numerical stability of circular hilbert transform and its application to signal decomposition abstract in this paper we propose a novel method of computing hilbert transform based on the mechanical quadrature method experiments show that the method outperforms the library function hilbert in matlab when the values of functions being handled are very large or approach to infinity that is a problem we have to deal with when we compute for instance outer functions as an application we use the method to obtain the unwinding series of signals which is a positive frequency decomposition of signals and is dependent of extraction of outer functions involving computation of hilbert transform the experimental results show better stability then we give the transient time frequency distribution of the unwinding series of signals finally experiments of noisy signals are given and the results show that the introduced method can well resist some disturbance

inferences from multinomial data learning about a bag of marbles a new method is proposed for making inferences from multinomial data in cases where there is no prior information a paradigm is the problem of predicting the colour of the next marble to be drawn from a bag whose contents are initially completely unknown in such problems we may be unable to formulate a sample space because we do not know what outcomes are possible this suggests an invariance principle inferences based on observations should not depend on the sample space in which the observations and future events of interest are represented objective bayesian methods do not satisfy this principle this paper describes a statistical model called the imprecise dirichlet model for drawing coherent inferences from multinomial data inferences are expressed in terms of posterior upper and lower probabilities the probabilities are initially vacuous reflecting prior ignorance but they become more precise as the number of observations increases this model does satisfy the invariance principle two sets of data are analysed in detail in the first example one red marble is observed in six drawings from a bag inferences from the imprecise dirichlet model are compared with objective bayesian and frequentist inferences the second example is an analysis of data from medical trials which compared two treatments for cardiorespiratory failure in newborn babies there are two problems to draw conclusions about which treatment is more effective and to decide when the randomized trials should be terminated this example shows how the imprecise dirichlet model can be used to analyse data in the form of a contingency table

multistate components assignment problem with optimal network reliability subject to assignment budget abstract the typical assignment problem for finding the optimal assignment of a set of components to a set of locations in a system has been widely studied in practical applications however this problem mainly focuses on maximizing the total profit or minimizing the total cost without considering component s failure in practice each component should be multistate due to failure partially failure or maintenance that is each component has several capacities with a probability distribution and may fail when a set of multistate components is assigned to a system the system can be treated as a stochastic flow network the network reliability is the probability that d units of homogenous commodity can be transmitted through the network successfully the multistate components assignment problem to maximize the network reliability is never discussed therefore this paper focuses on solving this problem under an assignment budget constraint in which each component has an assignment cost the network reliability under a components assignment can be evaluated in terms of minimal paths and state space decomposition subsequently an optimization method based on genetic algorithm is proposed the experimental results show that the proposed algorithm can be executed in a reasonable time

one armed bandit problems with covariates as does woodroofe we consider a bayesian sequential allocation between two treatments that incorporates a covariate the goal is to maximize the total discounted expected reward from an infinite population of patients although our model is more general than woodroofe s we are able to duplicate his main result the myopic rule is asymptotically optimal

a flexible numerical approach for quantification of epistemic uncertainty in the field of uncertainty quantification uq epistemic uncertainty often refers to the kind of uncertainty whose complete probabilistic description is not available largely due to our lack of knowledge about the uncertainty quantification of the impacts of epistemic uncertainty is naturally difficult because most of the existing stochastic tools rely on the specification of the probability distributions and thus do not readily apply to epistemic uncertainty and there have been few studies and methods to deal with epistemic uncertainty a recent work can be found in j jakeman m eldred d xiu numerical approach for quantification of epistemic uncertainty j comput phys 229 2010 4648 4663 where a framework for numerical treatment of epistemic uncertainty was proposed the method is based on solving an encapsulation problem without using any probability information in a hypercube that encapsulates the unknown epistemic probability space if more probabilistic information about the epistemic variables is known a posteriori the solution statistics can then be evaluated at post process steps in this paper we present a new method similar to that of jakeman et al but significantly extending its capabilities most notably the new method 1 does not require the encapsulation problem to be in a bounded domain such as a hypercube 2 does not require the solution of the encapsulation problem to converge point wise in the current formulation the encapsulation problem could reside in an unbounded domain and more importantly its numerical approximation could be sought in l p norm these features thus make the new approach more flexible and amicable to practical implementation both the mathematical framework and numerical analysis are presented to demonstrate the effectiveness of the new approach

