a constructive representation for the fourier dual of the zadoff chu sequences in this paper a complex matrix c consisting of a set of perfect sequences is studied the matrix c is constructed by taking the inverse discrete fourier transform idft of a diagonal matrix in which the diagonal elements comprise an arbitrary periodically perfect sequence gamma properties of the matrix c are presented in addition the fourier dual e of the matrix c is investigated when gamma is a zadoff chu sequence for the case of n even m 1 and g 0 an explicit representation for the matrix e is derived

holomorphic quantization on the torus and finite quantum mechanics we explicitly construct the quantization of classical linear maps of on toroidal phase space of arbitrary modulus using the holomorphic chiral version of the metaplectic representation we show that finite quantum mechanics fqm on tori of arbitrary integer discretization is a consistent restriction of the holomorphic quantization of to the subgroup being the principal congruent subgroup on a finite dimensional hilbert space the generators of the rotation group for arbitrary values of l are determined as well as their quantum mechanical eigenvalues and eigenstates

rational and polynomial matrix factorizations via recursive pole zero cancellation we develop a recursive algorithm for obtaining factorizations of the type r r1 r2 where all three matrices are rational and r1 is nonsingular moreover the factors r1 and r2 are such that either the poles of r1 1 and r2 are in a prescribed region of the complex plane or their zeros such factorizations cover the specific cases of coprime factorization inner outer factorization gcd extraction and many more the algorithm works on the state space or generalized state space realization of r and derives in a recursive fashion the corresponding realizations of the factors

a hierarchical bayesian model for combining multiple 2 x 2 tables using conditional likelihoods summary this paper introduces a hierarchical bayesian model for combining multiple 2 2 tables that allows the flexibility of different odds ratio estimates for different tables and at the same time allows the tables to borrow information from each other the proposed model however is different from a full bayesian model in that the nuisance parameters are eliminated by conditioning instead of integration the motivation is a more robust model and a faster and more stable gibbs algorithm we work out a gibbs scheme using the adaptive rejection sampling for log concave density and an algorithm for the mean and variance of the noncentral hypergeometric distribution the model is applied to a multicenter ulcer clinical trial

random partition distribution indexed by pairwise information abstractwe propose a random partition distribution indexed by pairwise similarity information such that partitions compatible with the similarities are given more probability the use of pairwise similarities in the form of distances is common in some clustering algorithms e g hierarchical clustering but we show how to use this type of information to define a prior partition distribution for flexible bayesian modeling a defining feature of the distribution is that it allocates probability among partitions within a given number of subsets but it does not shift probability among sets of partitions with different numbers of subsets our distribution places more probability on partitions that group similar items yet keeps the total probability of partitions with a given number of subsets constant the distribution of the number of subsets and its moments is available in closed form and is not a function of the similarities our formulation has an explicit probability mass function with a tractable

continuous time quantum walk on integer lattices and homogeneous trees this paper is concerned with the continuous time quantum walk on d and infinite homogeneous trees by using the generating function method we compute the limit of the average probability distribution for the general isotropic walk on and for nearest neighbor walks on d and infinite homogeneous trees in addition we compute the asymptotic approximation for the probability of the return to zero at time t in all these cases

facilitating the gibbs sampler the gibbs stopper and the griddy gibbs sampler abstract the article briefly reviews the history literature and form of the gibbs sampler an importance sampling device is proposed for converting the output of the gibbs sampler to a sample from the exact posterior this gibbs stopper technique is also useful for assessing convergence of the gibbs sampler for moderate sized problems also presented is an approach for implementing the gibbs sampler in nonconjugate situations the basic idea is to approximate the true cdf of each conditional distribution by a piecewise linear function and then sample from the approximation questions relating to the number of nodes in the approximation gap size between successive nodes and the treatment of unbounded intervals for a given conditional are discussed the methodology is illustrated using a genetic linkage model a nonlinear regression model and the cox model

