a quasi newton differential dynamic programming algorithm for discrete time optimal control we develop a quasi newton differential dynamic programming algorithm qddp for discrete time optimal control problems in the spirit of dynamic programming the quasi newton approximations are performed in a stagewise manner we establish the global convergence of the method and also show a superlinear convergence rate among other advantages of the qddp method second derivatives need not be calculated in theory the computational effort of each recursion grows proportionally to the number of stages n whereas with conventional quasi newton techniques which do not take advantage of the optimal control problem structure the growth is as n2 computational results are also reported

robust matched filters the problem of designing robust matched filters for situations in which there is uncertainty in the signal structure or noise statistics is considered two general aspects of this problem are treated first maximin robust designs are characterized for a general hilbert space formulation of the matched filtering problem and explicit solutions are given for two intuitively appealing models for uncertainty these results are seen to generalize earlier results for specific matched filtering problems the second general aspect treated is the application of the theoretical maximin results to the particular problem of designing filters to combat uncertain nonlinear channel distortion channel distortion is modeled by considering an unknown received signal which may differ in l 2 norm from the transmitted or nominal signal by no more than a fixed amount the effect of the channel distortion is seen to be equivalent to that of adding a white noise to the channel whose spectral height depends on the degree of distortion general expressions are developed for the determination of the robust filter and its performance and numerical results are presented for the case of baseband detection in gauss markov noise

consistency of spectral clustering consistency is a key property of all statistical procedures analyzing randomly sampled data surprisingly despite decades of work little is known about consistency of most clustering algorithms in this paper we investigate consistency of the popular family of spectral clustering algorithms which clusters the data with the help of eigenvectors of graph laplacian matrices we develop new methods to establish that for increasing sample size those eigenvectors converge to the eigenvectors of certain limit operators as a result we can prove that one of the two major classes of spectral clustering normalized clustering converges under very general conditions while the other unnormalized clustering is only consistent under strong additional assumptions which are not always satisfied in real data we conclude that our analysis provides strong evidence for the superiority of normalized spectral clustering

convergence rate analysis of the state increment dynamic programming method it is shown that if the discretization of the state space is sufficiently fine and if the limiting trajectory is an interior point of the admissible policies then the state increment dynamic programming technique sidp has linear convergence and the coefficient of convergence can be explicitly related to the control problem components in the course of this analysis it is seen that the sidp method is in essence a nonlinear generalization of the block gauss seidel algorithm for solving linear equations some consequences of this insight are suggested and a computational example comparing sidp with differential dynamic programming is offered

analytic representation of bayes labeling and bayes clustering operators for random labeled point processes clustering algorithms typically group points based on some similarity criterion but without reference to an underlying random process to make clustering algorithms rigorously predictive in fact there exists a probabilistic theory of clustering in the context of random labeled point sets in which clustering error is defined in terms of the process in the present paper given an underlying point process we develop a general analytic procedure for finding an optimal clustering operator the bayes clusterer that corresponds to the bayes classifier in classification theory we provide detailed solutions under gaussian models owing to computational complexity we also develop approximations of the bayes clusterer

bayesian minimum mean square error estimation for classification error part i definition and the bayesian mmse error estimator for discrete classification with the advent of high throughput genomic and proteomic technologies in conjunction with the difficulty in obtaining even moderately sized samples small sample classifier design has become a major issue in the biological and medical communities with small samples training data error estimation becomes mandatory yet none of the popular error estimation techniques have been rigorously designed based on statistical inference and optimization in this investigation we place classifier error estimation into the framework of optimal mean square error mse signal estimation in the presence of uncertainty which results in a bayesian approach to error estimation based on a parameterized family of feature label distributions with the prior distribution of the parameters governing the choice of feature label distribution these bayesian error estimators are optimal when averaged over a given family of distributions unbiased when averaged over a given family and all samples and analytically address a trade off between robustness modeling assumptions and accuracy minimum mean square error in this paper part i of a two part study we define the minimum mean square error mmse error estimator discuss its basic properties provide closed form analytic estimator representation for discrete classifiers with both non informative and informative prior distributions and examine the performance and robustness of the mmse error estimator via simulations in part ii of this paper in this same issue of ieee transactions on signal processing we address all of these issues in particular closed form representation for linear classification in the gaussian model with known and unknown covariance matrices for both the discrete and gaussian cases the mmse error estimator has especially good performance for distributions having moderate true errors

