filtering and frequency interpretations of singular spectrum analysis new filtering and spectral interpretations of singular spectrum analysis ssa are provided it is shown that the variables reconstructed from diagonal averaging of reduced rank approximations to the trajectory matrix can be obtained from a noncausal convolution filter with zero phase characteristics the reconstructed variables are readily constructed using a two pass filtering algorithm that is well known in the signal processing literature when the number of rows in the trajectory matrix is much larger than number of columns many results reported in the signal processing literature can be used to derive the properties of the resulting filters and their spectra new features of the reconstructed series are revealed using these results two examples are used to illustrate the results derived in this paper

embedding formulations and complexity for unions of polyhedra it is well known that selecting a good mixed integer programming mip formulation is crucial for effectively obtaining a solution with state of the art solvers although best practices and guidelines for constructing good formulations abound there is rarely a single systematic construction approach that leads to the best possible formulation here we introduce embedding formulations and complexity as a new mip formulation paradigm for systematically constructing formulations for disjunctive constraints that are optimal with respect to size more specifically they yield the smallest possible ideal formulation i e one whose lp relaxation has integral extreme points among all formulations that only use 0 1 auxiliary variables we use the paradigm to characterize optimal formulations for special ordered sets of type 2 and certain piecewise linear functions of two variables we also show that the resultant formulations can provide a significant computational advantage over all known formulations for pi

on the dimension of complex responses in nonlinear structural vibrations abstract the ability to accurately model engineering systems under extreme dynamic loads would prove a major breakthrough in many aspects of aerospace mechanical and civil engineering extreme loads frequently induce both nonlinearities and coupling which increase the complexity of the response and the computational cost of finite element models dimension reduction has recently gained traction and promises the ability to distill dynamic responses down to a minimal dimension without sacrificing accuracy in this context the dimensionality of a response is related to the number of modes needed in a reduced order model to accurately simulate the response thus an important step is characterizing the dimensionality of complex nonlinear responses of structures in this work the dimensionality of the nonlinear response of a post buckled beam is investigated significant detail is dedicated to carefully introducing the experiment the verification of a finite element model and the dimensionality estimation algorithm as it is hoped that this system may help serve as a benchmark test case it is shown that with minor modifications the method of false nearest neighbors can quantitatively distinguish between the response dimension of various snap through non snap through random and deterministic loads the state space dimension of the nonlinear system in question increased from 2 to 10 as the system response moved from simple low level harmonic to chaotic snap through beyond the problem studied herein the techniques developed will serve as a prescriptive guide in developing fast and accurate dimensionally reduced models of nonlinear systems and eventually as a tool for adaptive dimension reduction in numerical modeling the results are especially relevant in the aerospace industry for the design of thin structures such as beams panels and shells which are all capable of spatio temporally complex dynamic responses that are difficult and computationally expensive to model

operator theoretic framework for forecasting nonlinear time series with kernel analog techniques abstract kernel analog forecasting kaf alternatively known as kernel principal component regression is a kernel method used for nonparametric statistical forecasting of dynamically generated time series data this paper synthesizes descriptions of kernel methods and koopman operator theory in order to provide a single consistent account of kaf the framework presented here illuminates the property of the kaf method that under measure preserving and ergodic dynamics it consistently approximates the conditional expectation of observables that are acted upon by the koopman operator of the dynamical system and are conditioned on the observed data at forecast initialization more precisely kaf yields optimal predictions in the sense of minimal root mean square error with respect to the invariant measure in the asymptotic limit of large data the presented framework facilitates moreover the analysis of generalization error and quantification of uncertainty extensions of kaf to the construction of conditional variance and conditional probability functions as well as to non symmetric kernels are also shown illustrations of various aspects of kaf are provided with applications to simple examples namely a periodic flow on the circle and the chaotic lorenz 63 system

analytic hierarchy process for multi sensor data fusion based on belief function theory abstract multi sensor data fusion is an evolving technology whereby data from multiple sensor inputs are processed and combined the data derived from multiple sensors can however be uncertain imperfect and conflicting the present study is undertaken to help contribute to the continuous search for viable approaches to overcome the problems associated with data conflict and imperfection sensor readings represented by belief functions have to be fused according to their corresponding weights previous studies have often estimated the weights of sensor readings based on a single criterion mono criteria approaches for the assessment of sensor reading weights are however often unreliable and inadequate for the reflection of reality accordingly this work opts for the use of a multi criteria decision aid a modified analytical hierarchy process ahp that incorporates several criteria is proposed to determine the weights of a sensor reading set the approach relies on the automation of pairwise comparisons to eliminate subjectivity and reduce inconsistency it assesses the weight of each sensor reading and fuses the weighed readings obtained using a modified average combination rule the efficiency of this approach is evaluated in a target recognition context several tests sensitivity analysis and comparisons with other approaches available in the literature are described

a branch and cut algorithm without binary variables for nonconvex piecewise linear optimization we give a branch and cut algorithm for solving linear programs lps with continuous separable piecewise linear cost functions plfs models for plfs use continuous variables in special ordered sets of type 2 sos2 traditionally sos2 constraints are enforced by introducing auxiliary binary variables and other linear constraints on them alternatively we can enforce sos2 constraints by branching on them thus dispensing with auxiliary binary variables we explore this approach further by studying the inequality description of the convex hull of the feasible set of lps with plfs in the space of the continuous variables and using the new cuts in a branch and cut scheme without auxiliary binary variables we give two families of valid inequalities the first family is obtained by lifting the convexity constraints the second family consists of lifted cover inequalities finally we report computational results that demonstrate the effectiveness of our cuts and that branch and cut without auxiliary binary variables is significantly more practical than the traditional mixed integer programming approach

singular spectrum analysis in nonlinear dynamics with applications to paleoclimatic time series we distinguish between two dimensions of a dynamical system given by experimental time series statistical dimension gives a theoretical upper bound for the minimal number of degrees of freedom required to describe tje attractor up to the accuracy of the data taking into account sampling and noise problems the dynamical dimension is the intrinsic dimension of the attractor and does not depend on the quality of the data singular spectrum analysis ssa provides estimates of the statistical dimension ssa also describes the main physical phenomena reflected by the data it gives adaptive spectral filters associated with the dominant oscillations of the system and clarifies the noise characteristics of the data we apply ssa to four paleoclimatic records the principal climatic oscillations and the regime changes in their amplitude are detected about 10 degrees of freedom are statistically significant in the data large noise and insufficient sample length do not allow reliable estimates of the dynamical dimension