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

an improved algorithm for the computation of structural invariants of a system pencil and related geometric aspects in this paper we propose a new recursive algorithm for computing the staircase form of a matrix pencil and implicitly its kronecker structure the algorithm compares favorably to existing ones in terms of elegance versatility and complexity in particular the algorithm without any modification yields the structural invariants associated with a generalized state space system and its system pencil two related geometric aspects are also discussed we show that an appropriate choice of a set of nested spaces related to the pencil leads directly to the staircase form we extend the notion of deflating subspace to the singular pencil case c 1997 elsevier science b v

a problem of time in the multiplicative scheme for the n site hopper quantum measure theory qmt is an approach to quantum mechanics based on the path integral in which quantum theory is conceived of as a generalised stochastic process one of the postulates of qmt is that events with zero quantum measure do not occur however this is not sufficient to give a full picture of the quantum world determining the other postulates is a work in progress and this paper investigates a proposal called the multiplicative scheme for qmt in which the physical world corresponds essentially to a set of histories from the path integral this scheme is applied to sorkin s n site hopper a discrete unitary model of a single particle on a ring of n sites motivated by free schrodinger propagation it is shown that the multiplicative scheme s global features lead to the conclusion that no non trivial time finite event can occur

on the relationship between continuous and discrete time quantum walk quantum walk is one of the main tools for quantum algorithms defined by analogy to classical random walk a quantum walk is a time homogeneous quantum process on a graph both random and quantum walks can be defined either in continuous or discrete time but whereas a continuous time random walk can be obtained as the limit of a sequence of discrete time random walks the two types of quantum walk appear fundamentally different owing to the need for extra degrees of freedom in the discrete time case

an enhanced classical approach to graph isomorphism using continuous time quantum walk studies on graph isomorphism play an important role in graph research and graph isomorphism algorithms have a wide range of applications in image matching pattern recognition computer vision biochemistry and other fields previous research demonstrated that involving discrete time quantum walk in the graph isomorphism algorithm could achieve complexity o n7 for general graphs since quantum walk could be utilized as a new toolbox for solving graph problems we develop an enhanced classical approach to graph isomorphism using continuous time quantum walk which has lower complexity o n5 and can effectively distinguish the graphs that are generally considered difficult in addition we define a graph similarity measure based on the proposed algorithm which can be used for graph isomorphism and graph clustering in the experiment we test a wide variety of classes of graphs the results show that the algorithm has a wide range of applications rather than being limited to a specific type of graph

empirical bayes methods for combining likelihoods comment suppose that several independent experiments are observed each one yielding a likelihood l k k for a real valued parameter of interest k for example k might be the log odds ratio for a 2 x 2 table relating to the kth population in a series of medical experiments this article concerns the following empirical bayes question how can we combine all of the likelihoods l k to get an interval estimate for any one of the k s say 1 the results are presented in the form of a realistic computational scheme that allows model building and model checking in the spirit of a regression analysis no special mathematical forms are required for he priors or the likelihoods this scheme is designed to take advantage of recent methods that produce approximate numerical likelihoods l k k even in very complicated situations with all nuisance parameters eliminated the empirical bayes likelihood theory is extended to situations where the k s have a regression structure as well as an empirical bayes relationship most of the discussion is presented in terms of a hierarchical bayes model and concerns how such a model can be implemented without requiring large amounts of bayesian input frequentist approaches such as bias correction and robustness play a central role in the methodology

generalized linear mixed models for meta analysis we examine two strategies for meta analysis of a series of 2 x 2 tables with the odds ratio modelled as a linear combination of study level covariates and random effects representing between study variation penalized quasi likelihood pql an approximate inference technique for generalized linear mixed models and a linear model fitted by weighted least squares to the observed log odds ratios are used to estimate regression coefficients and dispersion parameters simulation results demonstrate that both methods perform adequate approximate inference under many conditions but that neither method works well in the presence of highly sparse data under certain conditions with small cell frequencies the pql method provides better inference

dynamics of continuous time quantum walks in restricted geometries we study quantum transport on finite discrete structures and we model the process by means of continuous time quantum walks a direct and effective comparison between quantum and classical walks can be attained based on the average displacement of the walker as a function of time indeed a fast growth of the average displacement can be advantageously exploited to build up efficient search algorithms by means of analytical and numerical investigations we show that the finiteness and the inhomogeneity of the substrate jointly weaken the quantum walk performance we further highlight the interplay between the quantum walk dynamics and the underlying topology by studying the temporal evolution of the transfer probability distribution and the lower bound of long time averages

trapping of continuous time quantum walks on erdos renyi graphs abstract we consider the coherent exciton transport modeled by continuous time quantum walks on erdos reny graphs in the presence of a random distribution of traps the role of trap concentration and of the substrate dilution is deepened showing that at long times and for intermediate degree of dilution the survival probability typically decays exponentially with a average decay rate which depends non monotonically on the graph connectivity when the degree of dilution is either very low or very high stationary states not affected by traps get more likely giving rise to a survival probability decaying to a finite value both these features constitute a qualitative difference with respect to the behavior found for classical walks

