bayesian feature selection with strongly regularizing priors maps to the ising model identifying small subsets of features that are relevant for prediction and classification tasks is a central problem in machine learning and statistics the feature selection task is especially important and computationally difficult for modern data sets where the number of features can be comparable to or even exceed the number of samples here we show that feature selection with bayesian inference takes a universal form and reduces to calculating the magnetizations of an ising model under some mild conditions our results exploit the observation that the evidence takes a universal form for strongly regularizing priors priors that have a large effect on the posterior probability even in the infinite data limit we derive explicit expressions for feature selection for generalized linear models a large class of statistical techniques that includes linear and logistic regression we illustrate the power of our approach by analyzing feature selection in a logistic regression based classifier trained to distinguish between the letters b and d in the notmnist data set

a finite element method for the simulation of strong and weak discontinuities in solid mechanics in this paper we introduce and analyze a finite element method for elasticity problems with interfaces the method allows for discontinuities internal to the elements in the approximation across the interface we propose a general approach that can handle both perfectly and imperfectly bonded interfaces without modifications of the code for the case of linear elasticity we show that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh we present numerical examples for the linear case as well as for contact and crack propagation model problems

distributed trace estimation under timing mismatch and channel distortion in conservative or complete trace based distributed fault diagnosis it is common to compute for each component a preliminary local estimate consisting of all possible traces that can generate the same local symptom i e a collection of sequences of observable events as the one being received from that component up to a specific time instant then communication among local trace estimators can be used to refine those preliminary local estimates an approach has been proposed by su and wonham to perform such refinement in terms of achieving global or local consistency among local estimates but that approach does not consider timing mismatch and channel distortion in the process of collecting local symptoms which may result in incorrect estimates in practical applications in this paper we will provide a new approach to handle trace estimation under timing mismatch and channel distortion

modeling three dimensional crack propagation a comparison of crack path tracking strategies the development of a new finite element technique for the simulation of discontinuous failure phenomena in three dimensions is the key objective of this study in contrast to the widely used extended finite element technique we apply a purely deformation based strategy based on an independent interpolation of the deformation field on both sides of the discontinuity this method has been applied successfully for two dimensional crack propagation problems in the past however when it comes to three dimensional failure phenomena it faces the same difficulties as the extended finite element method unlike in two dimensions the characterization for the three dimensional failure surface is non unique and the tracking of the discrete crack can be performed in several conceptually different ways in this work we review the four most common three dimensional crack tracking strategies we perform a systematic comparison in terms of standard algorithmic quality measures such as mesh independency efficiency robustness stability and computational cost moreover we discuss more specific issues such as crack path continuity and integratability in commercial finite element packages the features of the suggested crack tracking algorithms will be elaborated by means of characteristic benchmark problems in failure analysis copyright 2008 john wiley sons ltd

hp generalized fem and crack surface representation for non planar 3 d cracks a high order generalized finite element method gfem for non planar three dimensional crack surfaces is presented discontinuous p hierarchical enrichment functions are applied to strongly graded tetrahedral meshes automatically created around crack fronts the gfem is able to model a crack arbitrarily located within a finite element fe mesh and thus the proposed method allows fully automated fracture analysis using an existing fe discretization without cracks we also propose a crack surface representation that is independent of the underlying gfem discretization and controlled only by the physics of the problem the representation preserves continuity of the crack surface while being able to represent non planar non smooth crack surfaces inside of elements of any size the proposed representation also provides support for the implementation of accurate robust and computationally efficient numerical integration of the weak form over elements cut by the crack surface numerical simulations using the proposed gfem show high convergence rates of extracted stress intensity factors along non planar curved crack fronts and the robustness of the method copyright 2008 john wiley sons ltd