unified lagrangian formulation for solid and fluid mechanics and fsi problems abstract we present a lagrangian monolithic strategy for solving fluid structure interaction fsi problems the formulation is called unified because fluids and solids are solved using the same solution scheme and unknown variables the method is based on a mixed velocity pressure formulation each time step increment is solved via an iterative partitioned two step procedure the particle finite element method pfem is used for solving the fluid parts of the domain while for the solid ones the finite element method fem is employed both velocity and pressure fields are interpolated using linear shape functions for quasi incompressible materials the solution scheme is stabilized via the finite calculus fic method the stabilized elements for quasi incompressible hypoelastic solids and newtonian fluids are called vps s element and vps f element respectively other two non stabilized elements are derived for hypoelastic solids one is based on a velocity formulation v element and the other on a mixed velocity pressure scheme vp element the algorithms for coupling the solid elements with the vps f fluid element are explained in detail the unified formulation is validated by solving benchmark fsi problems and by comparing the numerical solution to the ones published in the literature

minimax linear observers and regulators for stochastic systems with uncertain second order statistics the problem of minimax design of linear observers and regulators for linear time varying multivariable stochastic systems with uncertain models of their second order statistics is treated in this paper general classes of allowable covariance matrices and means of the process and observation noises and of the random initial condition are considered a game formulation of the problem is adopted and it is shown that the optimal filter for the least favorable set of covariances is minimax robust for each of the filtering situations analyzed conditions satisfied by the saddle point solutions are given and their utility for finding the worst case covariances is illustrated by way of several examples of uncertainty classes of practical interest

on minimax robustness a general approach and applications the minimax approach to the design of systems that are robust with respect to modeling uncertainties is studied using a game theoretic formulation in which the performance functional and the sets of modeling uncertainties and admissible design policies are arbitrary the existence and characterization of minimax robust solutions that form saddle points are discussed through various methods that take into account several common features of the games encountered in applications in particular it is shown that if the performance functional and the uncertainty set are convex then a certain type of regularity condition on the functional is sufficient to ensure that the optimal strategy for a least favorable element of the uncertainty set is minimax robust the efficacy of the methods proposed for a general game is tested in the problems of matched filtering wiener filtering quadratic detection and output energy filtering in which uncertainties in their respective signal and noise models are assumed to exist these problems are analyzed in a common hilbert space framework and they serve to point out the advantages and limitations of the proposed techniques

a three dimensional numerical model for incompressible two phase flow of a granular bed submitted to a laminar shearing flow a numerical model for the simulation of incompressible two phase flows of a flat granular bed submitted to a laminar shearing flow is presented considering a two fluid model and a mixed fluid one the governing equations are discretized by a finite element method and a penalisation method is introduced to cope with the incompressibility constraint a regularisation technique is used to deal with the visco plastic behaviour of the granular phase validations are carried out on three flow test cases a bingham fluid between two infinite parallel planes a bingham fluid in a square lid driven cavity and a newtonian fluid over a granular bed in a two dimensional configuration for which we compare our numerical results with existing analytical or numerical results the accuracy and efficiency of the numerical models have been compared for the two formulations of the two phase flow model it turns out that the two fluid model requires ten times more cpu time than the mixed fluid one for a comparable accuracy which can be achieved provided one takes a smaller regularisation parameter in the latter model finally three dimensional computations are presented for the flow of a newtonian fluid over a granular bed in a square and circular cross section ducts

the discrete time maximum principle a survey and some new results in this paper we present a review of the development of the discrete maximum principle in the presentation the emphasis is on a geometrical interpretation the crucial assumptions in the theory developed are pointed out and the attempts to overcome the limitation in the resulting theorems ore exposed following the review we present a new approach to optimization of the multi stage optimization problems called the upper boundary approach the classical methods of solving this problem are shown to fit smoothly into the new approach moreover using this approach a number of new results have been developed among these a new generalized version of the discrete maximum principle the new version does not require the assumption of directional convexity