dissimilar behaviors of coherent exciton transport on scale free networks with identical degree sequence conventional wisdom is that the power law degree sequence has a profound impact on diverse dynamical processes taking place on scale free networks here we show that power law degree distribution alone is not sufficient to determine the behaviors of coherent exciton transport on scale free networks for this purpose we study coherent exciton transport on a class of scale free networks controlled by a tunable parameter q which have the same degree sequence independent of q but are very different in other structural properties determined by q such as average distance and fractality first through numerical determination of the time evolutions of return probabilities we compare in detail the dissimilarities in oscillation periods and oscillation amplitudes between two limiting cases of q 0 and q 1 second we demonstrate that in the network of q 0 up to the third generation the quantum transport problem between node groups partitioned by node degrees can be mapped onto a line furthermore we show that in the case of long time limit the transition probabilities in the networks of q 0 and q 1 exhibit different characteristic patterns with identical values finally we find that the degree averaged return probability decreases when the parameter q increases from 0 to 1 indicating that the stronger localization can be found in those networks with lower values of q our results suggest that it is far from enough to characterize the behaviors of coherent exciton transport on scale free networks merely by power law degree distribution

spectrum and diffusion for a class of tight binding models on hypercubes we propose a class of exactly solvable anisotropic tight binding models on an infinite dimensional hypercube the energy spectrum is computed analytically and is shown to be fractal and or absolutely continuous according to the value of the hopping parameters in both cases the spectral and diffusion exponents are derived the main result is that even if the spectrum is absolutely continuous the diffusion exponent for the wave packet may be anything between 0 and 1 depending upon the class of models

numerical solution to a descriptor discrete time algebraic riccati equation abstract we investigate the numerical solution of a special type of descriptor discrete time riccati equation involved in the solution of several key problems in robust control formulated under very general hypotheses necessary and sufficient existence conditions together with computable formulas are given for the stabilizing and antistabilizing solutions in terms of an associated matrix pencil two particular applications and numerical experiments of our results are included for squaring down with l norm preservation and j j spectral factorization both for a completely general discrete time system

mathcal h _ infty control problem for discrete time algebraic dynamical systems this paper considers the suboptimal mathcal h infty control problem for linear discrete time algebraic dynamical systems such systems can be formally described as linear and time invariant discrete time systems whose transfer function matrix is allowed to be improper or polynomial the parametrization of output feedback controllers is given in a realization based setting involving two generalized algebraic riccati equations and features the same elegant simplicity of the standard proper case two relevant numerical examples prove the effectiveness of our approach

a monte carlo implementation of the em algorithm and the poor man s data augmentation algorithms abstract the first part of this article presents the monte carlo implementation of the e step of the em algorithm given the current guess to the maximizer of the posterior distribution latent data patterns are generated from the conditional predictive distribution the expected value of the augmented log posterior is then updated as a mixture of augmented log posteriors mixed over the generated latent data patterns multiple imputations in the m step of the algorithm this mixture is maximized to obtain the update to the maximizer of the observed posterior the gradient and hessian of the observed log posterior are also expressed as mixtures mixed over the multiple imputations the relation between the monte carlo em mcem algorithm and the data augmentation algorithm is noted two modifications to the mcem algorithm the poor man s data augmentation algorithms which allow for the calculation of the entire posterior are then presented these approximations serve as diagnostics for the validity o

the intrinsic bayes factor for model selection and prediction abstract in the bayesian approach to model selection or hypothesis testing with models or hypotheses of differing dimensions it is typically not possible to utilize standard noninformative or default prior distributions this has led bayesians to use conventional proper prior distributions or crude approximations to bayes factors in this article we introduce a new criterion called the intrinsic bayes factor which is fully automatic in the sense of requiring only standard noninformative priors for its computation and yet seems to correspond to very reasonable actual bayes factors the criterion can be used for nested or nonnested models and for multiple model comparison and prediction from another perspective the development suggests a general definition of a reference prior for model comparison

unraveling the structure of treelike networks from first passage times of lazy random walkers we study the problem of random search in finite networks with a tree topology where it is expected that the distribution of the first passage time f t decays exponentially we show that the slope of the exponential tail is independent of the initial conditions of entering the tree in general and scales exponentially or as a power law with the extent of the tree l depending on the tendency p to jump toward the target node it is unfeasible to uniquely determine l and p from measuring the tail slope or the mean first passage time mfpt of an ordinary diffusion along the tree to unravel the structure we consider lazy random walkers that take steps with probability m when jumping on the nodes and return with probability q from the leaves by deriving an exact analytical expression for the mfpt of the intermittent random walk we verify that the structural information of the tree can be uniquely extracted by measuring the mfpt for two randomly chosen types of tracer particles with distinct experimental parameters m and q we also address the applicability of our approach in the presence of disorder in the structure of the tree or statistical uncertainty in the experimental parameters