two families of unit analytic signals with nonlinear phase abstract this paper focuses on constructing two families of unit analytic signals with nonlinear phase the first is the 2 periodic extension of the nonlinear fourier atoms viz e i a t a 1 t r where a t is the poisson kernel of the unit circle associated with a in the unit disc in the complex plane and satisfies a t 2 a t 2 and the second consists of e i a t a 1 t r that are the images of the nonlinear fourier atoms under cayley transform these unit analytic signals are mono components based on which one can define meaningful instantaneous frequency the pairs 1 a t and 1 a t form canonical pairs the real signals cos a t corresponding to the first family coincide with the notion of normalized intrinsic mode functions we finally point out that starting from nonlinear fourier atoms the gram schmidt procedure leads to laguerre bases

adaptive treatment allocation and the multi armed bandit problem a class of simple adaptive allocation rules is proposed for the problem often called the multi armed bandit problem of sampling x 1 cdots x n sequentially from k populations with densities belonging to an exponential family in order to maximize the expected value of the sum s n x 1 cdots x n these allocation rules are based on certain upper confidence bounds which are developed from boundary crossing theory for the k population parameters the rules are shown to be asymptotically optimal as n rightarrow infty from both bayesian and frequentist points of view monte carlo studies show that they also perform very well for moderate values of the horizon n

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

response surface bandits in this paper we define a response surface bandit as the sequential design problem that maximizes an expected bandit utility but where the outcomes y n are continuous and can be related through a response surface to a set of controllable variables x n x 1n x 2n x kn we link this problem to other traditional optimization problems from industrial engineering and to the traditional bandit problem we consider two approaches to the problem the first is based on a myopic sequential design the second approach uses the best design out of a family of designs related to upper bounds for the predicted surface the family includes myopic and sequential versions of d optimal designs these approaches can be generalized to more broadly defined sequential problems

extension of the concept of propositional deduction from classical logic to probability an overview of probability selection approaches abstract establishing a rigorous framework for propositional deduction which also agrees with what is termed commonsense reasoning poses a difficult challenge this paper is the first of a two part effort in considering the issue and proposing in future part 2 a particular approach via the use of second order probabilities i e distributions of probability measures as opposed to probability selection approaches especially that of maximum entropy and adams high probability schemes in the second order probability approach usually all probability distributions are assumed a priori to be either equally likely or more generally to be distributed via the dirichlet family up to the constraints involved in the premise set of the potential deduction considered

the prevision of a prevision abstract we prove that the result ex e e x y is true for bounded x when the usual concept of conditional expectation or prevision is replaced by an alternative definition reflecting an individual s actual beliefs concerning x after observing y we discuss the importance of this result to subjectivist theory

chirp transforms and chirp series abstract motivated by the recent work on the non harmonic fourier atoms initiated by t qian and the non harmonic fourier series which originated from the celebrated work of paley and wiener we introduce an integral version of the non harmonic fourier series called chirp transform as an integral transform with kernel e i t the chirp transform is an unitary isometry from l 2 r d onto l 2 r d and it can be explicitly defined in terms of generalized hermite polynomials the corresponding chirp series take e i n t as a basis which in some sense is dual to the theory of non harmonic fourier series which take e i n t as a basis the chirp version of the shannon sampling theorem and the poisson summation formula are also considered by dealing with sampling points which may non equally distributed since the chirp transform interchanges weighted derivatives into multiplications it plays a role in solving certain differential equations with variable coefficients in addition we extend t qian s theorem on the characterization of a measure to be a linear combination of a number of harmonic measures on the unit disc with positive integer coefficients to that with positive rational coefficients

