relative entropy optimization and its applications in this expository article we study optimization problems specified via linear and relative entropy inequalities such relative entropy programs reps are convex optimization problems as the relative entropy function is jointly convex with respect to both its arguments prominent families of convex programs such as geometric programs gps second order cone programs and entropy maximization problems are special cases of reps although reps are more general than these classes of problems we provide solutions based on reps to a range of problems such as permanent maximization robust optimization formulations of gps and hitting time estimation in dynamical systems we survey previous approaches to some of these problems and the limitations of those methods and we highlight the more powerful generalizations afforded by reps we conclude with a discussion of quantum analogs of the relative entropy function including a review of the similarities and distinctions with respect to the classical case we also describe a stylized application of quantum relative entropy optimization that exploits the joint convexity of the quantum relative entropy function

coupled map lattices with complex order parameter abstract we introduce and study coupled map lattices with complex state variable the dynamical regimes of the finite length systems are classified naturally in terms of a topological invariant the overall phase shift accumulated along the whole length at fixed time a stability analysis of the spatially uniform states is presented and the results of numerical simulations of the spatio temporal dynamics are discussed we demonstrate that fast amplitude evolution including regular and chaotic spatio temporal behavior takes place on the background of a slower phase evolution for large values of the topological invariant the phase dynamics may give rise to an instability which in some cases results in a jump of the system to another value of the invariant we also consider the formation of long lived bubbles i e local domains of complicated dynamics in the spatial regions of locally reduced phase gradient our coupled map lattice model and its generalizations may be useful for understanding the dynamics in a larger range of parameters for such nonlinear dissipative media which allow small amplitude description in terms of the complex ginzburg landau equation as well as for time delay feedback systems with nonzero central frequency of the generated signal

the expansion of functions under transformation and its application to optimization abstract this paper proposes the expansion of functions under transformation which represents infinite kinds of extensions of taylor s expansion based on this duffin s condensation formula is developed as a condensation formula of high order furthermore a theorem of efficiently solving mathematical programming by using the expansion of functions is proposed according to the condensation formula of high order two kinds of second order primal algorithms are proposed for solving generalized geometric programming with rapid and stable convergence which could be applied to a wide range of structural optimization problems finally an efficient fully stressed design method under the function transformation is proposed using these expansions of functions

estimation and inference with censored and ordered multinomial response data abstract we propose a new formulation of the statistical model and the use of the maximum entropy principle for recovering information when the dependent variable is censored or ordered this approach makes use of weak sampling assumptions and performs well over a range of non gaussian error distributions and ill posed and well posed problems analytical and illustrative monte carlo sampling results are presented

orthogonality conditions for tobit models with fixed effects and lagged dependent variables abstract this paper presents orthogonality conditions for censored regression models with fixed effects and lagged dependent variables the orthogonality conditions can be used to construct method of moments estimators of the parameters of the model nonlinear fixed effects models are usually estimated by maximum likelihood with the fixed effects treated as parameters to be estimated monte carlo results indicate that in a tobit model with fixed effects and lagged dependent variables the maximum likelihood estimator of the effect of the lagged dependent variable performs poorly the method of moments estimator based on the orthogonality conditions presented here however performs quite well

symmetrically trimmed least squares estimation for tobit models this paper proposes alternatives to maximum likelihood estimation of the censored and truncated regression models known to economists as tobit models the proposed estimators are based upon symmetric censoring or truncation of the upper tail of the distribution of the dependent variable unlike methods based on the assumption of identically distributed gaussian errors the estimators are semiparametric in the sense that they are consistent and asymptotically normal for a wide class of symmetric error distributions with heteroskedasticity of unknown form the paper gives the regularity conditions and proofs of these large sample properties demonstrates how to construct consistent estimators of the asymptotic covariance matrices and presents the results of a simulation study for the censored case extensions and limitations of the approach are also considered

second order method of generalized geometric programming for spatial frame optimization to design concrete sectional sizes of beams the optimization model of the spatial frame is transformed into a problem of ggp generalized geometric programming in terms of the duffin s condensation formula adopting the strategy of two stages the problem is solved by the structure stage and the elements stage alternately the first and the second order primal algorithm for the ggp which are based on the first and the second order expansions under the logarithmic transformation in the logarithmic space are applied in the elements stage and the structure stage respectively numerical results including a large scale structure of the electrostatic precipitator show satisfactory efficiency of the method

noisy collective behaviour in deterministic cellular automata we investigate cellular automata in four and five dimensions for which chate and manneville recently have found nontrivial collective behaviour more precisely though being fully deterministic the average magnetization seems to be periodic respectively quasiperiodic with superimposed noise whose amplitude decreases with system size we confirm this behaviour on very large systems and over very large times we analyse in detail the statistical properties of the noise systems on small lattices and or subject to additional external noise are metastable arguments by grinstein et al suggest that in the periodic case the infinite deterministic systems should be metastable too these arguments are generalized to quasiperiodic systems we find evidence that they do indeed apply but we find no direct evidence for metastability of large systems

