interpolation of precipitation under topographic influence at different time scales 1 in this paper new methodologies for interpolating rainfall data in individual time intervals ranging from a day to a year using gaussian copulas and unsymmetrical v copulas with a variety of treatments of altitude as an exogenous variable are described for shorter time aggregations zeros were treated as censored variables for each selected time step the marginal distributions of precipitation amounts were modeled using nonparametric density estimators while the spatial dependence structures were estimated using a maximum likelihood methodology the methodology was compared to other common geostatistical interpolators such as ordinary kriging and external drift kriging several measures of bias and error structure have been used to assess the efficacy of the methods in a range of comparative split sampling studies the data set chosen for the study comprises daily precipitation time series over 41 years in three regions in germany measured at more than 1200 locations over a large area 126 144 km2 among the many findings in the paper the ones that stand out are i correlation between precipitation and topography increases with the length of time interval and is significantly improved by directional smoothing of topography ii the copula methods are superior to kriging methods in terms of quality of interpolation bias and uncertainty estimation iii the treatment of zeros as censored variables improves interpolation quality for daily and pentad values monthly and annual data in this region present no dry periods iv the copula methods yield full conditional distributions of estimates at a target point in an interval improving substantially on the simple uncertainty estimates derived from kriging and v the gauss copula in particular performs best overall in terms of computational efficiency combined with useful error profiles in the interpolations and of all methods is the most realistic in its error estimates

stochastic reconstruction and interpolation of precipitation fields using combined information of commercial microwave links and rain gauges for the reconstruction and interpolation of precipitation fields we present the application of a stochastic approach called random mixing generated fields are based on a data set consisting of rain gauge observations and path averaged rain rates estimated using commercial microwave link cml derived information precipitation fields are received as linear combination of unconditional spatial random fields where the spatial dependence structure is described by copulas the weights of the linear combination are optimized such that the observations and the spatial structure of the precipitation observations are reproduced the innovation of the approach is that this strategy enables the simulation of ensembles of precipitation fields of any size each ensemble member is in concordance with the observed path averaged cml derived rain rates and additionally reflects the observed rainfall variability along the cml paths the ensemble spread allows additionally an estimation of the uncertainty of the reconstructed precipitation fields the method is demonstrated both for a synthetic data set and a real world data set in south germany while the synthetic example allows an evaluation against a known reference the second example demonstrates the applicability for real world observations generated precipitation fields of both examples reproduce the spatial precipitation pattern in good quality a performance evaluation of random mixing compared to ordinary kriging demonstrates an improvement of the reconstruction of the observed spatial variability random mixing is concluded to be a beneficial new approach for the provision of precipitation fields and ensembles of them in particular when different measurement types are combined

shannon entropy at avoided crossings in the quantum transition from order to chaos shannon entropy is studied for the series of avoided crossings that characterize the transition from order to chaos in quantum mechanics in order to be able to study jointly this entropy for discrete and continuous probability calculations have been performed on a quantized map the kicked harper map resulting in a different behavior as order chaos transition takes place for the discrete position representation and continuous coherent state representation cases this different behavior is analyzed in terms of the distribution of zeros of the husimi function

an exact renormalisation group for bloch electrons in a magnetic field bloch electrons in a magnetic field can be modelled by a one dimensional hamiltonian h h x p which is periodic in x and p when beta the ratio of planck s constant h to the area of a unit cell is a rational number p q the spectrum is a set of q bloch bands if beta is perturbed away from this rational value the spectrum becomes a cantor set but it is still possible to define a set of generalised bloch waves which form a complete basis set for a given band projecting these states into the band and taking matrix elements of the hamiltonian leads to a new effective hamiltonian h1v x p and planck constant h v describing the spectrum of the vth band since degrees of freedom have been eliminated by projecting into a band this is a renormalisation group rg transformation the rg transformation can be iterated indefinitely if the measure of the spectrum is zero or if beta is a liouville number the measure of the spectrum vanishes if h x p has centres of threefold or fourfold symmetry in the phase plane and the rg transformation explains the hierarchical structure of the spectrum observed in these cases

band husimi distributions and the classical quantum correspondence on the torus band husimi distributions bhds are introduced in the quantum chaos problem on a toral phase space in the framework of this phase space a quantum state must satisfy bloch boundary conditions bcs on a torus and the spectrum consists of a finite number of levels for given bcs as the bcs are varied a level broadens into a band the bhd for a band is defined as the uniform average of the husimi distributions for all the eigenstates in the band the generalized bhd for a set of adjacent bands is the average of the bhds associated with these bands bhds are shown to be closer in several aspects to classical distributions than husimi distributions for individual eigenstates the generalized bhd for two adjacent bands is shown to be approximately conserved in the passage through a degeneracy between the bands as a nonintegrability parameter is varied finally it is shown how generalized bhds can be defined so as to achieve physical continuity under small variations of the scaled planck constant a generalization of the topological chern index characterization of the classical quantum correspondence is then obtained

copula based geostatistical models for groundwater quality parameters 1 groundwater quality parameters exhibit considerable spatial variability geostatistical methods including the assessment of variograms are usually used to characterize this variability copulas offer an interesting opportunity to describe dependence structures for multivariate distributions bivariate empirical copulas can be used as an alternative to variograms and covariance functions for the description of the spatial variability rank correlations of these copulas express the strength of the dependence independently of the marginal distributions and thus offer an alternative to the variograms empirical copulas for four quality parameters chloride sulfate ph and nitrate obtained from a large scale groundwater quality measurement network in baden wurttemberg germany are calculated they indicate that the spatial dependence structure of the investigated parameters is not gaussian two theoretical copula based models are presented in this paper a gaussian and a non gaussian bootstrap based statistical tests using stochastic simulation of the multivariate distributions are used to investigate the appropriateness of the models according to the test results the gaussian copula is rejected for most of the parameters while the non gaussian alternative is not rejected in most cases