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

robust counterpart optimization for the redundancy allocation problem in series parallel systems with component mixing under uncertainty in this paper a robust optimization approach is used to solve the redundancy allocation problem rap in series parallel systems with component mixing where uncertainty exists in components reliabilities in real world the reliabilities of components are imprecisely estimated or the reliability of some components may vary due to some realistic factors therefore we may deal with a system where there are many components with uncertain values of reliabilities to deal with this problem for the first time a robust optimization approach is applied to rap with component mixing to produce a robust solution which is relatively insensitive with respect to uncertainty in reliability of components in addition the advantages of the proposed robust technique are illustrated by considering a series parallel system and finding the suitable redundancy levels and then monte carlo simulation is implemented to examine the quality of the robust solutions the results indicate that applying the proposed robust rap can be more reliable to determine system reliability in the designing phase of systems

an algebraic synthesis of the foundations of logic and probability abstract this paper develops a unified algebraic theory of logic and probability based upon an initial boolean algebra logic of propositions together with its extensionally associated boolean algebra of models probabilistic events that satisfy the axioms of the boolean algebra of propositions a proposition may be true in some models and false in others but each model must unambiguously assign true or false to each proposition thus the examples models in which different propositions are true may be all some or none according as those propositions are necessary possible or impossible a probability measure p on the collection of models events induces a probability measure on the propositions the crucial if then relation is defined so that p if p then q equals p q p the conditional probability of q given p this conditional probability is less than the probability of the material conditional q or not p unless p p 1 or p q p 1 at these two extremes the two propositional constructions coalesce thus an additional relation q p is needed in logic and probability namely q given p this is accomplished in the algebraic logic generated by the various sum ideals entailments of various propositions that may serve as the explicit condition of a conditional proposition q p the corresponding relation b a in the model realm defines the notion of a conditional event in this context of algebraic logic and model theory a new algebraic structure called the conditional closure l l of a boolean logic l is defined consisting of the ordered pairs q p of all propositions of l excluding those for which the condition p is equivalent to 0 that is impossible the conditional closure is not altogether a boolean algebra not altogether distributive for instance but it has many subalgebras that are boolean including l itself this paper contains partially assumed formulas for operating on the conditional propositions q p using and or not and of course if then this allows complex conditional expressions to be reduced to simple conditionals of boolean propositions which have a conditional probability an example calculation from the dice table illustrates how to simplify a compound conditional proposition and compute its probability the structure of l l is explored including the finite conditional closures of finite boolean logics formulas are given for the probabilistic difference between familiar conditional propositions that are equivalent in the two valued logic where all propositions are either necessary or impossible but not equivalent in the conditional closure of a logic with possible propositions the probability that a proposition p is a theorem true in all models is contrasted from the probability of the models in which the proposition is true the latter being p p while the former is p p 1 this leads to a natural connection with fuzzy set theory since p 1 can also be expressed as p 1 where 1 is the sum ideal filter of necessary propositions given the boolean axioms this paper ends with a representation of each conditional proposition q p as the p measurable two valued truth function of q restricted to those models that satisfy p

on upper and lower bounds for quantity of interest in problems subject to epistemic uncertainty in many problems uncertainty is a result of lack of knowledge and may not be modeled as random variables processes because of the lack of probability information this is often referred to as epistemic uncertainty and the traditional probabilistic approaches cannot be readily employed in this paper we present a method to compute upper and lower bounds for the quantity of interest of problems whose uncertain inputs are of epistemic type the method is based on a variational inequality of relative entropy the inequality applies to integrable functions and is a notable extension of an existing inequality in the literature the extension has more flexible applicability and allows one to derive bounds for quantities such as the statistical moments of the problems we present the theoretical derivation of the bounds along with numerical examples to illustrate their computations

a maximum entropy approach to nonmonotonic reasoning an approach to nonmonotonic reasoning that combines the principle of infinitesimal probabilities with that of maximum entropy thus extending the inferential power of the probabilistic interpretation of defaults is proposed a precise formalization of the consequences entailed by a conditional knowledge base is provided the computational machinery necessary for drawing these consequences is developed and the behavior of the maximum entropy approach is compared to related work in default reasoning the resulting formalism offers a compromise between two extremes the cautious approach based on the conditional interpretations of defaults and the bold approach based on minimizing abnormalities