pac bayesian analysis of co clustering and beyond we derive pac bayesian generalization bounds for supervised and unsupervised learning models based on clustering such as co clustering matrix tri factorization graphical models graph clustering and pairwise clustering we begin with the analysis of co clustering which is a widely used approach to the analysis of data matrices we distinguish among two tasks in matrix data analysis discriminative prediction of the missing entries in data matrices and estimation of the joint probability distribution of row and column variables in co occurrence matrices we derive pac bayesian generalization bounds for the expected out of sample performance of co clustering based solutions for these two tasks the analysis yields regularization terms that were absent in the previous formulations of co clustering the bounds suggest that the expected performance of co clustering is governed by a trade off between its empirical performance and the mutual information preserved by the cluster variables on row and column ids we derive an iterative projection algorithm for finding a local optimum of this trade off for discriminative prediction tasks this algorithm achieved state of the art performance in the movielens collaborative filtering task our co clustering model can also be seen as matrix tri factorization and the results provide generalization bounds regularization terms and new algorithms for this form of matrix factorization the analysis of co clustering is extended to tree shaped graphical models which can be used to analyze high dimensional tensors according to the bounds the generalization abilities of tree shaped graphical models depend on a trade off between their empirical data fit and the mutual information that is propagated up the tree levels we also formulate weighted graph clustering as a prediction problem given a subset of edge weights we analyze the ability of graph clustering to predict the remaining edge weights the analysis of co clustering easily extends to this problem and suggests that graph clustering should optimize the trade off between empirical data fit and the mutual information that clusters preserve on graph nodes

robust wiener kolmogorov theory a minimax formulation is considered for the problem of designing robust linear causal estimators of linear functions of discrete time wide sense stationary signals when knowledge of the signal and or noise spectra is inexact the solution is given under mild regularity conditions in terms of a least favorable pair of spectra thus reducing the minimax problem to a direct maximization problem which in many cases can be solved easily it is noted that this design method leads in particular to robust n step predictors robust causal filters and robust n lag smoothers the method of design is illustrated by a thorough development of the special case of one step noiseless prediction further solutions are given explicitly for the problem of robust causal filtering of an uncertain signal in white noise and numerical examples are given for this case which illustrate the effectiveness of this design

bayesian model averaging for linear regression models abstract we consider the problem of accounting for model uncertainty in linear regression models conditioning on a single selected model ignores model uncertainty and thus leads to the underestimation of uncertainty when making inferences about quantities of interest a bayesian solution to this problem involves averaging over all possible models i e combinations of predictors when making inferences about quantities of interest this approach is often not practical in this article we offer two alternative approaches first we describe an ad hoc procedure occam s window which indicates a small set of models over which a model average can be computed second we describe a markov chain monte carlo approach that directly approximates the exact solution in the presence of model uncertainty both of these model averaging procedures provide better predictive performance than any single model that might reasonably have been selected in the extreme case where there are many candidate predictors but

random set theory and problems of modeling the three or four dimensional world in which we live is full of objects to be measured and summarized very often a parsimonious finite collection of measurements is enough for scientific investigation into an object s genesis and evolution there is a growing need however to describe and model objects through their form as well as their size the purpose of this article is to show the potentials and limitations of a probabilistic and statistical approach collections of objects the data are assimilated to a random set the model whose parameters provide description and or explanation

derivation of stabilized equations for numerical solution of advective diffusive transport and fluid flow problems abstract the concept of the so called artificial or balancing diffusion used to stabilize the numerical solution of advective diffusive transport and fluid flow problems is revised in this paper it is shown that the standard forms of the balancing diffusion terms usually chosen in a heuristic manner can be naturally found by introducing higher order approximations in the derivation of the governing differential equations via standard conservation or equilibrium principles this allows us to reinterpret many stabilization algorithms and concepts used in every day practice by numerical analysts and also provides an expression for computing the stabilization parameter

a lagrangian nodal integration method for free surface fluid flows abstract we present a lagrangian nodal integration method for the simulation of newtonian and non newtonian free surface fluid flows the proposed nodal lagrangian method uses a finite element mesh to discretize the computational domain and to define the linear shape functions for the unknown nodal variables as in the standard particle finite element method pfem in this approach however the integrals are performed over nodal patches and not over elements and strains stresses are defined at nodes and not at gauss points this allows to limit the drawbacks associated with the remeshing and leads to a more accurate stress computation than in the classical elemental pfem several numerical tests in 2d and in 3d are presented to validate the proposed nodal pfem in all cases the method has shown a very good agreement with analytical solutions and with experimental and numerical results from the literature a thorough comparison between nodal and elemental pfems is also presented focusing on crucial issues such as solution accuracy convergence mass conservation and sensitivity to mesh distortion