characterization of a two parameter mixed mode electrochemical behavior regime using neural networks abstract we use nonlinear signal processing techniques based on artificial neural networks to construct a continuous time model set of ordinary differential equations odes from experimental observations of mixed mode oscillations during the galvanostatic oxidation of hydrogen on platinum in the presence of bismuth and chloride ions the data was in the form of time series of the potential for different values of the applied current and chloride ion concentration we use the model to reconstruct the experimental dynamics and to explore the associated bifurcation structures in phase space using numerical bifurcation techniques we locate stable and unstable periodic solutions calculate eigenvalues and identify bifurcation points this approach constitutes a promising data post processing procedure for investigating phase space and parameter space of real experimental systems it allows us to infer phase space structures which the experiments can only probe with limited measurement precision and only at a discrete number of operating parameter settings for example the fitted model suggests the existence of a sub critical hopf bifurcation near the range of parameters probed in the experiments this might explain the experimental difficulty in locating small amplitude simple oscillations

dimension measurement on high dimensional systems abstract using experimental data from a variety of laboratory electrical systems the upper limits on dimension measurement are examined and it is shown that contrary to standard scaling estimates it can be possible to reliably measure correlation dimensions larger than 10 the practical implications of the constraints on such a measurement are examined including the role of statistical errors geometrical artifacts dimension algorithm metric choice and the process power spectrum these ideas are applied to electrical 1 f noise from both macroscopic and microscopic sources to show that it cannot be explained by a deterministic model with fewer than roughly 20 degrees of freedom

convergence of the k 2 entropy for random noises with power law spectra abstract we discuss a counter example to the traditional expectation that stochastic processes lead to a non convergence of the k 2 entropy in computed or measured time series we consider a simple class of colored random noises with power law spectra which have already been shown to generate finite and predictable values of the correlation dimension we show that the k 2 entropy of these random noises converges as well these results imply that the observation of a finite or null value of the k 2 entropy in the analysis of data is not enough to infer that the system is dominated by a deterministic process such as low dimensional chaos

on the dempster shafer framework and new combination rules abstract we discuss the basic concepts of the dempster shafer approach basic probability assignments belief functions and probability functions we discuss how to represent various types of knowledge in this framework we discuss measures of entropy and specificity for belief structures we discuss the combination and extension of belief structures we introduce some concerns associated with the dempster rule of combination inherent in the normalization due to conflict we introduce two alternative techniques for combining belief structures the first uses dempster s rule while the second is based upon a modification of this rule we discuss the issue of credibility of a witness

a novel combination method for conflicting evidence based on inconsistent measurements dempster shafer d s evidence theory is a kind of effective tool for uncertain information fusion however the counter intuitive results are often obtained when the conflicting pieces of evidence are fused with dempster s combination rule in order to solve the existing counter intuitive problem more effectively and less conservatively in this paper we propose an improved combination method for the conflicting evidence based on inconsistent measurements firstly a new approach is proposed for measuring the conflict between two pieces of evidence then the conflicting evidence is revised by selecting discount coefficients moreover dempster s combination rule is significantly improved by the new conflict coefficients and the fusion results are acquired by the improved combination rule finally examples are given to illustrate the effectiveness and potential of the developed new techniques

secondary instability eof reduction and the transition to baroclinic chaos abstract high resolution numerical simulations illustrate how an initial baroclinic instability may become chaotic as the degree of supercritically is increased the route to chaos is via bifurcations to periodic and quasi periodic states but the spatial structures involved are much more complex than those assumed in previous low order models the fundamental participants in the transition can be educed by studying the symmetry breaking secondary instabilities of fixed points of the primary baroclinic instability problem these unstable disturbances to the equilibrium way baroclinic flow serve to eradicate the fundamental zonal currents reduced low dimensional models that replicate the full 10 4 mode computer simulations can be formulated by projecting the governing equations onto the eofs empirical orothogonal functions of the large scale calculations the successful constructions of such models using relatively few eofs appears to be related to the fact that the eofs are almost identical to the secondary instabilities of the primary baroclinic wave state and these secondary instabilities are in turn the primary participants in the supercritical periodic and quasiperiodic states

the combination of evidence in the transferable belief model a description of the transferable belief model which is used to quantify degrees of belief based on belief functions is given the impact of open and closed world assumption on conditioning is discussed the nature of the frame of discernment on which a degree of belief will be established is discussed a set of axioms justifying dempster s rule for the combination of belief functions induced by two distinct evidences is presented

topology from time series we describe methods for the study of topological properties of the invariant manifolds of experimental dynamical systems we explain how to compute such invariants as the euler characteristic and betti numbers using time series data and suggest a number of potential applications

models for stochastic climate prediction there has been a recent burst of activity in the atmosphere ocean sciences community in utilizing stable linear langevin stochastic models for the unresolved degree of freedom in stochastic climate prediction here several idealized models for stochastic climate modeling are introduced and analyzed through unambiguous mathematical theory this analysis demonstrates the potential need for more sophisticated models beyond stable linear langevin equations the new phenomena include the emergence of both unstable linear langevin stochastic models for the climate mean and the need to incorporate both suitable nonlinear effects and multiplicative noise in stochastic models under appropriate circumstances the strategy for stochastic climate modeling that emerges from this analysis is illustrated on an idealized example involving truncated barotropic flow on a beta plane with topography and a mean flow in this example the effect of the original 57 degrees of freedom is well represented by a theoretically predicted stochastic model with only 3 degrees of freedom

detecting switch dynamics in chaotic time waveform using a parametrized family of nonlinear predictors abstract an algorithm is presented for detecting switch dynamics in chaotic time waveform by the switch dynamics we mean that the chaotic time waveform is measured from a dynamical system whose bifurcation parameters are occasionally switched among a set of slightly different parameter values first the switched chaotic time waveform is divided into windows of short term time waveforms from the set of windowed time waveforms qualitatively similar parametrized family of nonlinear predictors is constructed qualitatively similar parametrized family means that the family of nonlinear predictors exhibits qualitatively similar bifurcation phenomena as the original by characterizing the windows of short term chaotic time waveforms in terms of the qualitative parameters of nonlinear predictors switch dynamics of their associated bifurcation parameters are detected for the lorenz equations the rossler equations and the mackey glass equations efficiency of the algorithm is demonstrated in the experiment chaotic time waveforms contaminated with observational noise is considered

recognizing chaotic time waveforms in terms of a parametrized family of nonlinear predictors abstract consider a chaotic dynamical system which exhibits a variety of chaotic time waveforms with a change in the bifurcation parameters this paper presents an algorithm for estimating the underlying bifurcation parameters of the chaotic time waveforms in experimental situation in which no a priori analytical knowledge of the dynamical system is available first we construct qualitatively similar parametrized family of nonlinear predictors only from several sets of chaotic time waveforms qualitatively similar parametrized family means that the family of nonlinear predictors exhibits qualitatively similar bifurcation phenomena as the original chaotic time waveforms are then characterized in terms of the qualitatively similar bifurcation parameters of the nonlinear predictors we call the characterization of chaotic time waveforms in terms of the underlying bifurcation parameters chaotic time waveform recognition several numerical experiments using the rossler equations show the efficiency of the algorithm the effect of observational noise included in chaotic time waveforms is also considered