maximum entropy and bayesian approaches to the ratio problem abstract maximum entropy and bayesian approaches provide superior estimates of a ratio of parameters as this paper illustrates using the classic nerlove model of agricultural supply providing extra information in the supports for the underlying parameters for generalized maximum entropy gme estimators or as an analytically derived prior distribution in zellner s minimum expected loss melo estimators and bayesian method of moments bmom estimators helps substantially simulations illustrate that gme melo and bmom estimators with conservative priors have much smaller mean square errors and average biases than do standard ordinary least squares or melo and bmom estimators with uninformative priors in addition a new estimator of the structural agricultural supply model provides estimates of parameters that cannot be obtained directly using traditional reduced form approaches

a totalistic three dimensional cellular automaton with quasiperiodic behaviour abstract a three dimensional deterministic totalistic cellular automation with non trivial quasiperiodic behaviour is presented different properties as intrinsic noise and influence of external noise are investigated an approach to an explanation of the phenomenon is discussed

semidefinite programming relaxations for semialgebraic problems a hierarchy of convex relaxations for semialgebraic problems is introduced for questions reducible to a finite number of polynomial equalities and inequalities it is shown how to construct a complete family of polynomially sized semidefinite programming conditions that prove infeasibility the main tools employed are a semidefinite programming formulation of the sum of squares decomposition for multivariate polynomials and some results from real algebraic geometry the techniques provide a constructive approach for finding bounded degree solutions to the positivstellensatz and are illustrated with examples from diverse application fields

cluster splitting bifurcation in a system of coupled maps abstract we consider cluster splitting bifurcations in a system of globally coupled maps as coupling parameter decreases at these transitions the number of clusters i e groups of elements with identical dynamics increases we demonstrate that different cascades of cluster splitting can occur depending on statistics of redistribution of the oscillators between new born clusters

pairwise difference estimators of censored and truncated regression models abstract this paper proposes a class of estimators of the semiparametric censored regression model under the assumption that the error terms are i i d and independent of the covariates the estimators exploit the fact that for a pair of observations a particular transformation of the censored variables depending upon the parameter vector and both covariate vectors will be identically distributed therefore the difference in the transformed dependent variables will be symmetrically distributed around zero when the transformation is evaluated at the true parameter vector an analogous class of estimators for the truncated regression model includes the bhattacharya chernoff and yang 1983 estimator as a special case the estimators are defined as minimizers of u processes so the large sample theory for classical m estimators is extended to this case conditions are given to ensure root n consistency and asymptotic normality of the estimators and a small scale simulation study for the censored regression estimator suggest that it will be well behaved in finite samples

pattern selection at high nonlinearity in a diffusively coupled logistic lattice a different pattern selection regime is shown to exist in regions of high nonlinearity in the diffusively coupled logistic lattice with nearest neighbor interaction for this regime the phase diagram of several prominent attractors is determined the results indicate that the spatiotemporal chaos in some of the regions so far believed to be areas of fully developed spatiotemporal chaos is of a transient nature

time evolution of coherent structures in networks of hindmarch rose neurons abstract in the regime of partial synchronization networks of diffusively coupled hindmarch rose neurons show coherent structures developing in a region of the phase space which is wider than in the correspondent single neuron such structures are kept without important changes during several bursting periods in this work we study the time evolution of these structures and their dynamical stability under damage this system may model the behavior of ensembles of neurons coupled through a bidirectional gap junction or in a broader sense it could also account for the molecular cascades present in the formation of flash and short time memory

a pseudo r2 measure for limited and qualitative dependent variable models abstract a pseudo r 2 measure for limited and qualitative dependent variable models is proposed a consistent estimator of the variance of the disturbance term is also suggested the pseudo r 2 measure is shown to have the same asymptotic limit as the conventional r 2 the measure is adapted to the logit model in an empirical example of female car ownership modeling the pseudo r 2 is applicable to a wide set of limited and qualitative dependent variable models and offers a valuable tool for model evaluation

long range order with local chaos in lattices of diffusively coupled odes abstract the existence of non trivial collective behavior in lattices of diffusively coupled differential equations is investigated for a two dimensional square lattice of rossler systems a rotating long range order is observed this case is best described in terms of a complex ginzburg landau cgl equation submitted to the local noise produced by the chaotic rossler units the parameters of this cgl equation are estimated to be in the so called benjamin feir stable region the collective oscillation regime thus corresponds to the linearly stable spatially homogeneous solution of the equivalent cgl equation the possibility of more complex collective behavior in similar systems is discussed

