the gaussian measure of shifted balls let be a centered gaussian measure on a hilbert spaceh and let b r subseteq h be the centered ball of radiusr 0 fora h and mathop lim limits t mathbf to mathbf infty mathbf r t t mathbf a we give the exact asymptotics of b r t t a ast also upper and lower bounds are given when is defined on an arbitrary separable banach space our results range from small deviation estimates to large deviation estimates

kolmogorov landau inequalities for monotone functions where llfll ess su if t kolmogorov 2 suceeded in finding the best possible constants in 1 where the norm is as in 2 except for isolated results no new progress was made until schoenberg and cavaretta 3 found the best possible constants for llfll su if f we propose to prove inequalities about various clases of monotone functions which yield as special cases pointwise inequalities of the form 1 for example

on quantum detection and the square root measurement we consider the problem of constructing measurements optimized to distinguish between a collection of possibly nonorthogonal quantum states we consider a collection of pure states and seek a positive operator valued measure povm consisting of rank one operators with measurement vectors closest in squared norm to the given states we compare our results to previous measurements suggested by peres and wootters 1991 and hausladen et al 1996 where we refer to the latter as the square root measurement srm we obtain a new characterization of the srm and prove that it is optimal in a least squares sense in addition we show that for a geometrically uniform state set the srm minimizes the probability of a detection error this generalizes a similar result of ban et al see int j theor phys vol 36 p 1269 88 1997

mills ratio monotonicity patterns and functional inequalities in this paper we study the monotonicity properties of some functions involving the mills ratio of the standard normal law from these we deduce some new functional inequalities involving the mills ratio and we show that the mills ratio is strictly completely monotonic at the end of this paper we present some turan type inequalities for mills ratio

simultaneous polar decomposition of rectangular complex matrices abstract a criterion for simultaneous polar decomposibility of two rectangular complex matrices is derived using the gl ordering of hauke and markiewicz j hauke a markiewicz on partial ordering on the set of rectangular matrices linear algebra appl 219 1995 187 193 a new characterization of this ordering is also given

quantum communication with coherent states quantum communication is studied under the cutoff rate criterion for transmission of m coherent states of real amplitude m 2 7 comparison with other measurement operators of interest such as the number and the quasi classical operators is made the effect of quantization of the decision level on the cutoff rate is considered

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

optimal tight frames and quantum measurement tight frames and rank one quantum measurements are shown to be intimately related in fact the family of normalized tight frames for the space in which a quantum mechanical system lies is precisely the family of rank one generalized quantum measurements on that space using this relationship frame theoretical analogs of various quantum mechanical concepts and results are developed the analog of a least squares quantum measurement is a tight frame that is closest in a least squares sense to a given set of vectors the least squares tight frame is found for both the case in which the scaling of the frame is specified constrained least squares frame clsf and the case in which the scaling is chosen to minimize the least squares error unconstrained least squares frame ulsf the well known canonical frame is shown to be proportional to the ulsf and to coincide with the clsf with a certain scaling

optimal distinction between non orthogonal quantum states given a finite set of linearly independent quantum states an observer who examines a single quantum system may sometimes identify its state with certainty however unless these quantum states are orthogonal there is a finite probability of failure a complete solution is given to the problem of optimal distinction of three states having arbitrary prior probabilities and arbitrary detection values a generalization to more than three states is outlined

nonuniform sampling and reconstruction in shift invariant spaces this article discusses modern techniques for nonuniform sampling and reconstruction of functions in shift invariant spaces it is a survey as well as a research paper and provides a unified framework for uniform and nonuniform sampling and reconstruction in shift invariant subspaces by bringing together wavelet theory frame theory reproducing kernel hilbert spaces approximation theory amalgam spaces and sampling inspired by applications taken from communication astronomy and medicine the following aspects will be emphasized a the sampling problem is well defined within the setting of shift invariant spaces b the general theory works in arbitrary dimension and for a broad class of generators c the reconstruction of a function from any sufficiently dense nonuniform sampling set is obtained by efficient iterative algorithms these algorithms converge geometrically and are robust in the presence of noise d to model the natural decay conditions of real signals and images the sampling theory is developed in weighted l p spaces

completely monotonic and related functions abstract we study completely monotonic and related functions whose firstnderivatives are definite on an interval let l ndenote the class of functions defined by f in cal l n leftrightarrow 1 k f k t ge0 qquad forall t 0 forall k 0 le k le n forn we writef l such functions are called completely monotonic on 0 we prove in particular that the implication f in cal l n rightarrow bigl forall alpha 1 colon f alpha in cal l n bigr is true for 0 n 5 but false forn 6 in contrast l lorch and d j newman j london math soc 2 28 1983 31 45 theorem 8 claimed this implication to be false forn 5 further we prove that the implication f in cal l rightarrow bigl forall alpha 1 colon f alpha in cal l n bigr is true for 0 n 6 but false forn 20

estimation of object motion parameters from noisy images an approach is presented for the estimation of object motion parameters based on a sequence of noisy images the problem considered is that of a rigid body undergoing unknown rotational and translational motion the measurement data consists of a sequence of noisy image coordinates of two or more object correspondence points by modeling the object dynamics as a function of time estimates of the model parameters including motion parameters can be extracted from the data using recursive and or batch techniques this permits a desired degree of smoothing to be achieved through the use of an arbitrarily large number of images some assumptions regarding object structure are presently made results are presented for a recursive estimation procedure the case considered here is that of a sequence of one dimensional images of a two dimensional object thus the object moves in one transverse dimension and in depth preserving the fundamental ambiguity of the central projection image model loss of depth information an iterated extended kalman filter is used for the recursive solution noise levels of 5 10 percent of the object image size are used approximate cramer rao lower bounds are derived for the model parameter estimates as a function of object trajectory and noise level this approach may be of use in situations where it is difficult to resolve large numbers of object match points but relatively long sequences of images 10 to 20 or more are available

