a statistical mechanical description of quantum entanglement we present a description of finite dimensional quantum entanglement based on a study of the space of all convex decompositions of a given density matrix on this space we construct a system of real polynomial equations describing separable states we further study this system using methods of statistical mechanics as an example we finally apply our techniques to werner states of two qubits and obtain a sufficient criterion for separability

separability of very noisy mixed states and implications for nmr quantum computing we give a constructive proof that all mixed states of n qubits in a sufficiently small neighborhood of the maximally mixed state are separable unentangled the construction provides an explicit representation of any such state as a mixture of product states we give upper and lower bounds on the size of the neighborhood which show that its extent decreases exponentially with the number of qubits the bounds show that no entanglement appears in the physical states at any stage of present nmr experiments though this result raises questions about nmr quantum computation further analysis would be necessary to assess the power of the general unitary transformations which are indeed implemented in these experiments in their action on separable states

improved dynamic dictionary matching in the dynamic dictionary matching problem a dictionary d contains a set of patterns that can change over time by insertion and deletion of individual patterns the user also presents text strings and asks for all occurrences of any patterns in the text the two main contributions of this paper are 1 a faster algorithm for dynamic string dictionary matching with bounded alphabets and 2 a dynamic dictionary matching algorithm for two dimensional texts and patterns the first contribution is based on an algorithm that solves the general problem of maintaining a sequence of well balanced parentheses under the operations insert delete and find nearest enclosing parenthesis pair the main new idea behind the second contribution is a novel method to efficiently manipulate failure links for two dimensional patterns

dynamic numerical models of stock market price from microscopic determinism to macroscopic randomness abstract a variant of threshold dynamics is introduced to model the behaviors of a large assembly of dealers in a stock market although the microscopic evolution dynamics is deterministic the collective behaviors such as market prices show seemingly stochastic fluctuations the statistical properties of market price change can be well approximated by a simple discrete langevin type equation with random amplification the macroscopic stochastic equation is solved both numerically and analytically showing that the market price change generally follow power law distributions in the steady state the reason for the appearance of rapid decay in the distribution tails are discussed

space efficient preprocessing schemes for range minimum queries on static arrays given a static array of n totally ordered objects the range minimum query problem is to build a data structure that allows us to answer efficiently subsequent on line queries of the form what is the position of a minimum element in the subarray ranging from i to j we focus on two settings where 1 the input array is available at query time and 2 the input array is available only at construction time in setting 1 we show new data structures a of size frac 2n c n theta bigl frac n lg lg n c n lg n bigr bits and query time o c n for any positive integer function c n in o bigl n varepsilon bigr for an arbitrary constant 0 varepsilon 1 or b with o nh k o n bits and o 1 query time where h k denotes the empirical entropy of k th order of the input array in setting 2 we give a data structure of size 2n o n bits and query time o 1 all data structures can be constructed in linear time and almost in place

dynamic lca queries on trees we show how to maintain a data structure on trees which allows for the following operations all in worst case constant time insertion of leaves and internal nodes deletion of leaves deletion of internal nodes with only one child determining the least common ancestor of any two nodes we also generalize the dietz sleator cup filling scheduling methodology which may be of independent interest

time optimal top k document retrieval let mathcal d be a collection of d documents which are strings over an alphabet of size sigma of total length n we describe a data structure that uses linear space and reports k most relevant documents that contain a query pattern p which is a string of length p packed in p log sigma n words in time o p log sigma n k this is optimal in the ram model in the general case where log d theta log n and involves a novel ram optimal suffix tree search our construction supports an ample set of important relevance measures such as the number of times p appears in a document called term frequency a fixed document importance and the minimal distance between two occurrences of p in a document when log d o log n we show how to reduce the space of the data structure from o n log n to o n log sigma log d log log n bits and to o n log sigma log d bits in the case of the popular term frequency measure of relevance at the price of an additive term o log varepsilon sigma n in the query time for any constant varepsilon 0 we also consider the dynamic scenario where documents can be inserted and deleted from the collection we obtain linear space and query time o p log log n 2 log sigma n log n k log log k whereas insertions and deletions require o log 1 varepsilon n time per symbol for any constant varepsilon 0 finally we consider an extended static scenario where an extra parameter mathtt par p d is defined and the query must retrieve only documents d such that mathtt par p d in tau 1 tau 2 where this range is specified at query time we solve these queries using linear space and o p log sigma n log 1 varepsilon n k log varepsilon n time for any constant varepsilon 0 our technique is to translate these top k problems into multidimensional geometric search problems as a bonus we describe some improvements to those problems

a generalized suffix tree and its un expected asymptotic behaviors suffix trees find several applications in computer science and telecommunications most notably in algorithms on strings data compressions and codes despite this very little is known about their typical behaviors in a probabilistic framework a family of suffix trees further called b suffix trees built from the first n suffixes of a random word is considered in this family a noncompact suffix tree i e such that every edge is labeled by a single symbol is represented by b 1 and a compact suffix tree i e without unary nodes is asymptotically equivalent to b to infty as n to infty several parameters of b suffix trees are studied namely the depth of a given suffix the depth of insertion the height and the shortest feasible path some new results concerning typical i e almost sure behaviors of these parameters are established these findings are used to obtain several insights into certain algorithms on words molecular biology and universal data compression schemes