supersensitivity due to uncertain boundary conditions summary we study the viscous burgers equation subject to perturbations on the boundary conditions two kinds of perturbations are considered deterministic and random for deterministic perturbations we show that small perturbations can result in o 1 changes in the location of the transition layer for random perturbations we solve the stochastic burgers equation using different approaches first we employ the jacobi polynomial chaos which is a subset of the generalized polynomial chaos for stochastic modeling converged numerical results are reported up to seven significant digits and we observe similar stochastic supersensitivity for the mean location of the transition layer subsequently we employ up to fourth order perturbation expansions we show that even with small random inputs the resolution of the perturbation method is relatively poor due to the larger stochastic responses in the output two types of distributions are considered uniform distribution and a truncated gaussian distribution with no tails various solution statistics including the spatial evolution of probability density function at steady state are studied copyright 2004 john wiley sons ltd

on instantaneous amplitude and phase of signals in many questions of signal processing it is important to use the concepts of instantaneous amplitude or phase of signals this is especially the case in communication systems with amplitude or frequency modulation these concepts are often introduced empirically however it is well known that the correct approach for this purpose is to use the concept of analytic signal starting from this point we show some examples of contradictions appearing when using other definitions of instantaneous amplitude or frequency that are commonly admitted this introduces the problem of characterizing pure amplitude modulated or pure phase modulated signals it is especially shown that whereas amplitude modulated signals can be characterized by spectral considerations this is no longer the case for phase modulated signals furthermore signals with constant amplitude have very specific properties which are analyzed in detail some consequences and extensions to random signals are finally discussed

study of boundary conditions in the iterative filtering method for the decomposition of nonstationary signals abstract nonstationary and non linear signals are ubiquitous in real life their decomposition and analysis is an important research topic of signal processing recently a new technique called iterative filtering has been developed with the goal of decomposing such signals into simple oscillatory components several papers have been devoted to the investigation of this technique from a mathematical point of view all these works start with the assumption that each compactly supported signal is extended periodically outside the boundaries in this work we tackle the problem of studying the influence of different boundary conditions on the decompositions produced by the iterative filtering method in particular the choice of boundary conditions gives rise to different types of structured matrices thus we describe their spectral properties and the convergence properties of iterative filtering algorithm when such matrices are involved numerical results on artificial and real life signals provide interesting insight on important aspects such as accuracy and error propagation of the proposed technique and pave the way for further promising developments

bayesian sequential estimation of the reliability of a parallel series system we give a risk averse solution to the problem of estimating the reliability of a parallel series system we adopt a beta binomial model for components reliabilities assuming that the total sample size for the experiment is fixed the allocation at subsystems or components level may be random based on the sampling schemes for parallel and series systems separately we propose a hybrid sequential scheme for the parallel series system asymptotic optimality of the bayes risk associated with quadratic loss is proved with the help of martingale convergence properties a comparison is given with the best fixed design with numerical examples

a sampling theorem for non bandlimited signals using generalized sinc functions a ladder shaped filter of two real parameters a 1 a 2 1 1 is introduced in this note the impulse response of the corresponding linear time invariant lti system is a generalized sinc function of two parameters consequently a generalized shannon type sampling theorem is established for a class of non bandlimited signals with special spectrum properties associated with a ladder shaped filter of two parameters finally a mathematical characterization for the class of non bandlimited signals satisfying the generalized sampling theorem is offered these signals are restrictions to the real line of certain analytic functions in stripped domains symmetric about the real axis in the complex plane for these signals their spectra in higher frequency bands are measured by the spectrum of their base bands

estimations of parameters in a three state reliability semi markov model maximum likelihood and bayes estimates of the parameters included in a three state semi markov reliability model are presented the renewal kernel which depends upon a vector of unknown parameters is used to define a semi markov process which can be used to describe some reliability model moreover some of the obtained results are compared with those obtained in other literature special case of the obtained results is presented

