on the equivalence of constrained and compound optimal designs abstract constrained and compound optimal designs represent two well known methods for dealing with multiple objectives in optimal design as reflected by two functionals 1 and 2 on the space of information matrices a constrained optimal design is constructed by optimizing 2 subject to a constraint on 1 and a compound design is found by optimizing a weighted average of the functionals 1 1 2 0 1 we show that these two approaches to handling multiple objectives are equivalent

resonant algebras and gravity the s expansion framework is analyzed in the context of a freedom in closing the multiplication tables for the abelian semigroups including the possibility of the zero element in the resonant decomposition and associating the lorentz generator with the semigroup identity element leads to a wide class of the expanded lie algebras introducing interesting modifications to the gauge gravity theories among the results we find all the maxwell algebras of type and the recently introduced the additional new examples complete the resulting generalization of the bosonic enlargements for an arbitrary number of the lorentz like and translational like generators some further prospects concerning enlarging the algebras are discussed along with providing all the necessary constituents for constructing the gravity actions based on the obtained results

a geometric characterization of c optimal designs for heteroscedastic regression we consider the common nonlinear regression model where the variance as well as the mean is a parametric function of the explanatory variables the c optimal design problem is investigated in the case when the parameters of both the mean and the variance function are of interest a geometric characterization of c optimal designs in this context is presented which generalizes the classical result of elfving 1952 for c optimal designs as in elfving s famous characterization c optimal designs can be described as representations of boundary points of a convex set however in the case where there appear parameters of interest in the variance the structure of the elfving set is dierent roughly speaking the elfving set corresponding to a heteroscedastic regression model is the convex hull of a set of ellipsoids induced by the underlying model and indexed by the design space the c optimal designs are characterized as representations of the points where the line in direction of the vector c intersects the boundary of the new elfving set the theory is illustrated in several examples including pharmacokinetic models with random eects

pathwise uniqueness for a degenerate stochastic differential equation we introduce a new method of proving pathwise uniqueness and we apply it to the degenerate stochastic differential equation dx t x t dw t where w t is a one dimensional brownian motion and e 0 1 2 weak uniqueness does not hold for the solution to this equation if one restricts attention however to those solutions that spend zero time at 0 then pathwise uniqueness does hold and a strong solution exists we also consider a class of stochastic differential equations with reflection

bayesian experimental design for multiple hypothesis testing abstract the problem of designing an optimal experiment for the purpose of performing one or more hypothesis tests is considered the bayesian decision theoretic approach is used to arrive at several new optimality criteria for this purpose for a single hypothesis test the resulting optimal designs are the well known optimal designs that minimize the posterior variance of the parameter being tested for multiple tests an experimental design must perform well under several competing criteria different approaches to achieving this goal are explored including constrained optimization and an additive weighted loss the resulting optimality criteria are sensitive not only to the posterior variances of the parameters under test but also to their prior means

optimal designs when the variance is a function of the mean summary we develop locally d optimal designs for nonlinear models when the variance of the response is a function of its mean using the two parameter michaelis menten model as an example we show that the optimal design depends on both the type of heteroscedasticity and the magnitude of the variation in addition our results suggest that the homoscedastic d optimal design has high efficiency under a broad class of heteroscedastic patterns and that it is fairly insensitive to nominal values of the parameters

d optimum designs for heteroscedastic linear models abstract the methods of optimum experimental design are applied to models in which the variance as well as the mean is a parametric function of explanatory variables extensions to standard optimality theory lead to designs when the parameters of both the mean and the variance functions or the parameters of only one function are of interest the theory also applies whether the mean and variance are functions of the same variables or of different variables although the mathematical foundations differ the example studied is a second order two factor response surface for the mean with a parametric nonlinear variance function the theory is used both for constructing designs and for checking optimality a major potential for application is to experimental design in off line quality control

structure of higher spin gauge interactions in a previous paper higher spin gauge field theory was formulated in an abstract way essentially only keeping enough machinery to discuss gauge invariance of an action the approach could be thought of as providing an interface or syntax toward an implementation or semantics yet to be constructed the structure then revealed turned out to be that of a strongly homotopy lie algebra in the present paper the framework will be connected to more conventional field theoretic concepts the fock complex vertex operator implementation of the interactions in the brst bv formulation of the theory will be elaborated the relation between the vertex order expansion and homological perturbation theory will be clarified a formal nonobstruction argument is reviewed the syntactically derived sh lie algebra structure is semantically mapped to the fock complex implementation and it is shown that the equations governing the higher order vertices are reproduced global symmetries and subsidiary conditions are discu

