unconditional security from noisy quantum storage we consider the implementation of two party cryptographic primitives based on the sole assumption that no large scale reliable quantum storage is available to the cheating party we construct novel protocols for oblivious transfer and bit commitment and prove that realistic noise levels provide security even against the most general attack such unconditional results were previously only known in the so called bounded storage model which is a special case of our setting our protocols can be implemented with present day hardware used for quantum key distribution in particular no quantum storage is required for the honest parties

a time domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems we study a class of time domain decomposition based methods for the numerical solution of large scale linear quadratic optimal control problems our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete time optimal control dtoc problem the optimality conditions for this dtoc problem lead to a linear block tridiagonal system the diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time subintervals this motivates the application of block gauss seidel gs type methods for the solution of the block tridiagonal systems numerical experiments show that the spectral radii of the block gs iteration matrices are larger than one for typical applications but that the eigenvalues of the iteration matrices decay to zero fast hence while the gs method is not expected to convergence for typical applications it can be effective as a preconditioner for krylov subspace methods this is confirmed by our numerical tests a byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block gs method applied to the dtoc optimality system

quantum achievability proof via collision relative entropy in this paper we provide a simple framework for deriving one shot achievable bounds for some problems in quantum information theory our framework is based on the joint convexity of the exponential of the collision relative entropy and is a partial quantum generalization of the technique of yassaee et al from classical information theory based on this framework we derive one shot achievable bounds for the problems of communication over classical quantum channels quantum hypothesis testing and classical data compression with quantum side information we argue that our one shot achievable bounds are strong enough to give the asymptotic achievable rates of these problems even up to the second order

robust protocols for securely expanding randomness and distributing keys using untrusted quantum devices randomness is a vital resource for modern day information processing especially for cryptography a wide range of applications critically rely on abundant high quality random numbers generated securely here we show how to expand a random seed at an exponential rate without trusting the underlying quantum devices our approach is secure against the most general adversaries and has the following new features cryptographic level of security tolerating a constant level of imprecision in devices requiring only unit size quantum memory for each device component in an honest implementation and allowing a large natural class of constructions for the protocol in conjunction with a recent work by chung et al l2014r it also leads to robust unbounded expansion using just 2 multipart devices when adapted for distributing cryptographic keys our method achieves for the first time exponential expansion combined with cryptographic security and noise tolerance the proof proceeds by showing that the renyi divergence of the outputs of the protocol for a specific bounding operator decreases linearly as the protocol iterates at the heart of the proof are a new uncertainty principle on quantum measurements and a method for simulating trusted measurements with untrusted devices

recent developments in nonparametric density estimation advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research and especially the development of nonparametric data analysis procedures in particular theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics such as nonparametric regression nonparametric discrimination and nonparametric pattern recognition this article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject the early density estimation methods such as the histogram kernel estimators and orthogonal series estimators are still very popular and recent research on them is described different types of restricted maximum likelihood density estimators including order restricted estimators maximum penalized likelihood estimators and sieve estimators are discussed where restrictions are imposed upon the class of densities or on the form of the likelihood function nonparametric density estimators that are data adaptive and lead to locally smoothed estimators are also discussed these include variable partition histograms estimators based on statistically equivalent blocks nearest neighbor estimators variable kernel estimators and adaptive kernel estimators for the multivariate case extensions of methods of univariate density estimation are usually straightforward but can be computationally expensive a method of multivariate density estimation that did not spring from a univariate generalization is described namely projection pursuit density estimation in which both dimensionality reduction and density estimation can be pursued at the same time finally some areas of related research are mentioned such as nonparametric estimation of functionals of a density robust parametric estimation semiparametric models and density estimation for censored and incomplete data directional and spherical data and density estimation for dependent sequences of observations