a note on performance limitations in bandit problems with side information we consider a sequential adaptive allocation problem which is formulated as a traditional two armed bandit problem but with one important modification at each time step t before selecting which arm to pull the decision maker has access to a random variable xt which provides information on the reward in each arm performance is measured as the fraction of time an inferior arm generating lower mean reward is pulled we derive a minimax lower bound that proves that in the absence of sufficient statistical diversity in the distribution of the covariate x a property that we shall refer to as lack of persistent excitation no policy can improve on the best achievable performance in the traditional bandit problem without side information

the wiener askey polynomial chaos for stochastic differential equations we present a new method for solving stochastic differential equations based on galerkin projections and extensions of wiener s polynomial chaos specifically we represent the stochastic processes with an optimum trial basis from the askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error several continuous and discrete processes are treated and numerical examples show substantial speed up compared to monte carlo simulations for low dimensional stochastic inputs

bandit problems with side observations an extension of the traditional two armed bandit problem is considered in which the decision maker has access to some side information before deciding which arm to pull at each time t before making a selection the decision maker is able to observe a random variable x sub t that provides some information on the rewards to be obtained the focus is on finding uniformly good rules that minimize the growth rate of the inferior sampling time and on quantifying how much the additional information helps various settings are considered and for each setting lower bounds on the achievable inferior sampling time are developed and asymptotically optimal adaptive schemes achieving these lower bounds are constructed

reliability equivalence with a basic series parallel system this paper extends the concept of reliability equivalence from simple series and parallel systems to some complex systems the reliability equivalence factors of a complex system are obtained we consider a radar system in an aircraft which consists of three independent and non identical components both survival function and mean time to failure are used as references of reliability equivalence the case of independent and identical components is studied as a special case theoretical comparisons among the used methods of improving the system reliability are introduced numerical examples are presented to interpret how one can utilize the obtained results

probability updating using second order probabilities and conditional event algebra abstract the second order probability technique is a procedure whereby an incompletely specified finite argument probability function is modeled as a random vector over the associated natural simplex of all possible probability functions of a fixed common number of arguments often the distribution of the random vector is assumed to be a uniform one as in the case of goodman s treatment of the probabilistic syllogism or penguin triangle problem 1998 but when compatibility with a non uniform prior distribution is sought the uniform random vector assumption must be replaced by a different one in a related but distinct direction conditional event algebra is a new mathematical tool which allows the direct incorporation of conditional relations expressed through conditional probabilities with other such conditional relations or unconditional events i r goodman h t nguyen journal of uncertainty fuzziness and knowledge based systems 3 3 1995 247 339 i r goodman r p mahler h t nguyen mathematics of data fusion kluwer academic publishers dordrecht holland 1997 the judy benjamin jb problem as originally posed by van fraasen british journal of philosophy of science 32 1981 375 379 has been recently addressed by grove and halpern g h proceedings of the 13th conference uncertainty in ai 1997 pp 208 214 and has elements in it conducive to analysis via both second order probability and conditional event algebra the problem involves the issue of how to update a particular event of interest having a known prior probability part of a known uniform prior probability function upon a known conditional probability statement when the latter is given through a probability function otherwise unknown and distinct from the prior probability function in the problem as stated the event of interest is disjoint from the antecedent event in the conditional probability statement g h make use of a trust principle in order to be able to apply in effect the second order probability technique with an associated uniform distribution g h s result differs sharply from that of van fraasen who employs instead a minimal cross entropy approach to the problem in that g h show no change in probability values between the prior and posterior assessments this paper considers in a more general context the application of the second order probability technique using the dirichlet family generalization of the uniform distribution over a simplex in updating an event upon a conditional probability statement when no such disjointness as in the jb problem holds and compatibility is sought with a non uniform prior when this is specialized to the disjoint event case even with a non uniform prior the independence result of g h extends to this context the jb problem is also considered via a conditional event algebra viewpoint which avoids the trust principle in conjunction with the second order probability technique and general agreement with that of g h s independence result is established for the case of disjoint event of interest from the antecedent and consequence of the conditional form these relations are also extended to a more general setting

