duality between smooth min and max entropies in classical and quantum information theory operational quantities such as the amount of randomness that can be extracted from a given source or the amount of space needed to store given data are normally characterized by one of two entropy measures called smooth min entropy and smooth max entropy respectively while both entropies are equal to the von neumann entropy in certain special cases e g asymptotically for many independent repetitions of the given data their values can differ arbitrarily in the general case in this paper a recently discovered duality relation between nonsmooth min and max entropies is extended to the smooth case more precisely it is shown that the smooth min entropy of a system a conditioned on a system b equals the negative of the smooth max entropy of a conditioned on a purifying system c this result immediately implies that certain operational quantities such as the amount of compression and the amount of randomness that can be extracted from given data are related we explain how such relations have applications in cryptographic security proofs

the effects of model selection on confidence intervals for the size of a closed population one encounters in the literature estimates of some rates of genetic and congenital disorders based on log linear methods to model possible interactions among sources often the analyst chooses the simplest model consistent with the data for estimation of the size of a closed population and calculates confidence intervals on the assumption that this simple model is correct however despite an apparent excellent fit of the data to such a model we note here that the resulting confidence intervals may well be misleading in that they can fail to provide an adequate coverage probability we illustrate this with a simulation for a hypothetical population based on data reported in the literature from three sources the simulated nominal 95 per cent confidence intervals contained the modelled population size only 30 per cent of the time only if external considerations justify the assumption of plausible interactions of sources would use of the simpler model s interval be justified

survival models for heterogeneous populations derived from stable distributions summary a new three parameter family of distributions on the positive numbers is proposed it includes the stable distributions on the positive numbers the gamma the degenerate and the inverse gaussian distributions the family is characterized by the laplace transform from which moments convolutions infinite divisibility unimodality and other properties are derived the density is complicated but a simple saddlepoint approximation is provided weibull and gompertz distributions are naturally mixed over some of the distributions the family is natural exponential in one of the parameters the distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations desirable properties of such distributions are discussed as an example survival after myocardial infarction is considered

an upper bound on the zero error list coding capacity presents an upper bound on the zero error list coding capacity of discrete memoryless channels using this bound we show that the list 3 capacity of the 4 3 channel is at most 0 3512 bits improving the best previous bound the relation of the bound to earlier similar bounds in particular to korner s 1986 graph entropy bound is discussed

an extreme form of superactivation for quantum zero error capacities the zero error capacity of a channel is the rate at which it can send information perfectly with zero probability of error and has long been studied in classical information theory we show that the zero error capacity of quantum channels exhibits an extreme form of nonadditivity one which is not possible for classical channels or even for the usual capacities of quantum channels by combining probabilistic arguments with algebraic geometry we prove that there exist channels and with no zero error classical capacity whatsoever but whose joint zero error quantum capacity is positive this striking effect is an extreme form of the superactivation phenomenon as it implies that both the classical and quantum zero error capacities of these channels can be superactivated simultaneously while being a strictly stronger property of capacities superactivation of the quantum zero error capacity was not previously known

the quantum capacity of channels with arbitrarily correlated noise we study optimal rates for quantum communication over a single use of a channel which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise the corresponding capacity is often referred to as the one shot quantum capacity in this paper we prove bounds on the one shot quantum capacity of an arbitrary channel this allows us to compute the quantum capacity of a channel with arbitrarily correlated noise in the limit of asymptotically many uses of the channel in the memoryless case we explicitly show that our results reduce to known expressions for the quantum capacity

the interpretation of multiplicative model parameters as standardized parameters under current conventions relative risk estimates obtained from multiplicative models are interpreted as estimates of a homogeneous effect such interpretations condition on the unverifiable assumption that the relative risk under study is homogeneous an assumption that is not likely to be correct even if the model fits well we propose that such estimates are better interpreted as estimates of standardized relative risks with a bias component that depends on the degree of model misspecification and on the study design to evaluate our proposal we present a study of the maximum likelihood estimators from poisson and logistic regression compared to the population standardized rate ratio the results indicate that our proposed interpretation would in practice be more cautious and accurate than the homogeneous effect interpretation

entanglement can increase asymptotic rates of zero error classical communication over classical channels it is known that the number of different classical messages which can be communicated with a single use of a classical channel with zero probability of decoding error can sometimes be increased by using entanglement shared between sender and receiver it has been an open question to determine whether entanglement can ever increase the zero error communication rates achievable in the limit of many channel uses in this paper we show by explicit examples that entanglement can indeed increase asymptotic zero error capacity even to the extent that it is equal to the normal capacity of the channel