a significance test for the lasso in the sparse linear regression setting we consider testing the significance of the predictor variable that enters the current lasso model in the sequence of models visited along the lasso solution path we propose a simple test statistic based on lasso fitted values called the covariance test statistic and show that when the true model is linear this statistic has an exp 1 asymptotic distribution under the null hypothesis the null being that all truly active variables are contained in the current lasso model our proof of this result for the special case of the first predictor to enter the model i e testing for a single significant predictor variable against the global null requires only weak assumptions on the predictor matrix x on the other hand our proof for a general step in the lasso path places further technical assumptions on x and the generative model but still allows for the important high dimensional case p n and does not necessarily require that the current lasso model achieves perfect recovery of the truly active variables of course for testing the significance of an additional variable between two nested linear models one typically uses the chi squared test comparing the drop in residual sum of squares rss to a formula see text distribution but when this additional variable is not fixed and has been chosen adaptively or greedily this test is no longer appropriate adaptivity makes the drop in rss stochastically much larger than formula see text under the null hypothesis our analysis explicitly accounts for adaptivity as it must since the lasso builds an adaptive sequence of linear models as the tuning parameter decreases in this analysis shrinkage plays a key role though additional variables are chosen adaptively the coefficients of lasso active variables are shrunken due to the formula see text penalty therefore the test statistic which is based on lasso fitted values is in a sense balanced by these two opposing properties adaptivity and shrinkage and its null distribution is tractable and asymptotically exp 1

on effective computation of supremal local supports in distributed diagnosis it may be useful to achieve local consistency among local estimates for that purpose the computational procedure for local consistency cplc was proposed to achieve the supremal local support which represents one type of local consistency it has been shown that if cplc terminates then the result is in fact the supremal local support however in this paper it is shown that even if all initial estimates are regular languages the termination of cplc is undecidable moreover these difficulties are not confined to this specific procedure it is undecidable whether the supremal local support corresponding to an arbitrary collection of regular initial languages is componentwise empty consequently the supremal local support is effectively uncomputable on the other hand a sufficient condition is given which guarantees that cplc terminates and that the supremal local support can be computed in time linear in the number of component diagnosers

arc and path consistence revisited mackworth and freuder have analyzed the time complexity of several constraint satisfaction algorithms 5 we present here new algorithms for arc and path consistency and show that the arc consistency algorithm is optimal in time complexity and of the same order space complexity as the earlier algorithms a refined solution for the path consistency problem is proposed however the space complexity of the path consistency algorithm makes it practicable only for small problems these algorithms are the result of the synthesis techniques used in image a general constraint satisfaction system and local consistency methods 3

occam factors and model independent bayesian learning of continuous distributions learning of a smooth but nonparametric probability density can be regularized using methods of quantum field theory we implement a field theoretic prior numerically test its efficacy and show that the data and the phase space factors arising from the integration over the model space determine the free parameter of the theory smoothness scale self consistently this persists even for distributions that are atypical in the prior and is a step towards a model independent theory for learning continuous distributions finally we point out that a wrong parametrization of a model family may sometimes be advantageous for small data sets

dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment summary a methodology is developed for switching from a continuum to a discrete discontinuity where the governing partial dierential equation loses hyperbolicity the approach is limited to rate independent materials so that the transition occurs on a set of measure zero the discrete discontinuity is treated by the extendednite element method xfem whereby arbitrary discontinuities can be incorporated in the model without remeshing loss of hyperbolicity is tracked by a hyperbolicity indicator that enables both the crack speed and crack direction to be determined for a given material model a new method was developed for the case when the discontinuity ends within an element it facilitates the modelling of crack tips that occur within an element in a dynamic setting the method is applied to several dynamic crack growth problems including the branching of cracks copyright 2003 john wiley sons ltd

probabilistic detection of fsm single state transition faults based on state occupancy measurements this note discusses a probabilistic methodology for detecting single permanent or transient functional changes in the state transition mechanism of a deterministic finite state machine fsm the associated probabilistic detector observes the empirical frequencies with which different states are occupied and detects faults by analyzing the discrepancy between the observed state occupancy measurements and the expected frequencies in addition to state occupancy measurements the detector requires a statistical characterization of the input but does not need to know the order with which states appear or the exact input sequence that is applied to the fsm these features can be useful in settings where the input state order may not be known due to synchronization communication or other constraints