cutoff rate for the m ary psk modulation channel with optimal quantum detection the cutoff rate r sub 0 of an optical channel transmitting m ary phase shift keyed coherent states is calculated for a receiver using the optimum quantum detector this is shown to be nearly equivalent when m 1 to a system that measures the phase of the received signal a closed form expression yielding a good approximation to r sub 0 is derived

a semidefinite program for distillable entanglement we show that the maximum fidelity obtained by a positive partial transpose p p t distillation protocol is given by the solution to a certain semidefinite program this gives a number of new lower and upper bounds on p p t distillable entanglement and thus new upper bounds on 2 locally distillable entanglement in the presence of symmetry the semidefinite program simplifies considerably becoming a linear program in the case of isotropic and werner states using these techniques we determine the p p t distillable entanglement of asymmetric werner states and maximally correlated states we conclude with a discussion of possible applications of semidefinite programming to quantum codes and 1 local distillation

minimum error discrimination between self symmetric mixed quantum state signals we derive some properties of minimum error measurements for mixed quantum state signals where a density operator itself has a certain symmetry in the first case we show that if there exists a regular normal operator that commutes with each density operator of mixed state signals then there exists an optimal measurement that consists of detection operators expressed as the direct sum of positive operators with supports in the eigenspaces of the regular normal operator in the second case we show that for abelian geometrically uniform state signals if a matrix which represents one of the signals in a certain basis has all real elements then the matrix which represents the corresponding detection operator of an optimal measurement in that basis also has all real elements in addition we discuss some examples of applications of these properties and derive analytical solutions of optimal measurements for special cases

an exact chi squared decomposition theorem for inverse gaussian variates on montre que la deviance d echelle d un echantillon normal inverse de dimension n peut etre exprimee comme la somme de n 1 variables khi deux independantes

least squares orthogonalization using semidefinite programming we consider the problem of constructing an optimal set of orthogonal vectors from a given set of vectors in a real hilbert space the vectors are chosen to minimize the sum of the squared norms of the errors between the constructed vectors and the given vectors we show that the design of the optimal vectors referred to as the least squares ls orthogonal vectors can be formulated as a semidefinite programming sdp problem using the many well known algorithms for solving sdps which are guaranteed to converge to the global optimum the ls vectors can be computed very efficiently in polynomial time within any desired accuracy by exploiting the connection between our problem and a quantum detection problem we derive a closed form analytical expression for the ls orthogonal vectors for vector sets with a broad class of symmetry properties specifically we consider geometrically uniform gu sets with a possibly non abelian generating group and compound gu sets which consist of subsets that are gu

evaluation of relative entropy of entanglement and derivation of optimal lewenstein sanpera decomposition of bell decomposable states via convex optimization abstract we provide an analytical expression for optimal lewenstein sanpera decomposition of bell decomposable states by using semi definite programming also using the karush kuhn tucker optimization method the minimum relative entropy of entanglement of bell decomposable states has been evaluated and it is shown that the same separable bell decomposable state lying at the boundary of convex set of separable bell decomposable states optimizes both lewenstein sanpera decomposition and relative entropy of entanglement

on the distinguishability of random quantum states we develop two analytic lower bounds on the probability of success p of identifying a state picked from a known ensemble of pure states a bound based on the pairwise inner products of the states and a bound based on the eigenvalues of their gram matrix we use the latter and results from random matrix theory to lower bound the asymptotic distinguishability of ensembles of n random quantum states in d dimensions where n d approaches a constant in particular for almost all ensembles of n states in n dimensions p 0 72 an application to distinguishing boolean functions the oracle identification problem in quantum computation is given

uniqueness and estimation of three dimensional motion parameters of rigid objects with curved surfaces two main results are established in this paper first we show that seven point correspondences are sufficient to uniquely determine from two perspective views the three dimensional motion parameters within a scale factor for the translations of a rigid object with curved surfaces the seven points should not be traversed by two planes with one plane containing the origin nor by a cone containing the origin second a set of essential parameters are introduced which uniquely determine the motion parameters up to a scale factor for the translations and can be estimated by solving a set of linear equations which are derived from the correspondences of eight image points the actual motion parameters can subsequently be determined by computing the singular value decomposition svd of a 3 3 matrix containing the essential parameters

theoretical explanation of observed decreasing failure rate pooled data on the times of successive failures of the air conditioning system of a fleet of jet airplanes seemed to indicate that the life distribution had a decreasing failure rate more refined analysis showed that the failure distribution for each airplane separately was exponential but with a different failure rate using the theorem that a mixture of distributions each having a non increasing failure rate e g a mixture of exponential distributions itself has a non increasing failure rate the apparent decreasing failure rate of the pooled air conditioning life distribution was satisfactorily explained the present study has implications in other areas where an observed decreasing failure rate may well be the result of mixing exponential distributions having different parameters

recovery of the 3 d location and motion of a rigid object through camera image an extended kalman filter approach this paper deals with the problem of locating a rigid object and estimating its motion in three dimensions this involves determining the position and orientation of the object at each instant when an image is captured by a camera and recovering the motion of the object between consecutive frames in the implementation scheme used here a sequence of camera images digitized at the sample instants is used as the initial input data measurements are made of the locations of certain features e g maximum curvature points of an image contour corners edges etc on the 2 d images to measure the feature locations a matching algorithm is used which produces correspondences between the features in the image and the object using the measured feature locations on the image an algorithm is developed to solve the location and motion problem the algorithm is an extended kalman filter modeled for this application