on off intermittency power spectrum and fractal properties of time series abstract some dynamical systems possess invariant submanifolds such that the dynamics restricted to the invariant submanifold is chaotic this situation arises in systems with a spatial symmetry or in the synchronization of chaotic oscillators the invariant submanifold could become unstable to perturbations in the transverse directions when a parameter of the system is changed through a critical blow out value this could result in an extreme form of temporally intermittent bursting called on off intermittency we propose a model that incorporates the universal features of systems that display on off intermittency we study this model both with and without additive noise and we derive scaling results for the power spectral density of the on off intermittent process and for the box counting dimension for the set of time intervals when the process takes on values above a given threshold we then present numerical simulations realizing these results

concurrence of mixed bipartite quantum states in arbitrary dimensions we derive a lower bound for the concurrence of mixed bipartite quantum states valid in arbitrary dimensions as a corollary a weaker purely algebraic estimate is found which detects mixed entangled states with a positive partial transpose

multiplicative processes and power laws takayasu sato and takayasu phys rev lett 79 966 1997 revisited the question of stochastic processes with multiplicative noise which have been studied in several different contexts over the past decades we focus on the regime found for a generic set of control parameters in which stochastic processes with multiplicative noise produce intermittency of a special kind characterized by a power law probability density distribution we briefly explain the physical mechanism leading to a power law probability distribution function and provide a list of references for these results dating back from a quarter of century we explain how the formulation in terms of the characteristic function developed by takayasu sato and takayasu can be extended to exponents ensuremath mu g2 which explains the reason for the lucky coincidence the multidimensional generalization of the results of takayasu sato and takayasu and the present status of the problem are briefly summarized the discovery of stretched exponential tails in the presence of the cutoff introduced by takayasu sato and takayasu is explained theoretically we end by briefly listing applications

averaging approach to phase coherence of uncoupled limit cycle oscillators receiving common random impulses populations of uncoupled limit cycle oscillators receiving common random impulses show various types of phase coherent states which are characterized by the distribution of phase differences between pairs of oscillators we develop a theory to predict the stationary distribution of pairwise phase differences from the phase response curve which quantitatively encapsulates the oscillator dynamics via averaging of the frobeniusperron equation describing the impulse driven oscillators the validity of our theory is confirmed by direct numerical simulations using the fitzhugh nagumo neural oscillator receiving common poisson impulses as an example

fine structure and complex exponents in power law distributions from random maps discrete scale invariance dsi has recently been documented in time to failure rupture earthquake processes and financial crashes in the fractal geometry of growth processes and in random systems the main signature of dsi is the presence of log periodic oscillations correcting the usual power laws corresponding to complex exponents log periodic structures are important because they reveal the presence of preferred scaling ratios of the underlying physical processes here we present new evidence of log periodicity overlaying the leading power law behavior of probability density distributions of affine random maps with parametric noise the log periodicity is due to intermittent amplifying multiplicative events we quantify precisely the progressive smoothing of the log periodic structures as the randomness increases and find a large robustness our results provide useful markers for the search of log periodicity in numerical and experimental data

complete inverted files for efficient text retrieval and analysis given a finite set of texts s w 1 w k over some fixed finite alphabet s a complete inverted file for s is an abstract data type that provides the functions find w which returns the longest prefix of w that occurs as a subword of a word in s freq w which returns the number of times w occurs in s and locations w which returns the set of positions where w occurs in s a data structure that implements a complete inverted file for s that occupies linear space and can be built in linear time using the uniform cost ram model is given using this data structure the time for each of the above query functions is optimal to accomplish this techniques from the theory of finite automata and the work on suffix trees are used to build a deterministic finite automaton that recognizes the set of all subwords of the set s this automaton is then annotated with additional information and compacted to facilitate the desired query functions the result is a data structure that is smaller and more flexible than the suffix tree

composed ensembles of random unitary matrices composed ensembles of random unitary matrices are defined via products of matrices each pertaining to a given canonical circular ensemble of dyson we investigate statistical properties of spectra of some composed ensembles and demonstrate their physical relevance we also discuss the methods of generating random matrices distributed according to invariant haar measure on the orthogonal and unitary group

transmission of information and herd behavior an application to financial markets we propose a model for stochastic formation of opinion clusters modeled by an evolving network and herd behavior to account for the observed fat tail distribution in returns of financial price data the only parameter of the model is h the rate of information dispersion per trade which is a measure of herding behavior for h below a critical h the system displays a power law distribution of the returns with exponential cutoff however for hg h an increase in the probability of large returns is found and may be associated with the occurrence of large crashes