element free galerkin methods for static and dynamic fracture abstract element free galerkin efg methods are presented and applied to static and dynamic fracture problems efg methods which are based on moving least square mls interpolants require only nodal data no element connectivity is needed the description of the geometry and numerical model of the problem consists only of a set of nodes and a description of exterior boundaries and interior boundaries from any cracks this makes the method particularly attractive for growing crack problems since only minimal remeshing is needed to follow crack growth in moving least square interpolants the dependent variable at any point is obtained by minimizing a function in terms of the nodal values of the dependent variable in the domain of influence of the point numerical examples involving fatigue crack growth and dynamic crack propagation are presented to illustrate the performance and potential of this method

diagnosis of discrete event systems from uncertain temporal observations observations play a major role in diagnosis the nature of an observation varies according to the class of the considered system in static systems an observation is the value of a variable at a single time point in dynamic continuous systems such a value is observed over a time interval in discrete event systems an observation consists of a sequence of temporally ordered events in any case what is observed is assumed not to be ambiguous this certainty principle whilst being a useful simplification for a variety of contexts may become inappropriate for a wide range of real systems where the communication between the system and the observer is either bound to generate spurious messages to randomly lose messages or to lose temporal constraints among them consequently the observation may be underconstrained to cope with this uncertainty a number of principles affecting both the observations and the modeled behavior of a system are introduced that are independent of any specific processing technique furthermore the notion of an uncertain temporal observation for discrete event systems is introduced and accommodated within a graph whose nodes are labeled by uncertain messages while edges define a partial temporal ordering among messages this way an uncertain observation implicitly defines a finite set of observations in the traditional sense thus solving an uncertain diagnostic problem amounts to solving at one time several traditional diagnostic problems the notion of an uncertain observation is further generalized to that of a complex observation both notions can be exploited by any diagnostic approach pertinent to discrete event systems complex observations are contextualized in the framework of diagnosis of active systems and substantiated by a sample application in the domain of power transmission networks

dynamic fracture using element free galerkin methods the element free galerkin method for dynamic crack propagation is described and applied to several problems this method is a gridless method which facilitates the modelling of growing crack problems because it does not require remeshing the growth of the crack is modelled by extending its surfaces the essential feature of the method is the use of moving least squares interpolants for the trial and test functions in these interpolants the dependent variable is obtained at any point by minimizing a weighted quadratic form involving the nodal variables within a small domain surrounding the point the discrete equations are obtained by a galerkin method the procedures for modelling dynamic crack propagation based on dynamic stress intensity factors are also described

parametric inference in the large data limit using maximally informative models motivated by data rich experiments in transcriptional regulation and sensory neuroscience we consider the following general problem in statistical inference when exposed to a high dimensional signal s a system of interest computes a representation r of that signal which is then observed through a noisy measurement m from a large number of signals and measurements we wish to infer the filter that maps s to r however the standard method for solving such problems likelihood based inference requires perfect a priori knowledge of the noise function mapping r to m in practice such noise functions are usually known only approximately if at all and using an incorrect noise function will typically bias the inferred filter here we show that in the large data limit this need for a precharacterized noise function can be circumvented by searching for filters that instead maximize the mutual information i m r between observed measurements and predicted representations moreover if the correct filter lies within the space of filters being explored maximizing mutual information becomes equivalent to simultaneously maximizing every dependence measure that satisfies the data processing inequality it is important to note that maximizing mutual information will typically leave a small number of directions in parameter space unconstrained we term these directions diffeomorphic modes and present an equation that allows these modes to be derived systematically the presence of diffeomorphic modes reflects a fundamental and nontrivial substructure within parameter space one that is obscured by standard likelihood based inference

