analytic torsion and holomorphic determinant bundles in this paper we prove that in the case of holomorphic locally kahler fibrations the analytic and algebraic geometry constructions of determinant bundles for direct images coincide we calculate the curvature of the holomorphic hermitian connection for the quillen metric on the determinant bundle we study the behavior of the quillen metric under change of metrics in the fibers and also on the twisting vector bundles we thus generalize the conformal anomaly formula to kahler manifolds of arbitrary dimension we also study the quillen metrics on determinants associated with exact sequences of vector bundles we prove that the quillen metric is smooth on the grothendieck knudsen mumford determinant for arbitrary holomorphic fibrations

analytic torsion and holomorphic determinant bundles i bott chern forms and analytic torsion we attach secondary invariants to any acyclic complex of holomorphic hermitian vector bundles on a complex manifold these were first introduced by bott and chern bot c our new definition uses quillen s superconnections we also give an axiomatic characterization of these classes these results will be used in bgs2 and bgs3 to study the determinant of the cohomology of a holomorphic vector bundle

designs for crossvalidating approximation models multifold crossvalidation is routinely used for assessing the prediction error of an approximation model for a black box function despite its popularity this method is known to have high variability to mitigate this drawback we propose an experimental design approach that borrows latin hypercube designs to construct a structured crossvalidation sample such that the input values in each fold achieve uniformity theoretical results show that the estimate of the prediction error of the proposed method has significantly smaller variability than its counterpart under independent and identically distributed sampling numerical examples corroborate the theoretical results copyright 2013 oxford university press

post fisherian experimentation from physical to virtual fisher s pioneering work in design of experiments has inspired further work with broader applications especially in industrial experimentation this article discusses three topics in physical experiments principles of effect hierarchy sparsity and heredity for factorial designs a new method called conditional main effect cme for de aliasing aliased effects and robust parameter design i also review the recent emergence of virtual experiments on a computer some major challenges in computer experiments which must go beyond fisherian principles are outlined

the higher twisted index theorem for foliations abstract given a gerbe l on the holonomy groupoid g of the foliation m f whose pull back to m is torsion we construct a connes map from the twisted dupont sullivan bicomplex of g to the cyclic complex of the l projective leafwise smoothing operators on m f our construction allows to couple the k theory analytic indices of l projective leafwise elliptic operators with the twisted cohomology of b g producing scalar higher invariants finally by adapting the bismut quillen superconnection approach we compute these higher twisted indices as integrals over the ambient manifold of the expected twisted characteristic classes

entropy based importance measure for uncertain model inputs in the information theory entropy is a measure of the uncertainty associated with a random variable to identify the important variables of a system subjected to many random variables a novel entropy based importance measure for random variables is proposed in this paper the method evaluates the effect of a random variable on the output responses by calculating the change of the entropy value this technique focuses on the influence of input uncertainty on the entropy of the output responses and can be easily extended to the case taking the correlations among the random variables into consideration besides the effect of a random variable within any partial region of interest can also be evaluated by the proposed global sensitivity indicator the mathematical properties of the proposed importance measure are investigated and proven in detail three simple numerical examples are employed to demonstrate the applicability of the new importance measure and then a probabilistic risk assessment model is us

kriging hyperparameter tuning strategies response surfaces have been extensively used as a method of building effective surrogate models of high fidelity computational simulations of the numerous types of response surface models kriging is perhaps one of the most effective due to its ability to model complicated responses through interpolation or regression of known data while providing an estimate of the error in its prediction there is however little information indicating the extent to which the hyperparameters of a kriging model need to be tuned for the resulting surrogate model to be effective the following paper addresses this issue by investigating how often and how well it is necessary to tune the hyperparameters of a kriging model as it is updated during an optimization process to this end an optimization benchmarking procedure is introduced and used to assess the performance of five different tuning strategies over a range of problem sizes the results of this benchmark demonstrate the performance gains that can be associated with reducing the complexity of the hyperparameter tuning process for complicated design problems the strategy of tuning hyperparameters only once after the initial design of experiments is shown to perform poorly