constant compositions in the sphere packing bound for classical quantum channels the sphere packing bound in the form given by shannon gallager and berlekamp was recently extended to classical quantum channels and it was shown that this creates a natural setting for combining probabilistic approaches with some combinatorial ones such as the lovasz theta function in this paper we extend the study to the case of constant composition codes we first extend the sphere packing bound for classical quantum channels to this case and we then show that the obtained result is related to a variation of the lovasz theta function studied by marton we then propose a further extension to the case of varying channels and codewords with a constant conditional composition given a particular sequence this extension is finally applied to auxiliary channels to deduce a bound which is useful in the low rate region and which can be interpreted as an extension of the elias bound

separation between quantum lovasz number and entanglement assisted zero error classical capacity quantum lovasz number is a quantum generalization of the lovasz number in graph theory it is the best known efficiently computable upper bound of the entanglement assisted zero error classical capacity of a quantum channel however it remains an intriguing open problem whether quantum entanglement can always enhance the zero error capacity to achieve the quantum lovasz number in this paper by constructing a particular class of qutrit to qutrit channels we show that there exists a strict gap between the entanglement assisted zero error capacity and the quantum lovasz number interestingly for this class of quantum channels the quantum generalization of fractional packing number is strictly larger than the zero error capacity assisted with feedback or no signaling correlations which differs from the case of classical channels

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

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

on zero error communication via quantum channels in the presence of noiseless feedback we initiate the study of zero error communication via quantum channels when the receiver and the sender have at their disposal a noiseless feedback channel of unlimited quantum capacity generalizing shannon s zero error communication theory with instantaneous feedback we first show that this capacity is only a function of the linear span of choi kraus operators of the channel which generalizes the bipartite equivocation graph of a classical channel and which we dub non commutative bipartite graph then we go on to show that the feedback assisted capacity is non zero allowing for a constant amount of activating noiseless communication if and only if the non commutative bipartite graph is non trivial and give a number of equivalent characterizations this result involves a far reaching extension of the conclusive exclusion of quantum states we then present an upper bound on the feedback assisted zero error capacity motivated by a conjecture originally made by shannon and proved later by ahlswede we demonstrate that this bound to have many good properties including being additive and given by a minimax formula we also prove a coding theorem showing that this quantity is the entanglement assisted capacity against an adversarially chosen channel from the set of all channels with the same choi kraus span which can also be interpreted as the feedback assisted unambiguous capacity the proof relies on a generalization of the postselection lemma de finetti reduction that allows to reflect additional constraints and which we believe to be of independent interest this capacity is a relaxation of the feedback assisted zero error capacity however we have to leave open the question of whether they coincide in general we illustrate our ideas with a number of examples including classical quantum channels and weyl diagonal channels and close with an extensive discussion of open questions

quantum computational networks the theory of quantum computational networks is the quantum generalization of the theory of logic circuits used in classical computing machines quantum gates are the generalization of classical logic gates a single type of gate the universal quantum gate together with quantum unit wires is adequate for constructing networks with any possible quantum computational property

a concordance test for independence in the presence of censoring an extension of the definition of kendall s coefficient of concordance is proposed for testing independence in bivariate censored survival times the test statistic counts the number of known concordances minus the number of known discordances the variance of the statistic is calculated for an random censorship model which however does not require independence of the components of the censoring distribution two examples are given

one shot classical data compression with quantum side information and the distillation of common randomness or secret keys the task of compressing classical information in the one shot scenario is studied in the setting where the decompressor additionally has access to some given quantum side information in this hybrid classical quantum version of the famous slepian wolf problem the smooth max entropy is found to govern the number of bits into which classical information can be compressed so that it can be reliably recovered from the compressed version and quantum side information combining this result with known results on privacy amplification then yields tight bounds on the amount of common randomness and secret key that can be recovered in one shot from hybrid classical quantum systems using one way classical communication

bayesian model averaging for linear regression models abstract we consider the problem of accounting for model uncertainty in linear regression models conditioning on a single selected model ignores model uncertainty and thus leads to the underestimation of uncertainty when making inferences about quantities of interest a bayesian solution to this problem involves averaging over all possible models i e combinations of predictors when making inferences about quantities of interest this approach is often not practical in this article we offer two alternative approaches first we describe an ad hoc procedure occam s window which indicates a small set of models over which a model average can be computed second we describe a markov chain monte carlo approach that directly approximates the exact solution in the presence of model uncertainty both of these model averaging procedures provide better predictive performance than any single model that might reasonably have been selected in the extreme case where there are many candidate predictors but