on the numerical modeling of granular material flows via the particle finite element method pfem abstract the aim of this work is to describe a numerical framework for reliably and robustly simulating the different kinematic conditions exhibited by granular materials while spreading from a stagnant condition when the material is at rest to a transition to granular flow and back to a deposit profile the gist of the employed modeling approach was already presented by the authors in a recent work cante et al 2014 but no proper description of the underlying numerical techniques was provided therein the present paper focuses precisely on the detailed discussion of such numerical techniques as well as on its rigorous validation with the experimental results obtained by lajeunesse et al 2004 the constitutive model is based on the concepts of large strains plasticity the yield surface is defined in terms of the drucker prager yield function endowed with a deviatoric plastic flow and the elastic part by a hypoelastic model the plastic flow condition is assumed nearly incompressible so a u p mixed formulation with a stabilization of the pressure term via the polynomial pressure projection ppp is employed the numerical scheme takes as starting point the particle finite element method pfem in which the spatial domain is continuously redefined by a different nodal reconnection generated by a delaunay triangulation in contrast to classical pfem approximations idelsohn et al 2004 in which the free boundary is obtained by a geometrical technique shape method in this work the boundary is treated as a material surface and the boundary nodes are removed or inserted by means of an error function one of the novelties of this work is the use of the so called impl ex hybrid integration technique to enhance the spectral properties of the algorithmic tangent moduli and thus reduce the number of iterations and robustness of the accompanying newton raphson solution algorithm compared with fully implicit schemes respectively the new set of numerical tools implemented in the pfem algorithm including new discretization techniques the use of a projection of the variables between meshes and the constraint of the free surface instead using classic shape allows us to eliminate the negative jacobians present during large deformation problems which is one of the drawbacks in the simulation of granular flows finally numerical results are compared with the experiments developed in lajeunesse et al 2004 where a granular mass initially confined in a cylindrical container is suddenly allowed to spread by the sudden removal of the container the study is carried out using different geometries with varying initial aspect ratios the excellent agreement between computed and experimental results convincingly demonstrates the reliability of the model to reproduce different kinematic conditions in transient and stationary regimes

model based evaluation of clustering validation measures a cluster operator takes a set of data points and partitions the points into clusters subsets as with any scientific model the scientific content of a cluster operator lies in its ability to predict results this ability is measured by its error rate relative to cluster formation to estimate the error of a cluster operator a sample of point sets is generated the algorithm is applied to each point set and the clusters evaluated relative to the known partition according to the distributions and then the errors are averaged over the point sets composing the sample many validity measures have been proposed for evaluating clustering results based on a single realization of the random point set process in this paper we consider a number of proposed validity measures and we examine how well they correlate with error rates across a number of clustering algorithms and random point set models validity measures fall broadly into three classes internal validation is based on calculating properties of the resulting clusters relative validation is based on comparisons of partitions generated by the same algorithm with different parameters or different subsets of the data and external validation compares the partition generated by the clustering algorithm and a given partition of the data to quantify the degree of similarity between the validation indices and the clustering errors we use kendall s rank correlation between their values our results indicate that overall the performance of validity indices is highly variable for complex models or when a clustering algorithm yields complex clusters both the internal and relative indices fail to predict the error of the algorithm some external indices appear to perform well whereas others do not we conclude that one should not put much faith in a validity score unless there is evidence either in terms of sufficient data for model estimation or prior model knowledge that a validity measure is well correlated to the error rate of the clustering algorithm

engineering applications of discrete time optimal control abstract many problems of design and operation of engineering systems can be formulated as optimal control problems where time has been discretisized this is also true even if time is not involved in the formulation of the problem but rather another one dimensional parameter this paper gives a review of some well known and new results in discrete time optimal control methods applicable to practical problem solving within engineering emphasis is placed on dynamic programming the classical maximum principle and generalized versions of the maximum principle for optimal control of discrete time systems several case studies will illustrate the applicability of the above mentioned methods

computational aspects of discrete time optimal control our opinion is that a little known technique called differential dynamicprogramming offers the potential of enormously expanding the scale of discrete time optimal control problems which are subject to numerical solution among the attractive features of this method are that no discretization of control or state space is used the memory requirements grow as m 2 and the computational requirements as m 3 with m being the dimension of the control variable the successive approximations converge globally under lenient smoothness assumptions and the convergence is quadratic if certain convexity assumptions hold the contribution of the present paper is to demonstrate the practical merit of differential dynamic programming by reporting computational solutions to problems having as many as forty control variables and no particularly convenient structure additionally we give a more algorithmically oriented presentation of the method than hitherto available extend the basic methodto the nonconvex case and give a proof of global convergence