sequential allocation for an estimation problem with ethical costs the problem of designing an experiment to estimate the difference between the means of two normal populations with unit variances is considered when the cost of drawing a sample from either population may depend on unknown parameters a quasi bayesian approach is adopted in which the mean difference is estimated by its maximum likelihood estimator but the design allocation rule is evaluated in bayesian decision theoretic terms a three stage procedure is proposed and its risk evaluated up to terms which are small compared to the cost of a single observation

a method for processing the unreliable expert judgments about parameters of probability distributions abstract a method for combining two types of judgments about an object analyzed which are elicited from experts is considered in the paper it is assumed that the probability distribution of a random variable is known but its parameters may be determined by experts the method is based on the use of the imprecise probability theory and allows us to take into account the quality of expert judgments heterogeneity and imprecision of information supplied by experts an approach for computing cautious expert beliefs under condition that the experts are unknown is studied numerical examples illustrate the proposed method

nontrivial harmonic waves with positive instantaneous frequency abstract the concept of time varying frequency is fundamental in communications and nature one description of a time varying frequency is the instantaneous frequency of a signal our concern is the design of analytic signals with nonlinear phase and positive instantaneous frequency in this paper a kind of nontrivial orthonormal harmonic waves are derived by applying the gram schmidt procedure to the blaschke products furthermore we show the orthonormal harmonic waves satisfy the analytic condition and have positive instantaneous frequencies which are tightly associated with the average frequencies of the two mono component analytic signals at each time as a consequence non stationary signals can be decomposed into the superposition of nontrivial harmonic waves related conclusions are established for the orthonormal analytic signals on the whole time range

analytic signals and harmonic measures abstract we prove that a sufficient and necessary condition for h e i s i e i s where h is hilbert transformation is a continuous and strictly increasing function with r 2 is that d s is a harmonic measure on the line the counterpart result for the periodic case is also established the study is motivated by and has significant impact to time frequency analysis especially to aspects of analytic signals inducing instantaneous amplitude and frequency as a by product we introduce the theory of hardy space preserving weighted trigonometric series and fourier transformations induced by harmonic measures in the respective contexts

nonmonotonic reasoning preferential models and cumulative logics abstract many systems that exhibit nonmonotonic behavior have been described and studied already in the literature the general notion of nonmonotonic reasoning though has almost always been described only negatively by the property it does not enjoy i e monotonicity we study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties we concentrate on a number of families of nonmonotonic consequence relations defined in the style of gentzen 13 both proof theoretic and semantic points of view are developed in parallel the former point of view was pioneered by gabbay 10 while the latter has been advocated by shoham 38 five such families are defined and characterized by representation theorems relating the two points of view one of the families of interest that of preferential relations turns out to have been studied by adams 2 the preferential models proposed here are a much stronger tool than adams probabilistic semantics the basic language used in this paper is that of propositional logic the extension of our results to first order predicate calculi and the study of the computational complexity of the decision problems described in this paper will be treated in another paper

arbitrary order hilbert spectral analysis for time series possessing scaling statistics comparison study with detrended fluctuation analysis and wavelet leaders in this paper we present an extended version of hilbert huang transform namely arbitrary order hilbert spectral analysis to characterize the scale invariant properties of a time series directly in an amplitude frequency space we first show numerically that due to a nonlinear distortion traditional methods require high order harmonic components to represent nonlinear processes except for the hilbert based method this will lead to an artificial energy flux from the low frequency large scale to the high frequency small scale part thus the power law if it exists is contaminated we then compare the hilbert method with structure functions sf detrended fluctuation analysis dfa and wavelet leader wl by analyzing fractional brownian motion and synthesized multifractal time series for the former simulation we find that all methods provide comparable results for the latter simulation we perform simulations with an intermittent parameter 0 15 we find that the sf underestimates scaling exponent when q 3 the hilbert method provides a slight underestimation when q 5 however both dfa and wl overestimate the scaling exponents when q 5 it seems that hilbert and dfa methods provide better singularity spectra than sf and wl we finally apply all methods to a passive scalar temperature data obtained from a jet experiment with a taylor s microscale reynolds number re 250 due to the presence of strong ramp cliff structures the sf fails to detect the power law behavior for the traditional method the ramp cliff structure causes a serious artificial energy flux from the low frequency large scale to the high frequency small scale part thus dfa and wl underestimate the scaling exponents however the hilbert method provides scaling exponents q quite close to the one for longitudinal velocity indicating a less intermittent passive scalar field than what was believed before 2011 american physical society