minute ahead stock price forecasting based on singular spectrum analysis and support vector regression abstract time series modeling and forecasting is an essential and hard task in financial engineering and optimization various models have been proposed in the literature and tested on daily data however a limited attention has been given to intraday data in this regard the current work presents a model for intraday stock price prediction that uses singular spectrum analysis ssa and support vector regression svr coupled with particle swarm optimization pso in particular the ssa decomposes stock price time series into a small number of independent components used as predictors the svr is applied to the task of forecasting and pso is employed to optimize svr parameters the performance of our proposed model is compared to the performance of four models widely used in financial prediction the wavelet transform wt coupled with feedforward neural network ffnn autoregressive moving average arma process polynomial regression polyreg and naive model finally the mean absolute error mae mean absolute percentage error mape and the root mean of squared errors rmse are used as main performance metrics by applying all models to six intraday stock price time series the forecasting results from simulations show that the presented ssa pso svr largely outperforms the conventional wt ffnn arma polynomial regression and naive model in terms of mae mape and rmse therefore our proposed predictive system ssa pso svr shows evident potential for noisy financial time series analysis and forecasting

on the detection of determinism in a time series the nonlinearly scaled distributions of the strengths of the orthogonal modes in the data of a time series are compared with that derived from its surrogate counterpart to assess its chaoticity or the stochastic nature chaoticity manifests in the relatively decreasing strengths of the weaker modes with increasing dimension of the orthogonal spaces mapping the process the distributions of the strengths of the modes for the data and the surrogate are compared statistically singular value decomposition is used for the implementation the ability of the proposed method to distinguish between chaotic and stochastic dynamics is demonstrated through a number of simulated series including linear and nonlinear stochastic noise and processes described by lorenz rossler and mackey glass equations henon map and ecological map and some real life examples

a comparison of mixed integer programming models for nonconvex piecewise linear cost minimization problems we study a generic minimization problem with separable nonconvex piecewise linear costs showing that the linear programming lp relaxation of three textbook mixed integer programming formulations each approximates the cost function by its lower convex envelope we also show a relationship between this result and classical lagrangian duality theory

on the non equivalence of observables in phase space reconstructions from recorded time series in practical problems of phase space reconstruction it is usually the case that the reconstruction is much easier using a particular recorded scalar variable this seems to contradict the general belief that all variables of a dynamical system are equivalent in phase space reconstruction problems this paper will argue that in many cases the choice of a particular scalar time series from which to reconstruct the original dynamics could be critical it is argued that different dynamical variables do not provide the same level of information observability of the underlying dynamics and as a consequence the quality of a global reconstruction critically depends on the recorded variable examples in which the choice of observables is critical are discussed and the level of information contained in a given variable is quantified in the case where the original system is known a clear example of such a situation arises in the r ossler system for which the performance of a global vector field reconstruction technique is investigated using time series of variables x y or z taken one at a time

low dimensional chaotic dynamics versus intrinsic stochastic noise a paradigm model several prototype models are introduced here which are designed to elucidate the interaction between heteroclinic low dimensional chaos in the projected nonlinear dynamics and intrinsic stochasticity induced by energy exchange with a bath of fast variables these models are built by coupling a four dimensional ode with known analytical properties including heteroclinic cycles with a suitable deterministic bath of fast variables a systematic strategy for stochastic mode reduction is applied to these models with 104 degrees of freedom to derive four dimensional reduced stochastic equations for the slow variables due to the internal chaotic dynamics of the slow variables the stochastic mode reduction strategy is very robust in this case and yields reduced models which accurately capture the statistical behavior of the original deterministic system furthermore it is also shown here that even in the regime of a weak coupling between the slow variables and the fast heat bath the detailed structure of the stochastic terms derived through the mode elimination procedure is essential for reproducing the statistical behavior of the slow dynamics

a stochastic model of indopacific sea surface temperature anomalies abstract it is often desirable to represent a rapidly varying physical process as stochastic forcing of some slower dynamical system a review of this approximation is presented the white noise limit of rapidly varying processes reduces the dynamical description of the affected slower systems to stochastic differential equations the properties of which are summarized as an application of stochastic differential equations we review the evidence that indopacific sea surface temperature anomalies sstas can be represented as a stable linear process driven by spatially coherent stochastic forcing an inversemodeling approach is used that is the relevant parameters of the best fit stable linear process are obtained from observations and given these parameters the assumptions of stability and linearity are subsequently tested an optimal initial structure for growth predicted by the model is found to occur approximately seven months before most of the major warm and cold el nino la nina events in the data record the optimal structure preferentially occurs in the boreal spring with the mature phase of the extreme event occurring in the subsequent late fall winter the best model to fit the observations including the dependence of the dynamical system on the annual cycle is driven by stochastic forcing with periodic statistics these statistics are inferred using a time dependent fluctuation dissipation relation the variation of the stochastic forcing with the annual cycle is not the same as that of the optimal initial structure yet when a linear numerical model is driven with the derived stochastic forcing the optimal structure including its variation with the annual cycle is recovered this implies that deterministic dynamics play an important role in setting up the optimal structure and therefore a mature phase of el nino may be predicted before the optimal structure actually appears

models for the piecewise linear unsplittable multicommodity flow problems abstract in this paper we consider multicommodity flow problems with unsplittable flows and piecewise linear routing costs we first focus on the case where the piecewise linear routing costs are convex we show that this problem is np hard for the general case but polynomially solvable when there is only one commodity we then propose a strengthened mixed integer programming formulation for the problem we show that the linear relaxation of this formulation always gives the optimal solution of the problem for the single commodity case we present a wide array of computational experiments showing this formulation also produces very tight linear programming bounds for the multi commodity case finally we also adapt our formulation for the non convex case our experimental results imply that the linear programming bounds for this case are only slightly weaker than the ones of state of the art models for the splittable flow version of the problem

a mathematical framework for stochastic climate models there has been a recent burst of activity in the atmosphere ocean sciences community in utilizing stable linear langevin stochastic models for the unresolved degrees of freedom in stochastic climate prediction here a systematic mathematical strategy for stochastic climate modeling is developed and some of the new phenomena in the resulting equations for the climate variables alone are explored the new phenomena include the emergence of both unstable linear langevin stochastic models for the climate mean variables and the need to incorporate both suitable nonlinear effects and multiplicative noise in stochastic models under appropriate circumstances all of these phenomena are derived from a systematic self consistent mathematical framework for eliminating the unresolved stochastic modes that is mathematically rigorous in a suitable asymptotic limit the theory is illustrated for general quadratically nonlinear equations where the explicit nature of the stochastic climate modeling procedure can be elucidated the feasibility of the approach is demonstrated for the truncated equations for barotropic flow with topography explicit concrete examples with the new phenomena are presented for the stochastically forced three mode interaction equations the conjecture of smith and waleffe phys fluids 11 1999 1608 1622 for stochastically forced three wave resonant equations in a suitable regime of damping and forcing is solved as a byproduct of the approach examples of idealized climate models arising from the highly inhomogeneous equilibrium statistical mechanics for geophysical flows are also utilized to demonstrate self consistency of the mathematical approach with the predictions of equilibrium statistical mechanics in particular for these examples the reduced stochastic modeling procedure for the climate variables alone is designed to reproduce both the climate mean and the energy spectrum of the climate variables c 2001 john wiley sons inc