universal fluctuations of zeros of chaotic wavefunctions wavefunctions of one and two dimensional quantum systems can be parametrized by a finite number of zeros lying in phase space we study correlations of these zeros for fully chaotic systems in terms of a statistical model based on random polynomials excellent agreement is found for the two point correlation function and nearest neighbour spacing distribution of this model and the results obtained for wavefunctions of dynamical systems we conjecture that these correlation functions are valid for any chaotic system after rescaling the phase space distances unfolding some consequences for the distribution of zeros due to time reversal symmetry are also discussed

an aggregate subgradient method for nonsmooth convex minimization a class of implementable algorithms is described for minimizing any convex not necessarily differentiable functionf of several variables the methods require only the calculation off and one subgradient off at designated points they generalize lemarechal s bundle method more specifically instead of using all previously computed subgradients in search direction finding subproblems that are quadratic programming problems the methods use an aggregate subgradient which is recursively updated as the algorithms proceed each algorithm yields a minimizing sequence of points and iff has any minimizers then this sequence converges to a solution of the problem particular members of this algorithm class terminate whenf is piecewise linear the methods are easy to implement and have flexible storage requirements and computational effort per iteration that can be controlled by a user

influence of soil structure and root water uptake strategy on unsaturated flow in heterogeneous media 1 we analyze the combined effects of the spatial variability of soil hydraulic properties and the water uptake by plant roots on unsaturated water flow for this analysis we use a simplified macroscopic root water uptake model which is usually applied only for homogeneous or layered soil and therefore we also determine whether it is applicable for multidimensional heterogeneous media analytical solutions for mean and variance of pressure head first order second moment approximations in layered media and numerical solutions of two dimensional 2 d autocorrelated multi gaussian and non multi gaussian parameter fields are analyzed for steady state and transient flow conditions for non gaussian topological features that have little influence on the mean and the variance of the pressure field if root water uptake is ignored we test whether the influence is significant if root water uptake is accounted for the results reveal that in field structures with large patches of coarse material local regions with pressure head values at the wilting point develop these are surrounded by wet material without a compensation mechanism for local stress the global transpiration demand is not met if local wilting occurs various compensation mechanisms are tested that depend respectively on the saturation the relative conductivity or a strategy where the deficit in the global uptake rate is equally distributed to unstressed locations the strategies lead to a global actual transpiration rate at the potential value and attenuate the formation of locally wilted areas wilted regions can however still occur and may be an artifact of the simplified model concept as root soil interactions are neglected therefore simplified macroscopic models for root water uptake should be used with caution in heterogeneous media

multivariate copula analysis toolbox mvcat describing dependence and underlying uncertainty using a bayesian framework we present a newly developed multivariate copula analysis toolbox mvcat which includes a wide range of copula families with different levels of complexity mvcat employs a bayesian framework with a residual based gaussian likelihood function for inferring copula parameters and estimating the underlying uncertainties the contribution of this paper is threefold a providing a bayesian framework to approximate the predictive uncertainties of fitted copulas b introducing a hybrid evolution markov chain monte carlo mcmc approach designed for numerical estimation of the posterior distribution of copula parameters and c enabling the community to explore a wide range of copulas and evaluate them relative to the fitting uncertainties we show that the commonly used local optimization methods for copula parameter estimation often get trapped in local minima the proposed method however addresses this limitation and improves describing the dependence structure mvcat also enables evaluation of uncertainties relative to the length of record which is fundamental to a wide range of applications such as multivariate frequency analysis

chaos revealing multiplicative representation of quantum eigenstates the quantisation of the two dimensional toric and spherical phase spaces is considered in analytic coherent state representations every pure quantum state admits therein a finite multiplicative parametrisation by the zeros of its husimi function for eigenstates of quantised systems this description explicitly reflects the nature of the underlying classical dynamics in the semiclassical regime the distribution of the zeros in the phase space becomes one dimensional for integrable systems and highly spread out conceivably uniform for chaotic systems this multiplicative representation thereby acquires a special relevance for semiclassical analysis in chaotic systems

equipartition of the eigenfunctions of quantized ergodic maps on the torus we give a simple proof of the equipartition of the eigenfunctions of a class of quantized ergodic area preserving maps on the torus examples are the irrational translations the skew translations the hyperbolic automorphisms and some of their perturbations

improved spatial prediction a combinatorial approach 1 this paper presents a combinatorial approach for improving spatial predictions first copulas are used to interpolate a spatially distributed point rainfall field to a uniform spatial grid it is observed that results vary substantially depending on the parameters chosen for interpolation leading to the hypothesis that it may be advantageous to estimate copula parameters locally or to combine local and global copula predictions it is found that by modifying the method of forecast combinations prediction errors in the spatial interpolation of rainfall can be reduced although this method of combining predictions is applied in the context of rainfall interpolation using local and global copula predictions it can be used on other spatial variables and interpolation methods