analytic fields on riemann surfaces ii the properties of analytic fields on a riemann surface represented by a branch covering of 1 are investigated in detail branch points are shown to correspond to the vertex operators with simple conformal properties as applications we compute determinants of bar partial j operators forzn symmetric surfaces and obtain various representations for the two loop measure in the bosonic string theory together with various identities for theta functions of hyperelliptic surfaces we also present an integral representation for the quantum part of the twist field correlation functions which describe propagation of the string on the orbifold background we also calculate the quantum part of the structure constants of the twist field operator algebra generalizing the results of dixon friedan martinec and shenker

dimensionality reduction using principal component analysis applied to the gradient the cost of dimensionality reduction in aerodynamic design applications involving high dimensional design spaces and computational fluid dynamics is often prohibitive in an attempt to overcome this challenge a new method for dimensionality reduction is presented that scales as p log p where p is the number of design variables it works by taking advantage of adjoint design methods to compute the covariance matrix of the gradient this information is then used with principal component analysis to develop a linear transformation that allows an aerodynamic optimization problem to be reformulated in an equivalent coordinate system of lower dimensionality to demonstrate its feasibility the method is tested on a two dimensional staggered airfoil problem intentionally chosen as an abstraction of a more realistic overwing nacelle integration problem and shown to exhibit similarities with the latter results show that the method rivals typical screening methods used in aerospace engineering in terms of eff

sensitivity analysis and stochastic simulations of non equilibrium plasma flow we study the parametric uncertainties involved in plasma flows and apply stochastic sensitivity analysis to rank the importance of all inputs to guide large scale stochastic simulations specifically we employ different gradient based sensitivity methods namely morris multi element probabilistic collocation method on sparse grids quasi monte carlo and monte carlo methods these approaches go beyond the standard one at a time sensitivity analysis and provide a measure of the non linear interaction effects for the uncertain inputs the objective is to perform systematic stochastic simulations of plasma flows treating only as stochastic processes the inputs with the highest sensitivity index hence reducing substantially the computational cost two plasma flow examples are presented to demonstrate the capability and efficiency of the stochastic sensitivity analysis the first one is a two fluid model in a shock tube whereas the second one is a one fluid two temperature model in flow past a cylinder copyright 2009 john wiley sons ltd

diffusions conditionnelles i hypoellipticite partielle this paper is devoted to the proof of certain results on conditional diffusions by using the malliavin calculus of variations it is shown that under minimal conditions on the vectors fields which define a two component diffusion xt zt and their lie brackets a s for any t 0 the conditional law of xt t 0 given b zs s t a c density

differential k theory and localization formula for eta invariants in this paper we obtain a localization formula in differential k theory for s 1 actions we establish a localization formula for equivariant eta invariants by combining this result with our extension of goette s result on the comparison of two types of equivariant eta invariants an important step in our approach is to construct a pre lambda ring structure in differential k theory

global anomalies on orbifolds we consider global anomalies for heterotic string theory formulated on orbifolds the vanishing of certain characteristic classes in group cohomology provides sufficient conditions for the absence of global anomalies for abelian orbifolds level matching implies these cohomology conditions so suffices for the absence of anomalies for nonabelian orbifolds level matching does not suffice and there are additional constraints we give some examples to illustrate these new constraints

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

the efficiencies of fractional factorial designs a frequently stated advantage of fractional factorial ff designs over one factor at a time 1fat designs is their high relative efficiency we study k factor 2k run designs where k is a power of 2 or is divisible by 4 for which the usually stated relative efficiency is k in favor of the resolution iv ff design over an orthogonal 1fat design we examine other ways to measure efficiency under main effects only modeling in the case when all factors are quantitative which enables rescaling of their settings if both designs are restricted to lie in smallest sized hypercubes or hyperspheres of equal volume then the relative efficiency of the ff design is 1 under the full model k effects active we also show that the designs are identical in an important sense the 1fat design can be rescaled and rotated to become a resolution iv ff design the primary advantage of the ff design lies in its projection properties if at most k factors are expected to be active then under equal volume designs the ef