amplitude equation approach to spatiotemporal dynamics of cardiac alternans amplitude equations are derived that describe the spatiotemporal dynamics of cardiac alternans during periodic pacing of one b echebarria and a karma phys rev lett 88 208101 2002 and two dimensional homogeneous tissue and one dimensional anatomical reentry in a ring of homogeneous tissue these equations provide a simple physical understanding of arrhythmogenic patterns of period doubling oscillations of action potential duration with a spatially varying phase and amplitude as well as explicit quantitative predictions that can be compared to ionic model simulations or experiments the form of the equations is expected to be valid for a large class of ionic models but the coefficients are derived analytically only for a two variable ionic model and calculated numerically for the original noble model of purkinje fiber action potential in paced tissue this theory explains the formation of spatially discordant alternans by a linear instability mechanism that produces a periodic pattern of out of phase domains of alternans the wavelength of this pattern equal to twice the spacing between nodes separating out of phase domains is shown to depend on three fundamental length scales that are determined by the strength of cell to cell coupling and conduction velocity cv restitution moreover the patterns of alternans can be either stationary with fixed nodes or traveling with moving nodes and hence quasiperiodic oscillations of action potential duration depending on the relative strength of the destabilizing effect of cv restitution and the stabilizing effect of diffusive coupling for the ring geometry we recover the results of courtemanche glass and keener phys rev lett 70 2182 1993 with two important modifications due to cell to cell diffusive coupling first this coupling breaks the degeneracy of an infinite dimensional hopf bifurcation such that the most unstable mode of alternans corresponds to the longest quantized wavelength of the ring second the hopf frequency which determines the velocity of the node along the ring depends both on the steepness of cv restitution and the strength of this coupling with the net result that quasiperiodic behavior can arise with a constant conduction velocity in both the paced geometries and the ring the onset of alternans is different in tissue than for a paced isolated cell the implications of these results for alternans dynamics during two dimensional reentry are briefly discussed

the lorenz fermi pasta ulam experiment we consider a chain of lorenz 63 systems connected through a local nearest neighbour coupling we refer to the resulting system as the lorenz fermi pasta ulamlattice because of its similarity to the celebrated experiment conducted by fermi pasta and ulam at large coupling strengths the systems synchronize to a global chaotic orbit of the lorenz attractor for smaller coupling the synchronized state loses stability instead steady spatially structured equilibrium states are observed these steady states are related to the heteroclinic orbits of the system describing stationary solutions to the partial differential equation that emerges on taking the continuum limit of the lattice notably these orbits connect saddle foci suggesting the existence of a multitude of such equilibria in relatively wide systems on lowering the coupling strength yet further the steady states lose stability in what appear to be always subcritical hopf bifurcations this can lead to a variety of time dependent states with fixed time averaged spatial structure such solutions can be limit cycles tori or possibly chaotic attractors cluster states can also occur though with less regularity consisting of lattices in which the elements are partitioned into families of synchronized subsystems ultimately for very weak coupling the lattice loses its time averaged spatial structure at this stage the properties of the lattice are probably chaotic and approximately scale with the lattice size suggesting that the system is essentially an ensemble of elements that evolve largely independent of one another the weak interaction however is sufficient to induce widespread coherent phases these are ephemeral states in which the dynamics of one or more subsystems takes a more regular form we present measures of the complexity of these incoherent lattices and discuss the concept of a dynamical horizon that is the distance along the lattice that one subsystem can effectively influence another and error propagation how the introduction of a disturbance in one subsystem becomes spread throughout the lattice 2000 elsevier science b v all rights reserved

censored regression quantiles abstract the object of this paper is to demonstrate how the lad estimation method for the censored regression model can be extended to more general quantiles in this paper the form of the conditional quantiles for the censored regression models is heuristically derived and discussed the resulting estimators of the regression coefficients which include the censored lad estimator as a special case are shown to be consistent and asymptotically normally distributed under appropriately translated versions of the corresponding assumptions for the former approach consistent estimation of the asymptotic covariance matrix when the error terms are i i d is also treated the paper discussed how several quantile estimators might be combined to improve efficiency when the error terms are identically distributed and how tests of homoskedasticity and symmetry of the error distribution can be constructed using particular differences of the estimated coefficients

periodic behavior of cellular automata i propose an explanation of the observation of a globally synchronized behavior of deterministic cellular automata and coupled map lattices together with local fluctuations

exploring collective behaviors with a multi attractor quartic map we simulate a 2d coupled map lattice formed by individual units consisting of a multi attractor quartic map we show that the interesting recently discovered non trivial collective behaviors where macroscopic quantities show well dened usually regular temporal evolution in spite of the presence of local disorder in space and time also exist over wide parameter domains in the presence of local periodic order in systems having more realistic units allowing coexistence of more than one attractor c 1998 elsevier science b v all rights reserved

chaos transition of soliton motion on a microstructured lattice abstract soliton motion on a damped driven one dimensional lattice is proposed the lattice model is made of a one dimensional chain equipped at each point with a rotatory molecule the set of coupled difference differential equations for the molecule rotation is obtained for the discrete system using a semi discrete kink solution for which its center of mass is considered as a collective variable we derive the equation of motion for the kink location we show that the kink location is then governed by the equation of the damped sinusoidally driven pendulum when the first order corrections are dropped by means of numerical simulations carried out directly on the lattice model the complex dynamics of the kink location is investigated and compared to that of the well known forced pendulum for some ranges of the control parameters the numerical simulations exhibit a cascade of odd subharmonic components as well as strange attractors which characterizes the chaotic behavior of the kink motion these results agree fairly well with the main features of the transition to chaos for the damped driven pendulum

