review of options for structural design sensitivity analysis part 1 linear systems the paper reviews options for structural design sensitivity analysis including global finite differences continuum derivatives discrete derivatives and computational or automated differentiation the objective is to put these different approaches to design sensitivity analysis in the context of accuracy and consistency computational cost and implementation options and effort linear static analysis and transient dynamic analysis are reviewed in a separate appendix special attention is paid to the semi analytical method a future paper will address design sensitivity analysis in nonlinear structural problems

interpretable dynamic treatment regimes abstractprecision medicine is currently a topic of great interest in clinical and intervention science a key component of precision medicine is that it is evidence based i e data driven and consequently there has been tremendous interest in estimation of precision medicine strategies using observational or randomized study data one way to formalize precision medicine is through a treatment regime which is a sequence of decision rules one per stage of clinical intervention that map up to date patient information to a recommended treatment an optimal treatment regime is defined as maximizing the mean of some cumulative clinical outcome if applied to a population of interest it is well known that even under simple generative models an optimal treatment regime can be a highly nonlinear function of patient information consequently a focal point of recent methodological research has been the development of flexible models for estimating optimal treatment regimes however in many settings estimati

on asymptotically correct timoshenko like anisotropic beam theory abstract this paper presents a finite element cross sectional beam analysis capable of capturing transverse shear effects the approach uses the variational asymptotic method and can handle beams of general cross sectional shape and arbitrary anisotropic material the work builds on previous works which deal with development of the classical beam theory which includes only extension torsion and bending a timoshenko like formulation is sought to achieve a refined theory with simple boundary conditions apart from some simple special cases it is shown that this problem is overdetermined however it is possible to obtain the best possible solution using the least squares minimization technique the geometrical meaning of the shear variable for this formulation is also derived results are found to be in good agreement with published results for the shear stiffness coefficients for both isotropic and anisotropic beams

automatic differentiation of numerical integration algorithms automatic differentiation ad is a technique for automatically augmenting computer programs with statements for the computation of derivatives this article discusses the application of automatic differentiation to numerical integration algorithms for ordinary differential equations odes in particular the ramifications of the fact that ad is applied not only to the solution of such an algorithm but to the solution procedure itself this subtle issue can lead to surprising results when ad tools are applied to variable stepsize variable order ode integrators the computation of the final time step plays a special role in determining the computed derivatives we investigate these issues using various integrators and suggest constructive approaches for obtaining the desired derivatives

sensitivity analysis of flexible multibody systems using composite materials components in this paper a general formulation for the computation of the first order analytical sensitivities based on the direct method using automatic differentiation of flexible multibody systems is presented the direct method for sensitivity calculation is obtained by differentiating the equations that define the response of the flexible multibody systems of composite materials with respect to the design variables which are the ply orientations of the laminated in order to appraise the benefits of the approach suggested and to highlight the risks of the procedure the analytical sensitivities are compared with the numerical results obtained by using the finite difference method for the beam composite material elements the section properties and their sensitivities are found using an asymptotic procedure that involves a two dimensional 2 d finite element analysis of their cross section the equations of the sensitivities are obtained by automatic differentiation and integrated in time simultaneously with the equations of motion of the multibody systems the equations of motion and the sensitivities of the flexible multibody system are solved and the accelerations velocities and the sensitivities of accelerations and velocities are integrated in time using a multi step multi order integration algorithm through the application of the methodology to two simple flexible multibody systems the difficulties and benefits of the procedure with respect to finite difference approaches or to the direct implementation of the analytic sensitivities are discussed copyright 2008 john wiley sons ltd

estimation and evaluation of linear individualized treatment rules to guarantee performance summary in clinical practice an informative and practically useful treatment rule should be simple and transparent however because simple rules are likely to be far from optimal effective methods to construct such rules must guarantee performance in terms of yielding the best clinical outcome highest reward among the class of simple rules under consideration furthermore it is important to evaluate the benefit of the derived rules on the whole sample and in pre specified subgroups e g vulnerable patients to achieve both goals we propose a robust machine learning method to estimate a linear treatment rule that is guaranteed to achieve optimal reward among the class of all linear rules we then develop a diagnostic measure and inference procedure to evaluate the benefit of the obtained rule and compare it with the rules estimated by other methods we provide theoretical justification for the proposed method and its inference procedure and we demonstrate via simulations its superior performance when compared to existing methods lastly we apply the method to the sequenced treatment alternatives to relieve depression star d trial on major depressive disorder and show that the estimated optimal linear rule provides a large benefit for mildly depressed and severely depressed patients but manifests a lack of fit for moderately depressed patients

tree based methods for individualized treatment regimes individualized treatment rules recommend treatments on the basis of individual patient characteristics a high quality treatment rule can produce better patient outcomes lower costs and less treatment burden if a treatment rule learned from data is to be used to inform clinical practice or provide scientific insight it is crucial that it be interpretable clinicians may be unwilling to implement models they do not understand and black box models may not be useful for guiding future research the canonical example of an interpretable prediction model is a decision tree we propose a method for estimating an optimal individualized treatment rule within the class of rules that are representable as decision trees the class of rules we consider is interpretable but expressive a novel feature of this problem is that the learning task is unsupervised as the optimal treatment for each patient is unknown and must be estimated the proposed method applies to both categorical and continuous treatments and produces favourable marginal mean outcomes in simulation experiments we illustrate it using data from a study of major depressive disorder