classical diffusion and quantum level velocities systematic deviations from random matrix theory we study the response of the quasienergy levels in the context of quantized chaotic systems through the level velocity variance and relate them to classical diffusion coefficients using detailed semiclassical analysis the systematic deviations from random matrix theory assuming independence of eigenvectors from eigenvalues are shown to be connected to classical higher order time correlations of the chaotic system we study the standard map as a specific example and thus the well known oscillatory behavior of the diffusion coefficient with respect to the parameter is reflected exactly in the oscillations of the variance of the level velocities we study the case of mixed phase space dynamics as well and note a transition in the scaling properties of the variance that occurs along with the classical transition to chaos

general quantization of canonical maps on a two torus canonical maps on a two torus in phase space are quantized under most general conditions recent results by keating et al 1999 nonlinearity 12 579 are thus fully extended in two directions a the translational component of a general canonical map is included in the quantization b all values of planck s constant consistent with the toral boundary conditions bcs are considered generically these values are rational numbers whose numerator must satisfy a number theoretical condition besides the condition on planck s constant the quantization is possible only for particular allowed bcs on the torus the general equation determining these bcs is derived allowed bcs may not exist in some cases representative examples are the irrational skew translations and kronecker maps exact versions of egorov s theorem are shown to hold under some conditions composition and representation properties of the quantization scheme are studied

on the zeros of the husimi distribution the basic features of the zeros of the husimi phase space density of a quantum eigenstate are discussed it is demonstrated that some special properties of the harmonic oscillator related to the number of zeros and their location within the classical energy shell are not valid for anharmonic potentials as illustrated by numerical examples for the morse oscillator also discussed is the distribution of zeros in quantum poincare sections for systems with two degrees of freedom

semiclassical asymptotics of perturbed cat maps we derive an exact representation for tr u n where u is the quantum propagator associated with an anosov perturbed cat map this takes the form of a sum over the fixed points of the n th iterate of the classical transformation the contribution of each one being given by an n fold multiple integral we focus in particular on the case when n 1 an asymptotic evaluation of the integral in question then leads to a complete semiclassical series expansion the first term of which corresponds to the gutzwiller tabor trace formula it is demonstrated that this series diverges but that summing it down to its least term provides an approximation to the quantum trace that is exponentially accurate in 1 a simple universal approximation to the late terms is then derived this explains the divergence of the semiclassical expansion in terms of complex tunnelling periodic orbits and implies the existence of unusual relations between different orbit actions it also allows us to recover the semiclassical contributions from the complex orbits explicitly using borel resummation these exponentially subdominant terms are shown to exhibit the stokes phenomenon which causes them to depend sensitively on the size of the perturbation parameter finally we develop an alternative expansion based on the orbits of the unperturbed cat map rather than diverging this is shown to converge absolutely thus making possible an exact calculation of the quantum trace using only classical mechanics its properties are however distinctly anti semiclassical

multivariate type g matern stochastic partial differential equation random fields for many applications with multivariate data random field models capturing departures from gaussianity within realizations are appropriate for this reason we formulate a new class of multivariate non gaussian models based on systems of stochastic partial differential equations with additive type g noise whose marginal covariance functions are of matern type we consider four increasingly flexible constructions of the noise where the first two are similar to existing copula based models in contrast with these the last two constructions can model non gaussian spatial data without replicates computationally efficient methods for likelihood based parameter estimation and probabilistic prediction are proposed and the flexibility of the models suggested is illustrated by numerical examples and two statistical applications less

exact eigenfunctions for a quantised map exact eigenfunctions for quantised linear maps on a torus are constructed a connection with the number of periodic orbits of the classical map is established it is shown that in the semiclassical limit the eigenfunctions become more and more random i e their correlation function approaches a delta function

streamflow prediction in ungauged catchments using copula based dissimilarity measures 1 there are many procedures in the available literature to perform prediction in ungauged basins commonly the euclidean metric is used as a proxy of the hydrologic dissimilarity here we propose a procedure to find a metric on the basis of dissimilarity measures that are estimated from pairwise empirical copula densities of runoff a metric is then defined in an transformed space of basin descriptors whose parameterization is obtained with a variance reducing technique a hydrologic model was run in an ungauged basin with sets of global parameters obtained from the k nearest neighboring donor basins using various metrics to take into account the uncertainty of its parameterization hydrologic model parameters were regionalized with a multiscale parameter regionalization technique whose transfer function parameters were found via calibration the streamflow in an ungauged basin was found as an ensemble streamflow prediction to account for the uncertainties of the transfer function parameters as well as those to define the metric this technique was applied in 38 german basins ranging in size from 70 to 4000 km2 for each basin a number of catchment descriptors and several climatic indices were quantified e g mean slope aspect shape factor mean elevation and mean monthly temperature in january among others daily streamflow time series correspond to the period from 1961 to 2000 simulated daily discharge was validated with a jackknife cross validation technique nash sutcliffe efficiencies obtained in this way ranged between 0 76 and 0 86 these results suggested that the proposed technique would produce reasonable results in ungauged basins

topological properties of quantum periodic hamiltonians we consider periodic quantum hamiltonians on the torus phase space harper like hamiltonians we calculate the topological chern index which characterizes each spectral band in the generic case this calculation is made by a semiclassical approach with the use of quasi modes as a result the chern index is equal to the homotopy of the path of these quasi modes on phase space as the floquet parameter of the band is varied it is quite interesting that the chern indices defined as topological quantum numbers can be expressed from simple properties of the classical trajectories