the stagewise kuhn tucker condition and differential dynamic programming the intention of this work is to describe and examine a differential dynamic programming ddp algorithm for constrained discrete time optimal control this algorithm has performed successfully on a large scale reservoir control problem 11 the present paper gives conditions under which convergence to the stationary policy is assured the convergence demonstration hinges upon a notion which we refer to as the stagewise kuhn tucker condition strategies generated to satisfy this condition determine policies which satisfy the conventional kuhn tucker condition this observation may be of wider importance in discrete optimal control theory for the stagewise condition might be a convenient criterion for constructing strategies

optimal classifiers with minimum expected error within a bayesian framework part ii properties and performance analysis in part i of this two part study we introduced a new optimal bayesian classification methodology that utilizes the same modeling framework proposed in bayesian minimum mean square error mmse error estimation optimal bayesian classification thus completes a bayesian theory of classification where both the classifier error and our estimate of the error may be simultaneously optimized and studied probabilistically within the assumed model having developed optimal bayesian classifiers in discrete and gaussian models in part i here we explore properties of optimal bayesian classifiers in particular invariance to invertible transformations convergence to the bayes classifier and a connection to bayesian robust classifiers we also explicitly derive optimal bayesian classifiers with non informative priors and explore relationships to linear and quadratic discriminant analysis lda and qda which may be viewed as plug in rules under gaussian modeling assumptions finally we present several simulations addressing the robustness of optimal bayesian classifiers to false modeling assumptions companion website http gsp tamu edu publications supplementary dalton12a

a dynamic planning technique for continuous activities under multiple resource constrains the solution technique developed in this paper integrates the simplex search algorithm into the recursive calculations of dynamic programming in order to mitigate the curse of dimensionality since differentiation is not required as a means of optimization procedure it is expected that this technique will have an important impact on planning problems such as the multiple resource allocation problems which involve nondifferentiable and or highly nonlinear performance functions applications of the technique to very complex problems seem to confirm the anticipated polynomial average performance

a probabilistic theory of clustering abstract data clustering is typically considered a subjective process which makes it problematic for instance how does one make statistical inferences based on clustering the matter is different with pattern classification for which two fundamental characteristics can be stated 1 the error of a classifier can be estimated using test data and 2 a classifier can be learned using training data this paper presents a probabilistic theory of clustering including both learning training and error estimation testing the theory is based on operators on random labeled point processes it includes an error criterion in the context of random point sets and representation of the bayes optimal cluster operator for a given random labeled point process training is illustrated using a nearest neighbor approach and trained cluster operators are compared to several classical clustering algorithms

optimal control of nonlinear groundwater hydraulics using differential dynamic programming optimal groundwater management models are based on the hydraulic equations of the aquifer system these equations relate the state variables of the groundwater system the head and the decision variables that control the magnitude location and timing of pumping or artificial recharge for the unconfined aquifer these management models are large scale nonlinear programming problems a differential dynamic programming ddp algorithm is used for unsteady nonlinear groundwater management problems due to the stagewise decomposition of ddp the dimensionality problems associated with embedding the hydraulic equations as constraints in the management model are significantly reduced in addition ddp shows a linear growth in computing effort with respect to the number of stages or planning periods and quadratic convergence several example problems illustrate the application of ddp to the optimal control of nonlinear groundwater hydraulics

on the effect of the bulk tangent matrix in partitioned solution schemes for nearly incompressible fluids the purpose of this paper is to study the effect of the bulk modulus on the iterative solution of free surface quasi incompressible fluids using a mixed partitioned scheme a practical rule to set up the value of a pseudo bulk modulus a priori in the tangent bulk stiffness matrix for improving the conditioning of the linear system of algebraic equations is also given the efficiency of the proposed strategy is tested in several problems analyzing the advantage of the modified bulk tangent matrix with regard to the stability of the pressure field the convergence rate and the computational speed of the analyses the technique has been tested on a finite calculus particle finite element method lagrangian formulation but it can be easily extended to other quasi incompressible stabilized finite element formulations copyright c 2014 john wiley sons ltd