a generalized finite element method for the simulation of three dimensional dynamic crack propagation this paper is aimed at presenting a partition of unity method for the simulation of three dimensional dynamic crack propagation the method is a variation of the partition of unity finite element method and hp cloud method in the context of crack simulation this method allows for modeling of arbitrary dynamic crack propagation without any remeshing of the domain in the proposed method the approximation spaces are constructed using a partition of unity pu and local enrichment functions the pu is provided by a combination of shepard and finite element partitions of unity this combination of pus allows the inclusion of arbitrary crack geometry in a model without any modification of the initial discretization it also avoids the problems associated with the integration of moving least squares or conventional shepard partitions of unity used in several meshless methods the local enrichment functions can be polynomials or customized functions these functions can efficiently approximate the singular fields around crack fronts the crack propagation is modeled by modifying the partition of unity along the crack surface and does not require continuous remeshings or mappings of solutions between consecutive meshes as the crack propagates in contrast with the boundary element method the proposed method can be applied to any class of problems solvable by the classical finite element method in addition the proposed method can be implemented into most finite element data bases several numerical examples demonstrating the main features and computational efficiency of the proposed method for dynamic crack propagation are presented

element local level set method for three dimensional dynamic crack growth summary an approximate level set method for three dimensional crack propagation is presented in this method the discontinuity surface in each cracked element is defined by element local level sets ellss the local level sets are generated by a fitting procedure that meets the fracture directionality and its continuity with the adjacent element crack surfaces in a least square sense a simple iterative procedure is introduced to improve the consistency of the generated element crack surface with those of the adjacent cracked elements the discrete discontinuity is treated by the phantom node method which is a simplified version of the extended finite element method xfem the ells method and the phantom node technology are combined for the solution of dynamic fracture problems numerical examples for three dimensional dynamic crack propagation are provided to demonstrate the effectiveness and robustness of the proposed method copyright q 2009 john wiley sons ltd

a uniform strain hexahedron and quadrilateral with orthogonal hourglass control the treatment of zero energy modes which arise due to one point integration of first order isoparametric finite elements is addressed a method for precisely isolating these modes for arbitrary geometry is developed two hourglass control schemes viscous and elastic are presented and examined in addition a convenient one point integration scheme which analytically integrates the element volume and uniform strain modes is presented

3d crack propagation in unreinforced concrete a two step algorithm for tracking 3d crack paths tensile failure of unreinforced concrete involves progressive micro cracking and the related strain softening can coalesce into geometrical discontinuities which separate the material advanced mechanical theories and numerical schemes are required to efficiently and adequately represent crack propagation in 3d in this paper we use the concept of strong discontinuities to model concrete failure we introduce a cohesive fracture process zone which is characterized by a transversely isotropic traction separation law we combine the cohesive crack concept with the partition of unity finite element method where the finite element space is enhanced by the heaviside function the concept is implemented for tetrahedral elements and the failure initialization is based on the simple non local rankine criterion for each element we assume the embedded discontinuity to be flat in the reference configuration which leads to a non smooth crack surfaces approximation in 3d in general different concepts for tracking non planar cracks in 3d are reviewed in addition we propose a two step algorithm for tracking the crack path where a predictor step defines discontinuities according to the non local failure criterion and a corrector step draws in non local information of the existing discontinuities in order to predict a closed 3d crack surface implementation details are provided the proposed framework is used to analyze the predictability of concrete failure by two benchmark examples i e the nooru moharned test and the brokenshire test we compare our numerical results which are mesh independent with experimental data and numerical results adopted from the literature

mass lumping strategies for x fem explicit dynamics application to crack propagation this paper deals with the numerical modelling of cracks in the dynamic case using the extended finite element method more precisely we are interested in explicit algorithms we prove that by using a specific lumping technique the critical time step is exactly the same as if no crack were present this somewhat improves a previous result for which the critical time step was reduced by a factor of square root of 2 from the case with no crack the new lumping technique is obtained by using a lumping strategy initially developed to handle elements containing voids to be precise the results obtained are valid only when the crack is modelled by the heaviside enrichment note also that the resulting lumped matrix is block diagonal blocks of size 2 2 for constant strain elements linear simplex elements the critical time step is not modified when the element is cut thanks to the lumped mass matrix the critical time step never tends to zero moreover the lumping techniques conserve kinetic energy for rigid motions in addition tensile stress waves do not propagate through the discontinuity hence the lumping techniques create neither error on kinetic energy conservation for rigid motions nor wave propagation through the crack both these techniques will be used in a numerical experiment copyright 2007 john wiley sons ltd