frame theoretic analysis of oversampled filter banks we provide a frame theoretic analysis of oversampled finite impulse response fir and infinite impulse response fir uniform filter banks fbs our analysis is based on a new relationship between the fbs polyphase matrices and the frame operator corresponding to an fb for a given oversampled analysis fb we present a parameterization of all synthesis fbs providing perfect reconstruction we find necessary and sufficient conditions for an oversampled fb to provide a frame expansion a new frame theoretic procedure for the design of paraunitary fbs from given nonparaunitary fbs is formulated we show that the frame bounds of an fb can be obtained by an eigen analysis of the polyphase matrices the relevance of the frame bounds as a characterization of important numerical properties of an fb is assessed by means of a stochastic sensitivity analysis we consider special cases in which the calculation of the frame bounds and synthesis filters is simplified finally simulation results are presented

geometrically uniform frames we introduce a new class of finite dimensional frames with strong symmetry properties called geometrically uniform gu frames that are defined over a finite abelian group of unitary matrices and are generated by a single generating vector the notion of gu frames is then extended to compound gu cgu frames which are generated by a finite abelian group of unitary matrices using multiple generating vectors the dual frame vectors and canonical tight frame vectors associated with gu frames are shown to be gu and therefore also generated by a single generating vector which can be computed very efficiently using a fourier transform ft defined over the generating group of the frame similarly the dual frame vectors and canonical tight frame vectors associated with cgu frames are shown to be cgu the impact of removing single or multiple elements from a gu frame is considered a systematic method for constructing optimal gu frames from a given set of frame vectors that are not gu is also developed finally the euclidean distance properties of gu frames are discussed and conditions are derived on the abelian group of unitary matrices to yield gu frames with strictly positive distance spectrum irrespective of the generating vector

performance of quantum data transmission systems in the presence of thermal noise in the literature the performance of quantum data transmission systems is usually evaluated in the absence of thermal noise a more realistic approach taking into account the thermal noise is intrinsically more difficult because it requires dealing with glauber coherent states in an infinite dimensional space in particular the exact evaluation of the optimal measurement operators is a very difficult task and numerical approximation is unavoidable the paper faces the problem by approximating the p representation of the noisy quantum states with a large but finite numbers of terms and applying to them the square root measurement srm approach comparisons with cases where the exact solution are known show that the srm approach gives quite accurate results as application the performance of quadrature amplitude modulation qam and phase shift keying psk systems is considered in spite of the fact that the srm approach is not optimal and overestimates the error probability also in these cases the quantum detection maintains its superiority with respect to the classical homodyne detection

bayes cost reduction algorithm in quantum hypothesis testing corresp an iterative procedure is described for reducing the bayes cost in decisions among m 2 quantum hypotheses by minimizing the average cost in binary decisions between all possible pairs of hypotheses the resulting decision strategy is a projection valued measure and yields an upper bound to the minimum attainable bayes cost from it is derived an algorithm for finding the optimum measurement states for choosing among m linearly independent pure states with minimum probability of error the method is also applied to decisions among m unimodal coherent quantum signals in thermal noise

the feasibility of motion and structure from noisy time varying image velocity information this research addresses the problem of noise sensitivity inherent in motion and structure algorithms the motion and structure paradigm is a two step process first we measure image velocities and perhaps their spatial and temporal derivatives are obtained from time varying image intensity data and second we use these data to compute the motion of a moving monocular observer in a stationary environment under perspective projection relative to a single 3 d planar surface the first contribution of this article is an algorithm that uses time varying image velocity information to compute the observer s translation and rotation and the normalized surface gradient of the 3 d planar surface the use of time varying image velocity information is an important tool in obtaining a more robust motion and structure calculation the second contribution of this article is an extensive error analysis of the motion and structure problem any motion and structure algorithm that uses image velocity information as its input should exhibit error sensitivity behavior compatible with the results reported here we perform an average and worst case error analysis for four types of image velocity information full and normal image velocities and full and normal sets of image velocity and its derivatives these derivatives are simply the coefficients of a truncated taylor series expansion about some point in space and time the main issues we address here are just how sensitive is a motion and structure computation in the presence of noisy input or alternately how accurate must our image velocity information be how much and what type of input data is needed and under what circumstances is motion and structure feasible that is when can we be sure that a motion and structure computation will produce usable results we base our answers on a numerical error analysis we conduct for a large number of motions

recursive estimation of time varying motion and structure parameters we present a computational framework for recovering both first order motion parameters observer direction of translation and observer rotation second order motion parameters observer rotational acceleration and relative depth maps from time varying optical flow we recover translation speed and acceleration in units which are scaled relative to the distance to the object our assumption is that the observer rotational motion is no more than second order in other words observer motion is either constant or has at most constant acceleration we examine the effect of noise on the solution of the motion and structure parameters this ensemble of unknowns comprises a solution to the classical structure and motion from optic flow problem our complete framework utilizes a method for interpreting the bilinear image velocity equation by solving simple systems of linear equations since our noise analysis yields uncertainty measures for each parameter a kalman filter is employed to incrementally integrate new measurements as they become available as each additional frame in the sequence is processed we conclude by analysing this reduction of uncertainty over time as the system converges to a stable solution for both synthetic and real image sequences