improving mass conservation in simulation of incompressible flows summary we propose a technique for improving mass conservation features of fractional step schemes applied to incompressible flows the method is illustrated by using a lagrangian fluid formulation where the mass loss effects are particularly apparent however the methodology is general and could be used for fixed grid approaches the idea consists in reflecting the incompressibility condition already in the intermediate velocity this is achieved by predicting the end of step pressure and using this prediction in the fractional momentum equation the resulting intermediate velocity field is thus much closer to the final incompressible one than that of the standard fractional step scheme in turn the predicted pressure can be used as the boundary condition necessary for the solution of the pressure poisson equation in case a continuous laplacian matrix is employed using this approximation of the end of step incompressible pressure as the essential boundary condition considerably improves the conservation of mass specially for the free surface flows of fluids with low viscosity the pressure prediction does not require the resolution of any additional equations system the efficiency of the method is shown in two examples the first one shows the performance of the method with respect to mass conservation the second one tests the method in a challenging fluid structure interaction benchmark which can be naturally resolved by using the presented approach copyright 2012 john wiley sons ltd

robust design of envelope constrained filters in the presence of input uncertainty the maximum robustness design of envelope constrained filters with uncertain input ecui is formulated as a minimax optimization problem in which the set of feasible filters is characterized by nonsmooth matrix inequalities an efficient design algorithm is developed to solve this problem by use of a newly developed transformation technique the attractive feature of this algorithm is that the ecui filter thus designed can allow for the greatest uncertainty in the input signal while still achieving the acceptable filter performance

polyhedrization of an arbitrary 3d point set abstract given a 3d point set the problem of defining the volume associated dividing it into a set of regions elements and defining a boundary surface is tackled several physical problems need to define volume domains boundary surfaces and approximating functions from a given point distribution this is for instance the case of particle methods in which all the information is the particle positions and there are not boundary surfaces definition until recently all the fem mesh generators were limited to the generation of simple elements as tetrahedral or hexahedral elements or triangular and quadrangular in 2d problems the reason of this limitation was the lack of any acceptable shape function to be used in other kind of geometrical elements nowadays there are several acceptable shape functions for a very large class of polyhedra these new shape functions together with a generalization of the delaunay tessellation presented in this paper gives an optimal marriage and a powerful tool to solve a large variety of physical problems by numerical methods the domain partition into polyhedra presented here is not a standard mesh generation the problem here is for a given node distribution to find a suitable boundary surface and a suitable mesh to be used in the solution of a physical problem by a numerical method to include new nodes or change their positions is not allowed

intrinsically optimal bayesian robust filtering when designing optimal filters it is often unrealistic to assume that the statistical model is known perfectly the issue is then to design a robust filter that is optimal relative to an uncertainty class of processes robust filter design has been treated from minimax best worst case performance and bayesian best average performance perspectives heretofore the bayesian approach has involved finding a model specific optimal filter one that is optimal for some model in the uncertainty class lifting this constraint we optimize over the full class from which the original optimal filters were obtained for instance over all linear filters by extending the original characteristics determining the filter such as the power spectral density to effective characteristics that apply across the uncertainty class we demonstrate for both linear and morphological filtering that an intrinsically optimal bayesian robust filter can be represented in the same form as the standard solution to the optimal filter except via the effective characteristics solutions for intrinsic bayesian robust filters are more transparent and intuitive than solutions for model specific filters and also less tedious because effective characteristics push through the spectral theory into the bayesian setting whereas solutions in the model specific case depend on grinding out the optimization

the particle finite element method a powerful tool to solve incompressible flows with free surfaces and breaking waves summary particle methods are those in which the problem is represented by a discrete number of particles each particle moves accordingly with its own mass and the external internal forces applied to it particle methods may be used for both discrete and continuous problems in this paper a particle method is used to solve the continuous fluid mechanics equations to evaluate the external applied forces on each particle the incompressible navier stokes equations using a lagrangian formulation are solved at each time step the interpolation functions are those used in the meshless finite element method and the time integration is introduced by an implicit fractional step method in this manner classical stabilization terms used in the momentum equations are unnecessary due to lack of convective terms in the lagrangian formulation once the forces are evaluated the particles move independently of the mesh all the information is transmitted by the particles fluid structure interaction problems including free fluid surfaces breaking waves and fluid particle separation may be easily solved with this methodology copyright 2004 john wiley sons ltd