contractions of low dimensional lie algebras theoretical background of continuous contractions of finite dimensional lie algebras is rigorously formulated and developed in particular known necessary criteria of contractions are collected and new criteria are proposed a number of requisite invariant and semi invariant quantities are calculated for wide classes of lie algebras including all low dimensional lie algebras an algorithm that allows one to handle one parametric contractions is presented and applied to low dimensional lie algebras as a result all one parametric continuous contractions for both the complex and real lie algebras of dimensions not greater than 4 are constructed with intensive usage of necessary criteria of contractions and with studying correspondence between real and complex cases levels and colevels of low dimensional lie algebras are discussed in detail properties of multiparametric and repeated contractions are also investigated

a bayesian analysis of kriging this article is concerned with predicting for gaussian random fields in a way that appropriately deals with uncertainty in the covariance function to this end we analyze the best linear unbiased prediction procedure within a bayesian framework particular attention is paid to the treatment of parameters in the covariance structure and their effect on the quality both real and perceived of the prediction these ideas are implemented using topographical data from davis

s expansion of higher order lie algebras by means of a generalization of the s expansion method we construct a procedure to obtain expanded higher order lie algebras it is shown that the direct product between an abelian semigroup s and a higher order lie algebra g is also a higher order lie algebra from this s expanded lie algebra are obtained resonant submultialgebras and reduced multialgebras of a resonant submultialgebra

the three dimensional real lie algebras and their contractions in this paper the general contractions of the three dimensional real lie algebras are determined a short summary will be given of the history definitions properties examples and applications of contractions of lie algebras so far mostly simple or generalized inonu wigner contractions have been used the three dimensional real lie algebras are classified in such a way that their general contractions can be easily read off all these contractions can be realized by generalized inonu wigner contractions which supports the argument that these are the interesting objects to study

a note on the de la garza phenomenon for locally optimal designs the celebrated de la garza phenomenon states that for a polynomial regression model of degree p 1 any optimal design can be based on at most p design points in a remarkable paper yang ann statist 38 2010 2499 2524 showed that this phenomenon exists in many locally optimal design problems for nonlinear models in the present note we present a different view point on these findings using results about moment theory and chebyshev systems in particular we show that this phenomenon occurs in an even larger class of models than considered so far

designing for a response transformation parameter summary we investigate d optimum designs for experiments in which a linear model holds after an unknown power transformation of the univariate response variable this is a departure from standard d optimal design in which an appropriate scale for the response is assumed known before data collection the design problem that we formulate is intrinsically nonlinear requiring characterization of likely parameter values several applications are presented to illustrate the importance of recognizing the role of response transformations at the design stage

bayesian prediction of deterministic functions with applications to the design and analysis of computer experiments abstract this article is concerned with prediction of a function y t over a multidimensional domain t given the function values at a set of sites t 1 t 2 t n in t and with the design that is with the selection of those sites the motivating application is the design and analysis of computer experiments where t determines the input to a computer model of a physical or behavioral system and y t is a response that is part of the output or is calculated from it following a bayesian formulation prior uncertainty about the function y is expressed by means of a random function y which is taken here to be a gaussian stochastic process the mean of the posterior process can be used as the prediction function t and the variance can be used as a measure of uncertainty this kind of approach has been used previously in bayesian interpolation and is strongly related to the kriging methods used in geostatistics here emphasis is placed on product linear and product cubic correlation func

bayesian estimation and experimental design in linear regression models estimation and design as a bayesian decision problem choice of a prior distribution conjugate prior distributions bayes estimation of the regression parameter optimality and robustness of the bayes estimator bayesian interpretation of estimators using non bayesian prior knowledge bayes estimation in case of prior ignorance further problems the design problem for the linear bayes estimator characterization of optimal designs construction of optimal continuous designs construction of exact optimal designs