bayesian calibration of computer models we consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models such models implemented as computer codes are often generic in the sense that by a suitable choice of some of the model s input parameters the code can be used to predict the behaviour of the system in a variety of specific applications however in any specific application the values of necessary parameters may be unknown in this case physical observations of the system in the specific context are used to learn about the unknown parameters the process of fitting the model to the observed data by adjusting the parameters is known as calibration calibration is typically effected by ad hoc fitting and after calibration the model is used with the fitted input values to predict the future behaviour of the system we present a bayesian calibration technique which improves on this traditional approach in two respects first the predictions allow for all sources of uncertainty including the remaining uncertainty over the fitted parameters second they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best fitting parameter values the method is illustrated by using data from a nuclear radiation release at tomsk and from a more complex simulated nuclear accident exercise

sensitivity analysis of distributed erosion models framework 1 we introduce the p r p procedure for analysis of distributed erosion models evaluating separate sensitivities to input fluxes precipitations p to the propensity of soil to surface flow runoff conditions r and to specific erosion properties descriptive parameters p for genericity and easier comparisons between models superparameters of equivalent slope and equivalent erodibility are assembled from innate descriptive parameters parameterization is reduced to four coded integers that are arguments of the soil loss function directional sensitivities are calculated in a deterministic way associated with any selected displacement in parameter space in this multistage and risk orientated procedure special emphasis is placed on trajectories from best case toward worst case scenarios involving one at a time variations and latin hypercube samples sensitivity maps are produced in the superparameter plane tracing risk isovalues and estimating the relative importance of the equivalent parameters and of their spatial distributions

regularisable and minimal orbits for group actions in infinite dimensions we introduce a class of regularisable infinite dimensional principal fibre bundles which includes fibre bundles arising in gauge field theories like yang mills and string theory and which generalise finite dimensional riemannian principal fibre bundles induced by an isometric action we show that the orbits of regularisable bundles have well defined both heat kernel and zeta function regularised volumes we introduce a notion of minimality for these orbits which extend the finite dimensional one our approach uses heat kernel methods and yields both heat kernel obtained via heat kernel regularisation and zeta function obtained via zeta function regularisation minimality for specific values of the parameter for each of these notions we give an infinite dimensional version of hsiang s theorem which extends the finite dimensional case interpreting minimal orbits as orbits with extremal regularised volume

gradient free active subspace construction using morris screening elementary effects among multivariate functions with high dimensional input spaces it is common for functions to vary more strongly in a few dominant directions related to a small number of highly influential parameters in such cases the input dimension may be greatly reduced by constructing a low dimensional response space that is aligned with the directions of strongest dominance this is the basis behind active subspace methods until recently gradient based methods have been employed to construct the active subspace we introduce a gradient free active subspace construction method that avoids the need to sample from the gradient which may not be available via construction of a coarse approximation to the gradient matrix by employing the concept of elementary effects from morris screening procedures in addition we introduce the use of adaptive step sizes and directions when constructing these elementary effects to allow for more accuracy in locally sensitive regions while still covering a substantial amount of the input space this increases algorithmic efficiency by avoiding function evaluations in directions in which the gradient is relatively flat to demonstrate the method we use an elliptic pde example with two correlation lengths to illustrate the effects of differing rates of singular value decay the gradient free active subspace method is compared to a local sensitivity analysis using coordinate reduction this problem is then modified to contain a clearly defined 10 dimensional active subspace for verification of our method on a more complex example

interpolated boundary conditions in plate bending problems using c1 curved finite elements abstract the purpose of this paper is to construct high order c 1 curved finite elements which are useful for the approximate solutions of plate bending problems with clamp or simply support boundary conditions over nonpolygon domains this kind of finite elements is defined over the exact domain of the problem and the corresponding approximate solution is also obtained over the original domain moreover the effect of the numerical quadrature schemes is studied

a note on c1 curved finite element abstract this paper shows that the c 1 curved finite element developed by bernadou 1 in general cannor satisfy the essential boundary conditions on approximate boundary furthermore a modified c 1 curved finite element is given which is compatible with the element of argyis triangle 3 and can satisfy the homogeneous dirichlet boundary conditions on approximate boundary

groupoids and an index theorem for conical pseudo manifolds we define an analytical index map and a topological index map for conical pseudomanifolds these constructions generalize the analogous constructions used by atiyah and singer in the proof of their topological index theorem for a smooth compact manifold m a main ingredient is a non commutative algebra that plays in our setting the role of c 0 t m we prove a thom isomorphism between non commutative algebras which gives a new example of wrong way functoriality in k theory we then give a new proof of the atiyah singer index theorem using deformation groupoids and show how it generalizes to conical pseudomanifolds we thus prove a topological index theorem for conical pseudomanifolds

