bell type inequalities for nonlocal resources we present bipartite bell type inequalities which allow the two partners to use some nonlocal resource such inequalities can only be violated if the parties use a resource which is more nonlocal than the one permitted by the inequality we introduce a family of n input nonlocal machines which are generalizations of the well known pr popescu rohrlich box then we construct bell type inequalities that cannot be violated by strategies that use one of these new machines finally we discuss implications for the simulation of quantum states

fuzzy texture unit and fuzzy texture spectrum for texture characterization an important problem that is necessary to face up to in texture characterization is that while the notion of texture is easy to grasp intuitively it is extremely difficult to quantify the texture spectrum methodology introduced by he and wang 1990 texture unit texture spectrum and texture analysis ieee trans on geoscience and remote sensing 28 4 1990 509 512 was initially used as a texture filtering approach and has been applied to texture characterization and texture classification showing promising discrimination performance in this paper we propose a texture characterization approach based on the texture spectrum methodology that for taking into account the vagueness introduced by noise and the different caption and digitation processes makes use of fuzzy techniques for defining the texture unit boxes

quantum probabilities for time extended alternatives we study the probability assignment for the outcomes of time extended measurements we construct the class operator that incorporates the information about a generic time smeared quantity these class operators are employed for the construction of positive operator valued measures for the time averaged quantities the scheme highlights the distinction between velocity and momentum in quantum theory propositions about velocity and momentum are represented by different class operators hence they define different probability measures we provide some examples we study the classical limit and we construct probabilities for generalized time extended phase space variables

modelling dependence within joint tail regions standard approaches for modelling dependence within joint tail regions are based on extreme value methods which assume max stability a particular form of joint tail dependence we develop joint tail models based on a broader class of dependence structure which provides a natural link between max stable models and weaker forms of dependence including independence and negative association this approach overcomes many of the problems that are encountered with standard methods and is the basis for a poisson process representation that generalizes existing bivariate results we apply the new techniques to simulated and environmental data and demonstrate the marked advantage that the new approach offers for joint tail extrapolation

multiple features data fusion method in color texture analysis a new algorithm is developed to represent colored texture by effectively merging the texture feature color feature together with spatial correlation of color and texture based on incomplete tree structured wavelet decomposition experiments are conducted on a set of 20 natural colored texture images in which multiple features fusion and classification performance are compared on the basis of the pyramid wavelet decomposition pwd incomplete tree structured wavelet decomposition ictswd and wavelet packet decomposition wpd class correct rates of multiple features fusion based on pwd is 85 78 and class correct rates based on wpd is 91 03 with the dimensionality increased exponentially however the dimensionality of feature fusion based on ictswd is descended greatly because of selective decomposition in subband which class correct rates is 90 63 it is demonstrated that multiple features fusion based on ictswd has better classification performance and anti noise ability than fusion based on pwd and wpd

modelling extreme multivariate events summary the classical treatment of multivariate extreme values is through componentwise ordering though in practice most interest is in actual extreme events here the point process of observations which are extreme in at least one component is considered parametric models for the dependence between components must satisfy certain constraints two new techniques for generating such models are presented aspects of the statistical estimation of the resulting models are discussed and are illustrated with an application to oceanographic data

continuous time and consistent histories we discuss the use of histories labelled by a continuous time in the approach to consistent histories quantum theory in which propositions about the history of the system are represented by projection operators on a hilbert space this extends earlier work by two of us c j isham and n linden j math phys 36 5392 5408 1995 where we showed how a continuous time parameter leads to a history algebra that is isomorphic to the canonical algebra of a quantum field theory we describe how the appropriate representation of the history algebra may be chosen by requiring the existence of projection operators that represent propositions about the time average of the energy we also show that the history description of quantum mechanics contains an operator corresponding to velocity that is quite distinct from the momentum operator finally the discussion is extended to give a preliminary account of quantum field theory in this approach to the consistent histories formalism

poincare invariance for continuous time histories we show that the relativistic analog of the two types of time translation in a nonrelativistic history theory is the existence of two distinct poincare groups the internal poincare group is analogous to the one that arises in the standard canonical quantization scheme the external poincare group is similar to the group that arises in a lagrangian description of the standard theory in particular it performs explicit changes of the space time foliation that is implicitly assumed in standard canonical field theory

markov chain models for threshold exceedances in recent research on extreme value statistics there has been an extensive development of threshold methods first in the univariate case and subsequently in the multivariate case as well in this paper an alternative methodology for extreme values of univariate time series is developed by assuming that the time series is markovian and using bivariate extreme value theory to suggest appropriate models for the transition distributions a new likelihood representation for threshold methods is presented which we apply to a markovian time series an important motivation for developing this kind of theory is the possibility of calculating probability distributions for functionals of extreme events we address this issue by showing how a theory of compound poisson limits for additive functionals can be combined with simulation to obtain numerical solutions for problems of practical interest the methods are illustrated by application to temperature data

the multivariate skew normal distribution summary the paper extends earlier work on the so called skew normal distribution a family of distributions including the normal but with an extra parameter to regulate skewness the present work introduces a multivariate parametric family such that the marginal densities are scalar skew normal and studies its properties with special emphasis on the bivariate case