a three dimensional numerical model for dense granular flows based on the µ i rheology this paper presents a three dimensional implementation of the so called i rheology to accurately and efficiently compute steady state dense granular flows the tricky pressure dependent visco plastic behaviour within an incompressible flow solver has been overcome using a regularisation technique along with a complete derivation of the incremental formulation associated with the newton raphson algorithm the computational accuracy and efficiency of the proposed numerical model have been assessed on two representative problems that have an analytical solution then two application examples dealing with actual lab experiments have also been considered the first one concerns a granular flow on a heap and the second one deals with the granular flow around a cylinder in both configurations the obtained computational results are in good agreement with available experimental data

model selection and accounting for model uncertainty in graphical models using occam s window abstract we consider the problem of model selection and accounting for model uncertainty in high dimensional contingency tables motivated by expert system applications the approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic p values leading to the selection of a single model inference is then conditional on the selected model the sampling properties of such a strategy are complex and the failure to take account of model uncertainty leads to underestimation of uncertainty about quantities of interest in principle a panacea is provided by the standard bayesian formalism that averages the posterior distributions of the quantity of interest under each of the models weighted by their posterior model probabilities furthermore this approach is optimal in the sense of maximizing predictive ability but this has not been used in practice because computing the posterior model probabilities is hard and the number of models is very large often greater than 1

on necessary optimality conditions in discrete control systems the paper deals with a nonlinear discrete time optimal control problem with a cost functional of terminal type using a new variation of the control and new properties of optimal controls we prove the linearised optimality conditions extending such classical optimality conditions along with this various optimality conditions of quasi singular controls are obtained finally the examples illustrating the rich content of the obtained results are illustrated

optimization of linear filters under power spectral density stabilization geometric mean filters compose a family of filters indexed by a parameter k varying between 0 and 1 they have been used to provide frequency based filtering that mitigates the noise suppression of the optimal linear wiener filter in the blurred signal plus noise model for k 0 and k 1 the geometric mean filter gives the inverse filter and the wiener filter for the model respectively the geometric mean for k 1 2 has previously been derived as the optimal linear filter for the model under power spectral density psd equalization this constraint requires the psd of the filtered signal to be equal to the psd of the uncorrupted signal that it estimates this paper defines the notion of psd stabilization in which the psd of the restored signal is equal to a predetermined function times the psd of the uncorrupted signal a particular parameterized stabilization function yields the geometric mean family as the optimal linear filter for the model under psd stabilization relative to unconstrained optimization geometric means are suboptimal however we consider a parameterized model for which the noise is such that the geometric mean filters provide optimal linear filtering in the altered signal plus noise model for which the geometric mean is optimal the blur is the same as the original model in which the geometric mean is defined but the noise psd is a function of the fourier transform of the blur and the psd of the original noise since the altered model depends on k we consider a robustness question what kind of suboptimality results from applying the geometric mean for k sub 1 to the model fur which the geometric mean for k sub 2 is optimal

the application of optimal control methodology to nonlinear programming problems dynamic programming techniques have proven to be more successful than alternative nonlinear programming algorithms for solving many discrete time optimal control problems the reason for this is that because of the stagewise decomposition which characterizes dynamic programming the computational burden grows approximately linearly with the numbern of decision times whereas the burden for other methods tends to grow faster e g n3 for newton s method the idea motivating the present study is that the advantages of dynamic programming can be brought to bear on classical nonlinear programming problems if only they can somehow be rephrased as optimal control problems

hierarchical clustering given confidence intervals of metric distances this paper considers metric the exact dissimilarities between pairs of points are not unknown but known to belong to some interval the goal is to study methods for the determination of hierarchical clusters i e a family of nested partitions indexed by a resolution parameter induced from the given distance intervals of the dissimilarities our construction of hierarchical clustering methods is based on defining admissible methods to be those methods that satisfy the axioms of value nodes in a metric space with two nodes are clustered together at the convex combination of the upper and lower bounds determined by a parameter and transformation when both distance bounds are reduced the output may become more clustered but not less two admissible methods are constructed and are shown to provide universal bounds in the space of admissible methods practical implications are explored by clustering moving points via snapshots and by clustering coauthorship networks representing collaboration between researchers from different communities the proposed clustering methods succeed in identifying underlying hierarchical clustering structures via the maximum and minimum distances in all snapshots as well as in differentiating collaboration patterns in journal publications between different research communities based on bounds of network distances