dimensions and entropies of strange attractors from a fluctuating dynamics approach abstract it is shown that the fluctuations in the divergence of near by trajectories on strictly deterministic strange attractors can be modelled by stochastic concepts in particular we propose kramers moyal type equations for correlation functions between points on the attractor the drift terms are the lyapunov exponents the diffusion terms depend on the above fluctuations from this we obtain bounds on generalized dimensions and entropies numerical results show that in nearly all studied cases henon map zaslavskii map mackey glass eq the attractors are fractal measures in the sense of farmer information dimension hausdorff dimension metric entropy topological entropy

a branch cut and price algorithm for the piecewise linear transportation problem abstract in this paper we present an exact solution method for the transportation problem with piecewise linear costs this problem is fundamental within supply chain management and is a straightforward extension of the fixed charge transportation problem we consider two dantzig wolfe reformulations and investigate their relative strength with respect to the linear programming lp relaxation both theoretical and practical through tests on a number of instances based on one of the proposed formulations we derive an exact method by branching and adding generalized upper bound constraints from violated cover inequalities the proposed solution method is tested on a set of randomly generated instances and compares favorably to solving the model using a standard formulation solved by a state of the art commercial solver

an experimental observation of a new type of intermittency abstract a novel hysteretic form of regular intermittency has been observed experimentally in a variant of the taylor couette problem where the fluid flow is confined between a stationary outer cylinder and a rotating inner cylinder and end plates the results cannot all be explained within the standard pomeau manneville classification of intermittency and an extension to this theory is proposed to account for the observed phenomena a satisfactory agreement is found between experiment and theory both for the reinjection burst frequency scaling law and the influence of noise on the regularity of the bursts

some extensions of radial basis functions and their applications in artificial intelligence abstract radial basis functions have recently found interesting applications in artificial intelligence and in particular in the problem of learning to perform a particular task from a set of examples however in many practical cases the radial basis functions method cannot be applied in a straight forward manner because it does not take into account some features that are typical of the problem of learning from examples in this paper we show some extensions of the standard theory introduced in order to deal with a large number of examples and with problems in which different variables play very different roles we present some examples and also point out some open problems

towards compatible triangulations we state the following conjecture any two planar n point sets that agree on the number of convex hull points can be triangulated in a compatible manner i e such that the resulting two triangulations are topologically equivalent we first describe a class of point sets which can be triangulated compatibly with any other set that satisfies the obvious size and shape restrictions the conjecture is then proved true for point sets with at most three interior points finally we demonstrate that adding a small number of extraneous points the number of interior points minus three always allows for compatible triangulations the linear bound extends to point sets of arbitrary size and shape

a multicriteria approach for analysis of conflicts in evidence theory we propose a new approach to model the conflict on dst as multi criteria problem we introduce a new subjective notion of conflict through a pseudo criteria analysis we present a numerical application of the proposed model based on 2 and 3 conflict measures therefore it is showed that is possible to capture conflict in dst using more that to 2 criteria dempster shafer theory dst or evidence theory is regarded as one of the leading theories for modeling uncertainty in imprecise situations the main advantage of this theory arises from the possibility of combining different bodies of evidence originally developed by using dempster s combination rule however this rule leads to counter intuitive results when the bodies of evidence conflict with each other to a high degree thus different combinations of conflict management rules have been developed over the years where regardless of the method used what should be identified first of all is the level of conflict between the bodies of evidence therefore different metrics were used to classify or quantify the conflict but no single one of these was successful because it is impracticable to represent all situations of conflict in this theory by using only one metric therefore the contribution of this article is to analyze conflict within dst by using a multi criteria analysis for which the multi criteria decision making mcdm method considered was electre tri on modeling the problem three classes of conflict low medium and high were considered to validate the model a numerical analysis was conducted that included the use of a method to point up conflict so as to infer parameters

statistical analysis of geopotential height gh timeseries based on tsallis non extensive statistical mechanics abstract in this paper we perform statistical analysis of time series deriving from earth s climate the time series are concerned with geopotential height gh and correspond to temporal and spatial components of the global distribution of month average values during the period 1948 2012 the analysis is based on tsallis non extensive statistical mechanics and in particular on the estimation of tsallis q triplet namely q stat q sens q rel the reconstructed phase space and the estimation of correlation dimension and the hurst exponent of rescaled range analysis r s the deviation of tsallis q triplet from unity indicates non gaussian tsallis q gaussian non extensive character with heavy tails probability density functions pdfs multifractal behavior and long range dependences for all timeseries considered also noticeable differences of the q triplet estimation found in the timeseries at distinct local or temporal regions moreover in the reconstructive phase space revealed a lower dimensional fractal set in the gh dynamical phase space strong self organization and the estimation of hurst exponent indicated multifractality non gaussianity and persistence the analysis is giving significant information identifying and characterizing the dynamical characteristics of the earth s climate

data driven non markovian closure models abstract this paper has two interrelated foci i obtaining stable and efficient data driven closure models by using a multivariate time series of partial observations from a large dimensional system and ii comparing these closure models with the optimal closures predicted by the mori zwanzig mz formalism of statistical physics multilayer stochastic models msms are introduced as both a generalization and a time continuous limit of existing multilevel regression based approaches to closure in a data driven setting these approaches include empirical model reduction emr as well as more recent multi layer modeling it is shown that the multilayer structure of msms can provide a natural markov approximation to the generalized langevin equation gle of the mz formalism a simple correlation based stopping criterion for an emr msm model is derived to assess how well it approximates the gle solution sufficient conditions are derived on the structure of the nonlinear cross interactions between the constitutive layers of a given msm to guarantee the existence of a global random attractor this existence ensures that no blow up can occur for a broad class of msm applications a class that includes non polynomial predictors and nonlinearities that do not necessarily preserve quadratic energy invariants the emr msm methodology is first applied to a conceptual nonlinear stochastic climate model of coupled slow and fast variables in which only slow variables are observed it is shown that the resulting closure model with energy conserving nonlinearities efficiently captures the main statistical features of the slow variables even when there is no formal scale separation and the fast variables are quite energetic second an msm is shown to successfully reproduce the statistics of a partially observed generalized lotka volterra model of population dynamics in its chaotic regime the challenges here include the rarity of strange attractors in the model s parameter space and the existence of multiple attractor basins with fractal boundaries the positivity constraint on the solutions components replaces here the quadratic energy preserving constraint of fluid flow problems and it successfully prevents blow up