a maximum entropy approach to recovering information from multinomial response data abstract the classical maximum entropy me approach to estimating the unknown parameters of a multinomial discrete choice problem which is equivalent to the maximum likelihood multinomial logit ml estimator is generalized the generalized maximum entropy gme model includes noise terms in the multinomial information constraints each noise term is modeled as the mean of a finite set of a priori known points in the interval 1 1 with unknown probabilities where no parametric assumptions about the error distribution are made a gme model for the multinomial probabilities and for the distributions associated with the noise terms is derived by maximizing the joint entropy of multinomial and noise distributions under the assumption of independence the gme formulation reduces to the me in the limit as the sample grows large or when no noise is included in the entropy maximization further even though the gme and the logit estimators are conceptually different the dual gme model is related to a gener

a new rectangle branch and pruning approach for generalized geometric programming generalized geometric programming ggp problem occurs frequently in engineering design and management in this paper a branch and pruning global optimization algorithm is proposed for ggp by utilizing some transformations a linear relaxation of the problem ggp is obtained based on the linear lower bound functions of objective and constraint functions inside some hyperrectangle region then a new pruning technique is given to accelerate the convergence of the given algorithm and this pruning technique offers the possibility to cut away a large part of the current investigated region in which there no exist global optimum solution the proposed algorithm which connects branch and bound method with the pruning technique successfully is convergent to the global minimum according to the successive refinement of the linear relaxation of feasible region of the objective function and the solutions of a series of linear relaxation problems and finally numerical experiment is given to illustrate the feasibility and efficiency of the proposed algorithm

coordinate based empirical likelihood like estimation in ill conditioned inverse problems in the context of a semiparametric regression model with underlying probability distribution unspecified an extremum estimator formulation is proposed that makes use of empirical likelihood and information theoretic estimation and inference concepts to mitigate the problem of an ill conditioned design matrix a squared error loss measure is used to assess estimator performance in finite samples in large samples the estimator can be designed to be consistent and asymptotically normal so that limiting chi squared distributions provide a basis for hypothesis tests and confidence intervals empirical risk results based on a large scale monte carlo sampling experiment suggest that the estimator has relative to traditional competitors superior finite sample properties under a squared error loss measure when the design matrix is ill conditioned

structure of complex periodic and chaotic media with spiral waves the spatiotemporal structure of reactive media supporting a solitary spiral wave is studied for systems where the local reaction law exhibits a period doubling cascade to chaos this structure is considerably more complex than that of simple period 1 oscillatory media as one moves from the core of the spiral wave the local dynamics takes the form of perturbed period doubled orbits whose character varies with spatial location relative to the core an important feature of these media is the existence of a curve where the local dynamics is effectively period 1 this curve arises as a consequence of the necessity to reconcile the conflict between the global topological organization of the medium induced by the presence of a spiral wave and the topological phase space structure of local orbits determined by the reaction rate law due to their general topological nature the phenomena described here should be observable in a broad class of systems with complex periodic behavior s1063 651x 96 12611 8

regression analysis with randomly right censored data this paper proposes a new estimator of the parameter vector in a linear regression model when the observations are randomly censored on the right and when the error distribution is unknown this estimator is explicitly defined and easily computable the paper contains sufficient conditions under which this estimator is mean square consistent and asymptotically normal a numerical example is given

condition for alternans and stability of the 1 1 response pattern in a memory model of paced cardiac dynamics we analyze a mathematical model of paced cardiac muscle consisting of a map relating the duration of an action potential to the preceding diastolic interval as well as the preceding action potential duration thereby containing some degree of memory the model displays rate dependent restitution so that the dynamic and s1 s2 restitution curves are different a manifestation of memory in the model we derive a criterion for the stability of the 1 1 response pattern displayed by this model it is found that the stability criterion depends on the slope of both the dynamic and s1 s2 restitution curves and that the pattern can be stable even when the individual slopes are greater or less than one we discuss the relation between the stability criterion and the slope of the constant bcl restitution curve the criterion can also be used to determine the bifurcation from the 1 1 response pattern to alternans we demonstrate that the criterion can be evaluated readily in experiments using a simple pacing protocol thus establishing a method for determining whether actual myocardium is accurately described by such a mapping model we illustrate our results by considering a specific map recently derived from a three current membrane model and find that the stability of the 1 1 pattern is accurately described by our criterion in addition a numerical experiment is performed using the three current model to illustrate the application of the pacing protocol and the evaluation of the criterion