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

space filling properties of good lattice point sets we study space filling properties of good lattice point sets and obtain some general theoretical results we show that linear level permutation does not decrease the minimum distance for good lattice point sets and we identify several classes of such sets with large minimum distance based on good lattice point sets some maximin distance designs are also constructed

eta invariants of dirac operators on foliated manifolds we define the eta function of dirac operators on foliated manifolds we show that the eta functions are regular at the origin thus defining corresponding eta invariants of foliated manifolds under the hypothesis of invertibility of the operator in question we prove the atiyah singer relative index theorem for dirac operators on foliated manifolds then we discuss the homotopy invariance of the index with respect to secondary data

factorial sampling plans for preliminary computational experiments a computational model is a representation of some physical or other system of interest first expressed mathematically and then implemented in the form of a computer program it may be viewed as a function of inputs that when evaluated produces outputs motivation for this article comes from computational models that are deterministic complicated enough to make classical mathematical analysis impractical and that have a moderate to large number of inputs the problem of designing computational experiments to determine which inputs have important effects on an output is considered the proposed experimental plans are composed of individually randomized one factor at a time designs and data analysis is based on the resulting random sample of observed elementary effects those changes in an output due solely to changes in a particular input advantages of this approach include a lack of reliance on assumptions of relative sparsity of important inputs monotonicity of outputs with respect to inputs or ad

twistor spaces and the general adiabatic expansions abstract we investigate the behavior of derivatives of the fundamental solution of a parabolic equation for the square of dirac operator on a twistor space when the metric is blown up in the base space direction such a blowing up operation is expected to be an effective method for extracting some intrinsic values from various geometric invariants most of whose cores consist of some derivatives of the fundamental solution

dimension reduction for aerodynamic design optimization the search for an optimal design in a high dimensional design space of a multivariate problem requires a sample size proportional or even exponential to the number of variables of the problem this curse of dimensionality places a computational burden on the cost of optimization especially when the problem uses expensive high fidelity simulations and may force one to try to reduce the dimensions of a problem traditional variable screening techniques reduce the dimensionality of the problem by removing variables that seem irrelevant to the design problem this practice fails when all the variables are equally relevant in the problem or when some variables are relevant only in some parts of the design space the present work describes a dimension reduction method called generative topographic mapping based on non linear latent models which transform a high dimensional data set into a low dimensional latent space without removing any variables it is first illustrated on a two dimensional branin function and then applied to a thirty dimensional airfoil problem the method is then compared with a global optimizer a genetic algorithm other dimension reduction methods principle component analysis and gaussian process latent variable models and with kriging surrogate models the method improves when the initial sample used for dimension reduction is filtered to contain only good designs

sensitivity analysis and identification of kinetic parameters in batch fermentation of glycerol a nonlinear dynamical system was established in our preceding work to describe the batch and continuous bioconversions of glycerol to 1 3 propanediol by klebsiella pneumoniae the purpose of this article is to analyze the sensitivity of kinetic parameters of the dynamical system and identify their values from experiment a global sensitivity analysis approach is constructed by combining the local technique with the monte carlo method with only those parameters of higher sensitivity as design variables we propose a parameter identification model and solve it by a gradient based simulated annealing algorithm numerical results show that our methods are feasible and efficient