low correlation sequences from linear combinations of characters pairs of binary sequences formed using linear combinations of multiplicative characters of finite fields are exhibited that when compared with a random sequence pairs simultaneously achieve significantly lower mean square autocorrelation values for each sequence in the pair and significantly lower mean square crosscorrelation values if we define crosscorrelation merit factor analogously to the usual merit factor for autocorrelation and if we define demerit factor as the reciprocal of merit factor then randomly selected binary sequence pairs are known to have an average crosscorrelation demerit factor of 1 our constructions provide sequence pairs with a crosscorrelation demerit factor significantly less than 1 and at the same time the autocorrelation demerit factors of the individual sequences can also be made significantly less than 1 which also indicates better than average performance the sequence pairs studied here provide combinations of autocorrelation and crosscorrelation performance that are not achievable using sequences formed from single characters such as maximal linear recursive sequences m sequences and legendre sequences in this paper exact asymptotic formulae are proved for the autocorrelation and crosscorrelation merit factors of sequence pairs formed using linear combinations of multiplicative characters data is presented that shows that the asymptotic behavior is closely approximated by sequences of modest length

efficient computation of root numbers and class numbers of parametrized families of real abelian number fields let k m be a parametrized family of simplest real cyclic cubic quartic quintic or sextic number fields of known regulators e g the so called simplest cubic and quartic fields associated with the polynomials p m x x3 mx2 m 3 x 1 and p m x x 4 mx 3 6x 2 mx 1 we give explicit formulas for powers of the gaussian sums attached to the characters associated with these simplest number fields we deduce a method for computing the exact values of these gaussian sums these values are then used to efficiently compute class numbers of simplest fields finally such class number computations yield many examples of real cyclotomic fields q p of prime conductors p 3 and class numbers h p greater than or equal to p however in accordance with vandiver s conjecture we found no example of p for which p divides h p

constructive solutions to spectral and inner outer factorizations with respect to the disk we use state space realizations to solve the spectral and inner outer factorization problems with respect to the unit disk formulated for a completely general rational matrix the algorithm is based on orthogonal transformations and standard reliable procedures for solving stein and riccati equations the formulas apply in particular to general descriptor systems or polynomial matrices the main novelty is that we allow for arbitrary rank poles and zeros on the unit circle or at infinity

quantum transport on two dimensional regular graphs we study the quantum mechanical transport on two dimensional graphs by means of continuous time quantum walks and analyse the effect of different boundary conditions bcs for periodic bcs in both directions i e for tori the problem can be treated in a large measure analytically some of these results carry over to graphs which obey open boundary conditions obcs such as cylinders or rectangles under obcs the long time transition probabilities lps also display asymmetries for certain graphs as a function of their particular sizes interestingly these effects do not show up in the marginal distributions obtained by summing the lps along one direction

minimal indices cancellation and rank revealing factorizations for rational matrix functions we study the problem of eliminating the minimal indices the indices of a minimal polynomial basis of the null space of a rational matrix function by multiplication with a suitably chosen invertible rational matrix function we derive the class of all invertible factors that dislocate the minimal indices to certain zero locations and feature minimal mcmillan degree we impose additional conditions on the factor like being j unitary or j inner either with respect to the imaginary axis or to the unit circle and characterize the classes of solutions en route we extend the well known rank revealing factorization of a constant matrix to rational matrix functions the results are completely general and apply in particular to matrices which are polynomial strictly proper or improper rank deficient with arbitrary poles and zeros including at infinity all characterization are made by using descriptor realizations while the associated computations are performed by employing constant unitary transformations and standard reliable procedures for eigenvalue assignment or for solving riccati equations

j factorizations of a general discrete time system abstract the problems of extending the j lossless conjugation the j j spectral factorization and the j j lossless factorization to a completely general discrete time system are considered existence conditions together with a numerically sound prototype algorithm for computing the factors are provided for a system having any type of singularity including arbitrary normal rank poles and zeros at infinity at zero or on the unit circle