modelling financial time series using multifractal random walks abstract multifractal random walks mrw correspond to simple solvable stochastic volatility processes moreover they provide a simple interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations we show that they are able to reproduce most of the recent empirical findings concerning financial time series no correlation between price variations long range volatility correlations and multifractal statistics

using pilot data to size a two arm randomized trial to find a nearly optimal personalized treatment strategy a personalized treatment strategy formalizes evidence based treatment selection by mapping patient information to a recommended treatment personalized treatment strategies can produce better patient outcomes while reducing cost and treatment burden thus among clinical and intervention scientists there is a growing interest in conducting randomized clinical trials when one of the primary aims is estimation of a personalized treatment strategy however at present there are no appropriate sample size formulae to assist in the design of such a trial furthermore because the sampling distribution of the estimated outcome under an estimated optimal treatment strategy can be highly sensitive to small perturbations in the underlying generative model sample size calculations based on standard uncorrected asymptotic approximations or computer simulations may not be reliable we offer a simple and robust method for powering a single stage two armed randomized clinical trial when the primary aim is estimating the optimal single stage personalized treatment strategy the proposed method is based on inverting a plugin projection confidence interval and is thereby regular and robust to small perturbations of the underlying generative model the proposed method requires elicitation of two clinically meaningful parameters from clinical scientists and uses data from a small pilot study to estimate nuisance parameters which are not easily elicited the method performs well in simulated experiments and is illustrated using data from a pilot study of time to conception and fertility awareness

limit lognormal multifractal as an exponential functional the limiting distribution of the limit lognormal multifractal first introduced by mandelbrot statistical models and turbulence m rosenblatt and c van atta eds lecture notes in physics 12 springer new york 1972 p 333 and constructed explicitly by bacry et al phys rev e 64 026103 2001 is investigated using its laplace transform a partial differential equation for the laplace transform is derived and it is shown that multifractality alone does not determine the limiting distribution the increments of the limit multifractal process are strongly stochastically dependent the precise nature of this stochastic dependence structure of increments sdsi is the determining characteristic of the limiting distribution the sdsi of the limit process is quantified by means of two integro differential relations obtained by renormalization in the sense of leipnik j aust math soc b 32 327 347 1991 one is interpreted as a counterpart of the star equation of mandelbrot and the other is shown to be an analogue of the classical girsanov theorem in the weak intermittency limit an approximate single variable equation for the laplace transform is obtained and successfully tested numerically by simulation

interactive model building for q learning evidence based rules for optimal treatment allocation are key components in the quest for efficient effective health care delivery q learning an approximate dynamic programming algorithm is a popular method for estimating optimal sequential decision rules from data q learning requires the modeling of nonsmooth nonmonotone transformations of the data complicating the search for adequately expressive yet parsimonious statistical models the default q learning working model is multiple linear regression which is not only provably misspecified under most data generating models but also results in nonregular regression estimators complicating inference we propose an alternative strategy for estimating optimal sequential decision rules for which the requisite statistical modeling does not depend on nonsmooth nonmonotone transformed data does not result in nonregular regression estimators is consistent under a broader array of data generation models than q learning results in estimated sequential decision rules that have better sampling properties and is amenable to established statistical approaches for exploratory data analysis model building and validation we derive the new method iq learning via an interchange in the order of certain steps in q learning in simulated experiments iq learning improves on q learning in terms of integrated mean squared error and power the method is illustrated using data from a study of major depressive disorder

calculation of sensitivity derivatives in thermal problems by finite differences the transient thermal analysis of large aerospace vehicles such as the space shuttle requires models with thousands of degrees of freedom the design of thermal protection systems for such vehicles requires the repetitive thermal analysis of the vehicle and the calculation of sensitivities derivatives of the transient response with respect to design parameters when the number of design parameters is large the cost of the sensitivity calculations may become prohibitive the present work is concerned with reducing the computational cost and errors in sensitivity calculations with one of the simplest available methods the finite difference approach a technique for calculating simultaneously the nominal and perturbed solutions required for the finite difference derivative is proposed an expression for the optimum value of the perturbation parameter is obtained which permits reducing the computational error an insulated cylinder is used as an example which demonstrates that significant improvements in accuracy and efficiency may be obtained