a two scale generalized finite element approach for modeling localized thermoplasticity summary predicting localized nonlinear thermoplastic behavior and residual stresses and deformations in structures subjected to intense heating is a prevalent challenge in a range of modern engineering applications the authors present a generalized finite element method targeted at this class of problems involving the solution of intrinsically parallelizable local boundary value problems to capture localized time dependent thermo elasto plastic behavior which is embedded in the coarse structural scale approximation via enrichment functions the method accommodates approximation spaces that evolve in between time or load steps while maintaining a fixed global mesh which avoids the need to map solutions and state variables on changing meshes typical of traditional adaptive approaches representative three dimensional examples exhibiting localized transient nonlinear thermal and thermomechanical effects are presented to demonstrate the advantages of the method with respect to available approaches especially in terms of its flexibility and potential for realistic future applications in this area parallelism of the approach is also discussed copyright 2016 john wiley sons ltd

finite elements with displacement interpolated embedded localization lines insensitive to mesh size and distortions a new finite element formulation aimed at the solution of problems involving strain localization is presented the proposed formulation incorporates displacement interpolated embedded localization lines results are shown to converge to an exact solution when the mesh is refined and also to be quite insensitive to mesh distortions

quadratically consistent one point qc1 quadrature for meshfree galerkin methods abstract a robust and efficient integration method named quadratically consistent one point qc1 scheme which evaluates the galerkin weak form only at the centers of background triangle elements cells is proposed for meshfree methods using quadratic basis the strain at the evaluation points is approximated by corrected smoothed nodal derivatives which are determined by a discrete form of the divergence theorem between nodal shape functions and their derivatives in taylor s expansion we prove that such smoothed nodal derivatives also meet the differentiation of the approximation consistency dac the same taylor s expansion is applied to the weak form and the smoothed nodal derivatives are used to compute the stiffness matrix the proposed qc1 scheme can pass both the linear and the quadratic patch tests exactly in a numerical sense several examples are provided to demonstrate its better numerical performance in terms of convergence accuracy efficiency and stability over other one point integration methods in the meshfree literature especially its superiority over the existing linearly consistent one point lc1 quadratures

time continuity in cohesive finite element modeling we introduce the notion of time continuity for the analysis of cohesive zone interface finite element models we focus on initially rigid models in which an interface is inactive until the traction across it reaches a critical level we argue that methods in this class are time discontinuous unless special provision is made for the opposite time discontinuity leads to pitfalls in numerical implementations oscillatory behavior non convergence in time and dependence on nonphysical regularization parameters these problems arise at least partly from the attempt to extend uniaxial traction displacement relationships to multiaxial loading we also argue that any formulation of a time continuous functional traction displacement cohesive model entails encoding the value of the traction components at incipient softening into the model we exhibit an example of such a model most of our numerical experiments concern explicit dynamics

a high order generalized fem for through the thickness branched cracks this paper presents high order implementations of a generalized finite element method for through the thickness three dimensional branched cracks this approach can accurately represent discontinuities such as triple joints in polycrystalline materials and branched cracks independently of the background finite element mesh representative problems are investigated to illustrate the accuracy of the method in combination with various discretizations and refinement strategies the combination of local refinement at crack fronts and high order continuous and discontinuous enrichments proves to be an excellent combination which can deliver convergence rates close to that of problems with smooth solutions copyright 2007 john wiley sons ltd

a simple method for crack growth in mixed mode with x fem abstract in this paper a new method for level set update is proposed in the context of crack propagation modeling with the extended finite element method x fem and level sets compared with the existing methods such as the resolution of the hamilton jacobi equations this new method is much simpler because it does not required complex manipulations of the level sets this method called the projection method uses both a classical discretization of the surface of the crack segments for 2d cracks and triangles for 3d cracks and a level set representation of the crack this discretization is updated with respect to the position of the new crack front then the level sets are re computed using the true distance to the new crack by an orthogonal projection of each node of the structure onto the new crack surface then numerical illustrations are given on 2d and 3d academic examples finally three illustrations are given on 3d industrial applications