an angular momentum approach to quadratic fourier transform hadamard matrices gauss sums mutually unbiased bases the unitary group and the pauli group the construction of unitary operator bases in a finite dimensional hilbert space is reviewed through a nonstandard approach combining angular momentum theory and representation theory of su 2 a single formula for the bases is obtained from a polar decomposition of su 2 and is analyzed in terms of cyclic groups quadratic fourier transforms hadamard matrices and generalized gauss sums weyl pairs generalized pauli operators and their application to the unitary group and the pauli group naturally arise in this approach

youla like parametrizations subject to qi subspace constraints consider that a linear time invariant lti plant is given and that we wish to design a stabilizing controller for it admissible controllers are lti and must belong to a pre selected subspace that may impose structural restrictions such as sparsity constraints the subspace is assumed to be quadratically invariant qi with respect to the plant which from prior results guarantees that there is a convex parametrization of all admissible stabilizing controllers provided that an initial admissible stable stabilizing controller is provided this paper addresses the previously unsolved problem of extending youla s classical parametrization so that it admits qi subspace constraints on the controller in contrast with prior parametrizations the one proposed here does not require initialization and it does not require the existence of a stable stabilizing controller the main idea is to cast the stabilizability constraint as an exact model matching problem with stability restrictions which can be tackled using existing methods furthermore we show that when it exists the solution of the exact model matching problem can be used to compute an admissible stabilizing controller applications of the proposed parametrization on the design of norm optimal controllers via convex methods are also explored an illustrative example is provided and a special case is discussed for which the exact model matching problem has a unique and easily computable solution

on the asymptotic connection between two exponential sums the relation between the exponential sums sn x p n 0n 1exp ixnp and t0 t0 x n p n 1 e n nexp ixnpe pn n where x 0 and p 0 is investigated it is demonstrated that there is an asymptotic connection as n which is found numerically to be valid provided the variable x satisfies the restriction xnp o n when p 1 the sum t0 is shown to be associated with a zeta function defined by z s n 1 exp i e an n s for real and a 0

approximate predictive likelihood summary a predictive likelihood is given which approximates both bayes and maximum likeli hood predictive inference by expansion of a posterior likelihood this synthesizes and extends previous results and is widely applicable the approximation usually differs from exact bayes posterior predictive density by op n 2 and from exact predictive likelihood by op n 1 but does not depend on the availability of prior information and is applicable when exact predictive likelihood cannot be found the results are applied to the prediction various treatments of the likelihood function form the basis of parametric inference but until recently few non bayesian attempts have been made to define versions of it suitable for prediction however lauritzen 1974 hinkley 1979 and more recently butler 1986 have proposed rather similar definitions of predictive likelihood based on the idea of conditioning on the value of a sufficient statistic unfortunately they apply only when sufficiency provides a genuine reduction of the data moreover even if for a given problem an exact predictive likelihood exists the calculations needed to derive it can be onerous this paper provides approximations to hinkley lauritzen predictive likelihood accur ate to op n 1 in many cases which are applicable in situations where maximum likelihood estimation is regular they also apply to problems which admit no exact predictive likelihood because sufficiency provides no real reduction of the data the approximations are derived from a posterior predictive density and may if prior informa tion is available be regarded as bayesian procedures their construction requires only the repeated maximization of a likelihood and evaluation of the observed information matrix at the maximum and is fast and accurate using usual numerical maximization methods there is a close connexion with the approximations to posterior moments and marginal densities given by tierney kadane 1986 who suggest the same approxima tion as used here but give no detailed results for prediction section 2 of this paper shows how laplace s method for integrals may be applied to a posterior predictive density to yield approximate predictive likelihood section 3 discusses a connection with conditional inference essentially the same approximation

zero cancellation for general rational matrix functions the problem of cancelling a specified part of the zeros of a completely general rational matrix function by multiplication with an appropriate invertible rational matrix function is investigated from different standpoints firstly the class of all factors that dislocate the zeros and feature minimal mcmillan degree are derived further necessary and sufficient existence conditions together with the construction of solutions are given when the factor fulfills additional assumptions like being j unitary or j inner either with respect to the imaginary axis or to the unit circle the main technical tool are centered realizations that deliver a sufficiently general conceptual support to cope with rational matrix functions which may be polynomial proper or improper rank deficient with arbitrary poles and zeros including at infinity a particular attention is paid to the numerically sound construction of solutions by employing at each stage unitary transformations reliable numerical algorithms for eigenvalue assignment and efficient lyapunov equation solvers