maximum entropy sampling and optimal bayesian experimental design when shannon entropy is used as a criterion in the optimal design of experiments advantage can be taken of the classical identity representing the joint entropy of parameters and observations as the sum of the marginal entropy of the observations and the preposterior conditional entropy of the parameters following previous work in which this idea was used in spatial sampling the method is applied to standard parameterized bayesian optimal experimental design under suitable conditions which include non linear as well as linear regression models it is shown in a few steps that maximizing the marginal entropy of the sample is equivalent to minimizing the preposterior entropy the usual bayesian criterion thus avoiding the use of conditional distributions it is shown using this marginal formulation that under normality assumptions every standard model which has a two point prior distribution on the parameters gives an optimal design supported on a single point other results include a new asymptotic formula which applies as the error variance is large and bounds on support size

scale invariances and lamperti transformations for stochastic processes scale invariant processes and hereafter processes with broken versions of this symmetry are studied by means of the lamperti transformation a one to one transformation linking stationary and self similar processes a general overview of the use of the transformation and of the stationary generators it builds is given for modelling and analysis of scale invariance we put an emphasis on generalizations to non strictly scale invariant situations the examples of discrete scale invariance and finite size scale invariance are developed by means of the lamperti transformation framework and some specific examples of processes with these generalized symmetries are given

expanding lie super algebras through abelian semigroups we propose an outgrowth of the expansion method introduced by de azcarraga et al nucl phys b 662 185 2003 the basic idea consists in considering the direct product between an abelian semigroup s and a lie algebra g general conditions under which relevant subalgebras can systematically be extracted from s g are given we show how for a particular choice of semigroup s the known cases of expanded algebras can be reobtained while new ones arise from different choices concrete examples including the m algebra and a d auria fre like superalgebra are considered finally we find explicit nontrace invariant tensors for these s expanded algebras which are essential ingredients in e g the formulation of supergravity theories in arbitrary space time dimensions

generating infinite dimensional algebras from loop algebras by expanding maurer cartan forms it is shown that the expansion methods developed in de azcarraga et al nucl phys b 662 185 2003 class quantum grav 21 s1375 2004 can be generalized so that they permit to study the expansion of algebras of loops both when the compact finite dimensional algebra and the algebra of loops have a decomposition into two subspaces

experimental designs for model discrimination abstract we present designs that perform well for several objectives simultaneously three different approaches are discussed to augment a given design in an optimal way to evaluate a mixture of the various criteria and to optimize one objective subject to achieving a prescribed efficiency level for the others our sample designs are for the situation of discriminating between a second and third degree polynomial fit under the d criterion and geometric mixtures of d criteria

bianchi spaces and their three dimensional isometries as s expansions of two dimensional isometries in this paper we show that certain three dimensional isometry algebras specifically those of type i ii iii and v according to bianchi s classification can be obtained as expansions of the isometries in two dimensions in particular we use the so called s expansion method which makes use of the finite abelian semigroups because it is the most general procedure known until now also it is explicitly shown why it is impossible to obtain the algebras of type iv vi ix as expansions from the isometry algebras in two dimensions all the results are checked with computer programs this procedure shows that the problem of how to relate by an expansion two lie algebras of different dimensions can be entirely solved in particular the procedure can be generalized to higher dimensions which could be useful for diverse physical applications as we discuss in our conclusions

dual formulation of the lie algebra s expansion procedure the expansion of a lie algebra entails finding a new bigger algebra g through a series of well defined steps from an original lie algebra g one incarnation of the method the so called s expansion involves the use of a finite abelian semigroup s to accomplish this task in this paper we put forward a dual formulation of the s expansion method which is based on the dual picture of a lie algebra given by the maurer cartan forms the dual version of the method is useful in finding a generalization to the case of a gauge free differential algebra which in turn is relevant for physical applications in e g supergravity it also sheds new light on the puzzling relation between two chern simons lagrangians for gravity in 2 1 dimensions namely the einstein hilbert lagrangian and the one for the so called exotic gravity

analyzing dispersion effects from replicated factorial experiments recent developments in quality engineering methods have led to considerable interest in the analysis of dispersion effects from designed experiments a commonly used method for identifying important dispersion effects from replicated experiments is based on least squares analysis of the logarithm of the within replication variance bartlett and kendall 1946 box and meyer 1986 introduced a pooling technique for unreplicated two level experiments we extend this to replicated two level experiments and compare its performance with the least squares analysis we show that both of these methods can be obtained as special cases of maximum likelihood estimation under normal theory the pooling technique is generally biased and is not recommended for model identification the least squares analysis performs well as a model identification tool but the estimators can be inefficient in such cases we recommend that the parameters of the identified submodel be estimated by maximum likelihood we derive some prop