comparative statics of the generalized maximum entropy estimator of the general linear model the generalized maximum entropy method of information recovery requires that an analyst provides prior information in the form of finite bounds on the permissible values of the regression coefficients and error values for its implementation using a new development in the method of comparative statics the sensitivity of the resulting coefficient and error estimates to the prior information is investigated a negative semidefinite matrix reminiscent of the slutsky matrix of neoclassical microeconomic theory is shown to characterize the said sensitivity and an upper bound for the rank of the matrix is derived

period doubling instability and memory in cardiac tissue theoretical studies have indicated that alternans period doubling instability of action potential duration is associated with a restitution relation with a slope or 1 however recent experimental findings suggest that the slope of the restitution relation is not necessarily predictive of alternans here we compared a return map memory model to action potential data from an ionic model and found that the memory model reproduced dynamics that could not be explained by a unidimensional restitution relation using linear stability analysis we determined the onset of the alternans in the memory model and confirmed that the slope of the restitution curve was not predictive

the effect of truncation on the identifiability of regression coefficients abstract when data are truncated and hence partly unobservable parameters identifiable under the complete observation may not be identifiable a class of distributions is characterized under which regression coefficients are unidentifiable by truncation of a dependent variable in the regression model in a class of strongly unimodal densities regression coefficients are shown to be unidentifiable only when the underlying distribution is proportional to the exponential distribution in support of the truncated observation the exponential double exponential and huber s least informative distribution for a location parameter are apparent examples of the distributions under which the unidentifiability can occur in a more restrictive class of symmetric and strongly unimodal densities the unidentifiability arises only when the error distribution has exponential tails and the degree of truncation is at least 50 the likelihood function becomes completely flat with respect to the regression coefficients and

a generalized information theoretical approach to tomographic reconstruction a generalized maximum entropy based approach to noisy inverse problems such as the abel problem tomography or deconvolution is presented in this generalized method instead of employing a regularization parameter each unknown parameter is redefined as a proper probability distribution within a certain pre specified support then the joint entropies of both the noise and signal probabilities are maximized subject to the observed data after developing the method information measures basic statistics and the covariance structure are developed as well this method is contrasted with other approaches and includes the classical maximum entropy formulation as a special case the method is then applied to the tomographic reconstruction of the soft x ray emissivity of the hot fusion plasma

adaptive estimation in time series regression models this work develops adaptive estimators for a linear regression model with serially correlated errors we show that these results continue to hold when the order of the arma process characterizing the errors is unknown the finite sample results are promising indicating that substantial efficiency gains may be possible for samples as small as 50 observations we use these estimators to investigate the behavior of the forward foreign exchange market

internal fluctuations period doubling and chemical chaos the effects of internal molecular fluctuations on period doubling bifurcations and chaotic band merging are studied in a well stirred reactive chemical system where spatial degrees of freedom play no role the calculations are carried out using a stochastic model based on reactive lattice gas cellular automata molecular fluctuations arising from reactive collisions are incorporated in the model and the mass action rate equations are recovered in the mean field limit large system sizes can be studied and permit the investigation of the internal noise scaling structure in the periodic and chaotic regimes for the willamowski r ossler system the noise scaling exponent is consistent with that found for one dimensional quadratic maps subject to external noise the model provides a means to study small non equilibrium reacting systems where fluctuations may not be neglected

geometric programming duals of channel capacity and rate distortion we show that the lagrange dual problems of the channel capacity problem with input cost and the rate distortion problem are simple geometric programs upper bounds on channel capacity and lower bounds on rate distortion can be efficiently generated from their duals for channel capacity the geometric programming dual characterization is shown to be equivalent to the minmax kullback leibler kl characterization in csiszar et al 1981 for rate distortion the geometric programming dual is extended to rate distortion with two sided state information a duality by mapping is then given between the lagrange dual problems of channel capacity with input cost and rate distortion which resolves several apparent asymmetries between their primal problems in the familiar form of mutual information optimization problems both the primal and dual problems can be interpreted in a common framework of free energy optimization from statistical physics

robust space time intermittency and 1 f noise abstract we investigate a type of intermittency that occurs in space as well as time studying a one dimensional lattice of coupled quadratic maps this system naturally forms spatial domains motion of the domain walls causes spatially localized changes from chaotic to almost periodic behavior the almost periodic phases have eigenvalues quite close to one resulting in long lived laminar bursts with a 1 f low frequency spectrum this behavior has aspects of both crutchfield and pomeau manneville intermittency unlike pomeau manneville however the behavior that we observe here is quite robust under changes of parameters

accelerating method of global optimization for signomial geometric programming abstract signomial geometric programming sgp has been an interesting problem for many authors recently many methods have been provided for finding locally optimal solutions of sgp but little progress has been made for global optimization of sgp in this paper we propose a new accelerating method for global optimization algorithm of sgp using a suitable deleting technique this technique offers a possibility to cut away a large part of the currently investigated region in which the globally optimal solution of sgp does not exist and can be seen as an accelerating device for global optimization algorithm of sgp problem compared with the method of shen and zhang global optimization of signomial geometric programming using linear relaxation appl math comput 150 2004 99 114 numerical results show that the computational efficiency is improved obviously by using this new technique in the number of iterations the required saving list length and the execution time of the algorithm