pegasos primal estimated sub gradient solver for svm we describe and analyze a simple and effective stochastic sub gradient descent algorithm for solving the optimization problem cast by support vector machines svm we prove that the number of iterations required to obtain a solution of accuracy epsilon is tilde o 1 epsilon where each iteration operates on a single training example in contrast previous analyses of stochastic gradient descent methods for svms require omega 1 epsilon 2 iterations as in previously devised svm solvers the number of iterations also scales linearly with 1 where is the regularization parameter of svm for a linear kernel the total run time of our method is tilde o d lambda epsilon where d is a bound on the number of non zero features in each example since the run time does not depend directly on the size of the training set the resulting algorithm is especially suited for learning from large datasets our approach also extends to non linear kernels while working solely on the primal objective function though in this case the runtime does depend linearly on the training set size our algorithm is particularly well suited for large text classification problems where we demonstrate an order of magnitude speedup over previous svm learning methods

geostatistical interpolation using copulas 1 in many applications of geostatistical methods the dependence structure of the investigated parameter is described solely with the variogram or covariance functions which are susceptible to measurement anomalies and implies the assumption of gaussian dependence moreover the kriging variance respects only observation density data geometry and the variogram model to address these problems we borrow the idea from copulas to depict the dependence structure without the influence of the marginal distribution the methodology and basic hypotheses for application of copulas as geostatistical methods are discussed and the gaussian copula as well as a non gaussian copula are used in this paper copula parameters are estimated using a division of the observations into multipoint subsets and a subsequent maximization of the corresponding likelihood function the interpolation is carried out with two different copulas where the expected and median values are calculated from the copulas conditioned with the nearby observations the full conditional copulas provide the estimation distributions for the unobserved locations and can be used to define confidence intervals which depend on both the observation geometry and values observations of a large scale groundwater quality measurement network in baden wurttemberg are used to demonstrate the methodology five groundwater quality parameters chloride nitrate ph sulfate and dissolved oxygen are investigated all five parameters show non gaussian dependence the copula based interpolation results of the five parameters are compared to the results of conventional ordinary and indicator kriging different statistical measures including mean squared error relative differences and probability scores are used to compare cross validation and split sampling results of the interpolation methods the non gaussian copulas give better results than the geostatistical interpolations validation of the confidence intervals shows that they are more realistic than the estimation variances obtained by ordinary kriging

a spatial markov model for the evolution of the joint distribution of groundwater age arrival time and velocity in heterogeneous media the evolution of the joint distribution of groundwater age velocity and arrival times based on a markov model for the velocities of fluid particles in heterogeneous porous media has been quantified an explicit evolution equation for the joint distribution of age arrival time and particle velocity is derived which is equivalent to a continuous time random walk for age velocity and arrival time the approach is fully parameterized by the correlation model and the distribution of groundwater flow velocities the transition probability for subsequent particle velocities along streamlines is implemented by a copula which is an efficient method to generate a correlated velocity series with prescribed marginal distribution we discuss different solution methods based on finite differences and random walk particle tracking the latter is based on continuous time random walks whose transition times are obtained kinematically from the flow velocities specifically we discuss a renormalization scheme to accelerate the particle tracking simulations based on the definition of aggregate particle transitions while at the same time renormalizing velocity correlation the impact of velocity correlation and velocity distribution on the evolution of age at different distances from the inlet plane is also studied at distances of the order of the correlation length persistent particle velocities give the same behavior as stochastic streamtube models for velocity distributions which give rise to transition times with finite variance the age distributions evolve toward an inverse gaussian for heavy tailed weighting times they evolve toward stable distribution as the distance from the inlet increases

generalized wannier function and renormalization of harper s equation harper s equation a model for bloch electrons in a magnetic field has a band spectrum when the dimensionless magnetic field beta is a rational number p q this paper considers the definition of generalized wannier functions which can be used to represent the bloch bands of the spectrum of the rational harper equation by means of a von neumann lattice one representation of these bloch bands can be extended to the irrational case and taking matrix elements in this basis leads to a renormalization group transformation acting on the hamiltonian the results in the present paper considerably extend a previous analysis of this renormalization group transformation in that the formalism is suitable for systematic calculations of the renormalized hamiltonian and that the transformation preserves the rotational symmetry of the harper hamiltonian in phase space

orbit bifurcations and spectral statistics systems whose phase space is mixed have been conjectured to exhibit quantum spectral correlations that are in the semiclassical limit a combination of poisson and random matrix with relative weightings determined by the corresponding measures of regular and chaotic orbits we here identify an additional component in long range spectral statistics associated with periodic orbit bifurcations which can be semiclassically large this is illustrated for a family of perturbed cat maps it has been conjectured that in the semiclassical limit the quantum spectral statistics of classically integrable systems are generically poissonian and that those of classically chaotic systems are generically given by the average over an appropriate random matrix ensemble 1 4 in between these two extremes lie systems whose phase space is mixed that is in which regular and irregular motion coexist such systems are said to exhibit soft chaos 5 for these it has been suggested that the quantum spectral statistics are a combination of poisson and random matrix with relative weightings determined by the corresponding measures of the regular and chaotic orbits 6 our purpose here is to identify in this case an additional component in the long range statistics that is associated with periodic orbit bifurcations and which can be semiclassically large a semiclassical theory for long range spectral statistics has been developed 1 7 9 based on gutzwiller s trace formula 10 which relates the quantum density of states d e d p n e en to classical periodic orbits