integration of accelerometer data filter analysis and design using riccati solutions the adjustment and integration of noisy accelerometer data is formulated as a discrete time optimal control problem which requires the minimization of a quadratic performance measure subject to linear dynamics the algebraic riccati equation associated with this problem is solved by expressing the entries of the riccati matrix explicitly in terms of the weights in the quadratic performance criterion steady state feedback gains are thus easily computed as functions of the weights the frequency domain analysis of the adjustment procedure provides the basis for selecting appropriate weights

optimal predictive model selection often the goal of model selection is to choose a model for future prediction and it is natural to measure the accuracy of a future prediction by squared error loss under the bayesian approach it is commonly perceived that the optimal predictive model is the model with highest posterior probability but this is not necessarily the case in this paper we show that for selection among normal linear models the optimal predictive model is often the median probability model which is defined as the model consisting of those variables which have overall posterior probability greater than or equal to 1 2 of being in a model the median probability model often differs from the highest probability model

unified lagrangian formulation for elastic solids and incompressible fluids application to fluid structure interaction problems via the pfem abstract we present a general lagrangian formulation for treating elastic solids and quasi fully incompressible fluids in a unified form the formulation allows to treat solid and fluid subdomains in a unified manner in fluid structure interaction fsi situations in our work the fsi problem is solved via the particle finite element method pfem the pfem is an effective technique for modeling complex interactions between floating and submerged bodies and free surface flows accounting for splashing of waves large motions of the bodies and frictional contact conditions applications of the unified lagrangian formulation to a number of fsi problems are given

3d regularized μ i rheology for granular flows simulation abstract this paper proposes two regularized models of the i rheology and shows their application to the numerical simulation of 3d dense granular flows the proposed regularizations are inspired by the papanastasiou and bercovier engleman methods typically used to approximate the bingham law the key idea is to keep limited the value of the apparent viscosity for low shear rates without introducing a fixed cutoff the proposed techniques are introduced into the particle finite element method pfem framework to deal with the large deformations expected in free surface granular flows after showing the numerical drawbacks associated to the standard i rheology the two regularization strategies are derived and discussed the regularized i rheology is then applied to the simulation of the collapse of 2d and 3d granular columns the numerical results show that the regularization techniques improve substantially the conditioning of the linear system without affecting the solution accuracy a good agreement with the experimental tests and other numerical methods is obtained in all the analyzed problems

a lagrangian finite element approach for the analysis of fluid structure interaction problems a lagrangian finite element method for the analysis of incompressible newtonian fluid flows based on a continuous re triangulation of the domain in the spirit of the so called particle finite element method is here revisited and applied to the analysis of the fluid phase in fluid structure interaction problems a new approach for the tracking of the interfaces between fluids and structures is proposed special attention is devoted to the mass conservation problem it is shown that despite its lagrangian nature the proposed combined finite element particle method is well suited for large deformation fluid structure interaction problems with evolving free surfaces and breaking waves the method is validated against the available analytical and numerical benchmarks copyright 2010 john wiley sons ltd

quantifying the objective cost of uncertainty in complex dynamical systems real world problems often involve complex systems that cannot be perfectly modeled or identified and many engineering applications aim to design operators that can perform reliably in the presence of such uncertainty in this paper we propose a novel bayesian framework for objective based uncertainty quantification uq which quantifies the uncertainty in a given system based on the expected increase of the operational cost that it induces this measure of uncertainty called mocu mean objective cost of uncertainty provides a practical way of quantifying the effect of various types of system uncertainties on the operation of interest furthermore the proposed uq framework provides a general mathematical basis for designing robust operators and it can be applied to diverse applications including robust filtering classification and control we demonstrate the utility and effectiveness of the proposed framework by applying it to the problem of robust structural intervention of gene regulatory networks an important application in translational genomics

robust multiple input matched filtering frequency and time domain results robust matched filtering is considered for multiple input systems with problems formulated in both frequency and time domains being given specific treatment robust solutions are found for bounded classes containing well defined but not exactly specified input characteristics several properties for some special cases of interest are examined and an example is given to illustrate the usefulness of the results finally the results are applied to a narrowband spatial array system for which the robust scheme has an interesting and useful characteristic