on some classes of bipartite unitary operators we investigate unitary operators acting on a tensor product space with the property that the quantum channels they generate via the stinespring dilation theorem are of a particular type independently of the state of the ancilla system in the stinespring relation the types of quantum channels we consider are those of interest in quantum information theory unitary conjugations constant channels unital channels mixed unitary channels ppt channels and en tanglement breaking channels for some of the classes of bipartite unitary operators corresponding to the above types of channels we provide explicit characterizations necessary and or sufficient conditions for membership and we compute the dimension of the corresponding algebraic variety inclusions between these classes are considered and we show that for small dimensions many of these sets are identical

zero error communication via quantum channels noncommutative graphs and a quantum lovasz number we study the quantum channel version of shannon s zero error capacity problem motivated by recent progress on this question we propose to consider a certain subspace of operators so called operator systems as the quantum generalization of the adjacency matrix in terms of which the zero error capacity of a quantum channel as well as the quantum and entanglement assisted zero error capacities can be formulated and for which we show some new basic properties most importantly we define a quantum version of lovasz famous function on general operator systems as the norm completion or stabilization of a naive generalization of we go on to show that this function upper bounds the number of entanglement assisted zero error messages that it is given by a semidefinite program whose dual we write down explicitly and that it is multiplicative with respect to the tensor product of operator systems corresponding to the tensor product of channels we explore various other properties of the new quantity which reduces to lovasz original in the classical case give several applications and propose to study the operator systems associated with channels as noncommutative graphs using the language of hilbert modules

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

a sharp continuity estimate for the von neumann entropy we derive an inequality relating the entropy difference between two quantum states to their trace norm distance sharpening a well known inequality due to fannes in our inequality equality can be attained for every prescribed value of the trace norm distance

zero error capacity under list decoding shannon s zero error channel capacities c sub of c sub o with and without noiseless feedback are generalized to list decoding the receiver lists l messages erring if the correct one is not listed the corresponding capacities c sub of l c sub o l are nondecreasing in l for an i letter input alphabet c sub of l attains its maximum at l i 1 a lower bound to c sub o l approaches that maximum as l increases

the operational meaning of min and max entropy in this paper we show that the conditional min entropy h min a b of a bipartite state rhoab is directly related to the maximum achievable overlap with a maximally entangled state if only local actions on the b part of rhoab are allowed in the special case where a is classical this overlap corresponds to the probability of guessing a given b in a similar vein we connect the conditional max entropy h max a b to the maximum fidelity of rhoab with a product state that is completely mixed on a in the case where a is classical this corresponds to the security of a when used as a secret key in the presence of an adversary holding b because min and max entropies are known to characterize information processing tasks such as randomness extraction and state merging our results establish a direct connection between these tasks and basic operational problems for example they imply that the logarithm of the probability of guessing a given b is a lower bound on the number of uniform secret bits that can be extracted from a relative to an adversary holding b

the quantum reverse shannon theorem based on one shot information theory the quantum reverse shannon theorem states that any quantum channel can be simulated by an unlimited amount of shared entanglement and an amount of classical communication equal to the channel s entanglement assisted classical capacity in this paper we provide a new proof of this theorem which has previously been proved by bennett devetak harrow shor and winter our proof has a clear structure being based on two recent information theoretic results one shot quantum state merging and the post selection technique for quantum channels

semidefinite programming strong converse bounds for classical capacity we investigate the classical communication over quantum channels when assisted by no signaling and positive partial transpose preserving ppt codes for which both the optimal success probability of a given transmission rate and the one shot epsilon error capacity are formalized as semidefinite programs sdps based on this we obtain improved sdp finite blocklength converse bounds of general quantum channels for entanglement assisted codes and unassisted codes furthermore we derive two sdp strong converse bounds for the classical capacity of general quantum channels for any code with a rate exceeding either of the two bounds of the channel the success probability vanishes exponentially fast as the number of channel uses increases in particular applying our efficiently computable bounds we derive an improved upper bound on the classical capacity of the amplitude damping channel we also establish the strong converse property for the classical and private capacities of a new class of quantum channels we finally study the zero error setting and provide efficiently computable upper bounds on the one shot zero error capacity of a general quantum channel