modeling complex geological structures with elementary training images and transform invariant distances 1 we present a new framework for multiple point simulation involving small and simple training images the use of transform invariant distances by applying random transformations expands the range of structures available in the simple patterns of the training image the training image is no longer regarded as a global conceptual geological model but rather a basic structural element of the subsurface complex geological structures are obtained whose spatial structure can be parameterized by adjusting the statistics of the random transformations on the basis of field data or geological context in most cases such parameterization is possible by adjusting two numbers only this method allows us to build models that 1 reproduce shapes corresponding to a desired prior geological concept and 2 are in phase with different types of field observations such as orientation hydrofacies or geophysical measurements the main advantage is that the training images are so simple that they can be easily built even in 3 d we apply the method on a synthetic example involving seismic data where the transformation parameters are data driven we also show examples where realistic 2 and 3 d structures are built from simplistic training images with transformation parameters inferred using a small number of orientation data

von neumann lattices of wannier functions for bloch electrons in a magnetic field the problem of bloch electrons in a magnetic field in two dimensions can be reduced to a one dimensional problem with a hamiltonian h that is a periodic function of x and p wannier functions can be defined for the sub bands of the spectrum of this effective hamiltonian when the chern class quantized hall conductance integer of the sub band is zero the weyl wigner formalism can be used to represent these wannier functions by a von neumann lattice it is shown how this von neumann lattice of wannier functions can be defined for irrational as well as rational magnetic fields an important benefit from using the weyl wigner formalism is that symmetries of the periodic potential are reflected by symmetries of the effective hamiltonian in phase space it is shown how the wannier functions can be defined so that their wigner functions have the point symmetries of the effective hamiltonian an example of how these results can prove useful is given if we take matrix elements of the hamiltonian between the wannier states of a sub band we derive a new effective hamiltonian describing this sub band which is again a periodic function of coordinate and momentum operators since by projecting onto a sub band we have also reduced the number of degrees of freedom this operation is a renormalization group transformation it is shown that the symmetry of the new effective hamiltonian in phase space is the same as that of the original one this preservation of symmetry helps to explain some unusual properties of the spectrum when the hamiltonian has fourfold symmetry

a version of the bundle idea for minimizing a nonsmooth function conceptual idea convergence analysis numerical results during recent years various proposals for the minimization of a nonsmooth functional have been made amongst these the bundle concept turned out to be an especially fruitful idea based on this concept a number of authors have developed codes that can successfully deal with nonsmooth problems the aim of the paper is to show that by adding some features of the trust region philosophy to the bundle concept the end result is a distinguished member of the bundle family with a more stable behaviour than some other bundle versions the reliability and efficiency of this code is demonstrated on the standard academic test examples and on some real life problems

a fast learning algorithm for deep belief nets we show how to use complementary priors to eliminate the explaining away effects that make inference difficult in densely connected belief nets that have many hidden layers using complementary priors we derive a fast greedy algorithm that can learn deep directed belief networks one layer at a time provided the top two layers form an undirected associative memory the fast greedy algorithm is used to initialize a slower learning procedure that fine tunes the weights using a contrastive version of the wake sleep algorithm after fine tuning a network with three hidden layers forms a very good generative model of the joint distribution of handwritten digit images and their labels this generative model gives better digit classification than the best discriminative learning algorithms the low dimensional manifolds on which the digits lie are modeled by long ravines in the free energy landscape of the top level associative memory and it is easy to explore these ravines by using the directed connections to display what the associative memory has in mind

bundle methods for regularized risk minimization a wide variety of machine learning problems can be described as minimizing a regularized risk functional with different algorithms using different notions of risk and different regularizers examples include linear support vector machines svms gaussian processes logistic regression conditional random fields crfs and lasso amongst others this paper describes the theory and implementation of a scalable and modular convex solver which solves all these estimation problems it can be parallelized on a cluster of workstations allows for data locality and can deal with regularizers such as l1 and l2 penalties in addition to the unified framework we present tight convergence bounds which show that our algorithm converges in o 1 e steps to e precision for general convex problems and in o log 1 e steps for continuously differentiable problems we demonstrate the performance of our general purpose solver on a variety of publicly available data sets

entropy copula method for single site monthly streamflow simulation 1 an entropy copula method is proposed for single site monthly streamflow simulation in this method the joint distribution of adjacent monthly streamflows is constructed using the copula method whereas the marginal distribution of streamflow for each month is derived using the entropy method then the conditional distribution is derived from which monthly streamflow is generated moment statistics of monthly streamflow such as mean standard deviation and skewness can be modeled by the entropy based marginal distribution while the dependence structure between streamflows of adjacent months can be modeled by the copula based joint distribution the proposed entropy copula method can be extended by incorporating an aggregate variable for modeling the interannual dependence application to the simulation of monthly streamflow from the colorado river illustrates the effectiveness of the proposed method

on a mapping approach to investigating the bootstrap accuracy a simple mapping approach is proposed to study the bootstrap accuracy in a rather general setting it is demonstrated that the bootstrap accuracy can be obtained through this method for a broad class of statistics to which the commonly used edgeworth expansion approach may not be successfully applied we then consider some examples to illustrate how this approach may be used to find the bootstrap accuracy and show the advantage of the bootstrap approximation over the gaussian approximation for the multivariate kolmogorov smirnov statistic we show the error of bootstrap approximation is as small as that of the gaussian approximation for the multivariate kernel type density estimate we obtain an order of the bootstrap error which is smaller than the order of the error of the gaussian approximation given in rio 1994 we also consider an application of the bootstrap accuracy for empirical process to that for the copula process