an enhanced logarithmic method for signomial programming with discrete variables abstract signomial programming problems with discrete variables spd appear widely in real life applications but they are hard to solve this paper proposes an enhanced logarithmic method to reformulate the spd problem as a mixed 0 1 linear program milp with a minimum number of binary variables and inequality constraints both of the theoretical analysis and numerical results strongly support its superior performance to other state of the art linearization methods we also extend the proposed method to linearize some more complicated problems involving product and fractional terms in discrete and continuous variables

global optimization of mixed integer quadratically constrained quadratic programs miqcqp through piecewise linear and edge concave relaxations we propose a deterministic global optimization approach whose novel contributions are rooted in the edge concave and piecewise linear underestimators to address nonconvex mixed integer quadratically constrained quadratic programs miqcqp to epsilon global optimality the facets of low dimensional n 3 edge concave aggregations dominating the termwise relaxation of miqcqp are introduced at every node of a branch and bound tree concave multivariable terms and sparsely distributed bilinear terms that do not participate in connected edge concave aggregations are addressed through piecewise linear relaxations extensive computational studies are presented for point packing problems standard and generalized pooling problems and examples from globallib meeraus globallib http www gamsworld org global globallib htm

phase portrait reconstruction using multivariate singular systems analysis abstract the singular systems analysis ssa method of broomhead and king is applied to the reconstruction of phase portraits from experimental time series of temperature measurements taken simultaneously at up to 16 probes within a rotating thermal convection experiment and used to characterize a number of different kinds of flow including the determination of their correlation dimension results are compared with equivalent reconstructions using more conventional method of delays embedding and ssa applied in the time domain only to data obtained from a single thermocouple probe multivariate ssa m ssa is shown to offer significantly improved reconstructions in terms of signal noise ratio and structural uniformity of the attractor over earlier methods this is due mainly to the ability of m ssa to combine simultaneously information sampling the complete range of the spatial cross correlation function in signals with complex spatio temporal structure

a computational analysis of multidimensional piecewise linear models with applications to oil production optimization production optimization of gas lifted oil wells under facility routing and pressure constraints is a challenging problem which has attracted the interest of operations engineers aiming to drive economic gains and scientists for its inherent complexity the hardness of this problem rests on the non linear characteristics of the multidimensional well production and pressure drop functions as well as the discrete routing decisions to this end this work develops several formulations in mixed integer linear programming milp using multidimensional piecewise linear models to approximate the non linear functions with domains spliced in hypercubes and simplexes computational and simulation analyses were performed considering a synthetic but realistic oil field modeled with a multiphase flow simulator the purpose of the analyses was to assess the relative performance of the milp formulations and their impact on the simulated oil production

extracting qualitative dynamics from experimental data abstract we consider the notion of qualitative information and the practicalities of extracting it from experimental data our approach based on a theorem of takens draws on ideas from the generalized theory of information known as singular system analysis due to bertero pike and co workers we illustrate our technique with numerical data from the chaotic regime of the lorenz model

the reduction of complex dynamical systems using principal interaction patterns abstract a method of constructing low dimensional nonlinear models capturing the main features of complex dynamical systems with many degrees of freedom is described the system is projected onto a linear subspace spanned by only a few characteristic spatial structures called principal interaction patterns pips the expansion coefficients are assumed to be governed by a nonlinear dynamical system the optimal low dimensional model is determined by identifying spatial modes and interaction coefficients describing their time evolution simultaneously according to a nonlinear variational principle the algorithm is applied to a two dimensional geophysical fluid system on the sphere the models based on principal interaction patterns are compared to models using empirical orthogonal functions eofs as basis functions a pip model using 12 patterns is capable of capturing the long term behaviour of the complete system monitored by second order statistics while in the case of eofs 17 modes are necessary

singular spectrum analysis a toolkit for short noisy chaotic signals abstract singular spectrum analysis ssa is developed further based on experience with applications to geophysical time series it is shown that ssa provides a crude but robust approximation of strange attractors by tori in the presence of noise the method works well for short noisy time series the lagged covariance matrix of the processes studied is the basis of ssa we select subsets of eigenelements and associated principal components pcs in order to provide i a noise reduction algorithm ii a detrending algorithm and iii an algorithm for the identification of oscillatory components reconstructed components rcs are developed to provide optimal reconstruction of a dynamic process at precise epochs rather than averaged over the window length of the analysis ssa is combined with advanced spectral analysis methods the maximum entropy method mem and the multi taper method mtm to refine the interpretation of oscillatory behavior a combined ssa mem method is also used for the prediction of selected subsets of rcs the entire toolkit is validated against a set of four prescribed time series generated by known processes quasi periodic or chaotic it is also applied to a time series of global surface air temperatures 130 years long which has attracted considerable attention in the context of the global warming issue and provides a severe test for noise reduction and prediction

combining various types of belief structures we first discuss the basic ideas of the dempster shafer belief structure we particularly emphasize the associated measures of plausibility and belief we discuss the cumulative distribution function associated with a belief structure we next turn to the issue of combining multiple belief structures two different types of combination of belief structures are investigated the first which we refer to as the fusion of belief structures occurs when the belief structures being combined are providing information about the same variable here we make use of the dempster rule the second type which we refer to as the joining of belief structures occurs when the belief structures being combined are providing information about different variables here we make use of a belief structures cumulative distribution function and the sklar theorem the classic belief structures typically have a finite number of focal elements here we began to look at belief structures which have a continuum of focal elements

variable disaggregation in network flow problems with piecewise linear costs we study mixed integer programming formulations based upon variable disaggregation for generic multicommodity network flow problems with nonconvex piecewise linear costs a problem class that arises frequently in many application domains in telecommunications transportation and logistics we present several structural results for these formulations and we analyze the results of extensive experiments on a large set of instances with various characteristics in particular we show that the linear programming relaxation of an extended disaggregated model approximates the objective function by its lower convex envelope in the space of commodity flows together the theoretical and computational results allow us to suggest which formulation might be the most appropriate depending on the characteristics of the problem instances

the piecewise linear optimization polytope new inequalities and intersection with semi continuous constraints we give new facets and valid inequalities for the separable piecewise linear optimization splo knapsack polytope we also extend the inequalities to the case in which some of the variables are semi continuous finally we give computational results that demonstrate their efficiency in solving difficult instances of splo and splo with semi continuous constraints