j j lossless factorization based on conjugation this paper is concerned with a derivation of the state space form of the j j lossless factorization which contains both the inner outer factorization and the spectral factorization of positive matrices as special cases also the j j lossless factorization gives a unified framework of h control theory we use the method of conjugation which makes the derivation much simpler than the previous literature most of which used the technique of j j spectral factorization a necessary and sufficient condition is represented in terms of two riccati equations one of which is degenerated

feynman s path integral and mutually unbiased bases our previous work on quantum mechanics in hilbert spaces of finite dimension n is applied to elucidate the deep meaning of feynman s path integral pointed out by g svetlichny he speculated that the secret of the feynman path integral may lie in the property of mutual unbiasedness of temporally proximal bases we confirm the corresponding property of the short time propagator by using a specially devised n n approximation of quantum mechanics in applied to our finite dimensional analogue of a free quantum particle

computation of general inner outer and spectral factorizations in this paper we solve two problems in linear systems theory the computation of the inner outer and spectral factorizations of a continuous time system considered in the most general setting we show that these factorization problems rely essentially on solving for the stabilizing solution a standard algebraic riccati equation of order usually much smaller than the mcmillan degree of the transfer function matrix of the system the proposed procedures are completely general being applicable for a polynomial proper improper system whose transfer function matrix could be rank deficient and could have poles zeros on the imaginary axis or at infinity as an application we discuss the extension to the case of rational matrices of the complete orthogonal decomposition of a constant matrix numerical refinements and examples illustrating the proposed approach are discussed in detail

controllability of system dynamics on networks quantum walks and random walks abstract we consider a model of system dynamics on networks consisting of a certain number of stations nodes connected by edges at every time step a certain quantity leaves the stations and gets re distributed among the neighboring stations preserving an appropriate norm one has the control at every station on the relative quantity which is sent to the various neighbors controllability is achieved when every possible distribution of the given quantity in a natural set can be obtained this general model includes in particular classical and quantum walks on graphs the case of quantum walks is treated in detail and it is proved that controllability is achieved if and only if the underlying graph is not bipartite this extends to general graphs a result previously proved in the literature for the case where the underlying graph is regular then extensions are presented to general systems modeling system dynamics on networks

noninformative priors for one parameter of many summary we consider the problem of constructing a prior that is noninformative for a single parameter in the presence of nuisance parameters our approach is to require that the resulting marginal posterior intervals have accurate frequentist coverage stein 1985 derived nonrigorously a sufficient condition for such a prior through the use of orthogonal parameters we give a general form for the class of priors satisfying stein s condition the priors are proportional to the square root of the information element for the parameter of interest times an arbitrary function of the nuisance parameters this is in contrast to jeffreys 1946 invariant prior for the overall parameter which is proportional to the square root of the determinant of the information matrix several examples are given and comparisons are made to the reference priors of bernardo 1979

controllability and observability of grid graphs via reduction and symmetries in this paper we investigate the controllability and observability properties of a family of linear dynamical systems whose structure is induced by the laplacian of a grid graph this analysis is motivated by several applications in network control and estimation quantum computation and discretization of partial differential equations specifically we characterize the structure of the grid eigenvectors by means of suitable decompositions of the graph for each eigenvalue based on its multiplicity and on suitable symmetries of the corresponding eigenvectors we provide necessary and sufficient conditions to characterize all and only the nodes from which the induced dynamical system is controllable observable we discuss the proposed criteria and show through suitable examples how such criteria reduce the complexity of the controllability respectively observability analysis of the grid

fractional bayes factors for model comparison bayesian comparison of models is achieved simply by calculation of posterior probabilities of the models themselves however there are difficulties with this approach when prior information about the parameters of the various models is weak partial bayes factors offer a resoiution of the problem by setting aside part of the data as a training sampie the training sampie is used to obtain an initiai informative posterior distribution of the parameters in each model model comparison is then based on a bayes factor calculated from the remaining data properties of partial bayes factors are discussed particularly in the context of weak prior information and they are found to have advantages over other proposed methods of model comparison a new variant of the partial bayes factor the fractional bayes factor is advocated on grounds of consistency simplicity robustness and coherence