parameter estimation by ensemble kalman filters with transformed data approach and application to hydraulic tomography 1 ensemble kalman filters enkfs are a successful tool for estimating state variables in atmospheric and oceanic sciences recent research has prepared the enkf for parameter estimation in groundwater applications enkfs are optimal in the sense of bayesian updating only if all involved variables are multivariate gaussian subsurface flow and transport state variables however generally do not show gaussian dependence on hydraulic log conductivity and among each other even if log conductivity is multi gaussian to improve enkfs in this context we apply nonlinear monotonic transformations to the observed states rendering them gaussian gaussian anamorphosis ga similar ideas have recently been presented by beal et al 2010 in the context of state estimation our work transfers and adapts this methodology to parameter estimation additionally we address the treatment of measurement errors in the transformation and provide several multivariate analysis tools to evaluate the expected usefulness of ga beforehand for illustration we present a first time application of an enkf to parameter estimation from 3 d hydraulic tomography in multi gaussian log conductivity fields results show that 1 ga achieves an implicit pseudolinearization of drawdown data as a function of log conductivity and 2 this makes both parameter identification and prediction of flow and transport more accurate combining enkfs with ga yields a computationally efficient tool for nonlinear inversion of data with improved accuracy this is an attractive benefit given that linearization free methods such as particle filters are computationally extremely demanding

on the algorithmic implementation of multiclass kernel based vector machines in this paper we describe the algorithmic implementation of multiclass kernel based vector machines our starting point is a generalized notion of the margin to multiclass problems using this notion we cast multiclass categorization problems as a constrained optimization problem with a quadratic objective function unlike most of previous approaches which typically decompose a multiclass problem into multiple independent binary classification tasks our notion of margin yields a direct method for training multiclass predictors by using the dual of the optimization problem we are able to incorporate kernels with a compact set of constraints and decompose the dual problem into multiple optimization problems of reduced size we describe an efficient fixed point algorithm for solving the reduced optimization problems and prove its convergence we then discuss technical details that yield significant running time improvements for large datasets finally we describe various experiments with our approach comparing it to previously studied kernel based methods our experiments indicate that for multiclass problems we attain state of the art accuracy

regularized bundle methods for convex and non convex risks machine learning is most often cast as an optimization problem ideally one expects a convex objective function to rely on efficient convex optimizers with nice guarantees such as no local optima yet non convexity is very frequent in practice and it may sometimes be inappropriate to look for convexity at any price alternatively one can decide not to limit a priori the modeling expressivity to models whose learning may be solved by convex optimization and rely on non convex optimization algorithms the main motivation of this work is to provide efficient and scalable algorithms for non convex optimization we focus on regularized unconstrained optimization problems which cover a large number of modern machine learning problems such as logistic regression conditional random fields large margin estimation etc we propose a novel algorithm for minimizing a regularized objective that is able to handle convex and non convex smooth and non smooth risks the algorithm is based on the cutting plane technique and on the idea of exploiting the regularization term in the objective function it may be thought as a limited memory extension of convex regularized bundle methods for dealing with convex and non convex risks in case the risk is convex the algorithm is proved to converge to a stationary solution with accuracy e with a rate o 1 e where is the regularization parameter of the objective function under the assumption of a lipschitz empirical risk in case the risk is not convex getting such a proof is more difficult and requires a stronger and more disputable assumption yet we provide experimental results on artificial test problems and on five standard and difficult machine learning problems that are cast as convex and non convex optimization problems that show how our algorithm compares well in practice with state of the art optimization algorithms

analytical relationship between gaussian and transformed gaussian spatially distributed fields 1 a transformation of a gaussian random field results in a change of the spatial dependence in simple terms the range and the shape of a variogram are different between an underlying gaussian and a transformed gaussian field there is a relationship between the underlying and the transformed spatial dependence this paper shows how this relationship can be expressed analytically rather than generating multidimensional random fields and conducting spatial statistical analysis we develop an accurate and efficient approach based on a unique mapping of the correlation coefficients of the original multi gaussian fields to the transformed correlation coefficients to evaluate the spatial correlation of transformed non gaussian random fields for any type of geostatistical parameterization such a mapping can also yield accurate estimation of the spatial correlation of the underlying gaussian field given the spatial correlation of the transformed field results indicate that 1 a nonlinear transformation of spatially distributed fields usually changes the spatial dependence structure and 2 the relationship between the dependence structures of the underlying and the transformed field can be expressed analytically and it is sufficient to do this in one dimension we use the developed approach to investigate the change of correlations of connected random fields generated by the absolute value transformation results show 1 the correlation lengths of the underlying gaussian fields are 1 67 and 2 64 times of those of transformed non gaussian fields for gaussian and exponential covariance models respectively 2 the anisotropic ratio does not change and 3 the anticorrelation in hole effect correlation models disappear

classical limit of the quantized hyperbolic toral automorphisms the canonical quantization of any hyperbolic symplectomorphisma of the 2 torus yields a periodic unitary operator on an dimenional hilbert space n 1 h we prove that this quantum system becomes ergodic and mixing at the classical limit n n prime which can be interchanged with the time average limit the recovery of the stochastic behaviour out of a periodic one is based on the same mechanism under which the uniform distribution of the classical periodic orbits reproduces the lebesgue measure the wigner functions of the eigenstates supported on the classical periodic orbits are indeed proved to become uniformly speread in phase space