weighted cautious conjunctive rule for belief functions combination denoeux proposed an operator called the cautious conjunctive rule ccr to combine non dogmatic belief functions i e the frame is considered a focal element from reliable dependent sources which can occur in practice however in cases such as uncertain multiple attribute and group decision analyses belief functions may denote data that vary in importance this paper extends ccr as a weighted ccr wccr to combine belief functions in consideration of their relative weights in such situations properties of wccr are analyzed proven and demonstrated using numerical examples in particular the consideration of relative weights enables wccr to combine dogmatic belief functions the normalized wccr is further constructed and used to assess the trustworthiness of a hospital information system employed in many hospitals in anhui province china

construction and analysis of differential equations from experimental time series of oscillatory systems abstract we propose a novel method to derive an autonomous system of ordinary differential equations from an experimental time series this model describe quantitatively transient behaviour of a system with limit cycle dynamics and is simplified to an evolution equation for the amplitude and frequency the landau equation in addition the model is used for a qualitative prediction of the influence of periodic excitation on the experimental system using the van der pol transformation and floquet theory in particular the instability of the locking solution including the hopf bifurcation the intermittency scenario and the period doubling cascade is considered the method of constructing a differential equation from an experimental time signal is successfully applied to a velocity fluctuation of the laminar periodic wake behind a circular cylinder

a new combination of evidence based on compromise dempster rule of combination is the standard way of combining multiple pieces of evidence given by independent sources of information however it aroused many controversies about its validity and many alternatives have been proposed the paper examines the model of combination in dempster s original paper and indicates that handling of the independence required among multiple pieces of evidence is strange from the viewpoint of semantics where the independence among occurrences of multiple pieces of information might be confused with the consistency among contents of the information the paper then proposes a new model of combination and a new rule of combination called combination by compromise as a consensus generator the properties of the proposed combination as well as several alternative combination methods proposed so far are discussed in the light of the drawbacks and advantages of dempster rule several numerical examples which demonstrate the properties are also shown the discussion and the examples suggest that the proposed combination produces the most preferable results among them from the viewpoints of consensus generation

structural investigation of piecewise linearized network flow problems in this work we study polyhedra in the context of network flow problems in which the flow value on each arc lies in one of several predefined intervals this is motivated by nonlinear problems on transportation networks where nonlinearities are handled by piecewise linear approximation or relaxation a common and established approach in many applications several methods for modeling piecewise linear functions which provide a complete description for a single network arc are known however in general this property is lost when considering multiple arcs we show how to strengthen the formulation for specific substructures consisting of multiple arcs by linear inequalities for the case of paths of degree two nodes we give a complete description of the polyhedron projected to the integer variables our model is based on but not limited to the connection between binary variables and flow variables that is used in the multiple choice method or the convex combination method we also show how to transfe

an approximate analytic solution of the lorenz equations multiple time perturbation theory is applied to the lorenz equations to obtain approximate solutions these solutions are used to obtain the form of the mapping relating two successive maxima of one of the variables of the equations good agreement is obtained with the numerical results presented by lorenz

faint phase synchronization detection through structured orthomax rotations in singular spectrum analysis multivariate singular spectrum analysis m ssa with a structured varimax rotation is a method that allows a deep characterization of phase synchronization ps phenomena in an almost automatic fashion it has been increasingly used in the study of ps in networks of nonlinear real world and numeric systems this paper investigates the impact of the other recently developed structured orthomax rotations on the m ssa ability to characterize ps the results show that by using the structured quartimax rotation a very faint and intermittent ps regime can be detected in contrast with the structured varimax which demands a stronger more consolidated ps regime this is due to the fact that the different rotations do not have the same efficiency in achieving a simple structure of the m ssa eigenvectors nevertheless for well established ps regimes the same robustness of the original m ssa approach against high levels of additive gaussian noise was found for the structured quartimax and biquartimax rotations however for all approaches we found an overshoot of the qualitative range for the ps onset due to noise

mixed integer models for the stationary case of gas network optimization a gas network basically consists of a set of compressors and valves that are connected by pipes the problem of gas network optimization deals with the question of how to optimize the flow of the gas and to use the compressors cost efficiently such that all demands of the gas network are satisfied this problem leads to a complex mixed integer nonlinear optimization problem we describe techniques for a piece wise linear approximation of the nonlinearities in this model resulting in a large mixed integer linear program we study sub polyhedra linking these piece wise linear approximations and show that the number of vertices is computationally tractable yielding exact separation algorithms suitable branching strategies complementing the separation algorithms are also presented our computational results demonstrate the success of this approach

switching based filter based on dempster s combination rule for image processing in this work a two pass switching rank ordered arithmetic mean tsram filter that preserves image details while effectively suppressing impulse noise is proposed to improve the performance of switching based median filters the proposed filter mechanism includes an efficient impulse detector based on the dempster shafer d s evidence theory and a rank ordered arithmetic mean filter that works by estimating the noise free ordered mean values excluding the current pixel a modified dempster s combination rule is applied to the impulse detector to improve filtering performance a simple switching median filter is included to perform second pass filtering experimental results show that the proposed filter outperforms many well accepted switching based median filters in terms of both noise suppression and detail preservation providing excellent robustness at various percentages of impulse noise

the transferable belief model abstract we describe the transferable belief model a model for representing quantified beliefs based on belief functions beliefs can be held at two levels 1 a credal level where beliefs are entertained and quantified by belief functions 2 a pignistic level where beliefs can be used to make decisions and are quantified by probability functions the relation between the belief function and the probability function when decisions must be made is derived and justified four paradigms are analyzed in order to compare bayesian upper and lower probability and the transferable belief approaches

using renyi parameter to improve the predictive power of singular value decomposition entropy on stock market abstract this paper generalizes the method of traditional singular value decomposition entropy by incorporating orders q of renyi entropy we analyze the predictive power of the entropy based on trajectory matrix using shanghai composite index and dow jones index data in both static test and dynamic test in the static test on sci results of global granger causality tests all turn out to be significant regardless of orders selected but this entropy fails to show much predictability in american stock market in the dynamic test we find that the predictive power can be significantly improved in sci by our generalized method but not in dji this suggests that noises and errors affect sci more frequently than dji in the end results obtained using different length of sliding window also corroborate this finding

an efficient algorithm for estimating noise covariances in distributed systems we present an efficient computational algorithm for estimating the noise covariance matrices of large linear discrete stochasticdynamic systems such systems arise typically by discretizing distributed parameter systems and their size renders computational efficiency a major consideration our adaptive filtering algorithm is based on the ideas of belanger and is algebraically equivalent to his algorithm the earlier algorithm however has computational complexity proportional to p6 where p is the number of observations of the system state while the new algorithm has complexity proportional to only p3 furthermore our formulation of noise covariance estimation as a secondary filter analogous to state estimation as a primary filter suggests several generalizations of the earlier algorithm the performance of the proposed algorithm is demonstrated for a distributed system arising in numerical weather prediction