hybrid reduced order modeling applied to nonlinear models summary reduced order modeling plays an indispensible role for most real world complex models the objective of this manuscript is to hybridize local and global sensitivity analysis methods to enable the application of reduced order modeling to complex nonlinear models often encountered in real system design and analysis calculations for example nuclear reactors this is achieved by first employing local variational methods to identify important nonlinear features of the original model that are required to reach a user defined accuracy for the reduced model this information is obtained by sampling local first order derivatives of a pseudoresponse utilizing a modified representation of an infinite series expansion around some reference point the resulting derivative information is aggregated in a subspace of dimension much less than the dimension of the input parameter space the accuracy of the reduced model can be mathematically quantified using a bounding norm next global sensitivity methods are employed to exhaustively search the reduced subspace for sensitivity information the theory and implementation details of the proposed method are exposed in this manuscript numerical tests based on prototype nonlinear functions and radiation transport models with many input parameters and many responses are conducted as proof of principle copyright 2012 john wiley sons ltd

the atiyah singer index theorem for families of dirac operators two heat equation proofs the purpose of this paper is to give two heat equation proofs of the index theorem of atiyah singer for a family of dirac operators

the atiyah singer theorems a probabilistic approach i the index theorem abstract the atiyah singer index theorem for classical elliptic complexes is proved by using probabilistic methods the general idea is to use a probabilistic construction of the heat equation kernel which permits the direct derivation of the index formulas without using the theory of invariants of gilkey stochastic calculus on the exterior algebra is then used to find the classical local formula for the index theorem the lefschetz fixed point formulas of atiyah singer will be proved in part ii

the mumford form and the polyakov measure in string theory an explicit formula is derived for the mumford form on the moduli space of algebraic curves according to the belavin knizhnik theorem this gives a formula for the polyakov bosonic string measure

a derivative based sensitivity measure of failure probability in the presence of epistemic and aleatory uncertainties in order to analyze the effect of the epistemic uncertainty of random variables distribution parameters on the safety of the structure system a novel sensitivity measure of the failure probability is constructed by integrating the derivative of failure probability in the parameter space compared with the variance based sensitivity index the new derivative based sensitivity measure can be evaluated with less computational cost it is noticed that the ranking of the new derivative based sensitivity measure is the same as that of the variance based one for the problem of the variance based sensitivity index with large computational cost the standard sobol s method is employed and the quasi monte carlo method and double loop point estimate method are then utilized to compute the derivative based sensitivity measure for comparison four examples are employed to demonstrate the reasonability of the proposed sensitivity measure and the efficiency of the proposed method

an index for gauge invariant operators and the dixmier douady invariant let g b be a bundle of compact lie groups acting on a fiber bundle y b in this paper we introduce and study gauge equivariant k theory groups k i g y these groups satisfy the usual properties of the equivariant k theory groups but also some new phenomena arise due to the topological non triviality of the bundle g b as an application we define a gauge equivariant index for a family of elliptic operators p b b b invariant with respect to the action of g b which in this approach is an element of k 0 g b we then give another definition of the gauge equivariant index as an element of k 0 c g the k theory group of the banach algebra c g we prove that k 0 c g k 0 g g and that the two definitions of the gauge equivariant index are equivalent the algebra c g is the algebra of continuous sections of a certain field of c algebras with non trivial dixmier douady invariant the gauge equivariant k theory groups are thus examples of twisted k theory groups which have recently turned out to be useful in the study of ramond ramond fields

the analysis of elliptic families i metrics and connections on determinant bundles in this paper we construct the quillen metric on the determinant bundle associated with a family of elliptic first order differential operators we also introduce a unitary connection on and calculate its curvature our results will be applied to the case of dirac operators in a forthcoming paper

the analysis of elliptic families ii dirac operators eta invariants and the holonomy theorem in this paper we specialize the results obtained in bf1 to the case of a family of dirac operators we first calculate the curvature of the unitary connection on the determinant bundle which we introduced in bf1

a simple algebraic derivation of the covariant anomaly and schwinger term an expression for the curvature of the covariant determinant line bundle is given in even dimensional space time the usefulness is guaranteed by its prediction of the covariant anomaly and schwinger term it allows a parallel derivation of the consistent anomaly and schwinger term and their covariant counterparts which clarifies the similarities and differences between them

construction of maximin distance latin squares and related latin hypercube designs summarymaximin distance latin hypercube designs are widely used in computer experiments yet their construction is challenging based on number theory and finite fields we propose three algebraic methods to construct maximin distance latin squares as special latin hypercube designs we develop lower bounds on their minimum distances the resulting latin squares and related latin hypercube designs have larger minimum distances than existing ones and are especially appealing for high dimensional applications