a faster cutting plane algorithm with accelerated line search for linear svm faster cutting plane algorithms with accelerated line search are proposed to solve linear svm it proposes a novel linear time line search solver while the existing strategy spends o mlogm time an optimized explicit piecewise linear function finding algorithm for multiclass linear svm is derived it can be proved to reduce the total svm training time experiments demonstrate the effectiveness of the proposed algorithm cutting plane algorithm cpa is a generalization of iterative first order gradient method in which the objective function is approximated successively by supporting hyperplanes cpa has been tailored to solve regularized loss minimization in machine learning by exploiting the regularization structure in particular for linear support vector machine svm embedding a line search procedure effectively remedies the fluctuations of function value and speeds up the convergence in practical issue however the existing line search strategy based on sorting algorithm takes o mlogm time in this paper we propose a more effective line search solver which spends only linear time it can be extended to multiclass svm in which an optimized explicit piecewise linear function finding algorithm is prearranged the total svm training time is proved to reduce theoretically and experiments consistently confirm the effectiveness of the proposed algorithms

gaussian and non gaussian inverse modeling of groundwater flow using copulas and random mixing this paper presents a new copula based methodology for gaussian and non gaussian inverse modeling of groundwater flow the presented approach is embedded in a monte carlo framework and it is based on the concept of mixing spatial random fields where a spatial copula serves as spatial dependence function the target conditional spatial distribution of hydraulic transmissivities is obtained as a linear combination of unconditional spatial fields the corresponding weights of this linear combination are chosen such that the combined field has the prescribed spatial variability and honors all the observations of hydraulic transmissivities the constraints related to hydraulic head observations are nonlinear in order to fulfill these constraints a connected domain in the weight space inside which all linear constraints are fulfilled is identified this domain is defined analytically and includes an infinite number of conditional fields i e conditioned on the observed hydraulic transmissivities and the nonlinear constraints can be fulfilled via minimization of the deviation of the modeled and the observed hydraulic heads this procedure enables the simulation of a great number of solutions for the inverse problem allowing a reasonable quantification of the associated uncertainties the methodology can be used for fields with gaussian copula dependence and fields with specific non gaussian copula dependence further arbitrary marginal distributions can be considered

vortex structure and characterization of quasiperiodic functions quasiperiodic functions qpfs are characterized by their full vortex structure in one unit cell this characterization is much finer and more sensitive than the topological one given by the total vorticity per unit cell the chern index it is shown that qpfs with an arbitrarily prescribed vortex structure exist by constructing explicitly such a standard qpf two qpfs with the same vortex structure are equivalent in the sense that their ratio is a function which is strictly periodic nonvanishing and at least continuous a general qpf can then be approximately reconstructed from its vortex structure on the basis of the standard qpf and the equivalence concept as another application of this concept a simple method is proposed for calculating the quasiperiodic eigenvectors of periodic matrices possible applications to the quantum chaos problem on a phase space torus are briefly discussed

extended and localized states of generalized kicked harper models basic properties of quantum states for generalized kicked harper models are studied using the phase space translational symmetry of the problem explicit expressions of the quasienergy qe states are derived for general rational values q p of a dimensionless ensuremath elzxh the quasienergies form p bands and the qe states are q fold degenerate with each band one can associate a pair of integers ensuremath sigma and ensuremath mu determined from the periodicity conditions of the qe states in the band for q 1 ensuremath sigma is exactly the chern index introduced by leboeuf et al phys rev lett 65 3076 1990 for a characterization of the classical quantum correspondence it is shown however that ensuremath sigma is always different from zero for qg1 the chern index characterization is then generalized by introducing localized quantum states associated in a natural way with ensuremath sigma 0 these states are formed from q qe bands with a total ensuremath sigma 0 and define q equivalent new bands each with ensuremath sigma 0 while these states are nonstationary they become stationary in the semiclassical limit p ensuremath rightarrow ensuremath infty

on the distribution of zeros of chaotic wavefunctions wavefunctions in a phase space representation can be expressed as entire functions of their zeros if the phase space is compact these zeros seem to hide a lot of relevant and explicit information about the underlying classical dynamics besides an understanding of their statistical properties may prove to be useful in the analytical calculations of the wavefunctions in quantum chaotic systems this motivates us to pursue the present study which by a numerical statistical analysis shows that both long range correlations as well as short range correlations exist between zeros while the latter turn out to be universal and parametric independent the former seem to be system dependent and are significantly affected by various parameters i e symmetry localization etc furthermore for the delocalized quantum dynamics the distribution of these zeros seem to mimic that of the zeros of the random functions as well as random polynomials

efficient pairwise composite likelihood estimation for spatial clustered data spatial clustered data refer to high dimensional correlated measurements collected from units or subjects that are spatially clustered such data arise frequently from studies in social and health sciences we propose a unified modeling framework termed as geocopula to characterize both large scale variation and small scale variation for various data types including continuous data binary data and count data as special cases to overcome challenges in the estimation and inference for the model parameters we propose an efficient composite likelihood approach in that the estimation efficiency is resulted from a construction of over identified joint composite estimating equations consequently the statistical theory for the proposed estimation is developed by extending the classical theory of the generalized method of moments a clear advantage of the proposed estimation method is the computation feasibility we conduct several simulation studies to assess the performance of the proposed models and estimation methods for both gaussian and binary spatial clustered data results show a clear improvement on estimation efficiency over the conventional composite likelihood method an illustrative data example is included to motivate and demonstrate the proposed method