on the large sample minimal coverage probability of confidence intervals after model selection we give a large sample analysis of the minimal coverage probability of the usual confidence intervals for regression parameters when the underlying model is chosen by a conservative or overconsistent model selection procedure we derive an upper bound for the large sample limit minimal coverage probability of such intervals that applies to a large class of model selection procedures including the akaike information criterion as well as various pretesting procedures this upper bound can be used as a safeguard to identify situations where the actual coverage probability can be far below the nominal level we illustrate that the asymptotic upper bound can be statistically meaningful even in rather small samples

one shot classical quantum capacity and hypothesis testing the one shot classical capacity of a quantum channel quantifies the amount of classical information that can be transmitted through a single use of the channel such that the error probability is below a certain threshold in this work we show that this capacity is well approximated by a relative entropy type measure defined via hypothesis testing combined with a quantum version of stein s lemma our results give a conceptually simple proof of the well known holevo schumacher westmoreland theorem for the capacity of memoryless channels more generally we obtain tight capacity formulas for arbitrary not necessarily memoryless channels

sample size in cluster randomized trials with time to event as the primary endpoint in cluster randomized trials groups of individuals clusters are randomized to the treatments or interventions to be compared in many of those trials the primary objective is to compare the time for an event to occur between randomized groups and the shared frailty model well fits clustered time to event data members of the same cluster tend to be more similar than members of different clusters causing correlations as correlations affect the power of a trial to detect intervention effects the clustered design has to be considered in planning the sample size in this publication we derive a sample size formula for clustered time to event data with constant marginal baseline hazards and correlation within clusters induced by a shared frailty term the sample size formula is easy to apply and can be interpreted as an extension of the widely used schoenfeld s formula accounting for the clustered design of the trial simulations confirm the validity of the formula and its use also for non constant marginal baseline hazards findings are illustrated on a cluster randomized trial investigating methods of disseminating quality improvement to addiction treatment centers in the usa copyright 2012 john wiley sons ltd

randomness in secret sharing and visual cryptography schemes secret sharing schemes allow a secret to be shared among a group of participants so that only qualified subsets of participants can recover the secret a visual cryptography scheme vcs is a special kind of secret sharing scheme in which the secret to share consists of an image and the shares consist of xeroxed transparencies which are stacked to recover the shared image in this paper we analyze the relationship between secret sharing schemes and vcss focusing our attention on the amount of randomness required to generate the shares we prove that secret sharing schemes for a set of secrets of size two bsss and vcss are equivalent with respect to the randomness indeed we show how to transform a bss for a given access structure into a vcs for the same access structure while preserving the randomness of the original scheme we provide both upper and lower bounds on the randomness of bsss all vcss presented in this paper allow a perfect reconstruction of black pixels

entanglement assisted capacity of a quantum channel and the reverse shannon theorem the entanglement assisted classical capacity of a noisy quantum channel c sub e is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel assuming that the sender and receiver have access to the resource of shared quantum entanglement which may be used up by the communication protocol we show that the capacity c sub e is given by an expression parallel to that for the capacity of a purely classical channel i e the maximum over channel inputs spl rho of the entropy of the channel input plus the entropy of the channel output minus their joint entropy the latter being defined as the entropy of an entangled purification of spl rho after half of it has passed through the channel we calculate entanglement assisted capacities for two interesting quantum channels the qubit amplitude damping channel and the bosonic channel with amplification attenuation and gaussian noise we discuss how many independent parameters are required to completely characterize the asymptotic behavior of a general quantum channel alone or in the presence of ancillary resources such as prior entanglement in the classical analog of entanglement assisted communication communication over a discrete memoryless channel dmc between parties who share prior random information we show that one parameter is sufficient i e that in the presence of prior shared random information all dmcs of equal capacity can simulate one another with unit asymptotic efficiency

an improved bound on the zero error list decoding capacity of the 4 3 channel we prove a new upper bound on the size of codes c subseteq 1 2 3 4 n with the property that every four distinct codewords in c have a coordinate where they all differ specifically we provide a self contained proof that such codes have size at most 2 6n 19 o n that is rate bounded asymptotically by 6 19 0 3158 measured in bits this improves the previous best upper bound of 0 3512 due to arikan 1994 which in turn improved the 0 375 bound that followed from general bounds for perfect hashing due to fredman and komlos 1984 and korner and marton 1988 finally using a combination of our approach with a simple idea which exploits powerful bounds on the minimum distance of codes in the hamming space we further improve the upper bound to 0 31477

distilling entanglement from arbitrary resources we obtain the general formula for the optimal rate at which singlets can be distilled from any given noisy and arbitrarily correlated entanglement resource by means of local operations and classical communication locc our formula obtained by employing the quantum information spectrum method reduces to that derived by devetak and winter proc r soc london ser a 461 207 2005 in the special case of an independent and identically distributed resource the proofs rely on a one shot version of the so called hashing bound which in turn provides bounds on the one shot distillable entanglement under general locc