distinguishing between low dimensional dynamics and randomness in measured time series the success of current attempts to distinguish between low dimensional chaos and random behavior in a time series of observations is considered first we discuss stationary stochastic processes which produce finite numerical estimates of the correlation dimension and k2 entropy under naive application of correlation integral methods we then consider several straightforward tests to evaluate whether correlation integral methods reflect the global geometry or the local fractal structure of the trajectory this determines whether the methods are applicable to a given series if they are we evaluate the significance of a particular result for example by considering the results of the analysis of stochastic signals with statistical properties similar to those of observed series from the examples considered it is clear that the correlation integral should not be used in isolation but as one of a collection of tools to distinguish chaos from stochasticity

reconstruction expansion as a geometry based framework for choosing proper delay times abstract the quality of attractor reconstruction using the method of delays is known to be sensitive to the delay parameter here we develop a new computationally efficient approach to choosing that quantifies reconstruction expansion from the identity line of the embedding space we show that reconstruction expansion is related to the concept of reconstruction signal strength and that increased expansion corresponds to diminished effects of measurement error thus reconstruction expansion represents a simple geometrical framework for choosing furthermore we describe the role of dynamical error in attractor expansion and argue that algorithms for determining should be considered as attempts at estimating an upper bound to the optimal delay

mixed integer linear optimization for optimal lift gas allocation with well separator routing abstract the lift gas allocation problem with well separator routing constraints is a mixed integer nonlinear program of considerable complexity to this end a mixed integer linear formulation compact is obtained by piecewise linearizing the nonlinear curves using binary variables to express the linearization and routing decisions a new formulation integrated combining the decisions on linearization and routing is developed by using a single binary variable the structures of both formulations are explored to generate lifted cover cuts numerical tests show that the solution of the integrated formulation using cutting plane generation is faster in spite of having more variables than the compact formulation

flow transitions resembling bifurcations of the logistic map in simulations of the baroclinic rotating annulus we present evidence for a sequence of bifurcations in simulations of the differentially heated baroclinic rotating annulus similar to bifurcations of the logistic map the met office oxford rotating annulus laboratory simulation morals code is used to construct a detailed numerical regime diagram for the annulus and the distribution of regimes in parameter space is discussed the bifurcations are observed in a sequence of runs at high temperature forcing identified by poincare sections of the dominant temperature mode amplitude time series higher order return maps and predictions using quadratic fits to the data are used to verify this result and lyapunov exponents are calculated to identify and quantify the chaotic parts of the sequence

approximating stable and unstable manifolds in experiments we introduce a procedure to reveal invariant stable and unstable manifolds given only experimental data we assume a model is not available and show how coordinate delay embedding coupled with invariant phase space regions can be used to construct stable and unstable manifolds of an embedded saddle we show that the method is able to capture the fine structure of the manifold is independent of dimension and is efficient relative to previous techniques

waves vs particles in the atmosphere s phase space a pathway to long range forecasting thirty years ago e n lorenz provided some approximate limits to atmospheric predictability the details in space and time of atmospheric flow fields are lost after about 10 days certain gross flow features recur however after times of the order of 10 50 days giving hope for their prediction over the last two decades numerous attempts have been made to predict these recurrent features the attempts have involved on the one hand systematic improvements in numerical weather prediction by increasing the spatial resolution and physical faithfulness in the detailed models used for this prediction on the other hand theoretical attempts motivated by the same goal have involved the study of the large scale atmospheric motions9 phase space and the inhomogeneities therein these coarse graining studies have addressed observed as well as simulated atmospheric data sets two distinct approaches have been used in these studies the episodic or intermittent and the oscillatory or periodic the intermittency approach describes multiple flow or weather regimes their persistence and recurrence and the markov chain of transitions among them the periodicity approach studies intraseasonal oscillations with periods of 15 70 days and their predictability we review these two approaches particles vs waves in the quantum physics analogy alluded to in the title of this article discuss their complementarity and outline unsolved problems

correlation of local stretchings as a way of characterising chaotic dynamics amid noise abstract a positive lyapunov exponent can result from either chaotic dynamics or noise as a possible means of assessing the degree to which the exponent is noise affected and as a possible index in its own right the localised divergence of two neighbouring trajectories from a fiducial trajectory is compared in the expectation of finding strong correlation when the source of stretching is deterministic chaos and little or no correlation when the source is coloured or uncoloured noise the method is applied to various equation systems and to a periodic time series from the self excited oscillation of flexible tube collapsed by external pressure and conveying a flow

modeling disjunctive constraints with a logarithmic number of binary variables and constraints many combinatorial constraints over continuous variables such as sos1 and sos2 constraints can be interpreted as disjunctive constraints that restrict the variables to lie in the union of a finite number of specially structured polyhedra known mixed integer binary formulations for these constraints have a number of binary variables and extra constraints linear in the number of polyhedra we give sufficient conditions for constructing formulations for these constraints with a number of binary variables and extra constraints logarithmic in the number of polyhedra using these conditions we introduce mixed integer binary formulations for sos1 and sos2 constraints that have a number of binary variables and extra constraints logarithmic in the number of continuous variables we also introduce the first mixed integer binary formulations for piecewise linear functions of one and two variables that use a number of binary variables and extra constraints logarithmic in the number of linear pieces of the functions we prove that the new formulations for piecewise linear functions have favorable tightness properties and present computational results showing that they can significantly outperform other mixed integer binary formulations

fitting piecewise linear continuous functions abstract we consider the problem of fitting a continuous piecewise linear function to a finite set of data points modeled as a mathematical program with convex objective we review some fitting problems that can be modeled as convex programs and then introduce mixed binary generalizations that allow variability in the regions defining the best fit function s domain we also study the additional constraints required to impose convexity on the best fit function

a priori tests of a stochastic mode reduction strategy several a priori tests of a systematic stochastic mode reduction procedure recently devised by the authors proc natl acad sci 96 1999 14687 commun pure appl math 54 2001 891 are developed here in this procedure reduced stochastic equations for a smaller collections of resolved variables are derived systematically for complex nonlinear systems with many degrees of freedom and a large collection of unresolved variables while the above approach is mathematically rigorous in the limit when the ratio of correlation times between the resolved and the unresolved variables is arbitrary small it is shown here on a systematic hierarchy of models that this ratio can be surprisingly big typically the systematic reduced stochastic modeling yields quantitatively realistic dynamics for ratios as large as 1 2 the examples studied here vary from instructive stochastic triad models to prototype complex systems with many degrees of freedom utilizing the truncated burgers hopf equations as a nonlinear heat bath systematic quantitative tests for the stochastic modeling procedure are developed here which involve the stationary distribution and the two time correlations for the second and fourth moments including the resolved variables and the energy in the resolved variables in an important illustrative example presented here the nonlinear original system involves 102 degrees of freedom and the reduced stochastic model predicted by the theory for two resolved variables involves both nonlinear interaction and multiplicative noises even for large value of the correlation time ratio of the order of 1 2 the reduced stochastic model with two degrees of freedom captures the essentially nonlinear and non gaussian statistics of the original nonlinear systems with 102 modes extremely well furthermore it is shown here that the standard regression fitting of the second order correlations alone fails to reproduce the nonlinear stochastic dynamics in this example 2002 elsevier science b v all rights reserved