are there realistically interpretable local theories although it rests on strongly established proofs the statement that no realistically interpretable local theory is compatible with some experimentally testable predictions of quantum mechanics seems at first sight to be incompatible with a few general ideas and clear cut statements occurring in recent theoretical work by griffiths omnes and ballentine and jarrett it is shown here that in fact none of the developments due to these authors can be considered as a realistically interpretable local theory so that there is no valid reason for suspecting that the existing proofs of the statement in question are all flawed

symmetry and history quantum theory an analog of wigner s theorem the basic ingredients of the consistent histories approach to quantum theory are a space up of history propositions and a space d of decoherence functionals in this article we consider such history quantum theories in the case where up is given by the set of projectors p v on some hilbert space v we define the notion of a physical symmetry of a history quantum theory pshqt and specify such objects exhaustively with the aid of an analog of wigner s theorem in order to prove this theorem we investigate the structure of d define the notion of an elementary decoherence functional and show that each decoherence functional can be expanded as a certain combination of these functionals we call two history quantum theories that are related by a pshqt physically equivalent and show explicitly in the case of history quantum mechanics how this notion is compatible with one that has appeared previously

dependence modelling for spatial extremes current dependence models for spatial extremes are based upon max stable processes within this class there are few inferentially viable models available and we propose one further model more problematic are the restrictive assumptions that must be made when using max stable processes to model dependence for spatial extremes it must be assumed that the dependence structure of the observed extremes is compatible with a limiting model that holds for all events more extreme than those that have already occurred this problem has long been acknowledged in the context of finite dimensional multivariate extremes in particular when data display dependence at observable levels but are independent in the limit we propose a flexible class of models that is suitable for such data in a spatial context in addition we consider the situation where the extremal dependence structure may vary with distance we apply our models to spatially referenced significant wave height data from the north sea finding evidence that their extremal structure is not compatible with a limiting dependence model

consistent quantum realism a reply to bassi and ghirardi a recent claim by bassi and ghirardi that the consistent decoherent histories approach cannot provide a realistic interpretation of quantum theory is shown to be based upon a misunderstanding of the single framework rule they have replaced the correct rule with a principle which directly contradicts it it is their assumptions not those of the consistent histories approach which lead to a logical contradiction

modelling across extremal dependence classes different dependence scenarios can arise in multivariate extremes entailing careful selection of an appropriate class of models in bivariate extremes the variables are either asymptotically dependent or are asymptotically independent most available statistical models suit one or other of these cases but not both resulting in a stage in the inference that is unaccounted for but can substantially impact subsequent extrapolation existing modelling solutions to this problem are either applicable only on sub domains or appeal to multiple limit theories we introduce a unified representation for bivariate extremes that encompasses a wide variety of dependence scenarios and applies when at least one variable is large our representation motivates a parametric model that encompasses both dependence classes we implement a simple version of this model and show that it performs well in a range of settings

completeness of decoherence functionals the basic ingredients of the consistent histories approach to a generalized quantum theory are histories and decoherence functionals the main aim of this program is to find and to study the behavior of consistent sets associated with a particular decoherence functional d in its recent formulation by isham quantum logic and the histories approach to quantum theory j math phys 35 2157 2185 1994 it is natural to identify the space up of propositions about histories with an orthoalgebra or lattice when up is given by the lattice of projectors p v in some hilbert space v consistent sets correspond to certain partitions of the unit operator in v into mutually orthogonal projectors 1 2 such that the function d is a probability distribution on the boolean algebra generated by 1 2 using the classification theorem for decoherence functionals proven in isham et al the classification of decoherence functionals an analog of gleason s theorem j math phys 35 6

bayesian modeling of air pollution extremes using nested multivariate max stable processes capturing the potentially strong dependence among the peak concentrations of multiple air pollutants across a spatial region is crucial for assessing the related public health risks in order to investigate the multivariate spatial dependence properties of air pollution extremes we introduce a new class of multivariate max stable processes our proposed model admits a hierarchical tree based formulation in which the data are conditionally independent given some latent nested positive stable random factors the hierarchical structure facilitates bayesian inference and offers a convenient and interpretable characterization we fit this nested multivariate max stable model to the maxima of air pollution concentrations and temperatures recorded at a number of sites in the los angeles area showing that the proposed model succeeds in capturing their complex tail dependence structure

unsupervised texture segmentation of images using tuned matched gabor filters recent studies have confirmed that the multichannel gabor decomposition represents an excellent tool for image segmentation and boundary detection unfortunately this approach when used for unsupervised image analysis tasks imposes excessive storage requirements due to the nonorthogonality of the basis functions and is computationally highly demanding in this correspondence we propose a novel method for efficient image analysis that uses tuned matched gabor filters the algorithmic determination of the parameters of the gabor filters is based on the analysis of spectral feature contrasts obtained from iterative computation of pyramidal gabor transforms with progressive dyadic decrease of elementary cell sizes the method requires no a priori knowledge of the analyzed image so that the analysis is unsupervised computer simulations applied to different classes of textures illustrate the matching property of the tuned gabor filters derived using our determination algorithm also their capability to extract significant image information and thus enable an easy and efficient low level image analysis will be demonstrated