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

finite size scaling for random walks on fractals random walks are simulated on finite stages of construction of regular fractal lattices it is proved that the mean square displacement rn2 obeys a finite size scaling hypothesis and the critical exponent nu w is estimated the efficiency of the method is proved when applied to finitely ramified fractals in which the problem is exactly solvable nu w is obtained with good accuracy approximately 1 for a class of infinitely ramified fractals the sierpinski carpets the results correct previous estimates based on simulations which did not use finite size scaling it is shown that nu w decreases when dc decreases with very small corrections due to other geometrical properties such as lacunarity the comparison with estimates of the ideal chain exponent nu c shows that the two problems are not equivalent on these fractals and that in general nu w nu c estimates of nu w with the same accuracy are obtained on two sierpinski pastry shells 2 df 3 where anomalous diffusion is also observed

using hilbert transform and classical chains to simulate quantum walks we propose a simulation strategy which uses a classical device of linearly coupled chain of springs to simulate quantum dynamics in particular quantum walks through this strategy we obtain the quantum wave function from the classical evolution specially this goal is achieved with the classical momenta of the particles on the chain and their hilbert transform from which we construct the many body momentum and hilbert transformed momentum pair correlation functions yielding the real and imaginary parts of the wave function respectively with such a wave function we show that the classical chain s energy and heat spreading densities can be related to the wave function s modulus square this relation provides a new perspective to understand ballistic heat transport the results here may give a definite answer to feynman s idea of using a classical device to simulate quantum physics

conjugation interpolation and model matching in h abstract the notion of conjugation is introduced to give a unified framework of algebraic operations connected to the analytic aspects of transfer functions two classes of conjugations are shown to be important one is the lossless conjugation that performs inner outer factorization and the other is the j lossless conjugation that solves the model matching problem related to h 8 control the solution of the model matching problem obtained by j lossless conjugation is regarded as the state space version of the directional interpolation theory and is much simpler than those obtained via the nehari approximation

computation of the general j j prime lossless factorization the j j lossless factorization problem for a generalized state space system whose transfer matrix is completely general is investigated the main novelty is that we remove all restrictive hypotheses and allow for arbitrary normal rank poles and zeros on the imaginary axis or at infinity the numerically sound formulas for the solution bear the same nice expressions and striking simplicity of the inner outer factorization and may be equally well applied for the j j spectral factorization

notions of controllability for bilinear multilevel quantum systems in this note we define four different notions of controllability of physical interest for multilevel quantum mechanical systems these notions involve the possibility of driving the evolution operator as well as the state of the system we establish the connections among these different notions as well as methods to verify controllability

recurrence and polya number of quantum walks we analyze the recurrence probability polya number for d dimensional unbiased quantum walks a sufficient condition for a quantum walk to be recurrent is derived as a by product we find a simple criterion for localization of quantum walks in contrast with classical walks where the polya number is characteristic for the given dimension the recurrence probability of a quantum walk depends in general on the topology of the walk choice of the coin and the initial state this allows us to change the character of the quantum walk from recurrent to transient by altering the initial state

coherent dynamics on hierarchical systems abstract we study the coherent transport modeled by continuous time quantum walks focussing on hierarchical structures for these we use husimi cacti lattices dual to the dendrimers we find that the transport depends strongly on the initial site of the excitation for systems of sizes n 21 we find that processes which start at central sites are nearly recurrent furthermore we compare the classical limiting probability distribution to the long time average of the quantum mechanical transition probability which shows characteristic patterns we succeed in finding a good lower bound for the space average of the quantum mechanical probability to be still or again at the initial site

littlewood polynomials with small l4 norm abstract littlewood asked how small the ratio f 4 f 2 where denotes the l norm on the unit circle can be for polynomials f having all coefficients in 1 1 as the degree tends to infinity since 1988 the least known asymptotic value of this ratio has been 7 6 4 which was conjectured to be minimum we disprove this conjecture by showing that there is a sequence of such polynomials derived from the fekete polynomials for which the limit of this ratio is less than 22 19 4

approximate bayesian inference in conditionally independent hierarchical models parametric empirical bayes models abstract we consider two stage models of the kind used in parametric empirical bayes peb methodology calling them conditionally independent hierarchical models we suppose that there are k units which may be experimental subjects cities study centers etcetera at the first stage the observation vectors yi for units i 1 k are independently distributed with densities p yi i or more generally p yi i at the second stage the unit specific parameter vectors i are iid with densities p i the peb approach proceeds by regarding the second stage distribution as a prior and noting that if were known inference about could be based on its posterior since is not known the simplest peb methods estimate the parameter by maximum likelihood or some variant and then treat as if it were known to be equal to this estimate although this procedure is sometimes satisfactory a well known defect is that it neglects the uncertainty due to the estimation of in this article w