observation of a strange attractor abstract phase space portraits have been constructed and analyzed for noisy nonperiodic data obtained in an experiment on a nonequilibrium homogeneous chemical reaction the phase space trajectories define a limit set that is an attractor following a perturbation the trajectory quickly returns to the attracting set this attracting set is shown to be strange nearby trajectories separate exponentially on the average moreover the poincare sections exhibit the stretching and folding that is characteristic of strange attractors

reconstructing bifurcation diagrams only from time waveforms abstract a simple algorithm is proposed for reconstructing bifurcation diagrams only from time waveforms of a dynamical system without knowing an explicit form of the dynamics and its dependence on the parameters reconstruction means that the obtained bifurcation diagram is qualitatively similar to that of the original system the algorithm consists of two steps first a nonlinear predictor is sought using a particular class of functions with many parameters second the karhunen loeve transform is used to find only significant parameters contributing the bifurcations the algorithm is tested against two families of dynamical system the henon family and the coupled logistic delayed logistic family

base 2 expansions for linearizing products of functions of discrete variables this paper presents an approach for representing functions of discrete variables and their products using logarithmic numbers of binary variables given a univariate function whose domain consists of n distinct values it begins by employing a base 2 expansion to express the function in terms of the ceiling of log2n binary and n continuous variables using linear restrictions to equate the functional values with the possible binary realizations the representation of the product of such a function with a nonnegative variable is handled via an appropriate scaling of the linear restrictions products of m functions are treated in an inductive manner from i 2 to m where each step i uses such a scaling to express the product of function i and a nonnegative variable denoting a translated version of the product of functions 1 through i 1 as a newly defined variable the resulting representations both in terms of one function and many are important for reformulating general discrete variables as binary and also for linearizing mixed integer generalized geometric and discrete nonlinear programs where it is desired to economize on the number of binary variables the approach provides insight into improves upon and subsumes related linearization methods for products of functions of discrete variables

reduced models of atmospheric low frequency variability parameter estimation and comparative performance abstract low frequency variability lfv of the atmosphere refers to its behavior on time scales of 10 100 days longer than the life cycle of a mid latitude cyclone but shorter than a season this behavior is still poorly understood and hard to predict the present study compares various model reduction strategies that help in deriving simplified models of lfv three distinct strategies are applied here to reduce a fairly realistic high dimensional quasi geostrophic 3 level qg3 atmospheric model to lower dimensions i an empirical dynamical method which retains only a few components in the projection of the full qg3 model equations onto a specified basis and finds the linear deterministic and the stochastic corrections empirically as in selten 1995 5 ii a purely dynamics based technique employing the stochastic mode reduction strategy of majda et al 2001 62 and iii a purely empirical multi level regression procedure which specifies the functional form of the reduced model and finds the model coefficients by multiple polynomial regression as in kravtsov et al 2005 3 the empirical dynamical and dynamical reduced models were further improved by sequential parameter estimation and benchmarked against multi level regression models the extended kalman filter was used for the parameter estimation overall the reduced models perform better when more statistical information is used in the model construction thus the purely empirical stochastic models with quadratic nonlinearity and additive noise reproduce very well the linear properties of the full qg3 model s lfv i e its autocorrelations and spectra as well as the nonlinear properties i e the persistent flow regimes that induce non gaussian features in the model s probability density function the empirical dynamical models capture the basic statistical properties of the full model s lfv such as the variance and integral correlation time scales of the leading lfv modes as well as some of the regime behavior features but fail to reproduce the detailed structure of autocorrelations and distort the statistics of the regimes dynamical models that use data assimilation corrections do capture the linear statistics to a degree comparable with that of empirical dynamical models but do much less well on the full qg3 model s nonlinear dynamics these results are discussed in terms of their implications for a better understanding and prediction of lfv

reconstructing attractors from filtered time series abstract in this paper we investigate the criteria necessary to reconstruct an attractor from a time series that has been passed through an iir filter to guarantee that the whole of the attractor is reconstructed requires uniform bounds on the contraction rate of the dynamics however we show that if we use a condition that is only based on the average contraction rates the lyapunov exponents then a set of high probability can still be reconstructed we argue that in practice this is all that is necessary

mixed integer models for nonseparable piecewise linear optimization unifying framework and extensions we study the modeling of nonconvex piecewise linear functions as mixed integer programming mip problems we review several new and existing mip formulations for continuous piecewise linear functions with special attention paid to multivariate nonseparable functions we compare these formulations with respect to their theoretical properties and their relative computational performance in addition we study the extension of these formulations to lower semicontinuous piecewise linear functions

combining uncertain information of differing modalities in this paper we consider approaches for combining separately possibilistic uncertainty probabilistic uncertainty and situations where both forms of uncertainty appear an approach to probability aggregation using rational consensus with equi weighting is developed this aggregation is analyzed with information measures as one way to assess combinations and understand the impact on uncertainty the analysis is based on combinations of bounding cases of probability distributions measures of conflict and the effect on information are developed next possibility transformations are used and illustrated by three representative possibility cases the resultant transformed probabilities are aggregated with general probability distributions and the result evaluated with information measures as before finally a general approach to combining possibility distributions directly using quality criteria is described an example is provided to illustrate the basic possibility distribution aggregation fusion developed

an ensemble kalman filter for statistical estimation of physics constrained nonlinear regression models a central issue in contemporary science is the development of nonlinear data driven statistical dynamical models for time series of noisy partial observations from nature or a complex model it has been established recently that ad hoc quadratic multi level regression models can have finite time blow up of statistical solutions and or pathological behavior of their invariant measure recently a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior here a new finite ensemble kalman filtering algorithm is developed for estimating the state the linear and nonlinear model coefficients the model and the observation noise covariances from available partial noisy observations of the state several stringent tests and applications of the method are developed here in the most complex application the perfect model has 57 degrees of freedom involving a zonal east west jet two topographic rossby waves and 54 nonlinearly interacting rossby waves the perfect model has significant non gaussian statistics in the zonal jet with blocked and unblocked regimes and a non gaussian skewed distribution due to interaction with the other 56 modes we only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation numerically we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion including the skew non gaussian distribution and autocorrelation decay on the other hand a similar stochastic model with zero memory levels fails to capture the crucial non gaussian behavior of the zonal jet from the perfect 57 mode model