the moment problem on compact semi algebraic sets in this chapter we begin the study of the multidimensional moment problem the passage to dimensions d 2 brings new difficulties and unexpected phenomena in sect 3 2 we derived solvability criteria of the moment problem on intervals in terms of positivity conditions it seems to be natural to look for similar characterizations in higher dimensions as well this leads us immediately into the realm of real algebraic geometry and to descriptions of positive polynomials on semi algebraic sets in this chapter we treat this approach for basic closed compact semi algebraic subsets of mathbb r d it turns out that for such sets there is a close interaction between the moment problem and positivstellensatze for strictly positive polynomials

least absolute deviations estimation for the censored regression model this paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression or censored tobit model the proposed estimator is a generalization of least absolute deviations estimation for the standard linear model and unlike estimation methods based on the assumption of normally distributed error terms the estimator is consistent and asymptotically normal for a wide class of error distributions and is also robust to heteroscedasticity the paper gives the regularity conditions and proofs of these large sample results and proposes classes of consistent estimators of the asymptotic covariance matrix for both homoscedastic and heteroscedastic disturbances

a global optimization using linear relaxation for generalized geometric programming many local optimal solution methods have been developed for solving generalized geometric programming ggp but up to now less work has been devoted to solving global optimization of ggp problem due to the inherent difficulty this paper considers the global minimum of ggp problems by utilizing an exponential variable transformation and the inherent property of the exponential function and some other techniques the initial nonlinear and nonconvex ggp problem is reduced to a sequence of linear programming problems the proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems test results indicate that the proposed algorithm is extremely robust and can be used successfully to solve the global minimum of ggp on a microcomputer

an adaptive empirical bayes estimator of the multivariate normal mean under quadratic loss abstract for shrinkage estimators to achieve significant risk improvement over their traditional competitors one must identify the region or subspace where the unknown location vector lies or is thought likely to lie a priori when vague or conflicting priors suggest that a broad class of estimators may be effective under a squared error loss measure new minimax or near minimax empirical bayes estimators are proposed that make use of stein s unbiased estimator of the risk to identify the optimum risk effective shrinkage estimator

relative entropy relaxations for signomial optimization signomial programs sps are optimization problems specified in terms of signomials which are weighted sums of exponentials composed with linear functionals of a decision variable sps are nonconvex optimization problems in general and families of np hard problems can be reduced to sps in this paper we describe a hierarchy of convex relaxations to obtain successively tighter lower bounds of the optimal value of sps this sequence of lower bounds is computed by solving increasingly larger sized relative entropy optimization problems which are convex programs specified in terms of linear and relative entropy functions our approach relies crucially on the observation that the relative entropy function by virtue of its joint convexity with respect to both arguments provides a convex parametrization of certain sets of globally nonnegative signomials with efficiently computable nonnegativity certificates via the arithmetic geometric mean inequality by appealing to representation theorems from real algeb

global optimization with polynomials and the problem of moments we consider the problem of finding the unconstrained global minimum of a real valued polynomial p x mathbb r n to mathbb r as well as the global minimum of p x in a compact set k defined by polynomial inequalities it is shown that this problem reduces to solving an often finite sequence of convex linear matrix inequality lmi problems a notion of karush kuhn tucker polynomials is introduced in a global optimality condition some illustrative examples are provided

on the asymptotic bias of the ordinary least squares estimator of the tobit model this paper presents a precise characterization of the bias of least squares in two limited dependent variable models the tobit model and the truncated regression model for the cases considered the method of moments can be used to correct the bias of ols for more general cases the results provide approximations which appear to be relatively robust 13 and o in this paper we present a precise characterization of that bias for the particular case in which xt as well as is normally distributed we also show that the bias of the ols slope estimator can be corrected by dividing each estimate by the sample proportion of nonlimit observations other structural parameters can be consistently estimated in a similar fashion we present some evidence on the effect of nonnormality with respect to the predictions obtained in the normal model the case in which the sample contains only nonlimit observation the truncated regression model is considered elsewhere olsen 7 we analyze the relationship between his results and ours and derive some predictions of the normal model with respect to the seriousness of truncation bias

estimation of limited dependent variable models by ordinary least squares and the method of moments abstract under certain conditions a broad class of qualitative and limited dependent variable models can be consistently estimated by the method of moments using a non iterative correction to the ordinary least squares estimator with only a small loss of efficiency compared to maximum likelihood estimation the class of models is that obtained from a classical multinormal regression by any type of censoring or truncation and includes the tobit probit two limit probit truncated regression and some variants of the sample selection models the paper derives the estimators and their asymptotic covariance matrices