statistics for near independence in multivariate extreme values we propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence we examine inference under the model and develop tests for independence of extremes of the marginal variables both when the thresholds are fixed and when they increase with the sample size motivated by results obtained from this model we give a new and widely applicable characterisation of dependence in the joint tail which includes existing models as special cases a new parameter which governs the form of dependence is of fundamental importance to this characterisation by estimating this parameter we develop a diagnostic test which assesses the applicability of bivariate extreme value joint tail models the methods are demonstrated through simulation and by analysing two previously published data sets

automatic surface inspection using wavelet reconstruction abstract in this paper we present a multiresolution approach for the inspection of local defects embedded in homogeneous textured surfaces the proposed method does not rely on the extraction of local textural features in a pixel by pixel basis it is based on an efficient image restoration scheme using the wavelet transforms by properly selecting the smooth subimage or the combination of detail subimages in different decomposition levels for backward wavelet transform the reconstructed image will remove regular repetitive texture patterns and enhance only local anomalies then a simple thresholding can be used to discriminate between defective regions and homogeneous regions in the reconstructed image this converts the difficult defect detection in complicated textured images into a simple binary thresholding in nontextured images effects of different wavelet bases the number of multiresolution levels the decomposed subimages used for reconstruction and the change in image rotation on defect detection are thoroughly evaluated and discussed based on the experiment on a variety of real textures including machined surfaces natural wood textile fabrics sandpaper and leather

symmetries of history quantum theories and decoherence functionals recently schreckenberg investigated symmetries in the context of history quantum theories in the case that the space of histories is given by the set of projectors on some finite dimensional hilbert space he obtained first a complete characterization of all physical symmetries of history quantum theories an analog of wigner s theorem and second a complete mathematical characterization of symmetries of single decoherence functionals in this paper we extend schreckenberg s results to the case where the underlying space of histories is given by the set of projectors on some infinite dimensional hilbert space

stochastic description for open quantum systems abstract a linear quantum brownian motion model with a general spectral density function is considered in the framework of the influence functional formalism a langevin equation can be introduced to describe the system s fully quantum properties even beyond the semiclassical regime in particular we show that the reduced wigner function for the system can be formally written as a double average over both the initial conditions and the stochastic source of the langevin equation this is exploited to provide a derivation of the master equation for the reduced density matrix alternative to those existing in the literature furthermore we prove that all the correlation functions obtained in the context of the stochastic description associated to the langevin equation actually correspond to quantum correlation functions for system observables in doing so we also compute the closed time path generating functional of the open system

texture classification using logical operators in this paper a new algorithm for texture classification based on logical operators is presented operators constructed from logical building blocks are convolved with texture images an optimal set of six operators are selected based on their texture discrimination ability the responses are then converted to standard deviation matrices computed over a sliding window zonal sampling features are computed from these matrices a feature selection process is applied and the new set of features are used for texture classification classification of several natural and synthetic texture images are presented demonstrating the excellent performance of the logical operator method the computational superiority and classification accuracy of the algorithm is demonstrated by comparison with other popular methods experiments with different classifiers and feature normalization are also presented the euclidean distance classifier is found to perform best with this algorithm the algorithm involves only convolutions and simple arithmetic in the various stages which allows faster implementations the algorithm is applicable to different types of classification problems which is demonstrated by segmentation of remote sensing images compressed and reconstructed images and industrial images

local likelihood estimation of complex tail dependence structures applied to u s precipitation extremes to disentangle the complex nonstationary dependence structure of precipitation extremes over the entire contiguous united states u s we propose a flexible local approach based on factor copula

the arrival time distribution the extended probability approaches we present a calculation of the arrival time probability distribution based on the extended probability as proposed by hartle 2008 phys rev a 78 012108 we show that two cases of the arrival time probability distribution can be used first we use the path decomposition expansion to discuss a fine grained history for which a particle has a first crossing x 0 at time the arrival time probability related to the probability current is obtained second we consider that the arrival time distribution is modeled by the first photon emitted from a two level atom the basic atom laser model the partition dynamic of this system is discussed each history is in the form of a coarse grained history we confirm that the arrival time probability distribution computed by this method agrees with that computed via the probability of no photon detection crucially the resulting arrival time distributions can be obtained without the restriction of the consistency condition

unsupervised texture segmentation using gabor filters abstract this paper presents a texture segmentation algorithm inspired by the multi channel filtering theory for visual information processing in the early stages of human visual system the channels are characterized by a bank of gabor filters that nearly uniformly covers the spatial frequency domain and a systematic filter selection scheme is proposed which is based on reconstruction of the input image from the filtered images texture features are obtained by subjecting each selected filtered image to a nonlinear transformation and computing a measure of energy in a window around each pixel a square error clustering algorithm is then used to integrate the feature images and produce a segmentation a simple procedure to incorporate spatial information in the clustering process is proposed a relative index is used to estimate the true number of texture categories

quantum chaos an entropy approach a new definition of the entropy of a given dynamical system and of an instrument describing the measurement process is proposed within the operational approach to quantum mechanics it generalizes other definitions of entropy in both the classical and quantum cases the kolmogorov sinai ks entropy is obtained for a classical system and the sharp measurement instrument for a quantum system and a coherent states instrument a new quantity coherent states entropy is defined it may be used to measure chaos in quantum mechanics the following correspondence principle is proved the upper limit of the coherent states entropy of a quantum map as 0 is less than or equal to the ks entropy of the corresponding classical map chaos umpire sits and by decision more imbroils the fray by which he reigns next him high arbiter chance governs all john milton paradise lost book ii