oversampled filter banks perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in l sup 2 z these frames are the subject of this paper first the necessary and sufficient conditions of a filter bank for implementing a frame or a tight frame expansion are established as well as a necessary and sufficient condition for perfect reconstruction using fir filters after an fir analysis complete parameterizations of oversampled filter banks satisfying these conditions are given further we study the condition under which the frame dual to the frame associated with an fir filter bank is also fir and give a parameterization of a class of filter banks satisfying this property then we focus on non subsampled filter banks non subsampled filter banks implement transforms similar to continuous time transforms and allow for very flexible design we investigate the relations of these filter banks to continuous time filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two channel filter banks that yield highly regular wavelets with a given number of vanishing moments

geometric quantum discord with bures distance the qubit case the minimal bures distance of a quantum state of a bipartite system ab to the set of classical states for subsystem a defines a geometric measure of quantum discord when a is a qubit we show that this geometric quantum discord is given in terms of the eigenvalues of a 2nb 2nb hermitian matrix nb being the hilbert space dimension of the other subsystem b as a first application we calculate the geometric discord for the output state of the dqc1 algorithm we find that it takes its highest value when the unitary matrix from which the algorithm computes the trace has its eigenvalues uniformly distributed on the unit circle modulo a symmetry with respect to the origin as a second application we derive an explicit formula for the geometric discord of a two qubit state with maximally mixed marginals and compare it with other measures of quantum correlations we also determine the closest classical states to

prediction limits for the inverse gaussian distribution prediction intervals for the inverse gaussian are obtained from both a frequentist and a bayesian viewpoint the frequentist intervals are obtained by constructing pivotals that have the x 2 and f distributions the method involves inversion of probability statements which results in two sided prediction intervals a bayesian predictive density is obtained using a vague prior from which one or two sided bayesian prediction intervals can be determined an example for which bayesian prediction limits are narrower than the frequentist is given

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

minimal entropy of states emerging from noisy quantum channels we consider the minimal entropy of qubit states transmitted through two uses of a noisy quantum channel which is modeled by the action of a completely positive trace preserving or stochastic map we provide strong support for the conjecture that this minimal entropy is additive namely that the minimum entropy can be achieved when product states are transmitted explicitly we prove that for a tensor product of two unital stochastic maps on qubit states using an entanglement that involves only states which emerge with minimal entropy cannot decrease the entropy below the minimum achievable using product states we give a separate argument based on the geometry of the image of the set of density matrices under stochastic maps which suggests that the minimal entropy conjecture holds for nonunital as well as for unital maps we also show that the maximal norm of the output states is multiplicative for most product maps on n qubit states including all those for which at least one map is unital for the class of unital channels on c sup 2 we show that additivity of minimal entropy implies that the holevo see ieee trans inform theory vol 44 p 269 73 1998 and russian math surv p 1295 1331 1999 capacity of the channel is additive over two inputs achievable with orthogonal states and equal to the shannon capacity this implies that superadditivity of the capacity is possible only for nonunital channels

a note on multivariate gaussian estimates an upper bound of multivariate gaussian probability for a general convex domain d is given based on a geometric observation the bound is sharper than known ones on multivariate mills ratio in many cases

two sided estimates of minimum error distinguishability of mixed quantum states via generalized holevo curlander bounds we prove a concise factor of 2 estimate for the failure rate of optimally distinguishing an arbitrary ensemble of mixed quantum states generalizing work of holevo theor probab appl 23 411 1978 and curlander ph d thesis mit 1979 a modification to the minimal principle of cocha and poor proceedings of the 6th international conference on quantum communication measurement and computing rinton princeton nj 2003 is used to derive a suboptimal measurement which has an error rate within a factor of 2 of the optimal by construction this measurement is quadratically weighted and has appeared as the first iterate of a sequence of measurements proposed by je ek et al phys rev a 65 060301 2002 unlike the so called pretty good measurement it coincides with holevo s asymptotically optimal measurement in the case of nonequiprobable pure states a quadratically weighted version of the measurement bound by barnum and knill j math phys 43 2097 2002 is proven bounds on the distingu

a semidefinite programming approach to optimal unambiguous discrimination of quantum states we consider the problem of unambiguous discrimination between a set of linearly independent pure quantum states we show that the design of the optimal measurement that minimizes the probability of an inconclusive result can be formulated as a semidefinite programming problem based on this formulation we develop a set of necessary and sufficient conditions for an optimal quantum measurement we show that the optimal measurement can be computed very efficiently in polynomial time by exploiting the many well known algorithms for solving semidefinite programs which are guaranteed to converge to the global optimum using the general conditions for optimality we derive necessary and sufficient conditions so that the measurement that results in an equal probability of an inconclusive result for each one of the quantum states is optimal we refer to this measurement as the equal probability measurement epm we then show that for any state set the prior probabilities of the states can be chosen such that the epm is optimal finally we consider state sets with strong symmetry properties and equal prior probabilities for which the epm is optimal we first consider geometrically uniform gu state sets that are defined over a group of unitary matrices and are generated by a single generating vector we then consider compound gu state sets which are generated by a group of unitary matrices using multiple generating vectors where the generating vectors satisfy a certain weighted norm constraint

square root measurement for quantum symmetric mixed state signals a certain class of mixed states artificially constructed that is used in quantum cryptography is crucial for representation of signals this correspondence shows that the square root measurement gives the optimal measurement for such a class of mixed states

least squares inner product shaping we develop methods that construct an optimal set of vectors with a specified inner product structure from a given set of vectors in a complex hilbert space the optimal vectors are chosen to minimize the sum of the squared norms of the errors between the constructed vectors and the given vectors four special cases are considered in the first the constructed vectors are orthonormal in the second they are orthogonal in the third the gram matrix of inner products of the constructed vectors is a circulant matrix as we show the vectors form a cyclic set in the fourth the gram matrix has the property that the rows are all permutations of each other the constructed vectors are shown to be geometrically uniform