scaling law for the maximal lyapunov exponent the authors study the scaling law for epsilon to 0 of the maximal lyapunov exponent for coupled chaotic map lattices and for products of random jacobi matrices to this purpose they develop approximate analytical treatments of the random matrix problem inspired by the theory of directed polymers in a random medium a type of mean field method and a tree approximation which introduces correlations the theoretical results suggest a leading mod log epsilon mod 1 increase in the maximal lyapunov exponent near epsilon 0 which is confirmed by numerical simulations also for coupled map lattices a dynamical mechanism responsible for this behaviour is investigated for a 2 2 random matrix model the theory also predicts a phase transition at a critical value of the coupling epsilon e which is not observed in numerical simulations and might be an artifact of the approximation

geometric programming for optimal positive linear systems this article studies the parameter tuning problem of positive linear systems for optimizing their stability properties we specifically show that under certain regularity assumptions on the parameterization the problem of finding the minimum cost parameters that achieve a given requirement on a system norm reduces to a geometric program which in turn can be exactly and efficiently solved by convex optimization the flexibility of geometric programming allows the state input and output matrices of the system to simultaneously depend on the parameters to be tuned the class of system norms under consideration includes the h 2 norm h infty norm hankel norm and schatten p norm also the parameter tuning problem for ensuring the robust stability of the system under structural uncertainties is shown to be solved by geometric programming the proposed optimization framework is further extended to delayed positive linear systems where it is shown that the parameter tuning problem jointly constrained by the exponential decay rate the mathcal l 1 gain and the mathcal l infty gain can be solved by convex optimization the assumption on the system parameterization is stated in terms of posynomial functions which form a broad class of functions and thus allow us to deal with various interesting positive linear systems arising from for example dynamical buffer networks and epidemic spreading processes we present numerical examples to illustrate the effectiveness of the proposed optimization framework

adjusted least squares estimates for the scaled regression coefficients with censored data abstract the ordinary least squares ols method is popular for analyzing linear regression models because of its simplicity in computation suppose that the regressor variables are stochastic and the dependent observations are censored we can prove that under very general design conditions the least squares ls method can still be useful in estimating the scaled regression coefficients of the general regression model y q xi i i 1 2 n provided that the censored response observations are properly weighted here is a constant is a 1 p row vector x i are p 1 column vectors of explanatory variables i are unobserved random errors and q is an arbitrary unknown function particularly we shall see that under stronger design conditions such as assuming that the regressor variables have elliptically symmetric distribution the ols estimator consistently estimates the scaled when the response observations are complete the model discussed here is not the usual nonlinear re

two step estimation of semiparametric censored regression models root n consistent estimators of the regression coecients in the linear censored regression model under conditional quantile restrictions on the error terms were pro posed by powell journal of econometrics 25 1984 303 325 32 1986a 143 155 while those estimators have desirable asymptotic properties under weak regularity conditions simulation studies have shown these estimators to exhibit a small sam ple bias in the opposite direction of the least squares bias for censored data this paper introduces two step estimators for these models which minimize convex objec tive functions and are designed to overcome thisnite sample bias the paper gives regularity conditions under which the proposed two step estimators are consistent and asymptotically normal a monte carlo study compares thenite sample behavior of the proposed methods with their one step counterparts 2001 elsevier science s a all rights reserved

chaotic behavior of an extended system abstract some general aspects of spatiotemporal chaos are considered with emphasis on long range correlations and response an attempt is made to characterize the statistical steady state of a chaotic system by analogy with the description of a system near thermal equilibrium the one dimensional kuramoto sivashinsky equation is considered as an example and our present understanding of its statistical behavior is reviewed

cooperative behavior of a chain of synaptically coupled chaotic neurons abstract a coupled linear chain of hindmarsh rose model neurons with reciprocal inhibition between neighboring neurons exhibited synchronous oscillations in which neighboring neurons burst out of phase and next nearest neighbor neurons burst in phase the bifurcations observed inside this out of phase regime were qualitatively the same for all chains with an even number of neurons and were similar to those observed in a single isolated cell although the organization of the behavior of a chain of coupled neurons was more regular than that of an isolated cell when noise was added to the synaptic coupling strengths there was less hysteresis in the system and many of the bifurcations with smaller basins of attraction were eliminated making the system even more regular these results suggest that in populations of bursting neurons with reciprocal inhibition the chaotic behavior found in single cells is suppressed

spatiotemporal chaos in the one dimensional complex ginzburg landau equation the dynamical behavior of a large one dimensional system obeying the cubic complex ginzburg landau equation is studied numerically as a function of parameters near a supercritical bifurcation two types of chaotic behavior can be distinguished beyond the benjamin feir instability a phase turbulence regime with a conserved phase winding number and no phase dislocations space time defects and a defect regime with a nonzero density of defects the transition between the two can either be continuous or discontinuous hysteretic depending on parameters the spatial decay of the phase correlation function is inferred to be exponential in both regimes with a sharp decrease of the correlation length upon entering the defect phase the temporal decay of correlations is exponential in the defect regime