decoherence and linear entropy increase in the quantum baker s map we show that the coarse grained quantum baker s map exhibits a linear entropy increase at an asymptotic rate given by the kolmogorov sinai entropy of the classical chaotic baker s map the starting point of our analysis is a symbolic representation of the map on a string of n qubits i e an n bit register of a quantum computer to coarse grain the quantum evolution we make use of the decoherent histories formalism as a by product we show that the condition of medium decoherence holds asymptotically for the coarse grained quantum baker s map

models and inference for uncertainty in extremal dependence conventionally modelling of multivariate extremes has been based on the class of multivariate extreme value distributions more recently other classes have been developed allowing for the possibility that whilst dependence is observed at finite levels the limit distribution is independent a number of articles have shown this development to be important for accurate estimation of the extremal properties both of theoretical processes and observed datasets it has also been shown that so far as dependence is concerned the choice between modelling with either asymptotically dependent or asymptotically independent distributions can be far more influential than model choice within either of these two classes in this paper we explore the issue of modelling across both classes examining in particular the effect of uncertainty caused by lack of knowledge about the status of asymptotic dependence this is achieved by new multivariate models whose parameter spaces are such that asymptotic dependence occurs on a boundary standard techniques in bayesian inference implemented through markov chain monte carlo enable inferences to be drawn that assign posterior probability mass to the boundary region the techniques are illustrated on a set of oceanographic data for which previous analyses have shown that it is difficult to resolve the question of asymptotic dependence status which is however important in model extrapolation

texture classification by wavelet packet signatures this correspondence introduces a new approach to characterize textures at multiple scales the performance of wavelet packet spaces are measured in terms of sensitivity and selectivity for the classification of twenty five natural textures both energy and entropy metrics were computed for each wavelet packet and incorporated into distinct scale space representations where each wavelet packet channel reflected a specific scale and orientation sensitivity wavelet packet representations for twenty five natural textures were classified without error by a simple two layer network classifier an analyzing function of large regularity d sub 20 was shown to be slightly more efficient in representation and discrimination than a similar function with fewer vanishing moments d sub 6 in addition energy representations computed from the standard wavelet decomposition alone 17 features provided classification without error for the twenty five textures included in our study the reliability exhibited by texture signatures based on wavelet packets analysis suggest that the multiresolution properties of such transforms are beneficial for accomplishing segmentation classification and subtle discrimination of texture

modeling spatial processes with unknown extremal dependence class abstractmany environmental processes exhibit weakening spatial dependence as events become more extreme well known limiting models such as max stable or generalized pareto processes cannot capture this which can lead to a preference for models that exhibit a property known as asymptotic independence however weakening dependence does not automatically imply asymptotic independence and whether the process is truly asymptotically in dependent is usually far from clear the distinction is key as it can have a large impact upon extrapolation that is the estimated probabilities of events more extreme than those observed in this work we present a single spatial model that is able to capture both dependence classes in a parsimonious manner and with a smooth transition between the two cases the model covers a wide range of possibilities from asymptotic independence through to complete dependence and permits weakening dependence of extremes even under asymptotic dependence censored likelihood based

continuous time histories observables probabilities phase space structure and the classical limit the continuous time histories program stems from the consistent histories approach to quantum theory and aims to provide a fully covariant formalism for quantum mechanics in this paper we examine some structural points of the formalism we demonstrate a general construction of history hilbert spaces and identify a large class of time averaged observables we pay particular attention to the construction of the decoherence functional the object that encodes probability information in the continuous time limit and its relation to the temporal structure of the theory phase space observables are introduced through the study of general representations of the history group which is the analog of the canonical group in the formalism we can also define a closed time path ctp generating functional for each observable which encodes the information of its correlation functions the phase space version of the ctp generating functional leads to the implementation of wigner weyl transforms that gives a description of quantum theory solely in terms of phase space histories these results allow the identification of an algorithm for going to the classical stochastic limit for a generic quantum system

a comparison of texture feature extraction using adaptive gabor filtering pyramidal and tree structured wavelet transforms in recent studies on image analysis an increasing effort has been carried out in the area of wavelet transform techniques for the discrimination and classification of textural images these methods compete with multichannel filtering techniques especially with the nonorthogonal and incomplete gabor filtering in this paper we introduce two feature extraction algorithms based on pyramidal and tree structured wavelet transforms and compare their performance with the feature extraction which employs adaptive gabor filtering this comparison is based on the segmentation results of several texture image examples using the identical segmentation algorithm for all three feature extraction methods the visible differences of the segmentation results are discussed and their algorithmic causes are analysed

two derivations of the master equation of quantum brownian motion central to many discussion of decoherence is a master equation for the reduced density matrix of a massive particle experiencing scattering from its surrounding environment such as that of joos and zeh such master equations enjoy a close relationship with spontaneous localization models like the grw model the aim of this paper is to present two derivations of the master equation the first derivation is a pedagogical model designed to illustrate the origins of the master equation as simply as possible focusing on physical principles and without the complications of s matrix theory this derivation may serve as a useful tutorial example for students attempting to learn this subject area the second is the opposite a very general derivation using non relativistic many body field theory it reduces to the equation of the type given by joos and zeh in the one particle sector but correcting certain numerical factors which have recently become significant in connection with experimental tests of decoherence this master equation also emphasizes the role of local number density as the preferred basis for decoherence in this model