numerical approach for quantification of epistemic uncertainty in the field of uncertainty quantification uncertainty in the governing equations may assume two forms aleatory uncertainty and epistemic uncertainty aleatory uncertainty can be characterised by known probability distributions whilst epistemic uncertainty arises from a lack of knowledge of probabilistic information while extensive research efforts have been devoted to the numerical treatment of aleatory uncertainty little attention has been given to the quantification of epistemic uncertainty in this paper we propose a numerical framework for quantification of epistemic uncertainty the proposed methodology does not require any probabilistic information on uncertain input parameters the method only necessitates an estimate of the range of the uncertain variables that encapsulates the true range of the input variables with overwhelming probability to quantify the epistemic uncertainty we solve an encapsulation problem which is a solution to the original governing equations defined on the estimated range of the input variables we discuss solution strategies for solving the encapsulation problem and the sufficient conditions under which the numerical solution can serve as a good estimator for capturing the effects of the epistemic uncertainty in the case where probability distributions of the epistemic variables become known a posteriori we can use the information to post process the solution and evaluate solution statistics convergence results are also established for such cases along with strategies for dealing with mixed aleatory and epistemic uncertainty several numerical examples are presented to demonstrate the procedure and properties of the proposed methodology

characterization of analytic phase signals in many cases a real valued signal g t may be associated with a complex valued signal a t e i q t the analytic signal associated with g t with the characteristic properties g t a t cos q t and h a cos q t a t sin q t using such obtained amplitude frequency modulation the instantaneous frequency of g t at the time t 0 may be defined to be q t 0 provided q t 0 0 the purpose of this note is to characterize in terms of analytic functions the unimodular functions f t c t is t c 2 t s 2 t 1 a e that satisfy hc t s t this corresponds to the case a t 1 in the above formulation we show that a unimodular function satisfies the required condition if and only if it is the boundary value of a so called inner function in the upper half complex plane we also give through an explicit formula a large class of functions of which the parametrization c t cos q t is available and the extra condition q t 0 a e is enjoyed this class of functions contains blaschke products in the upper half complex plane as a proper subclass studied by picinbono in 1

detecting intrinsic dynamics of traffic flow with recurrence analysis and empirical mode decomposition abstract in this paper we apply the empirical mode decomposition emd method to the recurrence plot rp and recurrence quantification analysis rqa to evaluate the frequency and time evolving dynamics of the traffic flow based on the cumulative intrinsic mode functions extracted by the emd the frequency evolving rp regarding different oscillation of modes suggests that apparent dynamics of the data considered are mainly dominated by its components of medium and low frequencies while severely affected by fast oscillated noises contained in the signal noises are then eliminated to analyze the intrinsic dynamics and consequently the denoised time evolving rqa diversely characterizes the properties of the signal and marks crucial points more accurately where white bands in the rp occur whereas a strongly qualitative agreement exists between all the non denoised rqa measures generally the emd combining with the recurrence analysis sheds more reliable abundant and inherent lights into the traffic flow which is meaningful to the empirical analysis of complex systems