circumventing storage limitations in variational data assimilation studies an application of pontryagin s maximum principle data assimilation is used to blend possibly incomplete or nonuniformly distributed spatio temporal observational data into geophysical models used extensively in engineering control theory applications data assimilation has been introduced relatively recently into meteorological forecasting natural resource recovery modeling and climate dynamics variational data assimilation is a promising assimilation technique in which it is assumed that the optimal state of the system is an extrema of a carefully chosen cost function provided that an adjoint model is available the required model gradient can be computed by integrating the model forward and its adjoint backward the gradient is then used to extremize the cost function with a suitable iterative or conjugate gradient solver the problem addressed in this study is the explosive growth in both on line computer memory and remote storage requirements of computing the gradient by the forward adjoint technique which characterizes large scale assimilation studies storage limitations impose severe limitation on the size of assimilation studies even on the largest computers by using a recursive strategy a schedule can be constructed that enables the forward adjoint model runs to be performed in such a way that storage requirements can be traded for longer computational times this generally applicable strategy enables data assimilation studies on significantly larger domains than would otherwise be possible given the particular hardware constraints without compromising the outcome in any way furthermore it is shown that this tradeoff is indeed viable and that when the schedule is optimized the storage and computational times grow at most logarithmically

quantum to classical randomness extractors the goal of randomness extraction is to distill almost perfect randomness from a weak source of randomness when the source yields a classical string x many extractor constructions are known yet when considering a physical randomness source x is itself ultimately the result of a measurement on an underlying quantum system when characterizing the power of a source to supply randomness it is hence natural to ask how much classical randomness we can extract from a quantum system to tackle this question we here take on the study of quantum to classical randomness extractors qc extractors we provide constructions of qc extractors based on measurements in a full set of mutually unbiased bases mubs and certain single qubit measurements the latter are particularly appealing since they are not only easy to implement but also appear throughout quantum cryptography we proceed to prove an upper bound on the maximum amount of randomness that we could hope to extract from any quantum state some of our qc extractors almost match this bound we show two applications of our results first we show that any qc extractor gives rise to entropic uncertainty relations with respect to quantum side information such relations were previously only known for two measurements in particular we obtain strong relations in terms of the von neumann shannon entropy as well as the min entropy for measurements in almost unitary two designs a full set of mubs and single qubit measurements in three mubs each second we resolve the central open question in the noisy storage model by linking security to the quantum capacity of the adversary s storage device more precisely we show that any two party cryptographic primitives can be implemented securely as long as the adversary s storage device has sufficiently low quantum capacity our protocol does not need any quantum storage to implement and is technologically feasible using present day technology

quantum logarithmic sobolev inequalities and rapid mixing a family of logarithmic sobolev inequalities on finite dimensional quantum state spaces is introduced the framework of non commutative lp spaces is reviewed and the relationship between quantum logarithmic sobolev inequalities and the hypercontractivity of quantum semigroups is discussed this relationship is central for the derivation of lower bounds for the logarithmic sobolev ls constants essential results for the family of inequalities are proved and we show an upper bound to the generalized ls constant in terms of the spectral gap of the generator of the semigroup these inequalities provide a framework for the derivation of improved bounds on the convergence time of quantum dynamical semigroups when the ls constant and the spectral gap are of the same order convergence bounds on finite dimensional state spaces are particularly relevant for the field of quantum information theory we provide a number of examples where improved bounds on the mixing time of several semigroups are obtained incl

some asymptotic properties of kernel estimators of a density function in case of censored data on considere l adaptation de l estimateur du noyau a des donnees censurees en utilisant l estimateur de kaplan meier

a schwarz domain decomposition method with gradient projection for optimal control governed by elliptic partial differential equations a b s t r a c t a domain decomposition method ddm is presented to solve the distributed optimal control problem the optimal control problem essentially couples an elliptic partial differential equation with respect to the state variable and a variational inequality with respect to the constrained control variable the proposed algorithm called sa gp algorithm consists of two iterative stages in the inner loops the schwarz alternating method sa is applied to solve the state and co state variables and in the outer loops the gradient projection algorithm gp is adopted to obtain the control variable convergence of iterations depends on both the outer and the inner loops which are coupled and affected by each other in the classical iteration algorithms a given tolerance would be reached after sufficiently many iteration steps but more iterations lead to huge computational cost for solving constrained optimal control problems most of the computational cost is used to solve pdes in this paper a proposed iterative number independent of the tolerance is used in the inner loops so as to save a lot of computational cost the convergence rate of l 2 error of control variable is derived also the analysis on how to choose the proposed iteration number in the inner loops is given some numerical experiments are performed to verify the theoretical results