logical reformulation of quantum mechanics iv projectors in semiclassical physics this is a technical paper providing the proofs of three useful theorems playing a central role in two kinds of physical applications an explicit logical and mathematical formulation of the interpretation of quantum mechanics and the corresponding description of irreversibility the appendix contains a brief mathematical introduction to microlocal analysis three theorems are derived in the text a associating a projector in hilbert space with a macroscopic regular cell in classical phase space b specifying the algebra of the projectors associated with different cells c showing the connection between the classical motion of cells and the schrodinger evolution of projectors for a class of regular hamiltonians corresponding approximately to deterministic systems as described within the framework of quantum mechanics applications to the interpretation of quantum mechanics are given and the consequences for irreversibility will be given later

a bell inequality analog in quantum measure theory one obtains bell s inequalities if one posits a hypothetical joint probability distribution or measure whose marginals yield the probabilities produced by the spin measurements in question the existence of a joint measure is in turn equivalent to a certain causality condition known as screening off we show that if one assumes more generally a joint quantal measure or decoherence functional one obtains instead an analogous inequality weaker by a factor of the proof of this tsirel son inequality is geometrical and rests on the possibility of associating a hilbert space to any strongly positive quantal measure these results lead both to a question does a joint measure follow from some quantal analog of screening off and to the observation that non contextual hidden variables are viable in histories based quantum mechanics even if they are excluded classically

numerical evidence for approximate consistency and markovianity of some quantum histories in a class of finite closed spin systems closed quantum systems obey the schrodinger equation whereas nonequilibrium behavior of many systems is routinely described in terms of classical markovian stochastic processes evidently there are fundamental differences between those two types of behavior we discuss the conditions under which the unitary dynamics may be mapped onto pertinent classical stochastic processes this is first principally addressed based on the notions of consistency and markovianity numerical data are presented that show that the above conditions are to good approximation fulfilled for heisenberg type spin models comprising 12 20 spins the accuracy to which these conditions are met increases with system size

quantum dynamics without the wavefunction when suitably generalized and interpreted the path integral offers an alternative to the more familiar quantal formalism based on state vectors self adjoint operators and external observers mathematically one generalizes the path integral as propagator to a quantal measure on the space of all conceivable worlds and this generalized measure expresses the dynamics or law of motion of the theory much as wiener measure expresses the dynamics of brownian motion within such histories based schemes new and more realistic possibilities open up for resolving the philosophical problems of the state vector formalism in particular one can dispense with the need for external agents by locating the predictive content of in its sets of measure zero such sets are to be precluded but unrestricted application of this rule engenders contradictions one possible response would remove the contradictions by circumscribing the application of the preclusion concept another response more in the tradition of quantum logic would accommodate the contradictions by dualizing to a space of co events and effectively identifying reality with an element of this dual space

quantum equilibrium and the origin of absolute uncertainty what is randomness probability certainty knowledge these are old and difficult questions and we shall not focus on them here nonetheless we shall obtain sharp striking conclusions concerning the relationship between these concepts

comparison of texture features based on gabor filters texture features that are based on the local power spectrum obtained by a bank of gabor filters are compared the features differ in the type of nonlinear post processing which is applied to the local power spectrum the following features are considered gabor energy complex moments and grating cell operator features the capability of the corresponding operators to produce distinct feature vector clusters for different textures is compared using two methods the fisher 1923 criterion and the classification result comparison both methods give consistent results the grating cell operator gives the best discrimination and segmentation results the texture detection capabilities of the operators and their robustness to nontexture features are also compared the grating cell operator is the only one that selectively responds only to texture and does not give false response to nontexture features such as object contours

linearly positive histories probabilities for a robust family of sequences of quantum events non negative probabilities that obey the sum rules may be assigned to a much wider family of sets of histories than decohering histories the resulting linearly positive histories avoid the highly restrictive decoherence conditions and yet give the same probabilities when those conditions apply thus linearly positive histories are a broad extension of decohering histories moreover the resulting theory is manifestly time reversal invariant

the classical limit for a class of quantum baker s maps we show that the class of quantum baker s maps defined by schack and caves have the proper classical limit provided the number of momentum bits approaches infinity this is done by deriving a semi classical approximation to the coherent state propagator

likelihood based inference for max stable processes the last decade has seen max stable processes emerge as a common tool for the statistical modeling of spatial extremes however their application is complicated due to the unavailability of the multivariate density function and so likelihood based methods remain far from providing a complete and flexible framework for inference in this article we develop inferentially practical likelihood based methods for fitting max stable processes derived from a composite likelihood approach the procedure is sufficiently reliable and versatile to permit the simultaneous modeling of marginal and dependence parameters in the spatial context at a moderate computational cost the utility of this methodology is examined via simulation and illustrated by the analysis of united states precipitation extremes

the action operator for continuous time histories we define the action operator for the consistent histories formalism as the quantum analog of the classical action functional for the simple harmonic oscillator case we conclude that the action operator is the generator of time transformations and is associated with the two types of time evolution of the standard quantum theory the wave packet reduction and the unitary time evolution we construct the corresponding classical histories and demonstrate the relevance with the quantum histories finally we show the relation of the action operator to the decoherence functional