generating higher order lie algebras by expanding maurer cartan forms by means of a generalization of the maurer cartan expansion method we construct a procedure to obtain expanded higher order lie algebras the expanded higher order maurer cartan equations for the case g v0 v1 are found a dual formulation for the s expansion multialgebra procedure is also considered the expanded higher order maurer cartan equations are recovered from s expansion formalism by choosing a special semigroup this dual method could be useful in finding a generalization to the case of a generalized free differential algebra which may be relevant for physical applications in e g higher spin gauge theories

geometrical aspects of the lie algebra s expansion procedure in this article it is shown that s expansion procedure affects the geometry of a lie group changing it and leading us to the geometry of another lie group with higher dimensionality a method for determining the semigroup which would provide a lie algebra from another is outlined via an example finally it is proved that a lie algebra obtained from another lie algebra via s expansion is a non simple lie algebra

a new structure for analyzing discrete scale invariant processes covariance and spectra improving the efficiency of discrete scale invariant dsi sequence we consider some flexible sampling of a continuous time dsi process on positive real line with scale greater than one this sampling has the advantage to have a corresponding multi dimensional self similar process this enables us to obtain spectral representation of such sampled dsi process and corresponding spectral density matrix by imposing wide sense markov property on the dsi process we show that the covariance function and the spectral density matrix are characterized by variances and covariances of adjacent samples in the first scale interval finally we present an example as simple brownian motion and provide its simulations to clarify this study we also study the performance of this structure on the s p500 indices for some special period too

heteroscedastic g optimal designs this paper addresses the issue of constructing large sample g optimal designs when the variability of the response varies across a compact design space a useful characterization theorem is presented along with a computer algorithm for generating heteroscedastic g optimal designs to facilitate comparisons between d and g optimal designs atwood s inequality for comparing d and g efficiencies in homoscedastic models is generalized to heteroscedastic models some robustness properties of these designs are presented

a jump type sde approach to real valued self similar markov processes in his 1972 paper john lamperti characterized all positive self similar markov processes as time changes of exponentials of levy processes in the past decade the problem of classifying all non negative self similar markov processes that do not necessarily have zero as a trap has been solved gradually via connections to ladder height processes and excursion theory motivated by a recent article of chaumont rivero panti we classify via jump type sdes the symmetric real valued self similar markov processes that only decrease the absolute value by jumps and leave zero continuously our construction of these self similar processes involves a pseudo excursion construction and singular stochastic calculus arguments ensuring that solutions to the sdes spend zero time at zero to avoid problems caused by a bang bang drift

the usefulness of optimum experimental designs optimum experimental designs were originally developed by kiefer mainly for response surface models this survey of recent developments emphasizes potential or actual usefulness for linear models the construction of exact designs particularly over irregular design regions is stressed as is the blocking of response surface designs other important areas include systematic designs that are robust against trend and designs for mixtures with irregular design regions several industrial examples are mentioned both d and c optimum designs are found for a non linear model of the economic response of cereal production to fertilizer level the c optimum design being for the conditions of maximum economic return locally optimum and bayesian designs are both described similar results for generalized linear models lead to designs for the ld 95 in a logistic model in which male and female subjects respond differently designs with structure in the variance suggest alternatives to the potentially wasteful product designs of taguchi designs for sequential clinical trials to include random balance are presented the last section outlines some applications including life testing and models in which time is a factor

optimal data augmentation strategies for additive models abstract consider an experiment where the factors are measured on a continuous scale and suppose that the experimenter is permitted to augment the existing observations with one or more new data points bondar s universal optimality criterion u optimality suggests that the problem is best studied in the eigenvector coordinate system we proceed by showing how to construct new points that first equate and then jointly increase the smaller eigenvalues of the crossproduct of the independent variables we discuss the limitations of design augmentation strategies based solely on the crossproduct matrix our goals are to equate and minimize the variances of the estimated regression coefficients keep the new points constrained in a prespecified experimental region use as much of the information in the original points as possible and keep the number of required new points as small as possible we offer several data augmentation strategies to meet these requirements as u optimality subsumes each of the d a