analytic and topological torsion for manifolds with boundary and symmetry letg be a finite group acting on a riemannian manifoldm by isometries we introduce analytic torsion an m m1 v r z repr g pl torsion pl m m1 v k1 rg poincare torsion pd m m1 v k1 rg and euler characteristic m m1 v repr g for m the disjoint union of m1 and m2 and v an equivariant coefficient system the analytic torsionis defined in terms of the spectrum of the laplace operator the pl torsionis based on the cellular chain complex and poincare torsionmeasures the failure of equivariant poincare duality in the pl setting which does hold in the analytic context denote by repr g the subgroup of repr g generated by the irreducible representations of real or complex type we define an isomorphism

β1 curved finite elements with numerical integration for thin plate and thin shell problems part 2 approximation of thin plate and thin shell problems abstract in this paper we study the approximation of solutions of linear thin shell problems formulated on plane reference domains with curved boundary according to the model of w t koiter sufficient conditions are given which preserve the order of convergence of the method these conditions involve both the approximation of the components of the displacement with straight and curved finite element families of class 1 and the degree of accuracy of the numerical quadrature schemes we conclude by examining various examples as a particular case we apply the results to plate bending problems

the residue of the global η function at the origin where i dvol x l denotes the riemannian measure on m using the calculus of pseudo differential operators depending upon a complex parameter which was developed by seeley 9 one can show that both q s x p and r s p can be meromorphically extended to the complex plane with simple poles at s m n u for n 0 the residues of l s x p at the poles for n 0 m are given by local formulas in the jets of the total symbol of p we define

sensitivity and uncertainty analysis for flexoelectric nanostructures abstract in this paper sensitivity analysis has been applied to identify the key input parameters influencing the energy conversion factor ecf of flexoelectric materials the governing equations of flexoelectricity are modeled by a nurbs based iga formulation exploiting their higher order continuity and hence avoiding a complex mixed formulation the examined input parameters include model and material properties and the sampling has been obtained using the latin hypercube sampling lhs method in the probability space the sensitivity of the model output to each of the input parameters at different aspect ratios of the beam is quantified by three various common methods i e morris one at a time moat pce sobol and extended fourier amplitude sensitivity test efast the numerical results indicate that the flexoelectric constants are the most dominant factors influencing the uncertainties in the energy conversion factor in particular the transversal flexoelectric coefficient h 12 moreover the model parameters also show considerable interaction effects of the material properties

orthogonal central composite designs of the third order in the evaluation of sensitivity and plant growth simulation models abstract the u s department of agriculture has used response surface techniques as applied by baker and bargmann 1981 to plant process simulation models as an aid in the identification of interrelationships among yield and various single valued and functional parameters orthogonal cubic surfaces have provided insight into higher order relationships as well as a measure of the relative sensitivity of yield to experimentally determined parameter values several examples investigate the effectiveness of those higher order surfaces and illustrate how less precise and less costly measurements may be possible in building and using these simulation models

bayesian sparse polynomial chaos expansion for global sensitivity analysis polynomial chaos expansions are frequently used by engineers and modellers for uncertainty and sensitivity analyses of computer models they allow representing the input output relations of computer models usually only a few terms are really relevant in such a representation it is a challenge to infer the best sparse polynomial chaos expansion of a given model input output data set in the present article sparse polynomial chaos expansions are investigated for global sensitivity analysis of computer model responses a new bayesian approach is proposed to perform this task based on the kashyap information criterion for model selection the efficiency of the proposed algorithm is assessed on several benchmarks before applying the algorithm to identify the most relevant inputs of a double diffusive convection model

multi fidelity optimization via surrogate modelling this paper demonstrates the application of correlated gaussian process based approximations to optimization where multiple levels of analysis are available using an extension to the geostatistical method of co kriging an exchange algorithm is used to choose which points of the search space to sample within each level of analysis the derivation of the co kriging equations is presented in an intuitive manner along with a new variance estimator to account for varying degrees of computational noise in the multiple levels of analysis a multi fidelity wing optimization is used to demonstrate the methodology