information is a physical entity abstract this paper associated with a broader conference talk on the fundamental physical limits of information handling emphasizes the aspects still least appreciated information is not an abstract entity but exists only through a physical representation thus tying it to all the restrictions and possibilities of our real physical universe the mathematician s vision of an unlimited sequence of totally reliable operations is unlikely to be implementable in this real universe speculative remarks about the possible impact of that on the ultimate nature of the laws of physics are included

a topos formulation of history quantum theory topos theory has been suggested by doring and isham as an alternative mathematical structure with which to formulate physical theories in particular it has been used to reformulate standard quantum mechanics in such a way that a novel type of logic is used to represent propositions in this paper we extend this formulation to include temporally ordered collections of propositions as opposed to single time propositions that is to say we have developed a quantum history formalism in the language of topos theory where truth values can be assigned to temporal propositions we analyze the extent to which such truth values can be derived from the truth values of the constituent single time propositions

popescu rohrlich boxes in quantum measure theory two results are proved at the quantal level in sorkin s hierarchy of measure theories one is a strengthening of an existing bound on the correlations in the epr bohm set up under the assumption that the probabilities admit a strongly positive joint quantal measure it is also proved that any set of no signalling probabilities for two distant experimenters with a choice of two alternative experiments each and two possible outcomes per experiment admits a joint quantal measure though one that is not necessarily strongly positive

nonlinear operator for oriented texture texture is an important part of the visual world of animals and humans and their visual systems successfully detect discriminate and segment texture relatively recently progress was made concerning structures in the brain that are presumably responsible for texture processing neurophysiologists reported on the discovery of a new type of orientation selective neuron in areas v1 and v2 of the visual cortex of monkeys which they called grating cells such cells respond vigorously to a grating of bars of appropriate orientation position and periodicity in contrast to other orientation selective cells grating cells respond very weakly or not at all to single bars which do not make part of a grating elsewhere we proposed a nonlinear model of this type of cell and demonstrated the advantages of grating cells with respect to the separation of texture and form information in this paper we use grating cell operators to obtain features and compare these operators in texture analysis tasks with commonly used feature extracting operators such as gabor energy and co occurrence matrix operators for a quantitative comparison of the discrimination properties of the concerned operators a new method is proposed which is based on the fisher 1923 linear discriminant and the fisher criterion the operators are also qualitatively compared with respect to their ability to separate texture from form information and their suitability for texture segmentation

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

factor copula models for replicated spatial data abstractwe propose a new copula model that can be used with replicated spatial data unlike the multivariate normal copula the proposed copula is based on the assumption that a common factor exists and affects the joint dependence of all measurements of the process moreover the proposed copula can model tail dependence and tail asymmetry the model is parameterized in terms of a covariance function that may be chosen from the many models proposed in the literature such as the matern model for some choice of common factors the joint copula density is given in closed form and therefore likelihood estimation is very fast in the general case one dimensional numerical integration is needed to calculate the likelihood but estimation is still reasonably fast even with large datasets we use simulation studies to show the wide range of dependence structures that can be generated by the proposed model with different choices of common factors we apply the proposed model to spatial temperature data and com

super quantum measures on effect algebras with the riesz decomposition properties we give one basis of the space of super quantum measures on finite effect algebras with the riesz decomposition properties rdp for short then we prove that the super quantum measures and quantum interference functions on finite effect algebras with the rdp are determined each other at last we investigate the relationships between the super quantum measures and the diagonally positive signed measures on finite effect algebras with the rdp in detail

estimation of husler reiss distributions and brown resnick processes summary estimation of extreme value parameters from observations in the max domain of attraction of a multivariate max stable distribution commonly uses aggregated data such as block maxima multivariate peaks over threshold methods in contrast exploit additional information from the non aggregated large observations we introduce an approach based on peaks over thresholds that provides several new estimators for processes in the max domain of attraction of the frequently used husler reiss model and its spatial extension brown resnick processes the method relies on increments t0 conditional on t0 exceeding a high threshold where t0 is a fixed location when the marginals are standardized to the gumbel distribution these increments asymptotically form a gaussian process resulting in computationally simple estimates of the husler reiss parameter matrix and particularly enables parametric inference for brown resnick processes based on high dimensional multivariate densities this is a major advantage over composite likelihood methods that are commonly used in spatial extreme value statistics since they rely only on bivariate densities a simulation study compares the performance of the new estimators with other commonly used methods as an application we fit a non isotropic brown resnick process to the extremes of 12 year data of daily wind speed measurements

logical reformulation of quantum mechanics i foundations the basic rules of quantum mechanics are reformulated they deal primarily with individual systems and do not assume that every ket may represent a physical state the customary kinematic and dynamic rules then allow to construct consistent boolean logics describing the history of a system following essentially griffiths proposal logical implication is defined within these logics the multiplicity of which reflects the complementary principle only one interpretative rule of quantum mechanics is necessary in such a framework it states that these logics providebona fide foundations for the description of a quantum system and for reasoning about it one attempts to build up classical physics including classical logic on these quantum foundations the resulting theory of measurement needs not to statea priori that the eigenvalues of an observable have to be the results of individual measurements nor to assume wave packet reduction both these properties can be obtained as consequences of the basic rules one also needs not to postulate that every observable is measurable even in principle a proposition calculus is obtained allowing in principle the replacement of the discussion of problems concerned with the practical interpretation of experiments by due calculations