an extended quasi likelihood function summary wedderburn s original definition of quasi likelihood for generalized linear models is extended to allow the comparison of variance functions as well as those of linear predictors and link functions the relationship between generalized linear models and the use of transformations of the response variable is explored and the ideas are illustrated by three examples generalized linear models by allowing the full distributional assumption about the random component in the model to be replaced by a much weaker assumption in which only the first and second moments were defined in making this extension wedderburn widened the scope of generalized linear models in a way very similar to that of gauss when he replaced the assumption of normality in classical linear models by that of equal variance for generalized linear models with distributions in the exponential family likelihood ratio and score tests are used for testing hypotheses concerning nested subsets of covariates in the linear predictor and for assessing hypothesized link functions these methods are also applicable with wedderburn s form of quasi likelihood however neither of these methods is suitable for the comparison of different variance functions in this paper we introduce an extended quasi likelihood function which allows for the comparison of various forms of all the components of a generalized linear model i e the linear predictor the link function and the variance function we then apply the ideas to the analysis of several sets of data

combined algorithm to compute d optimal designs algorithmic techniques for computing optimal designs continue being a need in the optimal experimental design field the increasing interest in finding the optimal experimental conditions makes that new methods are demanded for more complex frameworks showing more realistic situations numerical techniques are often the unique viable option for computing these designs since to tackle analytically the problem results impracticable in most of cases wynn fedorov algorithm multiplicative algorithm and their modifications are the more frequently used methods in the literature for computing d optimal designs however they are not always suitable and efficient to compute optimal designs since their procedures are very limited by the computational requirements a new algorithm to obtain d optimal designs is proposed in this paper it is based on combining suitable strategies followed by the traditional algorithms a proof of the convergence is provided and several numerical examples are presented to illustrate its improved results

diagnostics for heteroscedasticity in regression summary for the usual regression model without replication we provide a diagnostic test for heteroscedasticity based on the score statistic a graphical procedure to complement the score test is also presented some key u ords influence linear model residual score test diagnostic methods in linear regression are used to examine the appropriateness of assumptions underlying the modelling process and to locate unusual characteristics of the data that may influence conclusions the recent literature on diagnostics is dominated by studies of methods for the detection of influential observations cook weisberg 1982 provide a review diagnostics for the relevance of specific assumptions however have not received the same degree of attention even though these may be of equal importance our purpose here is to provide appropriate diagnostic techniques to aid in an assessment of the validity of the usual assumption of homoscedasticity when little or no replication is present available methods for studying this assumption include both graphical and nongraphical procedures the usual graphical procedure consists of plotting the ordinary least squares residuals against fitted values or an explanatory variable a megaphone shaped pattern is taken as evidence that the variance depends on the quantity plotted on tlle abscissa weisberg 1980 chapter 6 in 3 we suggest several ways in which this

minimax adjustment technique and fuzzy information abstract in this paper the minimax adjustment technique is generalized to fuzzy information sets using a quadratic loss function and specific ellipsoidal constraints the case of fuzzy information can be reduced to the case of crisp information here the minimax adjustment technique is equivalent to a projection method furthermore a characterization of the solution is given being not far away from an explicit representation applications to statistics and to economics are presented

bayesian d optimal designs on a fixed number of design points for heteroscedastic polynomial models summary we consider design issues in a polynomial regression model where the variance of the response depends on the independent variable exponentially however this dependence is not known precisely and additional parameters are required in the model our design criteria permit various subsets of the parameters to be estimated with different emphasis bayesian d optimal designs on a compact interval with the number of support points restricted to be one more than the degree of the polynomial are found analytically for a large class of priors these designs may or may not be optimal within the class of all designs depending on the prior distribution

lowest dimensional example on non universality of generalized inonu wigner contractions abstract we prove that there exists just one pair of complex four dimensional lie algebras such that a well defined contraction among them is not equivalent to a generalized iw contraction or to a one parametric subgroup degeneration in conventional algebraic terms over the field of real numbers this pair of algebras is split into two pairs with the same contracted algebra the example we constructed demonstrates that even in the dimension four generalized iw contractions are not sufficient for realizing all possible contractions and this is the lowest dimension in which generalized iw contractions are not universal moreover this is also the first example of nonexistence of generalized iw contraction for the case when the contracted algebra is not characteristically nilpotent and therefore admits nontrivial diagonal derivations the lower bound equal to three of nonnegative integer parameter exponents which are sufficient to realize all generalized iw contractions of four dimensional lie algebras is also found