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

simple capture recapture models permitting unequal catchability and variable sampling effort we consider two capture recapture models that imply that the logit of the probability of capture is an additive function of an animal catchability parameter and a parameter reflecting the sampling effort the models are special cases of the rasch model and satisfy the property of quasi symmetry one model is log linear and the other is a latent class model for the log linear model point and interval estimates of the population size are easily obtained using standard software such as glim

goodness of fit based confidence intervals for estimates of the size of a closed population methods for estimating the size of a closed population often consist of fitting some model e g a log linear model to data with a missing cell corresponding to the members of the population missed by all reporting sources although the use of the asymptotic standard error is the usual method for forming confidence intervals for the population total the sample sizes are not always large enough to produce valid confidence intervals we propose a method for forming confidence intervals based upon changes in a goodness of fit statistic associated with changes in trial values of the population total

zero error channel capacity and simulation assisted by non local correlations the theory of zero error communication is re examined in the broader setting of using one classical channel to simulate another exactly in the presence of various classes of nonsignalling correlations between sender and receiver i e shared randomness shared entanglement and arbitrary nonsignalling correlations when the channel being simulated is noiseless this is zero error coding assisted by correlations when the resource channel is noiseless it is the reverse problem of simulating a noisy channel exactly by a noiseless one assisted by correlations in both cases separations between the power of the different classes of assisting correlations are exhibited for finite block lengths the most striking result here is that entanglement can assist in zero error communication in the large block length limit shared randomness is shown to be just as powerful as arbitrary nonsignalling correlations for exact simulation but not for asymptotic zero error coding for assistance by arbitrary nonsignalling correlations linear programming formulas for the asymptotic capacity and simulation rates are derived the former being equal for channels with nonzero unassisted capacity to the feedback assisted zero error capacity derived by shannon finally a kind of reversibility between nonsignalling assisted zero error capacity and exact simulation is observed mirroring the usual reverse shannon theorem

model selection and accounting for model uncertainty in graphical models using occam s window abstract we consider the problem of model selection and accounting for model uncertainty in high dimensional contingency tables motivated by expert system applications the approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic p values leading to the selection of a single model inference is then conditional on the selected model the sampling properties of such a strategy are complex and the failure to take account of model uncertainty leads to underestimation of uncertainty about quantities of interest in principle a panacea is provided by the standard bayesian formalism that averages the posterior distributions of the quantity of interest under each of the models weighted by their posterior model probabilities furthermore this approach is optimal in the sense of maximizing predictive ability but this has not been used in practice because computing the posterior model probabilities is hard and the number of models is very large often greater than 1

a bivariate cure mixture approach for modeling familial association in diseases summary for modeling correlation in familial diseases with variable ages at onset we propose a bivariate model that incorporates two types of pairwise association one between the lifetime risk or the overall susceptibility of two individuals and one between the ages at onset between two susceptible individuals for estimation we consider a two stage estimation procedure similar to that of shih 1998 biometrics 54 1115 1128 we evaluate the properties of the estimators through simulations and compare the performance with that from a bivariate survival model that allows correlation between ages at onset only we apply the methodology to breast cancer using the kinship data from the washington ashkenazi study we also discuss potential applications of the proposed method in the area of cure modeling

a bivariate survival model with compound poisson frailty a correlated frailty model is suggested for analysis of bivariate time to event data the model is an extension of the correlated power variance function pvf frailty model correlated three parameter frailty model j epidemiol biostat 1999 4 53 60 it is based on a bivariate extension of the compound poisson frailty model in univariate survival analysis ann appl probab 1992 4 951 972 it allows for a non susceptible fraction of zero frailty in the population overcoming the common assumption in survival analysis that all individuals are susceptible to the event under study the model contains the correlated gamma frailty model and the correlated inverse gaussian frailty model as special cases a maximum likelihood estimation procedure for the parameters is presented and its properties are studied in a small simulation study this model is applied to breast cancer incidence data of swedish twins the proportion of women susceptible to breast cancer is estimated to be 15 per cent