can a quantum state over time resemble a quantum state at a single time the standard formalism of quantum theory treats space and time in fundamentally different ways in particular a composite system at a given time is represented by a joint state but the formalism does not prescribe a joint state for a composite of systems at different times if there were a way of defining such a joint state this would potentially permit a more even handed treatment of space and time and would strengthen the existing analogy between quantum states and classical probability distributions under the assumption that the joint state over time is an operator on the tensor product of single time hilbert spaces we analyse various proposals for such a joint state including one due to leifer and spekkens one due to fitzsimons jones and vedral and another based on discrete wigner functions finding various problems with each we identify five criteria for a quantum joint state over time to satisfy if it is to play a role similar to the standard joint state for a composite system that it is a hermitian operator on the tensor product of the single time hilbert spaces that it represents probabilistic mixing appropriately that it has the appropriate classical limit that it has the appropriate single time marginals that composing over multiple time steps is associative we show that no construction satisfies all these requirements if hermiticity is dropped then there is an essentially unique construction that satisfies the remaining four criteria

efficient inference and simulation for elliptical pareto processes recent advances in extreme value theory have established ell pareto processes as the natural limits for extreme events defined in terms of exceedances of a risk functional here we provide methods for the practical modelling of data based on a tractable yet flexible dependence model we introduce the class of elliptical ell pareto processes which arise as the limit of threshold exceedances of certain elliptical processes characterized by a correlation function and a shape parameter an efficient inference method based on maximizing a full likelihood with partial censoring is developed novel procedures for exact conditional and unconditional simulation are proposed these ideas are illustrated using precipitation extremes in switzerland

complex probabilities on r n as real probabilities on c n and an application to path integrals we establish a necessary and sufficient condition for averages over complex valued weight functions on r n to be represented as statistical averages over real non negative probability weights on c n using this result we show that many path integrals for time ordered expectation values of bosonic degrees of freedom in real valued time can be expressed as statistical averages over ensembles of paths with complex valued coordinates and then speculate on possible consequences of this result for the relation between quantum and classical mechanics

contrary quantum histories and contrary inferences abstract in the context of the quantum histories approach to quantum mechanics we define a contrary relation between quantum histories generalizing the standard definition of contrary quantum properties using this contrary relation we study the possibility of inferring contrary quantum histories we consider the quantum histories approach with three different consistency conditions weak medium and global consistency conditions for the first two conditions we show that it is possible to infer contrary histories from different families of histories in accordance with previous results for global consistency condition we prove that it is not possible to infer contrary histories

consistent histories and the interpretation of quantum mechanics the usual formula for transition probabilities in nonrelativistic quantum mechanics is generalized to yield conditional probabilities for selected sequences of events at several different times called consistent histories through a criterion which ensures that within limits which are explicitly defined within the formalism classical rules for probabilities are satisfied the interpretive scheme which results is applicable to closed isolated quantum systems is explicitly independent of the sense of time i e past and future can be interchanged has no need for wave function collapse makes no reference to processes of measurement though it can be used to analyze such processes and can be applied to sequences of microscopic or macroscopic events or both as long as the mathematical condition of consistency is satisfied when applied to appropriate macroscopic events it appears to yield the same answers as other interpretative schemes for standard quantum mechanics though from a different point of view which avoids the conceptual difficulties which are sometimes thought to require reference to conscious observers or classical apparatus

how to calculate decoherence matrices numerically abstract a central object in the interpretation of quantum mechanics of closed systems is the decoherence matrix but only for a very small number of models one is able to give explicit expressions for its elements so numerical methods are required unfortunately the dimensions of these matrices are usually very high which makes also a direct numerical calculation impossible in this paper i will develop an algorithm that combines the numerical calculation of the elements of the decoherence matrix with a permanent estimation if the chosen histories are almost decoherent the algorithm will provide the diagonal and maybe some near to diagonal elements only in this case within numerical errors we can assume that all not calculated elements are smaller than a given threshold if the histories are coherent the algorithm has to calculate too much data there exist too much non vanishing elements and the success depends mainly on the available computer time as an example i apply this procedure to the caldeira leggett model

a theory of proximity based clustering structure detection by optimization abstract in this paper a systematic optimization approach for clustering proximity or similarity data is developed starting from fundamental invariance and robustness properties a set of axioms is proposed and discussed to distinguish different cluster compactness and separation criteria the approach covers the case of sparse proximity matrices and is extended to nested partitionings for hierarchical data clustering to solve the associated optimization problems a rigorous mathematical framework for deterministic annealing and mean field approximation is presented efficient optimization heuristics are derived in a canonical way which also clarifies the relation to stochastic optimization by gibbs sampling similarity based clustering techniques have a broad range of possible applications in computer vision pattern recognition and data analysis as a major practical application we present a novel approach to the problem of unsupervised texture segmentation which relies on statistical tests as a measure of homogeneity the quality of the algorithms is empirically evaluated on a large collection of brodatz like micro texture mondrians and on a set of real word images to demonstrate the broad usefulness of the theory of proximity based clustering the performances of different criteria and algorithms are compared on an information retrieval task for a document database the superiority of optimization algorithms for clustering is supported by extensive experiments