a predictive approach to the bayesian design problem with application to normal regression models a predictive decision theoretic approach is developed for the bayesian design problem the loss functions used are fair bayes or proper scoring rules and are quadratic measures of distance between probability measures optimal bayesian designs are those which minimise the preposterior risk for the decision problem such designs typically depend on both the prior distribution and the loss function the results are applied to certain normal regression models where explicit optimal designs are constructed

weak convergence of positive self similar markov processes and overshoots of levy processes using lamperti s relationship between levy processes and positive self similar markov processes pssmp we study the weak convergence of the law x of a pssmp starting at x 0 in the skorohod space of cadlag paths when x tends to 0 to do so we first give conditions which allow us to construct a cadlag markov process x 0 starting from 0 which stays positive and verifies the scaling property then we establish necessary and sufficient conditions for the laws x to converge weakly to the law of x 0 as x goes to 0 in particular this answers a question raised by lamperti z wahrsch verw gebiete 22 1972 205 225 about the feller property for pssmp at x 0

some guidelines for constructing exact d optimal designs on convex design spaces some problems unique to the construction of n point d optimal designs on convex design spaces are considered multiple point augmentation and exchange algorithms are shown to be more costly and less efficient than the analogous single point procedures moreover some recommendations for improving single point methods are given finally empirical evidence is found that supports the galil and kiefer option for constructing initial designs and powell s optimization method for design augmentation

linear regression analysis using the relative squared error abstract in order to determine estimators and predictors in a generalized linear regression model we apply a suitably defined relative squared error instead of the most frequently used absolute squared error the general solution of a matrix problem is derived leading to minimax estimators and predictors furthermore we consider an important special case where an analogon to a well known relation between estimators and predictors holds and where generalized least squares estimators as well as kuks olman and ridge estimators play a prominent role

stability of the overshoot for levy processes we give equivalences for conditions like x t r r rightarrow 1 and x t r allowbreak r rightarrow 1 where the convergence is in probability or almost sure both as r rightarrow 0 and r rightarrow infty where x is a l e vy process and t r and t r are the first exit times of x out of the strip t y t 0 y leq r and half plane t y t 0 y leq r respectively we also show using a result of kesten that x t r r rightarrow 1 a s as r to 0 is equivalent to x creeping across a level

miscellanea a note on bayesian design for the normal linear model with unknown error variance summary the bayesian theory of optimal experimental design for the normal linear model has been developed under the assumption of known variance the insensitivity of specific design criteria to prior assumptions on the variance distribution has been demonstrated in special cases but a general result showing the way in which bayesian optimal designs are affected by prior information on the variance is lacking this note proves that bayesian designs are insensitive to information about

fluctuation theory and exit systems for positive self similar markov processes for a positive self similar markov process x we construct a local time for the random set of times where the process reaches its past supremum using this local time we describe an exit system for the excursions of x out of its past supremum next we define and study the ladder process r h associated to a positive self similar markov process x namely a bivariate markov process with a scaling property whose coordinates are the right inverse of the local time of the random set and the process x sampled on the local time scale the process r h is described in terms of a ladder process linked to the levy process associated to x via lamperti s transformation in the case where x never hits 0 and the upward ladder height process is not arithmetic and has finite mean we prove the finite dimensional convergence of r h as the starting point of x tends to 0 finally we use these results to provide an alternative proof to the weak convergence of x as the starting point tends to 0 our approach allows us to address two issues that remained open in caballero and chaumont ann probab 34 2006 1012 1034 namely how to remove a redundant hypothesis and how to provide a formula for the entrance law of x in the case where the underlying levy process oscillates

extinction time of non markovian self similar processes persistence annihilation of jumps and the frechet distribution we start by providing an explicit characterization and analytical properties including the persistence phenomena of the distribution of the extinction time mathbb t of a class of non markovian self similar stochastic processes with two sided jumps that we introduce as a stochastic time change of markovian self similar processes for a suitably chosen time change we observe for classes with two sided jumps the following surprising facts on the one hand all the mathbb t s within a class have the same law which we identify in a simple form for all classes and reduces in the spectrally positive case to the frechet distribution on the other hand each of its distribution corresponds to the law of an extinction time of a single markov process without positive jumps leaving the interpretation that the time change has annihilated the effect of positive jumps the example of the non markovian processes associated to levy stable processes is detailed