3 d motion estimation understanding and prediction from noisy image sequences this paper presents an approach to understanding general 3 d motion of a rigid body from image sequences based on dynamics a locally constant angular momentum lcam model is introduced the model is local in the sense that it is applied to a limited number of image frames at a time specifically the model constrains the motion over a local frame subsequence to be a superposition of precession and translation thus the instantaneous rotation axis of the object is allowed to change through the subsequence the trajectory of the rotation center is approximated by a vector polynomial the parameters of the model evolve in time so that they can adapt to long term changes in motion characteristics the nature and parameters of short term motion can be estimated continuously with the goal of understanding motion through the image sequence the estimation algorithm presented in this paper is linear i e the algorithm consists of solving simultaneous linear equations based on the assumption that the motion is smooth object positions and motion in the near future can be predicted and short missing subsequences can be recovered noise smoothing is achieved by overdetermination and a leastsquares criterion the framework is flexible in the sense that it allows both overdetermination in number of feature points and the number of image frames

upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination we consider the multiple hypothesis testing problem for symmetric quantum state discrimination between r given states 1 r by splitting up the overall test into multiple binary tests in various ways we obtain a number of upper bounds on the optimal error probability in terms of the binary error probabilities these upper bounds allow us to deduce various bounds on the asymptotic error rate for which it has been hypothesized that it is given by the multi hypothesis quantum chernoff bound or chernoff divergence c 1 r as recently introduced by nussbaum and szkola in analogy with salikhov s classical multi hypothesis chernoff bound this quantity is defined as the minimum of the pairwise binary chernoff divergences minj kc j k it was known already that the optimal asymptotic rate must lie between c 3 and c and that for certain classes of sets of states the bound is actually achieved it was known to be achieved in particular when the state pair that is closest together in chernoff dive

vehicle type motion estimation from multi frame images a model for vehicle type motion which assumes that the motion is a rotation around an axis through the vehicle center followed by a forward translation along the main axis of the vehicle is proposed when the rotation and the amplitude of translation are constant this type of motion is shown to be equivalent to a constant camera centered motion this indicates that a constant motion in the conventional camera centered model which is commonly considered to be artificial can in fact be a reasonable model in real life it is shown that a constant vehicle type motion can be interpreted as a constant screw motion a linear algorithm for estimating constant vehicle type motion is presented and experiments using real scene images are included as an extension vehicle type motion with constant rotation and constantly accelerated translation is discussed

inequalities for real powers of completely monotonic functions let lndenote the class of functions defined byf ln 1 kf k t 0 t 0 k 0 k n forn we writef l functions in l are called completely monotonic on 0 we derive several inequalities involving completely monotonic functions in particular we prove that the implicationf l 1 f ln is true for 0 n 7 but false forn 13

covariance shaping least squares estimation a new linear estimator is proposed which we refer to as the covariance shaping least squares csls estimator for estimating a set of unknown deterministic parameters x observed through a known linear transformation h and corrupted by additive noise the csls estimator is a biased estimator directed at improving the performance of the traditional least squares ls estimator by choosing the estimate of x to minimize the weighted total error variance in the observations subject to a constraint on the covariance of the estimation error so that we control the dynamic range and spectral shape of the covariance of the estimation error the presented csls estimator is shown to achieve the cramer rao lower bound for biased estimators furthermore analysis of the mean squared error mse of both the csls estimator and the ls estimator demonstrates that the covariance of the estimation error can be chosen such that there is a threshold snr below which the csls estimator yields a lower mse than the ls estimator for all values of x as we show some of the well known modifications of the ls estimator can be formulated as csls estimators this allows us to interpret these estimators as the estimators that minimize the total error variance in the observations among all linear estimators with the same covariance

on some identities and inequalities for frames in hilbert spaces we give new parseval type identities and inequalities for frames in hilbert spaces our results generalize the remarkable results obtained recently by r balan p g casazza d edidin and g kutyniok

direct methods for recovering motion we have developed direct methods for recovering the motion of an observer in a static environment in the case of pure rotation pure translation and arbitrary motion when the rotation is known some of these methods are based on the minimization of the difference between the observed time derivative of brightness and that predicted from the spatial brightness gradient given the estimated motion we minimize the square of the integral of this difference taken over the image region of interest other methods presented here exploit the fact that surfaces have to be in front of the observer in order to be seen

quantum detection and mutual information for qam and psk signals we analyze the performance of the error probability and the mutual information for quadrature amplitude modulation qam and phase shift keying systems based on quantum detection theory it is shown that the quantum receiver called square root measurement gives about 5 7 db improvement in power in comparison with the classical one furthermore we show that the quantum qam system can achieve the same reliability as the conventional intensity modulation direct detection im dd system with almost equal power compressing the required bandwidth while the reliability is degraded in general