a delay equation representation of pulse circulation on a ring in excitable media this paper develops a theory for pulse circulation on a ring in a continuous excitable medium simulations of a partial differential equation pde modeling propagation of electrical pulses on a one dimensional ring of cardiac tissue are presented the dynamics of the circulating pulse in this excitable medium are reduced to a single integral delay equation stability conditions for steady circulation are obtained and estimates are derived for the wavelength growth rate and asymptotic amplitude of oscillating solutions near the transition from steady rotation to oscillatory pulse dynamics the analytical results agree with simulations of the delay equation and the pde model and uncover previously uncharted solutions of the pde equations

renormalization group for strongly coupled maps systems of strongly coupled chaotic maps generically exhibit collective behavior emerging out of extensive chaos we show how the well known renormalization group rg of unimodal maps can be extended to the coupled systems and in particular to coupled map lattices cmls with local diffusive coupling the rg relation derived for cmls is nonperturbative i e not restricted to a particular class of configurations nor to some vanishingly small region of parameter space after defining the strong coupling limit in which the rg applies to almost all asymptotic solutions we first present the simple case of coupled tent maps we then turn to the general case of unimodal maps coupled by diffusive coupling operators satisfying basic properties extending the formal approach developed by collet and eckmann for single maps we finally discuss and illustrate the general consequences of the rg cmls are shown to share universal properties in the space continuous limit which emerges naturally as the group is iterated we prove that the scaling properly ties of the local map carry to the coupled systems with an additional scaling factor of length scales implied by the synchronous updating of these dynamical systems this explains various scaling laws and self similar features previously observed numerically

lower bounds for polynomials using geometric programming we make use of a result of hurwitz j reine angew math 108 1891 pp 266 268 and reznick math ann 283 1989 pp 431 464 and a consequence of this result due to fidalgo and kovacec math z 269 2011 pp 629 645 to establish in theorem 2 3 a new sufficient condition for a polynomial f in mathbb r x 1 dots x n of even degree to be a sum of squares theorem 2 3 yields as special cases the results of ghasemi and marshall in arch math basel 95 2010 pp 343 353 and consequently also those of fidalgo and kovacec and lasserre arch math basel 89 2007 pp 390 398 we apply theorem 2 3 to obtain a new lower bound f textrm gp for f and we explain how f textrm gp can be computed using geometric programming the lower bound f textrm gp is generally not as good as the lower bound f textrm sos introduced by lasserre siam j optim 11 2001 pp 796 817 and parrilo and sturmfels algorithmic and quantitative real algebraic geometry ams provid

global optimization of signomial geometric programming using linear relaxation various local optimization approaches have been developed for solving signomial geometric programming sgp problems but up to now less work has been devoted to solving global optimization of sgp due to the inherent difficulty this paper considers the global minimum of sgp that arise in various practice problems by utilizing an exponential variable transformation and tangential hypersurfaces and convex envelop approximations a linear relaxation of sgp is then obtained thus initial nonconvex nonlinear problem sgp is reduced to a sequence of linear programming problems through the successive refinement of a linear relaxation of feasible region of the objective function the proposed algorithm is convergent to the global minimum of sgp by means of the subsequent solutions of a series of linear programming problems test results indicate that the proposed algorithm is extremely robust and can be used successfully to solve global minimum of sgp on a microcomputer

dynamics at the interface dividing collective chaotic and synchronized periodic states in a cml abstract a study is developed focusing the loss of stability of the interface dividing two regions of different spatial patterns on a coupled map lattice using coupling as the parameter guiding the transition these patterns are constructed over local periodic chaotic attractors generating regions of synchronized collective behavior the discrete feature of the underlying lattice the anisotropy that stems from such discreteness and its possible change to an isotropic system through coupling with large number of neighbors are also investigated

linearization method of global optimization for generalized geometric programming many methods for solving generalized geometric programming ggp problem can only find locally optimal solutions but up to now less work has been devoted to solving global optimization of ggp due to the inherent difficulty this paper gives a method for finding the globally optimal solutions of ggp utilizing an exponentially variable transformation and some other techniques the initial nonlinear and nonconvex ggp problem is reduced to a sequence of linear programming problems the proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems several ggp examples in the literatures are tested to demonstrate that the proposed method can systematically solve these examples to find the global optimum within a prespecified error

universality and scaling of period doubling bifurcations in a dissipative distributed medium abstract a homogeneous medium consisting of nonlinear elements demonstrating transition to chaos via period doubling bifurcations is considered the coupling between the elements is supposed to be of a dissipative type i e it tends to equalize their instantaneous states using the renormalization group approach the following scaling law for weakly inhomogeneous states near the critical point is obtained at each period doubling the spatial scale increases by 2 on the basis of this law the scaling hypotheses for the transition to chaos in the semi infinite and finite systems are proposed the scaling properties are verified by the numerical calculations with a simple model