higher order simple lie algebras it is shown that the non trivial cocycles on simple lie algebras may be used to introduce antisymmetric multibrackets which lead to higher order lie algebras the definition of which is given their generalised jacobi identities turn out to be satisfied by the antisymmetric tensors or higher order structure constants which characterise the lie algebra cocycles this analysis allows us to present a classification of the higher order simple lie algebras as well as a constructive procedure for them our results are synthesised by the introduction of a single complete brst operator associated with each simple algebra

infinite s expansion with ideal subtraction and some applications according to the literature the s expansion procedure involving a finite semigroup is valid no matter what the structure of the original lie super algebra is however when something about the structure of the starting super algebra is known and when certain particular conditions are met the s expansion method with its features of resonance and reduction is able not only to lead to several kinds of expanded super algebras but also to reproduce the effects of the standard as well as the generalized inonu wigner contraction in the present paper we propose a new prescription for s expansion involving an infinite abelian semigroup s and the subtraction of an infinite ideal subalgebra we show that the subtraction of the infinite ideal subalgebra corresponds to a reduction our approach is a generalization of the finite s expansion procedure presented in the literature and it offers an alternative view of the generalized inonu wigner contraction we then show how to write the invariant tensors of

contractions of lie algebras generalized inonu wigner contractions versus graded contractions recently a new notion of contraction has been introduced the purely algebraically defined graded contractions that fall into two disjoint classes continuous and discrete our main result is that all continuous graded contractions can be realized by generalized inonu wigner contractions furthermore we give a complete characterization of the discrete graded contractions via certain higher order identities inherent to the grading group

optimal bayesian designs for models with partially specified heteroscedastic structure we consider the problem of finding a nonsequential optimal design for estimating parameters in a generalized exponential growth model this problem is solved by first considering polynomial regression models with error variances that depend on the covariate value and unknown parameters a bayesian approach is adopted and optimal bayesian designs supported on a minimal number of support points for estimating the coefficients in the polynomial model are found analytically for some criteria the optimal bayesian designs depend only on the expectation of the prior but generally their dependence includes the derivative of the logarithm of the laplace transform of a measure induced by the prior the optimal design for the generalized exponential growth model is then determined from these optimal bayesian designs

law of the absorption time of some positive self similar markov processes let x be a spectrally negative self similar markov process with 0 as an absorbing state in this paper we show that the distribution of the absorption time is absolutely continuous with an infinitely continuously differentiable density we provide a power series and a contour integral representation of this density then by means of probabilistic arguments we deduce some interesting analytical properties satisfied by these functions which include for instance several types of hypergeometric functions we also give several characterizations of the kesten s constant appearing in the study of the asymptotic tail distribution of the absorbtion time we end the paper by detailing some known and new examples in particular we offer an alternative proof of the recent result obtained by bernyk dalang and peskir ann probab 36 2008 1777 1789 regarding the law of the maximum of spectrally positive levy stable processes

spectral analysis of multi dimensional self similar markov processes in this paper we consider a discrete scale invariant dsi process x t t r with scale l 1 we consider a fixed number of observations in every scale say t and acquire our samples at discrete points k k w where is obtained by the equality l t and w 0 1 we thus provide a discrete time scale invariant dt si process x with the parameter space k k w we find the spectral representation of the covariance function of such a dt si process by providing the harmonic like representation of multi dimensional self similar processes spectral density functions of them are presented we assume that the process x t t r is also markov in the wide sense and provide a discrete time scale invariant markov dt sim process with the above scheme of sampling we present an example of the dt sim process simple brownian motion by the above sampling scheme and verify our results finally we find the spectral density matrix of such a dt sim process and show that its associated t dimensional self similar markov process is fully specified by rhj 1 rjh 0 j 0 1 t 1 where rhj is the covariance function of jth and j th observations of the process

the equivalence of constrained and weighted designs in multiple objective design problems abstract several competing objectives may be relevant in the design of an experiment the competing objectives may not be easy to characterize in a single optimality criterion one approach to these design problems has been to weight each criterion and find the design that optimizes the weighted average of the criteria an alternative approach has been to optimize one criterion subject to constraints on the other criteria an equivalence theorem is presented for the bayesian constrained design problem equivalence theorems are essential in verifying optimality of proposed designs especially when as in most nonlinear design problems numerical optimization is required this theorem is used to show that the results of cook and wong on the equivalence of the weighted and constrained problems apply much more generally the results are applied to bayesian nonlinear design problems with several objectives