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

adaptive subgradient methods for online learning and stochastic optimization we present a new family of subgradient methods that dynamically incorporate knowledge of the geometry of the data observed in earlier iterations to perform more informative gradient based learning metaphorically the adaptation allows us to find needles in haystacks in the form of very predictive but rarely seen features our paradigm stems from recent advances in stochastic optimization and online learning which employ proximal functions to control the gradient steps of the algorithm we describe and analyze an apparatus for adaptively modifying the proximal function which significantly simplifies setting a learning rate and results in regret guarantees that are provably as good as the best proximal function that can be chosen in hindsight we give several efficient algorithms for empirical risk minimization problems with common and important regularization functions and domain constraints we experimentally study our theoretical analysis and show that adaptive subgradient methods outperform state of the art yet non adaptive subgradient algorithms

bayesian assessment of the expected data impact on prediction confidence in optimal sampling design 1 incorporating hydro geo logical data such as head and tracer data into stochastic models of subsurface flow and transport helps to reduce prediction uncertainty because of financial limitations for investigation campaigns information needs toward modeling or prediction goals should be satisfied efficiently and rationally optimal design techniques find the best one among a set of investigation strategies they optimize the expected impact of data on prediction confidence or related objectives prior to data collection we introduce a new optimal design method called predia gnosis preposterior data impact assessor predia derives the relevant probability distributions and measures of data utility within a fully bayesian generalized flexible and accurate framework it extends the bootstrap filter bf and related frameworks to optimal design by marginalizing utility measures over the yet unknown data values predia is a strictly formal information processing scheme free of linearizations it works with arbitrary simulation tools provides full flexibility concerning measurement types linear nonlinear direct indirect allows for any desired task driven formulations and can account for various sources of uncertainty e g heterogeneity geostatistical assumptions boundary conditions measurement values model structure uncertainty a large class of model errors via bayesian geostatistics and model averaging existing methods fail to simultaneously provide these crucial advantages which our method buys at relatively higher computational costs we demonstrate the applicability and advantages of predia over conventional linearized methods in a synthetic example of subsurface transport in the example we show that informative data is often invisible for linearized methods that confuse zero correlation with statistical independence hence predia will often lead to substantially better sampling designs finally we extend our example to specifically highlight the consideration of conceptual model uncertainty

multivariate hydrological frequency analysis using copulas 1 this article presents the modeling of multivariate extreme values using copulas our approach allows us to model the dependence structure independently of the marginal distributions which is not possible with standard classical methods the methodology has been applied on two different problems in hydrology the first application is concerned with the combined risk in the framework of frequency analysis four copulas have been tested on peak flows from the watershed of peribonka in quebec canada the second application relates to the joint modeling of peak flows and volumes three copulas have been applied to the watershed of the rimouski river in quebec canada this approach using copulas is promising since it allows us to take into account a wide range of correlation which can happen in hydrology

antiresonance and localization in quantum dynamics the phenomenon of quantum antiresonance qar i e exactly periodic recurrences in quantum dynamics is studied in a large class of nonintegrable systems the modulated kicked rotors mkrs it is shown that asymptotic exponential localization generally occurs for eta a scaled hbar in the infinitesimal vicinity of qar points eta 0 the localization length xi 0 is determined from the analytical properties of the kicking potential this qar localization is associated in some cases with an integrable limit of the corresponding classical systems the mkr dynamical problem is mapped into pseudorandom tight binding models exhibiting dynamical localization dl by considering exactly solvable cases numerical evidence is given that qar localization is an excellent approximation to dl sufficiently close to qar the transition from qar localization to dl in a semiclassical regime as eta is varied is studied it is shown that this transition takes place via a gradual reduction of the influence of the analyticity of the potential on the analyticity of the eigenstates as the level of chaos is increased

signature of chaotic diffusion in band spectra we investigate the two point correlations in the band spectra of periodic systems that exhibit chaotic diffusion in the classical limit in terms of form factors with the winding number as a spatial argument for times below the heisenberg time they contain the full space time dependence of the classical propagator they approach constant asymptotes via a regime reflecting quantal ballistic motion where they decay by a factor proportional to the number of unit cells we derive a universal scaling function for the long time behavior in the limit of long chains our results are consistent with expressions obtained by field theoretical methods they are substantiated by numerical studies of the kicked rotor and a billiard chain

quantization of a class of piecewise affine transformations on the torus we present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of chaoticity the systems to be quantized are piecewise affine maps on the two torus viewed as phase space and include the automorphisms translations and skew translations we then treat some discontinuous transformations such as the baker map and the sawtooth like maps our approach extends some ideas from geometric quantization and it is both conceptually and calculationally simple

on the quantisation of arnold s cat characterises the quantisation ua of the classical map a in sl 2 z using the heisenberg group constructs the eigenstates for n perfect square where 2 pi n and shows that the fourier components of the wigner functions of a complete set of eigenstates go to zero for n p2 p prime p to infinity a hyperbolic

chaotic eigenfunctions in phase space we study individual eigenstates of quantized area preserving maps on the 2 torus which are classically chaotic in order to analyze their semiclassical behavior we use the bargmann husimi representations for quantum states as well as their stellar parametrization which encodes states through a minimal set of points in phase space the constellation of zeros of the husimi density we rigorously prove that a semiclassical uniform distribution of husimi densities on the torus entails a similar equidistribution for the corresponding constellations we deduce from this property a universal behavior for the phase patterns of chaotic bargmann eigenfunctions which is reminiscent of the wkb approximation for eigenstates of integrable systems though in a weaker sense in order to obtain more precise information on chaotic eigenconstellations we then model their properties by ensembles of random states generalizing former results on the 2 sphere to the torus geometry this approach yields statistical predictions for the constellations which fit quite well the chaotic data we finally observe that specific dynamical information e g the presence of high peaks like scars in husimi densities can be recovered from the knowledge of a few long wavelength fourier coefficients which therefore appear as valuable order parameters at the level of individual chaotic eigenfunctions