continuous time quantum walks on nonorientable surfaces analytical solutions for mobius strips and klein bottles in this paper we present an extensive analytical study of continuous time quantum walks ctqws occurring on two dimensional lattices under various boundary conditions focusing on the m n lattice wrapped on mobius strips and klein bottles which are featured by the twisted boundary conditions we find that the eigenvalue spectra and transport efficiency both quantum mechanical and classical for the two structures show comparable results with those for other well known two dimensional lattices including rectangles cylinders and tori we also demonstrate that the behaviors of ctqws depend on the initial node of the excitation and the network size both on short and long timescales in addition we discover the asymmetric behaviors of limiting probabilities for mobius strips and klein bottles which are quite different from each other and are also compared to those discovered in other two dimensional networks our work provides a comprehensive understanding of recent results about ctqws on two dimensional lattices and sheds light on quantum dynamics on lattices especially those with different boundary conditions

eigenvalue spectrum of transition matrix of dual sierpinski gaskets and its applications the eigenvalue spectrum of the transition matrix of a network contains much information about its structural properties and is related to the behavior of various dynamical processes performed on it in this paper we study the eigenvalues of the transition matrix of the dual sierpinski gaskets embedded in d dimensional euclidean spaces we obtain all the eigenvalues as well as their corresponding degeneracies by making use of the spectral decimation technique we then apply the obtained eigenvalues to determine the exact number of spanning trees in the studied fractals and derive an explicit formula of the eigentime identity for random walks taking place on them

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

assessing robustness of intrinsic tests of independence in two way contingency tables for testing nested hypotheses from a bayesian standpoint a desirable condition is that the prior for the alternative model concentrates mass around the smaller or null model for testing independence in contingency tables the intrinsic priors satisfy this requirement furthermore the degree of concentration of the priors is controlled by a discrete parameter t the training sample size which plays an important role in the resulting answer in this article we report on the robustness of the tests of independence for small or moderate sample sizes in contingency tables with respect to intrinsic priors with different degrees of concentration around the null we compare these tests to frequentist tests and other robust bayes tests for large sample sizes robustness is achieved because the intrinsic bayesian tests are consistent examples using real and simulated data are given supplemental materials technical details and data sets are available online

non stationary quantum walks on the cycle we consider quantum walks on the cycle in the non stationary case where the coin operation is allowed to change at each time step we characterize in algebraic terms the set of possible state transfers and prove that as opposed to the stationary case the associate probability distribution may converge to a uniform distribution among the nodes of the associated graph

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

symmetrization of the hurwitz zeta function and dirichlet l functions we consider the hurwitz zeta function z s a and form two parts zc and zk by symmetric and antisymmetric combinations of z s a a ndz s 1ka we consider the properties of zc and zk and then show that each may be decomposed into parts denoted by p and n each of which obeys a functional equation of the dirichlet l type with a multiplicative factor of k1 for the functions n we show the results of this procedure for rational az p q with qz1 2 3 4 5 6 7 8 10 and demonstrate that the functions p and n have some of the key properties of dirichlet l functions

analysis of quantum walks with time varying coin on d dimensional lattices in this paper we present a study of discrete time quantum walks whose underlying graph is a d dimensional lattice the dynamical behavior of these systems is of current interest because of their applications in quantum information theory as tools to design quantum algorithms we assume that at each step of the walk evolution the coin transformation is allowed to change so that we can use it as a control variable to drive the evolution in a desired manner we give an exact description of the possible evolutions and of the set of possible states that can be achieved with such a system in particular we show that it is possible to go from a state where there is probability 1 for the walker to be found in a vertex to a state where all the vertices have equal probability we also prove a number of properties of the set of admissible states in terms of the number of steps needed to obtain them we provide explicit algorithms for state transfer in low dimensional cases as well as results that allow to reduce algorithms on two dimensional lattices to algorithms on the one dimensional lattice the cycle

time evolution of continuous time quantum walks on dynamical percolation graphs we study the time evolution of continuous time quantum walks on randomly changing graphs at certain moments edges of the graph appear or disappear with a given probability as in percolation we treat this problem in a strong noise limit we focus on the case when the time interval between the subsequent changes of the graph tends to zero we derive explicit formulae for the general evolution in this limit we find that the percolation in this limit causes an effective time rescaling independently of the graph and the initial state of the walk the time is rescaled by the probability of keeping an edge both the individual trajectories for a single system and average properties with a superoperator formalism are discussed we give an analytical proof for our theorem and we also present results from the numerical simulations of the phenomena for different graphs we also analyze the effect of finite step size on the evolution