robust and efficient designs for the michaelis menten model for the michaelis menten model we determine designs that maximize the minimum of the d efficiencies over a certain interval for the nonlinear parameter the best two point designs can be found explicitly and a characterization is given when these designs are optimal within the class of all designs in most cases of practical interest the determined designs are highly efficient and robust with respect to misspecification of the nonlinear parameter the results are illustrated and applied in an example of a hormone receptor assay

coherent dispersion criteria for optimal experimental design we characterize those coherent design criteria which depend only on the dispersion matrix assumed proper and nonsingular of the state of nature which may be a parameter vector or a set of future observables and describe the associated decision problems connections are established with the classical approach to optimal design theory for the normal linear model based on concave functions of the information matrix implications of the theory for more general models are also considered

bayes optimal designs for two and three level factorial experiments abstract two and three level factorial designs are often used for exploratory experiments with many independent variables the purpose of such experiments is to estimate the effects of all active independent variables and their interactions for reasons of economy or other constraints only a fraction of the full number of experimental settings of the independent variables may be run precluding the separate data based estimation of all the effects in this situation of relatively sparse data and many unknown parameters the benefits of reliable prior information used in the estimation and experimental design can be especially significant in this article exact bayes optimal designs of two and three level fractional factorial experiments and of blocked two and three level factorial experiments are derived the optimality criteria used in this process are versions of the bayes criterion introduced by duncan and degroot it is shown that the classical fractional factorial designs for the 2k experime

on construction of markov processes let be the time of hitting 0 for a standard markov process x t with state space 0 probabilities px and sub probability operators ptf x ex f x t t 0 sp t t s conversely given s one may construct an excursion or characteristic measure on path space and a poisson point process y k ito and s watanabe refer to the possibility of using y to construct an extension having the prescribed entrance law in this paper we verify that under quite general conditions this is indeed possible

a generalized action for 2 1 dimensional chern simons gravity we show that the so called semi simple extended poincare ssep algebra in d dimensions can be obtained from the anti de sitter algebra by means of the s expansion procedure with an appropriate semigroup s a general prescription is given for computing casimir operators for s expanded algebras and the method is exemplified for the ssep algebra the s expansion method also allows us to extract the corresponding invariant tensor for the ssep algebra which is a key ingredient in the construction of a generalized action for chern simons gravity in 2 1 dimensions

general properties of the expansion methods of lie algebras the study of the relation between lie algebras and groups and especially the derivation of new algebras from them is a problem of great interest in mathematics and physics because finding a new lie group from an already known one also means that a new physical theory can be obtained from a known one one of the procedures that allow us to do so is called expansion of lie algebras and has been recently used in different physical applications particularly in gauge theories of gravity here we report on further developments of this method required to understand in a deeper way their consequences in physical theories we have found theorems related to the preservation of some properties of the algebras under expansions that can be used as criteria and more specifically as necessary conditions to know if two arbitrary lie algebras can be related by some expansion mechanism formal aspects such as the cartan decomposition of the expanded algebras are also discussed finally an instructive example that allows us to check explicitly all our theoretical results is also provided

e optimal designs for rational models in this paper experimental designs for a rational model y p x q x e are investigated where p x o 1 x p x p and q x 1 p 1 x p q x q are polynomials and e is a random error two approaches bayesian d optimal and bayesian optimal design for extrapolation are examined the first criterion maximizes the expected increase in shannon information provided by the experiment asymptotically and the second minimizes the asymptotic variance of the maximum likelihood estimator mle of the mean response at an extrapolation point x e corresponding locally optimal designs are also discussed conditions are derived under which a p q 1 point design is a locally d optimal design the bayesian d optimal design is shown to be independent of the parameters in p x and to be equally weighted at each support point if the number of support points is the same as the number of parameters in the model the existence and uniqueness of the locally optimal design for extrapolation are proven the number of support points for the locally optimal design for extrapolation is exactly p q 1 these p q 1 design points are proved to be independent of the extrapolation point x e and the parameters in p x the corresponding weights are also independent of the parameters in p x but depend on x e and are not equal