searching for important factors in simulation models with many factors sequential bifurcation abstract this paper deals with the problem of screening that is how to find the important factors in simulation models that have many for example 300 factors also called simulation parameters or input variables screening assumes that only a few factors are really important parsimony principle this paper solves the screening problem by a novel technique called sequential bifurcation this technique is both effective and efficient that is it does find all important factors yet it requires relatively few simulation runs the technique is demonstrated through a realistic case study concerning a complicated simulation model called image this simulation models the greenhouse phenomenon the worldwide increase of temperatures this case study gives surprising results the technique identifies some factors as being important that the ecological experts initially thought to be unimportant sequential bifurcation assumes that the input output behavior of the simulation model may be approximated by a first order polynomial main effects possibly augmented with interactions between factors the technique is sequential that is it specifies and analyzes simulation runs one after the other

transformations and invariance in the sensitivity analysis of computer experiments summary monotonic transformations are widely employed in statistics and data analysis in computer experiments they are often used to gain accuracy in the estimation of global sensitivity statistics however one faces the question of interpreting results that are obtained on the transformed data back on the original data the situation is even more complex in computer experiments because transformations alter the model input output mapping and distort the estimators this work demonstrates that the problem can be solved by utilizing statistics which are monotonic transformation invariant to do so we offer an investigation into the families of metrics either based on densities or on cumulative distribution functions that are monotonic transformation invariant and we introduce a new generalized family of metrics numerical experiments show that transformations allow numerical convergence in the estimates of global sensitivity statistics both invariant and not in cases in which it would otherwise be impossible to obtain convergence however one fully exploits the increased numerical accuracy if the global sensitivity statistic is monotonic transformation invariant conversely estimators of measures that do not have this invariance property might lead to misleading deductions

the holonomy of the determinant of cohomology of an algebraic bundle the purpose of this note is to remark that theorem 3 7 in 1 when combined with the work of bismut and freed 2 leads in the algebraic case to an improvement of both results concerning the holonomy of determinant line bundles

a flexible uncertainty quantification method for linearly coupled multi physics systems abstract this paper presents a novel approach to building an integrated uncertainty quantification uq methodology suitable for modern day component based approach for multi physics simulation development our hybrid uq methodology supports independent development of the most suitable uq method intrusive or non intrusive for each physics module by providing an algorithmic framework to couple these stochastic modules for propagating global uncertainties we address algorithmic and computational issues associated with the construction of this hybrid framework we demonstrate the utility of such a framework on a practical application involving a linearly coupled multi species reactive transport model

a search grid for parameter optimization as a byproduct of model sensitivity analysis inverse problem solving i e the retrieval of optimal values of model parameters from experimental data remains a bottleneck for modelers therefore a large variety of heuristic optimization algorithms has been developed to deal with the inverse problem however in some cases the use of a grid search may be more appropriate or simply more practical in this paper an approach is presented to improve the selection of the grid points to be evaluated and which does not depend on the knowledge or availability of the underlying model equations it is suggested that using the information acquired through a sensitivity analysis can lead to better grid search results using the sensitivity analysis information a gauss newton like matrix is constructed and the eigenvalues and eigenvectors of this matrix are employed to transform naive search grids into better thought out ones after a theoretical analysis of the approach some computational experiments are performed using a simple linear model as well as more complex nonlinear models

a quantitative model independent method for global sensitivity analysis of model output a new method for sensitivity analysis sa of model output is introduced it is based on the fourier amplitude sensitivity test fast and allows the computation of the total contribution of each input factor to the output s variance the term total here means that the factor s main effect as well as all the interaction terms involving that factor are included although computationally different the very same measure of sensitivity is offered by the indices of sobol the main advantages of the extended fast are its robustness especially at low sample size and its computational efficiency the computational aspects of the extended fast are described these include 1 the definition of new sets of parametric equations for the search curve exploring the input space 2 the selection of frequencies for the parametric equations and 3 the procedure adopted to estimate the total contributions we also address the limitations of other global sa methods and suggest that the total effect indices are id