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

designing optimal quantum detectors via semidefinite programming we consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing among a collection of quantum states represented by a set of density operators we show that the design of the optimal detector can be formulated as a semidefinite programming problem based on this formulation we derive a set of necessary and sufficient conditions for an optimal quantum measurement we then show that the optimal measurement can be found by solving a standard convex semidefinite program by exploiting the many well known algorithms for solving semidefinite programs which are guaranteed to converge to the global optimum the optimal measurement can be computed very efficiently in polynomial time within any desired accuracy using the semidefinite programming formulation we also show that the rank of each optimal measurement operator is no larger than the rank of the corresponding density operator in particular if the quantum state ensemble is a pure state ensemble consisting of not necessarily independent rank one density operators then we show that the optimal measurement is a pure state measurement consisting of rank one measurement operators

two sided bounds on minimum error quantum measurement on the reversibility of quantum dynamics and on maximum overlap using directional iterates in a unified framework we estimate the following quantities of interest in quantum information theory 1 the minimum error distinguishability of arbitrary ensembles of mixed quantum states 2 the approximate reversibility of quantum dynamics in terms of entanglement fidelity this is referred to as channel adapted quantum error recovery when applied to the composition of an encoding operation and a noise channel 3 the maximum overlap between a bipartite pure quantum state and a bipartite mixed state that may be achieved by applying a local quantum operation to one part of the mixed state and 4 the conditional min entropy of bipartite quantum states a refined version of the author s techniques j tyson j math phys 50 032016 2009 for bounding the first quantity is employed to give two sided estimates of the remaining three quantities we obtain a closed form approximate reversal channel using a state dependent kraus decomposition our reversal may be interpreted as a quadratically

distinguishing separable and entangled states we show how to design families of operational criteria that distinguish entangled from separable quantum states the simplest of these tests corresponds to the well known peres horodecki positive partial transpose ppt criterion and the more complicated tests are strictly stronger the new criteria are tractable due to powerful computational and theoretical methods for the class of convex optimization problems known as semidefinite programs we successfully applied the results to many low dimensional states from the literature where the ppt test fails as a by product of the criteria we provide an explicit construction of the corresponding entanglement witnesses

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

the accuracy of the computation of optical flow and of the recovery of motion parameters the accuracy and the dependence on parameters of a general scheme for the analysis of time varying image sequences are discussed the approach is able to produce vector fields from which it is possible to recover 3 d motion parameters such as time to collision and angular velocity the numerical stability of the computed optical flow and the dependence of the recovery of 3 d motion parameters on spatial and temporal filtering is investigated by considering optical flows computed on subsampled images or along single scanlines it is also possible to recover 3 d motion parameters from reduced optical flows an adequate estimate of time to collision can be obtained from sequences of images with spatial resolution reduced to 128 128 pixels or from sequences of single scanlines passing near the focus of expansion the use of kalman filtering increases the accuracy and the robustness of the estimation of motion parameters the proposed approach seems to be able to provide not only a theoretical background but also practical tools that are adequate for the analysis of time varying image sequences

theory of quantum pulse position modulation and related numerical problems the paper deals with quantum pulse position modulation ppm both in the absence pure states and in the presence mixed states of thermal noise using the glauber representation of coherent laser radiation the objective is to find optimal or suboptimal measurement operators and to evaluate the corresponding error probability for ppm the correct formulation of quantum states is given by the tensorial product of m identical hilbert spaces where m is the ppm order the presence of mixed states due to thermal noise generates an optimization problem involving matrices of huge dimensions which already for 4 ppm are of the order of ten thousand to overcome this computational complexity the currently available methods of quantum detection which are based on explicit results convex linear programming and square root measurement are compared to find the computationally less expensive one in this paper a fundamental role is played by the geometrically uniform symmetry of the quantum ppm format the evaluation of error probability confirms the vast superiority of the quantum detection over its classical counterpart

approximating mills ratio abstract consider the mills ratio f x 1 x x x 0 where is the density function of the standard gaussian law and its cumulative distribution we introduce a general procedure to approximate f on the whole 0 which allows to prove interesting properties where f is involved as applications we present a new proof that 1 f is strictly convex and we give new sharp bounds of f involving rational functions functions with square roots or exponential terms also chernoff type bounds for the gaussian q function are studied

geometrically uniform codes a signal space code c is defined as geometrically uniform if for any two code sequences in c there exists an isometry that maps one sequence into the other while leaving the code c invariant geometrical uniformity a strong kind of symmetry implies such properties as a the distance profiles from code sequences in c to all other code sequences are all the same and b all voronoi regions of code sequences in c have the same shape it is stronger than ungerboeck zehavi wolf symmetry or calderbank sloane regularity nonetheless most known good classes of signal space codes are shown to be generalized coset codes and therefore geometrically uniform including a lattice type trellis codes based on lattice partitions lambda lambda such that z sup n lambda lambda 4z sup n is a lattice partition chain and b phase shift keying psk type trellis codes based on up to four way partitions of a 2 sup n psk signal set

three dimensional motion computation and object segmentation in a long sequence of stereo frames we address the problem of computing the three dimensional motions of objects in a long sequence of stereo frames our approach is bottom up and consists of two levels the first level deals with the tracking of 3d tokens from frame to frame and the estimation of their kinematics the processing is completely parallel for each token the second level groups tokens into objects based on their kinematic parameters controls the processing at the low level to cope with problems such as occlusion disappearance and appearance of tokens and provides information to other components of the system we have implemented this approach using 3d line segments obtained from stereo as the tokens we use classical kinematics and derive closed form solutions for some special but useful cases of motions the motion computation problem is then formulated as a tracking problem in order to apply the extended kalman filter the tracking is performed in a prediction matching update loop in which multiple matches can be handled tokens are labeled by a number called its support of existence which measures their adequation to the measurements if this number goes beyond a threshold the token disappears the individual line segments can be grouped into rigid objects according to the similarity of their kinematic parameters experiments using synthetic and real data have been carried out and the results found to be quite good