multifractal stationary random measures and multifractal random walks with log infinitely divisible scaling laws we define a large class of continuous time multifractal random measures and processes with arbitrary log infinitely divisible exact or asymptotic scaling law these processes generalize within a unified framework both the recently defined log normal multifractal random walk j f muzy j delour and e bacry eur j phys b 17 537 2000 e bacry j delour and j f muzy phys rev e 64 026103 2001 and the log poisson product of cylindrical pulses j barral and b b mandelbrot cowles foundation discussion paper no 1287 2001 unpublished our construction is based on some continuous stochastic multiplication as introduced in f schmitt and d marsan eur j phys b 20 3 2001 from coarse to fine scales that can be seen as a continuous interpolation of discrete multiplicative cascades we prove the stochastic convergence of the defined processes and study their main statistical properties the question of genericity universality of limit multifractal processes is addressed within this new framework we finally provide a method for numerical simulations and discuss some specific examples

on the limit lognormal and other limit log infinitely divisible laws the limit log infinitely divisible multifractals of muzy and bacry phys rev e 66 056121 2002 are reviewed and shown to possess novel invariance relations that translate into functional feynman kac equations for the corresponding probability distributions in the special case of the limit lognormal process of mandelbrot in statistical models and turbulence m rosenblatt c van atta eds springer new york 1972 the limit distribution is represented exactly in an operator form using the technique of intermittency expansions a novel representation for the mellin transform of the limit distribution is derived and related to the hurwitz zeta function for application the cumulants of the logarithm of the limit lognormal distribution are computed explicitly

the importance of the selberg integral it has been remarked that a fair measure of the impact of atle selberg s work is the number of mathematical terms that bear his name one of these is the selberg integral an n dimensional generalization of the euler beta integral we trace its sudden rise to prominence initiated by a question to selberg from enrico bombieri more than thirty years after its initial publication in quick succession the selberg integral was used to prove an outstanding conjecture in random matrix theory and cases of the macdonald conjectures it further initiated the study of q analogues which in turn enriched the macdonald conjectures we review these developments and proceed to exhibit the sustained prominence of the selberg integral as evidenced by its central role in random matrix theory calogero sutherland quantum many body systems knizhnik zamolodchikov equations and multivariable orthogonal polynomial theory

functional feynman kac equations for limit lognormal multifractals a novel technique of functional feynman kac equations is developed for the probability distribution of the limit lognormal multifractal process introduced by mandelbrot in statistical models and turbulence m rosenblatt and c van atta eds springer new york 1972 and constructed explicitly by bacry delour and muzy phys rev e 64 026103 2001 the distribution of the process is known to be determined by the complicated stochastic dependence structure of its increments sdsi it is shown that the sdsi has two separate layers of complexity that can be captured in a precise way by a pair of functional feynman kac equations for the laplace transform exact solutions are obtained as power series expansions in the intermittency parameter using a novel intermittency differentiation rule the expansion of the moments gives a new representation of the selberg integral

multifractal random walk we introduce a class of multifractal processes referred to as multifractal random walks mrws to our knowledge it is the first multifractal process with continuous dilation invariance properties and stationary increments mrws are very attractive alternative processes to classical cascadelike multifractal models since they do not involve any particular scale ratio the mrws are indexed by four parameters that are shown to control in a very direct way the multifractal spectrum and the correlation structure of the increments we briefly explain how in the same way one can build stationary multifractal processes or positive random measures

interactive q learning for quantiles abstracta dynamic treatment regime is a sequence of decision rules each of which recommends treatment based on features of patient medical history such as past treatments and outcomes existing methods for estimating optimal dynamic treatment regimes from data optimize the mean of a response variable however the mean may not always be the most appropriate summary of performance we derive estimators of decision rules for optimizing probabilities and quantiles computed with respect to the response distribution for two stage binary treatment settings this enables estimation of dynamic treatment regimes that optimize the cumulative distribution function of the response at a prespecified point or a prespecified quantile of the response distribution such as the median the proposed methods perform favorably in simulation experiments we illustrate our approach with data from a sequentially randomized trial where the primary outcome is remission of depression symptoms supplementary materials for this arti

mellin transform of the limit lognormal distribution the technique of intermittency expansions is applied to derive an exact formal power series representation for the mellin transform of the probability distribution of the limit lognormal multifractal process the negative integral moments are computed by a novel product formula of selberg type the power series is summed in general by means of its small intermittency asymptotic the resulting integral formula for the mellin transform is conjectured to be valid at all levels of intermittency the conjecture is verified partially by proving that the integral formula reproduces known results for the positive and negative integral moments of the limit lognormal distribution and gives a valid characteristic function of the levy khinchine type for the logarithm of the distribution the moment problem for the logarithm of the distribution is shown to be determinate whereas the moment problems for the distribution and its reciprocal are shown to be indeterminate the conjecture is used to represent the mellin transform as an infinite product of gamma factors generalizing selberg s finite product the conjectured probability density functions of the limit lognormal distribution and its logarithm are computed numerically by the inverse fourier transform

optimal dynamic treatment regimes summary a dynamic treatment regime is a list of decision rules one per time interval for how the level of treatment will be tailored through time to an individual s changing status the goal of this paper is to use experimental or observational data to estimate decision regimes that result in a maximal mean response to explicate our objective and to state the assumptions we use the potential outcomes model the method proposed makes smooth parametric assumptions only on quantities that are directly relevant to the goal of estimating the optimal rules we illustrate the methodology proposed via a small simulation