efficient inference for spatial extreme value processes associated to log gaussian random functions max stable processes arise as the only possible nontrivial limits for maxima of affinely normalized identically distributed stochastic processes and thus form an important class of models for the extreme values of spatial processes until recently inference for max stable processes has been restricted to the use of pairwise composite likelihoods due to intractability of higher dimensional distributions in this work we consider random fields that are in the domain of attraction of a widely used class of max stable processes namely those constructed via manipulation of log gaussian random functions for this class we exploit limiting d dimensional multivariate poisson process intensities of the underlying process for inference on all d vectors exceeding a high marginal threshold in at least one component employing a censoring scheme to incorporate information below the marginal threshold we also consider the d dimensional distributions for the equivalent max stable process and perform full likelihood inference by exploiting the methods of stephenson tawn 2005 where information on the occurrence times of extreme events is shown to dramatically simplify the likelihood the stephenson tawn likelihood is in fact simply a special case of the censored poisson process likelihood we assess the improvements in inference from both methods over pairwise likelihood methodology by simulation

the classification of decoherence functionals an analog of gleason s theorem gell mann and hartle have proposed a significant generalization of quantum theory with a scheme whose basic ingredients are histories and decoherence functionals within this scheme it is natural to identify the space up of propositions about histories with an orthoalgebra or lattice this raises the important problem of classifying the decoherence functionals in the case where up is the lattice of projectors p v in some hilbert space v in effect one seeks the history analog of gleason s famous theorem in standard quantum theory in the present article the solution to this problem for the case where v is finite dimensional is presented in particular it is shown that every decoherence functional d p v can be written in the form d trv v x for some operator x on the tensor product space v v

from classical to quantum mechanics how to translate physical ideas into mathematical language following previous works by e prugovecki physica a 91a 202 1978 and stochastic quantum mechanics and quantum space time reidel dordrecht 1986 on common features of classical and quantum mechanics we develop a unified mathematical framework for classical and quantum mechanics based on l2 spaces over classical phase space in order to investigate to what extent quantum mechanics can be obtained as a simple modification of classical mechanics on both logical and analytical levels to obtain this unified framework we split quantum theory in two parts i general quantum axiomatics a system is described by a state in a hilbert space observables are self adjoints operators and so on and ii quantum mechanics proper that specifies the hilbert space as l2 rn the heisenberg rule pi qj i ij with p i the free hamiltonian h 2 2m and so on we show that general quantum axiomatics up to a supplementary axiom of classicity can be used as a nonstandard mathematical ground to formula

decoherent histories and realism we reconsider the decoherent histories approach to quantum mechanics and analyze some problems related to its interpretation which we believe have not been adequately clarified by its proponents we put forward some assumptions which in our opinion are necessary for a realistic interpretation of the probabilities that the formalism attaches to decoherent histories we prove that such assumptions unless one limits the set of the decoherent families which can be taken into account lead to a logical contradiction the line of reasoning we follow is conceptually different from other arguments which have been presented and which have been rejected by the supporters of the decoherent histories approach the conclusion is that the decoherent histories approach to be considered as an interesting realistic alternative to the orthodox interpretation of quantum mechanics requires the identification of a mathematically precise criterion to characterize an appropriate set of decoherent families which does not give rise to any problem

the stationary bootstrap abstract this article introduces a resampling procedure called the stationary bootstrap as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on weakly dependent stationary observations previously a technique based on resampling blocks of consecutive observations was introduced to construct confidence intervals for a parameter of the m dimensional joint distribution of m consecutive observations where m is fixed this procedure has been generalized by constructing a blocks of blocks resampling scheme that yields asymptotically valid procedures even for a multivariate parameter of the whole i e infinite dimensional joint distribution of the stationary sequence of observations these methods share the construction of resampling blocks of observations to form a pseudo time series so that the statistic of interest may be recalculated based on the resampled data set but in the context of applying this method to stationary data it is natural

unsupervised segmentation of ultrasonic liver images by multiresolution fractal feature vector the feasibility of selecting fractal feature vector based on multiresolution analysis to segment suspicious abnormal regions of ultrasonic liver images is described in this paper the proposed feature extraction algorithm is based on the spatial frequency decomposition and fractal geometry segmentation of various liver diseases reveals that the fractal feature vector based on multiresolution analysis is trustworthy a quantitative characterization based on the proposed unsupervised segmentation algorithm can be utilized to establish an automatic computer aided diagnostic system as well to increase the visual interpretation capability of ultrasonic liver image for junior physicians off line learning software is developed to investigate the visual criteria

about the notion of truth in quantum mechanics the meaning of truth in quantum mechanics is considered in order to respond to some objections raised by b d espagnat against a logical interpretation of quantum mechanics recently proposed by the author a complete answer is given it is shown that not only can factual data be said to be true but also some of their logical consequences so that the definition of truth given by heisenberg is both extended and refined some nontrue but reliable propositions may also be used but they are somewhat arbitrary because of the complementarity principle for instance the propositions expressing wave packet reduction can be either true or reliable according to the case under study separability is also discussed as far as the true properties of an individual system are concerned quantum mechanics is separable

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