functional approach to data structures and its use in multidimensional searching we establish new upper bounds on the complexity of multidimensional searching our results include in particular linear size data structures for range and rectangle counting in two dimensions with logarithmic query time more generally we give improved data structures for rectangle problems in any dimension in a static as well as a dynamic setting several of the algorithms we give are simple to implement and might be the solutions of choice in practice central to this paper is the nonstandard approach followed to achieve these results at its root we find a redefinition of data structures in terms of functional specifications

asymptotic power law of moments in a random multiplicative process with weak additive noise it is well known that a random multiplicative process with weak additive noise generates a power law probability distribution it has recently been recognized that this process exhibits another type of power law the moment of the stochastic variable scales as a function of the additive noise strength we clarify the mechanism for this power law behavior of moments by treating a simple langevin type model both approximately and exactly and argue this mechanism is universal we also discuss the relevance of our findings to noisy on off intermittency and to singular spatio temporal chaos recently observed in systems of non locally coupled elements

optimal external memory interval management in this paper we present the external interval tree an optimal external memory data structure for answering stabbing queries on a set of dynamically maintained intervals the external interval tree can be used in an optimal solution to the dynamic interval management problem which is a central problem for object oriented and temporal databases and for constraint logic programming part of the structure uses a weight balancing technique for efficient worst case manipulation of balanced trees which is of independent interest the external interval tree as well as our new balancing technique have recently been used to develop several efficient external data structures

space efficient data analysis queries on grids we consider various data analysis queries on two dimensional points we give new space time tradeoffs over previous work on geometric queries such as dominance and rectangle visibility and on semigroup and group queries such as sum average variance minimum and maximum we also introduce new solutions to queries less frequently considered in the literature such as two dimensional quantiles majorities successor predecessor mode and various top k queries considering static and dynamic scenarios

stochastic resonance of a periodically driven neuron under non gaussian noise abstract we investigate the first passage time statistics of the integrate fire neuron model driven by a sub threshold harmonic signal superposed with a non gaussian noise here we considered the noise as the result of a random multiplicative process displaced from the origin by an additive term such a mechanism generates a power law distributed noise whose characteristic decay exponent can be finely tuned we performed numerical simulations to analyze the influence of the noise non gaussian character on the stochastic resonance condition we found that when the noise deviates from gaussian statistics the resonance condition occurs at weaker noise intensities achieving a minimum at a finite value of the distribution function decay exponent we discuss the possible relevance of this feature to the efficiency of the firing dynamics of biological neurons as the present result indicates that neurons would require a lower noise level to detect a sub threshold signal when its statistics departs from gaussian

a family of indecomposable positive linear maps based on entangled quantum states abstract we introduce a new family of indecomposable positive linear maps based on entangled quantum states central to our construction is the notion of an unextendible product basis the construction lets us create indecomposable positive linear maps in matrix algebras of arbitrary high dimension

hilbert s 17th problem and the quantumness of states a state of a quantum system can be regarded as classical quantum with respect to measurements of a set of canonical observables if and only if there exists does not exist a well defined positive phase space distribution the so called glauber sudarshan p representation we derive a family of classicality criteria that requires that the averages of positive functions calculated using p representation must be positive for polynomial functions these criteria are related to hilbert s 17th problem and have physical meaning of generalized squeezing conditions alternatively they may be interpreted as nonclassicality witnesses we show that every generic nonclassical state can be detected by a polynomial that is a sum of squares of other polynomials we introduce a very natural hierarchy of states regarding their degree of quantumness which we relate to the minimal degree of a sum of squares polynomial that detects them

unextendible product bases and bound entanglement an unextendible product basis upb for a multipartite quantum system is an incomplete orthogonal product basis whose complementary subspace contains no product state we give examples of upbs and show that the uniform mixed state over the subspace complementary to any upb is a bound entangled state we exhibit a tripartite 2 3 2 3 2 upb whose complementary mixed state has tripartite entanglement but no bipartite entanglement i e all three corresponding 2 3 4 bipartite mixed states are unentangled we show that members of a upb are not perfectly distinguishable by local positive operator valued measurements and classical communication s0031 9007 99 09360 6

power law distributions in random multiplicative processes with non gaussian colored multipliers abstract one class of universal mechanisms that generate power law probability distributions is that of random multiplicative processes in this paper we consider a multiplicative langevin equation driven by non gaussian colored multipliers we analytically derive a formula that relates the power law exponent to the statistics of the multipliers and numerically confirm its validity using multiplicative noise generated by chaotic dynamical systems and by a two valued markov process we also investigate the relationship between our treatment and the large deviation analysis of time series and demonstrate the appearance of log periodic fluctuations superimposed on the power law distribution due to the non gaussian nature of the multipliers

positive maps positive polynomials and entanglement witnesses we link the study of positive quantum maps block positive operators and entanglement witnesses with problems related to multivariate polynomials for instance we show how indecomposable block positive operators relate to biquadratic forms that are not sums of squares although the general problem of describing the set of positive maps remains open in some particular cases we solve the corresponding polynomial inequalities and obtain explicit conditions for positivity