computation of failure probability subject to epistemic uncertainty computing failure probability is a fundamental task in many important practical problems the computation its numerical challenges aside naturally requires knowledge of the probability distribution of the underlying random inputs on the other hand for many complex systems it is often not possible to have complete information about the probability distributions in such cases the uncertainty is often referred to as epistemic uncertainty and straightforward computation of the failure probability is not available in this paper we develop a method to estimate both the upper bound and the lower bound of the failure probability subject to epistemic uncertainty the bounds are rigorously derived using the variational formulas for relative entropy we examine in detail the properties of the bounds and present numerical algorithms to efficiently compute them

randomized allocation with nonparametric estimation for a multi armed bandit problem with covariates we study a multi armed bandit problem in a setting where covariates are available we take a nonparametric approach to estimate the functional relationship between the response reward and the covariates the estimated relationships and appropriate randomization are used to select a good arm to play for a greater expected reward randomization helps balance the tendency to trust the currently most promising arm with further exploration of other arms it is shown that with some familiar nonparametric methods e g histogram the proposed strategy is strongly consistent in the sense that the accumulated reward is asymptotically equivalent to that based on the best arm which depends on the covariates almost surely 1 introduction multi armed bandit problems have been extensively studied in probability and statistics in the past few decades and still receive considerable interest in these and related fields readers are referred to berry and fristedt 1985 and gittins 1989 and the references cited therein for the history many elegant results and applications in clinical trials scheduling and other industrial problems some recent developments have been reported in for example lai and yakowitz 1995 who considered the situation in which observations are dependent berry chen zame heath and shepp 1997 who considered infinitely many arms and auer cesa bianchi freund and schapire 1995 who considered worst case performances in classic bandit problems each arm sequentially generates rewards based on a distribution with some unknown parameters and one needs to sequentially select one arm to play for the maximum expected reward in a majority of the earlier work no auxiliary information beyond the observed rewards was considered when selecting an arm to play exceptions include woodroofe 1979 sarkar 1991 and clayton 1989 who considered one armed bandit problems with covariates the first two papers studied bayesian sequential allocation in non bernoulli bandit models with parametric frameworks and showed that the myopic rule is asymptotically optimal the third studied bernoulli bandit problems

analytic unit quadrature signals with nonlinear phase abstract the notion of intrinsic mode functions imfs in the algorithm of hilbert huang transform hht n e huang z shen s r long m c wu h h shih q zheng n c yen c c tung h h liu the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis proc r soc london a 454 1998 903 995 is essentially an engineering description in relation to mono components of nonlinear and non stationary signals in this note we prove a version of bedrosian s theorem on the unit circle we give a sufficient condition together with an example for nonlinear phases t that make the unit quadrature signals e i t to be analytic we also establish a corresponding relationship between the periodic and non periodic signals on the whole time range

a hybrid detrending method for fractional gaussian noise abstract determining trend and implementing detrending operations are important steps in data analysis yet there is neither precise definition of trend nor any logical algorithm for extracting it in this paper we propose a hybrid detrending method hdm which is based on the empirical mode decomposition emd and the detrended fluctuation analysis dfa our method can remove the polynomial and sinusoidal trends from the fractional gaussian noise fgn background we illustrate the method by selected examples from artificial time series and climate data in comparison with existing frequency domain based detrending methods our method is a posteriori the trend defined by our method is only derived from the data further our method also preserves the scaling behavior of the original signals

an efficient method for uncertainty propagation using fuzzy sets in the field of uncertainty quantification uq propagation of uncertainty is one of the most important tasks as it is essential to almost all uq analysis while many numerical methods have been developed for uncertainty propagation in probabilistic framework much less has been discussed in the nonprobabilistic framework which is important whenever one does not possess sufficient data or knowledge of the underlying systems in this paper we focus on the use of fuzzy sets to model uncertainty and their propagation through physical systems in particular we develop a numerical strategy that can efficiently propagate fuzzy sets in complex systems the method utilizes an accurate approximation model for the solution over the support of the input fuzzy sets and then retrieves the output fuzzy set information via the approximation model by doing so the method becomes highly efficient as the only simulation cost is in the construction of the approximation model in particular we discuss the use of ortho