estimation of multivariate frailty models using penalized partial likelihood summary there exists a growing literature on the estimation of gamma distributed multiplicative shared frailty models there is however often a need to model more complicated frailty structures but attempts to extend gamma frailties run into complications motivated by hip replacement data with a more complicated dependence structure we propose a model based on multiplicative frailties with a multivariate log normal joint distribution we give a justification and an estimation procedure for this generally structured frailty model which is a generalization of the one presented by mcgilchrist 1993 biometrics49 221 225 the estimation is based on laplace approximation of the likelihood function this leads to estimating equations based on a penalized fixed effects partial likelihood where the marginal distribution of the frailty terms determines the penalty term the tuning parameters of the penalty function i e the frailty variances are estimated by maximizing an approximate profile likelihood the performance of the approximation is evaluated by simulation and the frailty model is fitted to the hip replacement data

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

exact and asymptotic inference for the size of a population on montre que la vraisemblance a un maximum local unique et que l algorithme iteratif propose converge vers celui ci

semidefinite programming converse bounds for quantum communication we derive several efficiently computable converse bounds for quantum communication over quantum channels in both the one shot and asymptotic regime first we derive one shot semidefinite programming sdp converse bounds on the amount of quantum information that can be transmitted over a single use of a quantum channel which improve the previous bound from tomamichel berta renes nat commun 7 2016 as applications we study quantum communication over depolarizing channels and amplitude damping channels with finite resources second we find an sdp strong converse bound for the quantum capacity of an arbitrary quantum channel which means the fidelity of any sequence of codes with a rate exceeding this bound will vanish exponentially fast as the number of channel uses increases furthermore we prove that the sdp strong converse bound improves the partial transposition bound introduced by holevo and werner third we prove that this sdp strong converse bound is equal to the so called max rains information which is an analog to the rains information introduced in tomamichel wilde winter ieee trans inf theory 63 715 2017 our sdp strong converse bound is weaker than the rains information but it is efficiently computable for general quantum channels

no signalling assisted zero error capacity of quantum channels and an information theoretic interpretation of the lovasz number we study the one shot zero error classical capacity of a quantum channel assisted by quantum no signalling correlations and the reverse problem of exact simulation of a prescribed channel by a noiseless classical one quantum no signalling correlations are viewed as two input and two output completely positive and trace preserving maps with linear constraints enforcing that the device cannot signal both problems lead to simple semidefinite programmes sdps that depend only on the choi kraus operator space of the channel in particular we show that the zero error classical simulation cost is precisely the conditional min entropy of the choi jamiolkowski matrix of the given channel the zero error classical capacity is given by a similar looking but different sdp the asymptotic zero error classical capacity is the regularization of this sdp and in general we do not know of any simple form interestingly however for the class of classical quantum channels we show that the asymptotic capacity is given by a much simpler sdp which coincides with a semidefinite generalization of the fractional packing number suggested earlier by aram harrow this finally results in an operational interpretation of the celebrated lovasz vartheta function of a graph as the zero error classical capacity of the graph assisted by quantum no signalling correlations the first information theoretic interpretation of the lovasz number

bayesian methods for estimation of the size of a closed population summary a bayesian methodology for estimating the size of a closed population from multiple incomplete administrative lists is proposed the approach allows for a variety of dependence structures between the lists can make use of covariates and explicitly accounts for model uncertainty interval estimates from this approach are compared to frequentist and previously published bayesian approaches several examples are considered

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

one shot rates for entanglement manipulation under non entangling maps we obtain expressions for the optimal rates of one shot entanglement manipulation under operations which generate a negligible amount of entanglement as the optimal rates for entanglement distillation and dilution in this paradigm we obtain the max and min relative entropies of entanglement the two logarithmic robustnesses of entanglement and smoothed versions thereof this gives a new operational meaning to these entanglement measures moreover by considering the limit of many identical copies of the shared entangled state we partially recover the recently found reversibility of entanglement manipulation under the class of operations which asymptotically do not generate entanglement

general theory of environment assisted entanglement distillation we evaluate the one shot entanglement of assistance for an arbitrary bipartite state this yields another interesting result namely a characterization of the one shot distillable entanglement of a bipartite pure state this result is shown to be stronger than that obtained by specializing the one shot hashing bound to pure states finally we show how the one shot result yields the operational interpretation of the asymptotic entanglement of assistance proved by smolin and coworkers