non planar 3d crack growth by the extended finite element and level sets part i mechanical model a methodology for solving three dimensional crack problems with geometries that are independent of the mesh is described the method is based on the extended finite element method in which the crack discontinuity is introduced as a heaviside step function via a partition of unity in addition branch functions are introduced for all elements containing the crack front the branch functions include asymptotic near tip fields that improve the accuracy of the method the crack geometry is described by two signed distance functions which in turn can be defined by nodal values consequently no explicit representation of the crack is needed examples for three dimensional elastostatic problems are given and compared to analytic and benchmark solutions the method is readily extendable to inelastic fracture problems copyright 2002 john wiley sons ltd

compiling constraint satisfaction problems reference lia article 1999 003doi 10 1016 s0004 3702 99 00077 6view record in web of science record created on 2006 12 13 modified on 2017 05 12

analysis of three dimensional crack initiation and propagation using the extended finite element method an erratum has been published for this article in international journal for numerical methods in engineering 2005 63 8 1228 we present a new formulation and a numerical procedure for the quasi static analysis of three dimensional crack propagation in brittle and quasi brittle solids the extended finite element method xfem is combined with linear tetrahedral elements a viscosity regularized continuum damage constitutive model is used and coupled with the xfem formulation resulting in a regularized crack band version of xfem the evolving discontinuity surface is discretized through a c0 surface formed by the union of the triangles and quadrilaterals that separate each cracked element in two the element s properties allow a closed form integration and a particularly efficient implementation allowing large scale 3d problems to be studied several examples of crack propagation are shown illustrating the good results that can be achieved copyright 2005 john wiley sons ltd

non planar 3d crack growth by the extended finite element and level sets part ii level set update we present a level set method for treating the growth of non planar three dimensional cracks the crack is defined by two almost orthogonal level sets signed distance functions one of them describes the crack as a two dimensional surface in a three dimensional space and the second is used to describe the one dimensional crack front which is the intersection of the two level sets a hamilton jacobi equation is used to update the level sets a velocity extension is developed that preserves the old crack surface and can accurately generate the growing surface the technique is coupled with the extended finite element method which approximates the displacement field with a discontinuous partition of unity this displacement field is constructed directly in terms of the level sets so the discretization by finite elements requires no explicit representation of the crack surface numerical experiments show the robustness of the method both in accuracy and in treating cracks with significant changes in topology copyright 2002 john wiley sons ltd

global and local consistencies in distributed fault diagnosis for discrete event systems in this paper we present a unified framework for distributed diagnosis we first introduce the concepts of global and local consistency in terms of supremal global and local supports then present two distributed diagnosis problems based on them after that we provide algorithms to achieve supremal global and local supports respectively and discuss in detail the advantages and disadvantages of each finally we present an industrial example to demonstrate our distributed diagnosis approach

fault diagnosis in discrete event systems framework and model reduction a state based approach for online passive fault diagnosis in systems modeled as finite state automata is presented in this framework the system and the diagnoser the fault detection system do not have to be initialized at the same time furthermore no information about the state or even the condition failure status of the system before the initiation of diagnosis is required the design of the fault detection system in the worst case has exponential complexity a model reduction scheme with polynomial time complexity is introduced to reduce the computational complexity of the design diagnosability of failures is studied and necessary and sufficient conditions for failure diagnosability are derived

statistical inference occam s razor and statistical mechanics on the space of probability distributions the task of parametric model selection is cast in terms of a statistical mechanics on the space of probability distributions using the techniques of low temperature expansions i arrive at a systematic series for the bayesian posterior probability of a model family that significantly extends known results in the literature in particular i arrive at a precise understanding of how occam s razor the principle that simpler models should be preferred until the data justify more complex models is automatically embodied by probability theory these results require a measure on the space of model parameters and i derive and discuss an interpretation of jeffreys prior distribution as a uniform prior over the distributions indexed by a family finally i derive a theoretical index of the complexity of a parametric family relative to some true distribution that i call the razor of the model the form of the razor immediately suggests several interesting questions in the theory of learning that can be studied using the techniques of statistical mechanics