entanglement sampling and applications a natural measure for the amount of quantum information that a physical system e holds about another system a a 1 ldots a n is given by the min entropy rm h min a e in particular the min entropy measures the amount of entanglement between e and a and is the relevant measure when analyzing a wide variety of problems ranging from randomness extraction in quantum cryptography decoupling used in channel coding to physical processes such as thermalization or the thermodynamic work cost or gain of erasing a quantum system as such it is a central question to determine the behavior of the min entropy after some process mathcal m is applied to the system a here we introduce a new generic tool relating the resulting min entropy to the original one and apply it to several settings of interest a simple example of such a process is the one of sampling where a subset s of the systems a 1 ldots a n is selected at random our tool allows us to quantify the entanglement that e has with the selected systems a s i e rm h min a s es as a function of the original rm h min a e we give two applications of this result first it directly provides the first local quantum to classical randomness extractors for use in quantum cryptography as well as decoupling operations acting on only a small fraction a s of the input a moreover it gives lower bounds on the dimension of k out of n fully quantum random access encodings another natural example of such a process is a measurement in e g bb84 bases commonly used in quantum cryptography we establish the first entropic uncertainty relations with quantum side information that are nontrivial whenever e is not maximally entangled with a as a consequence we are able to prove optimality of quantum cryptographic schemes in the noisy storage model this model allows for the secure implementation of two party cryptographic primitives under the assumption that the adversary cannot store quantum information perfectly a special case is the bounded quantum storage model bqsm which assumes that the adversary s quantum memory device is noise free but limited in size ever since the inception of the bqsm it has been a vexing open question to determine whether the security is possible as long as the adversary can only store strictly less than the number of qubits n transmitted during the protocol here we show that security is even possible as long as the adversary s device is not larger than n o log 2 n qubits which finally settles the fundamental limits of the bqsm

decoupling with random quantum circuits decoupling has become a central concept in quantum information theory with applications including proving coding theorems randomness extraction and the study of conditions for reaching thermal equilibrium however our understanding of the dynamics that lead to decoupling is limited in fact the only families of transformations that are known to lead to decoupling are approximate unitary two designs i e measures over the unitary group that behave like the haar measure as far as the first two moments are concerned such families include for example random quantum circuits with o n2 gates where n is the number of qubits in the system under consideration in fact all known constructions of decoupling circuits use n2 gates here we prove that random quantum circuits with o n log2n gates satisfy an essentially optimal decoupling theorem in addition these circuits can be implemented in depth o log3n this proves that decoupling can happen in a time that scales polylogarithmically in the number of particles in the system provided all the particles are allowed to interact our proof does not proceed by showing that such circuits are approximate two designs in the usual sense but rather we directly analyze the decoupling property

sampling of min entropy relative to quantum knowledge let x1 xn be a sequence of n classical random variables and consider a sample xs1 xsr of r n positions selected at random then except with exponentially in r small probability the min entropy hmin xs1 xsr of the sample is not smaller than roughly a fraction r n of the overall entropy hmin x1 xn which is optimal here we show that this statement originally proved in s vadhan lncs 2729 springer 2003 for the purely classical case is still true if the min entropy hmin is measured relative to a quantum system because min entropy quantifies the amount of randomness that can be extracted from a given random variable our result can be used to prove the soundness of locally computable extractors in a context where side information might be quantum mechanical in particular it implies that key agreement in the bounded storage model using a standard sample and hash protocol is fully secure against quantum adversaries thus solving a long standing open problem

dynamics and approximations of a velocity tracking problem for the navier stokes flows with piecewise distributed controls we study the dynamics of a piecewise in time distributed optimal control problem for the navier stokes equations which models velocity tracking over time we also study the dynamics of semidiscrete and fully discrete approximations of this velocity tracking problem we prove that the rates of velocity tracking are exponential some computational results are presented which reinforces the theoretical results derived

multiple imputation for simple estimation of the hazard function based on interval censored data a data augmentation algorithm is presented for estimating the hazard function and pointwise variability intervals based on interval censored data the algorithm extends that proposed by tanner and wong for grouped right censored data to interval censored data it applies multiple imputation and local likelihood methods to obtain smooth non parametric estimates for the hazard function this approach considerably simplifies the problem of estimation for interval censored data as it transforms it into the more tractable problem of estimation for right censored data the method is illustrated for two real data sets times to breast cosmesis deterioration and times to hiv 1 infection for individuals with haemophilia simulations are presented to assess the effects of various parameters on the estimates and their variances

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

a note on the variable kernel estimator of the hazard function from randomly censored data in a recent paper tanner and wong 1983b a family of data based nonparametric hazard estimators was introduced several of these estimators were studied in an extensive simulation experiment the estimator which allows for variable bandwidth was found to have a superior performance in this note sufficient conditions for the variable kernel estimator to be strongly consistent are presented

review papers recent developments in nonparametric density estimation abstract advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research and especially the development of nonparametric data analysis procedures in particular theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics such as nonparametric regression nonparametric discrimination and nonparametric pattern recognition this article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject the early density estimation methods such as the histogram kernel estimators and orthogonal series estimators are still very popular and recent research on them is described different types of restricted maximum likelihood density estimators including order restricted estimators maximum penalized likelihood estimators and sieve estimators are discussed where re

local convergence of empirical measures in the random censorship situation with application to density and rate estimators on etudie les deviations locales de la mesure empirique definie par l estimateur de kaplan meier 1958 pour la fonction de survie

the estimation of the hazard function from randomly censored data by the kernel method by convolution smoothing of the empirical hazards a kernel estimate of the hazard function from censored data is obtained small and large sample expressions for the mean and the variance of the estimator are given conditions for asymptotic normality are investigated using the hajek projection method

dense quantum coding and quantum finite automata we consider the possibility of encoding m classical bits into many fewer n quantum bits qubits so that an arbitrary bit from the original m bits can be recovered with good probability we show that nontrivial quantum codes exist that have no classical counterparts on the other hand we show that quantum encoding cannot save more than a logarithmic additive factor over the best classical encoding the proof is based on an entropy coalescence principle that is obtained by viewing holevo s theorem from a new perspective in the existing implementations of quantum computing qubits are a very expensive resource moreover it is difficult to reinitialize existing bits during the computation in particular reinitialization is impossible in nmr quantum computing which is perhaps the most advanced implementation of quantum computing at the moment this motivates the study of quantum computation with restricted memory and no reinitialization that is of quantum finite automata it was known that there are languages that are recognized by quantum finite automata with sizes exponentially smaller than those of corresponding classical automata here we apply our technique to show the surprising result that there are languages for which quantum finite automata take exponentially more states than those of corresponding classical automata

density and hazard rate estimation for censored data via strong representation of the kaplan meier estimator we study the estimation of a density and a hazard rate function based on censored data by the kernel smoothing method our technique is facilitated by a recent result of lo and singh 1986 which establishes a strong uniform approximation of the kaplan meier estimator by an average of independent random variables note that the approximation is carried out on the original probability space which should be distinguished from the hungarian embedding approach pointwise strong consistency and a law of iterated logarithm are derived as well as the mean squared error expression and asymptotic normality which is obtain using a more traditional method as compared with the hajek projection employed by tanner and wong 1983

the superlinear convergence behaviour of gmres abstract gmres is a rather popular iterative method for the solution of nonsingular nonsymmetric linear systems it is well known that gmres often has a so called superlinear convergence behaviour i e the rate of convergence seems to improve as the iteration proceeds for the conjugate gradients method this phenomenon has been related to a modest degree of convergence of the ritz values it has been observed in experiments that for gmres too changes in the convergence behaviour seem to be related to the convergence of ritz values in this paper we prove that as soon as eigenvalues of the original operator are sufficiently well approximated by ritz values gmres from then on converges at least as fast as for a related system in which these eigenvalues and their eigenvector components are missing

on quantum fidelities and channel capacities for the discrete memoryless quantum channel we show the equivalence of two different notions of quantum channel capacity that which uses the entanglement fidelity as its criterion for success in transmission and that which uses the minimum fidelity of pure states in a subspace of the input hilbert space as its criterion as a corollary any source with entropy rate less than the capacity may be transmitted with high entanglement fidelity we also show that a restricted class of encodings is sufficient to transmit any quantum source which may be transmitted on a given channel this enables us to simplify a known upper bound for the channel capacity it also enables us to show that the availability of an auxiliary classical channel from encoder to decoder does not increase the quantum capacity

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

estimating regression parameters using linear rank tests for censored data a class of estimates for regression parameters in a linear model with right censored data is proposed these estimates are derived by using linear rank tests for right censored data as estimating equations they are shown to be consistent and asymptotically normal with covariance matrix for which estimates are proposed efficient estimates within this class are derived together with conditions when they are fully efficient 0 introduction the problem of estimating regression coefficients using ranks has received much attention in the literature for uncensored data and the results are summarized very nicely in hettmansperger 1984 there has also been some work with censored data for the two sample problem specifically louis 1981 considered estimation of a scale change between two distributions with the use of a log rank test whereas wei and gail 1983 generalize to other linear rank tests as well we shall consider the general problem of multiple linear regression and show how linear rank tests can be used as estimating equations the resulting linear rank estimates will be shown to be asymptotically normal with variances that can be estimated consistently we shall also look at the efficiency of these estimates under various situations

hazard function estimators a simulation study kernel based methods for the smooth non parametric estimation of the hazard function have received considerable attention in the statistical literature although the mathematical properties of the kernel based hazard estimators have been carefully studied their statistical properties have not we reviewed various kernel based methods for hazard function estimation from right censored data and compared the statistical properties of these estimators through computer simulations our simulations covered seven distributions three levels of random censoring four types of bandwidth functions two sample sizes and three types of boundary correction we conducted a total of 504 simulation experiments with 500 independent samples each our results confirmed the advantages of two recent innovations in kernel estimation boundary correction and locally optimal bandwidths the median relative improvement decrease in mean square error over fixed bandwidth estimators without boundary correction was 3 per cent for fixed bandwidth estimators with left boundary correction 52 per cent locally optimal bandwidths without boundary correction and 66 per cent for locally optimal bandwidths with left boundary correction the locally optimal bandwidth estimators with left boundary correction also outperformed three previously published and publicly available algorithms with median relative improvements in mean square error of 31 per cent 77 per cent and 80 per cent

uncertainty relation for smooth entropies uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted while established uncertainty relations apply to cases where the predictions are based on purely classical data e g a description of the system s state before measurement an extended relation which remains valid in the presence of quantum information has been proposed recently berta et al nature phys 6 659 2010 here we generalize this uncertainty relation to one formulated in terms of smooth entropies since these entropies measure operational quantities such as extractable secret key length our uncertainty relation is of immediate practical use to illustrate this we show that it directly implies security of quantum key distribution protocols our security claim remains valid even if the implemented measurement devices deviate arbitrarily from the theoretical model

entanglement cost of quantum channels the entanglement cost of a quantum channel is the minimal rate at which entanglement between sender and receiver is needed in order to simulate many copies of a quantum channel in the presence of free classical communication in this paper we show how to express this quantity as a regularized optimization of the entanglement formation over states that can be generated between sender and receiver our formula is the channel analog of a well known formula for the entanglement cost of quantum states in terms of the entanglement of formation and shares a similar relation to the recently shattered hope for additivity the entanglement cost of a quantum channel can be seen as the analog of the quantum reverse shannon theorem in the case where free classical communication is allowed the techniques used in the proof of our result are then also inspired by a recent proof of the quantum reverse shannon theorem and feature the one shot formalism for quantum information theory the postselection technique for quantum channels as well as sion s minimax theorem we discuss two applications of our result first we are able to link the security in the noisy storage model to a problem of sending quantum rather than classical information through the adversary s storage device this not only improves the range of parameters where security can be shown but also allows us to prove security for storage devices for which no results were known before second our result has consequences for the study of the strong converse quantum capacity here we show that any coding scheme that sends quantum information through a quantum channel at a rate larger than the entanglement cost of the channel has an exponentially small fidelity

one shot decoupling if a quantum system a which is initially correlated to another system e undergoes an evolution separated from e then the correlation to e generally decreases here we study the conditions under which the correlation disappears almost completely resulting in a decoupling of a from e we give a criterion for decoupling in terms of two smooth entropies one quantifying the amount of initial correlation between a and e and the other characterizing the mapping that describes the evolution of a the criterion applies to arbitrary such mappings in the general one shot setting furthermore the criterion is tight for mappings that satisfy certain natural conditions one shot decoupling has a number of applications both in physics and information theory e g as a building block for quantum information processing protocols as an example we give a one shot state merging protocol and show that it is essentially optimal in terms of its entanglement consumption production

a low rank in time approach to pde constrained optimization the solution of time dependent pde constrained optimization problems is a challenging task in numerical analysis and applied mathematics all at once discretizations and corresponding solvers provide efficient methods to robustly solve the arising discretized equations one of the drawbacks of this approach is the high storage demand for the vectors representing the discrete space time cylinder here we introduce a low rank in time technique that exploits the low rank nature of the solution the theoretical foundations for this approach originate in the numerical treatment of matrix equations and can be carried over to pde constrained optimization we illustrate how three different problems can be rewritten and used within a low rank krylov subspace solver with appropriate preconditioning

time domain decomposition of optimal control problems for the wave equation we consider the problem of boundary optimal control of a wave equation with boundary dissipation by the way of time domain decomposition of the corresponding optimality system we develop an iterative algorithm which shows that the decomposed optimality system corresponds to local in time optimal control problems which can be treated in parallel we show convergence of the algorithm finally we provide a time discretization which is reminiscent of an instantaneous control scheme we thereby also contribute to the problem of convergence of such schemes

numerical solution of a flow control problem vorticity reduction by dynamic boundary action in order to laminarize an unsteady internal flow the vorticity field is minimized in a least squares sense using an optimal control approach the flow model is the navier stokes equation for a viscous incompressible fluid and the flow is controlled by suction and blowing on a part of the boundary a quasi newton method is used for the minimization of a quadratic objective function involving a measure of the vorticity and a regularization term the navier stokes equations are approximated using a finite difference scheme in time and finite element approximations in space accurate expressions for the gradient of the discrete objective function are needed to obtain a satisfactory convergence rate of the minimization algorithm therefore first order necessary conditions for a minimizer of the objective function are derived in the fully discrete case a memory saving device is discussed without which problems of any realistic size especially in three space dimensions would remain computationally intractable the feasibility of the optimal control approach for flow control problems is demonstrated by numerical experiments for a two dimensional flow in a rectangular cavity at a reynolds number high enough for nonlinear effects to be important

efficient time domain decomposition algorithms for parabolic pde constrained optimization problems abstract optimization with time dependent partial differential equations pdes as constraints appears in many science and engineering applications the associated first order necessary optimality system consists of one forward and one backward time dependent pde coupled with optimality conditions an optimization process by using the one shot method determines the optimal control state and adjoint state at once with the cost of solving a large scale fully discrete optimality system hence such a one shot method could easily become computationally prohibitive when the time span is long or time step is small to overcome this difficulty we propose several time domain decomposition algorithms for improving the computational efficiency of the one shot method in these algorithms the optimality system is split into many small subsystems over a much smaller time interval which are coupled by appropriate continuity matching conditions both one level and two level multiplicative and additive schwarz algorithms are developed for iteratively solving the decomposed subsystems in parallel in particular the convergence of the one level non overlapping algorithms is proved the effectiveness of our proposed algorithms is demonstrated by both 1d and 2d numerical experiments where the developed two level algorithms show convergence rates that are scalable with respect to the number of subdomains

linear regression analysis for multivariate failure time observations abstract in this article we consider the case that each patient in a longitudinal study may experience two or more distinct failures the corresponding failure times which are possible censored are recorded for each patient the logarithm of each marginal failure time is assumed to be linearly related to its covariates however the distributional form of the error term in the model does not have to be specified in the analysis furthermore no specific structure of dependence among the distinct failure times on each subject has to be imposed various linear regression methods for analyzing multivariate failure time observations are proposed our procedures do not involve the unstable nonparametric hazard function estimation extensive numerical studies are conducted to evaluate the new proposals recommendations are also made for their practical usage