoff and hoeffding bounds for product states to a setting when both the null hypothesis and the alternative hypothesis can be correlated states on a spin chain our results apply to states satisfying a certain factorization property typical examples are the global gibbs states of translation invariant finite range interactions as well as certain finitely correlated states

fluctuations in the zeros of differentiable gaussian processes the stochastic point processes formed by the zero crossings or extremal points of differentiable stationary gaussian processes are studied as a function of their autocorrelation function the properties of these point processes are mapped to the space formed by the parameters appearing in the autocorrelation function their adopted form being sensitive to the structure of the autocorrelation function principally in the vicinity of the origin the distribution for the number of zeros occurring in an asymptotically large interval are approximately negative binomial or binomial depending upon whether the relative variance or fano factor is greater or less than unity the correlation properties of the zeros are such that they are repelled from each other or are antibunched if the autocorrelation function of the gaussian process is characterized by a single scale size but occur in clusters if more than one characteristic scale size is present the intervals between zeros can be interpreted in terms of the autocorrelation function of the zeros themselves when bunching occurs the interval density becomes bimodal indicating the interval sizes within and between the clusters the interevent periods are statistically dependent on one another with densities whose asymptotic behavior is governed by that of the autocorrelation function of the gaussian process at large delay times poisson distributed fluctuations of the zeros occur only exceptionally but never form a poisson process

strong converse for the classical capacity of entanglement breaking and hadamard channels via a sandwiched renyi relative entropy a strong converse theorem for the classical capacity of a quantum channel states that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of communication exceeds the classical capacity of the channel along with a corresponding achievability statement for rates below the capacity such a strong converse theorem enhances our understanding of the capacity as a very sharp dividing line between achievable and unachievable rates of communication here we show that such a strong converse theorem holds for the classical capacity of all entanglement breaking channels and all hadamard channels the complementary channels of the former these results follow by bounding the success probability in terms of a sandwiched renyi relative entropy by showing that this quantity is subadditive for all entanglement breaking and hadamard channels and by relating this quantity to the holevo capacity prior results regarding strong converse theorems for particular covariant channels emerge as a special case of our results

on the minimum output entropy of random orthogonal quantum channels we consider the sequences of random quantum channels defined by using the stinespring formula with haar distributed random orthogonal matrices for any fixed sequence of input states we study the asymptotic eigenvalue distribution of the outputs through the tensor powers of random channels we show that the input states achieving minimum output entropy are tensor products of maximally entangled states bell states when the tensor power is even this phenomenon is completely different from the one for random quantum channels constructed from haar distributed random unitary matrices which leads us to formulate some conjectures about the regularized minimum output entropy

word hyperbolic dehn surgery in the late 1970 s thurston dramatically changed the nature of 3 manifold theory with the introduction of his geometrisation conjecture and by proving it in the case of haken 3 manifolds 23 the conjecture for general closed orientable 3 manifolds remains perhaps the most important unsolved problem in the subject a weaker form of the conjecture 19 deals with the fundamental group of a closed orientable 3 manifold it proposes that either it contains z z as a subgroup or it is word hyperbolic in the sense of gromov 11 word hyperbolic groups are precisely those groups which satisfy a linear isoperimetric inequality they are of fundamental importance in geometric group theory and have very many useful properties