continuous and discrete wavelet transforms this paper is an expository survey of results on integral representations and discrete sum expansions of functions in l 2 bf r in terms of coherent states two types of coherent states are considered weyl heisenberg coherent states which arise from translations and modulations of a single function and affine coherent states called wavelets which arise as translations and dilations of a single function in each case it is shown how to represent any function in l 2 bf r as a sum or integral of these states most of the paper is a survey of literature most notably the work of i daubechies a grossmann and j morlet a few results of the authors are included

an optimal whitening approach to linear multiuser detection we propose a new linear multiuser receiver for synchronous code division multiple access cdma systems referred to as the orthogonal multiuser omu receiver unlike the linear minimum mean squared error mmse receiver the omu receiver depends only on the signature vectors and does not require knowledge of the received amplitudes or the channel signal to noise ratio snr several equivalent representations of the receiver are developed with different implications in terms of implementation in the first the receiver consists of a decorrelator demodulator followed by an optimal whitening transformation on a space formed by the signatures in the second the receiver consists of a bank of correlators with correlating vectors that are projections of a set of orthogonal vectors and are closest in a least squares sense to the decorrelator vectors and also closest in a least squares sense to the signature vectors in the third the receiver consists of a single user matched filter mf followed by an optimal whitening transformation on a space formed by the signatures we derive exact and approximate expressions for the probability of bit error as well as the asymptotic signal to interference noise ratio sinr in the large system limit the analysis suggests that over a wide range of channel parameters the omu receiver can outperform both the decorrelator and the single user mf and perform similarly to the linear mmse receiver despite not knowing the channel parameters

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

some new upper and lower bounds for the mills ratio abstract in this paper we present new upper and lower bounds for the mills ratio of the standard gaussian law several different methods are used to derive these new bounds one of the methods reproduces the bounds of several different authors in previous works as special cases and is a very general method that produces many new bounds one of the bounds can be written in terms of hyperbolic sine and inverse hyperbolic sine functions some of the bounds involve exponential functions and are improved versions of previously proposed bounds or are improved versions of the new bounds introduced earlier in this paper some results from reliability theory and jensen s inequality are used to improve determinantal inequalities some open problems are discussed and conjectures are made

state discrimination with post measurement information we introduce a new state discrimination problem in which we are given additional information about the state after the measurement or more generally after a quantum memory bound applies the following special case plays an important role in quantum cryptographic protocols in the bounded storage model given a string x encoded in an unknown basis chosen from a set of mutually unbiased bases mubs you may perform any measurement but then store at most q qubits of quantum information and an unlimited amount of classical information later on you learn which basis was used how well can you compute a function f x of x given the initial measurement outcome the q qubits and the additional basis information we first show a lower bound on the success probability for any balanced function and any number of mutually unbiased bases beating the naive strategy of simply guessing the basis we then show that for two bases any boolean function f x can be computed perfectly if you are allowed to store just a single qubit independent of the number of possible input strings x however we show how to construct three bases such that you need to store all qubits in order to compute f x perfectly we then investigate how much advantage the additional basis information can give for a boolean function to this end we prove optimal bounds for the success probability for the and and the xor function for up to three mutually unbiased bases our result shows that the gap in success probability can be maximal without the basis information you can never do better than guessing the basis but with this information you can compute f x perfectly we also give an example where the extra information does not give any advantage at all

a multi frame approach to visual motion perception one of the main issues in the area of motion estimation given the correspondences of some features in a sequence of images is sensitivity to error in the input the main way to attack the problem as with several other problems in science and engineering is redundancy in the data up to now all the algorithms developed either used two frames or depended on assumptions about the motion or the shape of the scene we present in this paper an algorithm based on multiple frames that employs only the rigidity assumption is simple and mathematically elegant and experimentally proves to be a major improvement over the two frame algorithms the algorithm does minimization of the squared error which we prove equivalent to an eigenvalue minimization problem one of the side effects of this mean square method is that the algorithm can have a very descriptive physical interpretation in terms of the loaded spring model

direct passive navigation in this correspondence we show how to recover the motion of an observer relative to a planar surface from image brightness derivatives we do not compute the optical flow as an intermediate step only the spatial and temporal brightness gradients at a minimum of eight points we first present two iterative schemes for solving nine nonlinear equations in terms of the motion and surface parameters that are derived from a least squares fomulation an initial pass over the relevant image region is used to accumulate a number of moments of the image brightness derivatives all of the quantities used in the iteration are efficiently computed from these totals without the need to refer back to the image we then show that either of two possible solutions can be obtained in closed form we first solve a linear matrix equation for the elements of a 3 3 matrix the eigenvalue decomposition of the symmetric part of the matrix is then used to compute the motion parameters and the plane orientation a new compact notation allows us to show easily that there are at most two planar solutions

multiple interpretations of a pair of images of a surface it is known that if two optical images of a visually textured surface projected from finitely separated viewpoints allow more than one 3d interpretation then the surface must be part of a quadric passing through the two viewpoints it is here shown that this quadric is either a plane or a ruled surface of a type first considered by maybank in a study of ambiguous optic flow fields and that in the latter case three is the maximum number of distinct interpretations that the two images can sustain

finding optimal solutions for generalized quantum state discrimination problems we study an optimal quantum measurement for generalized quantum state discrimination problems which include the problem of finding an optimal measurement maximizing the average success probability with and without a fixed rate of inconclusive results and the problem of finding an optimal measurement in the neyman pearson strategy we show that for any generalized quantum state discrimination problem there is a corresponding minimum error discrimination problem sharing the same optimal measurement we propose an approach in which the optimal measurement is obtained by solving the corresponding minimum error discrimination problem and clarify the relationship between optimal solutions to the original and the corresponding problems with which one can obtain an optimal solution to the original problem in some cases moreover as an example of application of our approach we present an algorithm for numerically obtaining optimal solutions to generalized quantum state discrimination problems

certain approximations to achieve sharp lower and upper bounds for the mills ratio of the inverse gaussian distribution abstract in this note we prove new complete monotonicity properties of some functions associated with the inverse gaussian distribution based on these properties we present some lower and upper bounds with explicit expressions for the mills ratio of the inverse gaussian distribution finally for demonstrating the efficiency of our estimates some numerical computations are provided

geometric coherence and quantum state discrimination the operational meaning of coherence measure lies at the very heart of the coherence theory in this paper we provide an operational interpretation for geometric coherence by proving that the geometric coherence of a quantum state is equal to the minimum error probability to discriminate a set of pure states with von neumann measurement on the other hand we also show that a task to ambiguously discriminate a set of linearly independent pure states can be regarded as a problem of calculating geometric coherence that is we reveal an equivalence relation between ambiguous quantum state discrimination and geometric coherence based on this equivalence moreover we improve the upper bound for geometric coherence and give the explicit expression of geometric coherence for a class of states besides we establish a complementarity relation of geometric coherence and path distinguishability with which the relationship between l 1 norm of coherence and geometric coherence is obtained finally with geometric coherence we study multiple copies of quantum state discrimination and give an example to show how to discriminate two pure states

optimal detection of symmetric mixed quantum states we develop a sufficient condition for the least squares measurement lsm or the square root measurement to minimize the probability of a detection error when distinguishing between a collection of mixed quantum states using this condition we derive the optimal measurement for state sets with a broad class of symmetries we first consider geometrically uniform gu state sets with a possibly non abelian generating group and show that if the generator satisfies a weighted norm constraint then the lsm is optimal in particular for pure state gu ensembles the lsm is shown to be optimal for arbitrary gu state sets we show that the optimal measurement operators are gu with generator that can be computed very efficiently in polynomial time within any desired accuracy we then consider compound gu cgu state sets which consist of subsets that are gu when the generators satisfy a certain constraint the lsm is again optimal for arbitrary cgu state sets the optimal measurement operators are shown to be cgu with generators that can be computed efficiently in polynomial time

on shrinking and boundedly complete schauder frames of banach spaces this paper studies schauder frames in banach spaces a concept which is a natural generalization of frames in hilbert spaces and schauder bases in banach spaces the associated minimal and maximal spaces are introduced as are shrinking and boundedly complete schauder frames our main results extend the classical duality theorems on bases to the situation of schauder frames in particular we will generalize james results on shrinking and boundedly complete bases to frames secondly we will extend his characterization of the reflexivity of spaces with unconditional bases to spaces with unconditional frames

motion fields are hardly ever ambiguous there has been much concern with ambiguity in the recovery of motion and structure from time varying images i show here that the class of surfaces leading to ambiguous motion fields is extremely restricted only certain hyperboloids of one sheet and some degenerate forms qualify furthermore the viewer must be on the surface for it to lead to a potentially ambiguous motion field thus the motion field over an appreciable image region almost always uniquely defines the instantaneous translational and rotational velocities as well as the shape of the surface up to a scale factor

closed form solutions to image flow equations for 3d structure and motion a major source of three dimensional 3d information about objects in the world is available to the observer in the form of time varying imagery relative motion between textured objects and the observer generates a time varying optic array at the image from which image motion of contours edge fragments and feature points can be extracted these dynamic features serve to sample the underlying image flow field new closed form solutions are given for the structure and motion of planar and curved surface patches from monocular image flow and its derivatives through second order both planar and curved surface solutions require at most the solution of a cubic equation the analytic solution for curved surface patches combines the transformation of longuet higgins and prazdny 25 with the planar surface solution of subbarao and waxman 43 new insights regarding uniqueness of solutions also emerge thus the structure motion coincidence of waxman and ullman 54 is interpreted as the duality of tangent plane solutions the multiplicity of transformation angles up to three is related to the sign of the gaussian curvature of the surface patch ovoid patches i e bowls are shown to possess a unique transform angle though they are subject to the local structure motion coincidence thus ovoid patches almost always yield a unique 3d interpretation in general ambiguous solutions can be resolved by requiring continuity of the solution over time

a new general asymptotic formula for the mills ratio of the skew generalized normal distribution abstract in this paper we establish some lower and upper bounds with explicit expressions for the mills ratio of the skew generalized normal distribution and for demonstrating the efficiency of our estimates some numerical computations are provided

noise reduction in tight weyl heisenberg frames the functions g that give rise to tight weyl heisenberg frames based on time and frequency discretization steps q sub 0 and p sub 0 with p sub 0 q sub 0 2 pi k k in n are characterized and the noise reducing properties of such frames are examined it is shown that when the frame coefficients c sub m n f of a function f are subject to stationary noise n the average squared l sup 2 norm of the corresponding noise contribution to the reconstruction of f is down by a factor proportional to k sup 2 for a fixed number of sample points also a measure of local error of the reconstruction is introduced as opposed to the global l sup 2 error for a given noise n formulae are derived for the optimal choice or choices of the basis function g in the sense of minimizing this local error

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed