random matrix eigenvalue problems in structural dynamics natural frequencies and mode shapes play a fundamental role in the dynamic characteristics of linear structural systems considering that the system parameters are known only probabilistically we obtain the moments and the probability density functions of the eigenvalues of discrete linear stochastic dynamic systems current methods to deal with such problems are dominated by mean centred perturbation based methods here two new approaches are proposed the first approach is based on a perturbation expansion of the eigenvalues about an optimal point which is best in some sense the second approach is based on an asymptotic approximation of multidimensional integrals a closed form expression is derived for a general rth order moment of the eigenvalues two approaches are presented to obtain the probability density functions of the eigenvalues the first is based on the maximum entropy method and the second is based on a chi square distribution both approaches result in simple closed form expressions which can be easily calculated the proposed methods are applied to two problems and the analytical results are compared with monte carlo simulations it is expected that the small randomness assumption usually employed in mean centred perturbation based methods can be relaxed considerably using these methods

on semi analytical probabilistic finite element method for homogenization of the periodic fiber reinforced composites the main aim of this paper is a development of the semi analytical probabilistic version of the finite element method fem related to the homogenization problem this approach is based on the global version of the response function method and symbolic integral calculation of basic probabilistic moments of the homogenized tensor and is applied in conjunction with the effective modules method it originates from the generalized stochastic perturbation based fem where taylor expansion with random parameters is not necessary now and is simply replaced with the integration of the response functions the hybrid computational implementation of the system maple with homogenization oriented fem code mcceff is invented to provide probabilistic analysis of the homogenized elasticity tensor for the periodic fiber reinforced composites although numerical illustration deals with a homogenization of a composite with material properties defined as gaussian random variables other composite parameters as well as other probabilistic distributions may be taken into account the methodology is independent of the boundary value problem considered and may be useful for general numerical solutions using finite or boundary elements finite differences or volumes as well as for meshless numerical strategies copyright 2011 john wiley sons ltd

extension of the certain generalized stresses method for the stochastic analysis of homogeneous and laminated shells abstract the paper presents an extension of the certain generalized stresses method cgsm for the static finite element analysis of homogeneous and laminated shells with variability the basic assumption is that the generalized stresses do not depend on input parameters perturbation the cgsm is a non intrusive method that requires only one finite element analysis with some load cases to calculate the variability of mechanical quantities of interest the uncertain input parameters are material and physical properties uniform random parameters as well as random fields are considered the displacements statistical results mean value standard deviation and distribution are obtained by monte carlo simulations using a semi analytical formula two examples are treated the scordelis lo shell roof and an automotive windscreen the method provides results of good quality and is very economical from a computational time point of view

finding similar consensus between trees an algorithm and a distance hierarchy abstract the problem of finding this similar consensus also known as the largest approximately common substructures of two trees arises in many pattern recognition applications this paper presents a dynamic programming algorithm to solve the problem based on the distance measure originated from tanaka and tanaka the algorithm runs as fast as the best known algorithm for comparing two trees using tanaka s distance measure when the allowed distance between the common substructures is a constant independent of the input trees in addition we establish a hierarchy among tanaka s distance measure and three other edit based distance measures published in the literature

local estimates for parabolic difference operators abstract we prove a local maximum principle and weak harnack inequality for parabolic difference inequalities analogous to previous work on elliptic difference inequalities as applications we have discrete analogues of the holder and harnack estimates of krylov and safonov and results pertaining to the stability of discrete scheme for nonlinear parabolic problems extending previous work on elliptic equations

modeling uncertainty in steady state diffusion problems via generalized polynomial chaos abstract we present a generalized polynomial chaos algorithm for the solution of stochastic elliptic partial differential equations subject to uncertain inputs in particular we focus on the solution of the poisson equation with random diffusivity forcing and boundary conditions the stochastic input and solution are represented spectrally by employing the orthogonal polynomial functionals from the askey scheme as a generalization of the original polynomial chaos idea of wiener amer j math 60 1938 897 a galerkin projection in random space is applied to derive the equations in the weak form the resulting set of deterministic equations for each random mode is solved iteratively by a block gauss seidel iteration technique both discrete and continuous random distributions are considered and convergence is verified in model problems and against monte carlo simulations

reduction of dimensions in random elastic soil medium abstract the paper deals with an application of the plane strain analysis in a stochastic three dimensional soil medium in a framework of random elasticity theory the geostatical state of stresses and the problem of a unit force acting in a statistically homogeneous half space are considered only the modulus of elasticity is considered to be random and is modelled as a three dimensional 3 d homogeneous random field as the result of imposed constrains due to the plane strain assumption the additional body and surface forces are induced in order to determine them additional equations must be introduced the equations in a form of constrain relations are proposed in this paper these equations are also valid for a case of uniformly distributed external loading first the two dimensional 2 d problem and its reduction to the uni axial strain state for the gravity forces and uniform unlimited surface loading is considered then it is generalised into a 2 d schematization of the 3 d state next the problem of a unit force acting in a statistically homogeneous half space is considered for a 3 d state of stress and strain the resulting stresses are compared with those for a 2 d state these stresses for the multidimensional state of strain and stress are presented as a sum of two components the first one reflects plane strain state stresses and is given in a form of a 3 d random field this term allows for incorporating a spatial 3 d soil variability into a two dimensional analysis the second component can be treated as a correction term and it represents the longitudinal influence of a 3 d analysis some numerical results are presented in this paper the proposed method can be regarded as a framework for further research aiming at application to a variety of geotechnical problems for which the plane strain state is assumed

stochastic boundary elements for two dimensional potential flow in homogeneous domains abstract a stochastic boundary element formulation is presented for the analysis of two dimensional steady state potential flow through homogeneous domains the operator of the governing differential equation is assumed to be random and is described by a set of correlated random variables the perturbation method in conjunction with the boundary element method is employed to derive the systems of equations for the unknown boundary variables and their respective first and second order derivatives with respect to the random variables these quantities are then used to calculate the desired response statistics a general procedure is developed which is next applied for the specific cases of random geometric configuration and random material parameter the random geometric configuration is modeled using a finite set of correlated random variables the random material parameter is modeled as a homogeneous random field which allows the use of deterministic fundamental solutions and integral representations for homogeneous domains the random field is first discretized into a set of correlated random variables and then the general procedure is applied a transformation of the correlated random variables into an uncorrelated set is performed to reduce the number of numerical operations the results for the boundary variables are used to calculate the response statistics of internal potentials these calculations require the modeling of the interior of the domain under consideration several models for representing the interior of the domain are presented for both random configuration and random material parameter and their influence on the response statistics is analysed distributed sources are considered in the present study using the particular integral approach a number of numerical examples are presented to demonstrate the validity of the present formulations the results obtained from the present analyses are compared with those obtained from monte carlo simulations with 5000 samples and a good agreement of results is observed

reliability analysis of randomly vibrating structures with parameter uncertainties the problem of reliability analysis of randomly driven stochastically parametered vibrating structures is considered the excitation components are assumed to be jointly stationary gaussian random processes the randomness in structural parameters is modelled through a vector of mutually correlated non gaussian random variables the structure is defined to be safe if a set of response quantities remain within prescribed thresholds over a given duration of time an approximation for the failure probability conditioned on structure randomness is first formulated in terms of recently developed multivariate extreme value distributions an estimate of the unconditional failure probability is subsequently obtained using a method based on taylor series expansion this has involved the evaluation of gradients of the multivariate extreme value distribution conditioned on structure random variables with respect to the basic variables analytical and numerical techniques for computing these gradients have been discussed issues related to the accuracy of the proposed method have been examined the proposed method has applications in reliability analysis of vibrating structural series systems where different failure modes are mutually dependent illustrative examples presented include the seismic fragility analysis of a piping network in a nuclear power plant

computation of heat conduction in materials with random variable thermophysical properties a method for the direct computation of mean values and variances of the temperature in conduction heated objects with random variable thermophysical properties is presented this method is based on a taylor expansion of the finite element formulation of the heat conduction equation and offers a powerful alternative to the computationally expensive monte carlo method both steady state and transient problems are considered some example problems are solved and the results discussed the simulations indicate that the variability of the thermophysical properties may cause a considerable variability of the temperature within the heated object this may have important consequences on the design of heating operations in food process engineering

long duration response evaluation of linear structural system with random system properties using time dependent polynomial chaos abstract polynomial chaos pc is one of the popular methods for approximate evaluation of responses of stochastic structural mechanics problems in the case of a structural system under dynamic loading the pc method is combined with a time integration scheme the pc method with galerkin projection converts the stochastic pde to a set of simultaneous deterministic pde which can be solved using any standard time integration scheme however the convergence of responses is known to fail for long duration time integration problem due to the development of unacceptable error in calculated response the probability density functions of the responses are not of constant type as the time progresses however in the case of generalized pc gpc these are approximated using initially considered gpc thus loses its efficiency time dependent general polynomial chaos tdgpc can be considered to overcome these difficulties where polynomials are generated on the fly to match with the pdf of the responses the present study considered an investigation of structural mechanics responses with both gaussian and non gaussian random system properties under dynamic loading using tdgpc an adaptive updation scheme based on the rms value of the coefficients of pc expansion is investigated for a proper updation of pc expansion the curse of dimensionality of pc expansion is addressed by considering only the dominant components of the responses evaluated using kl expansion further starting with lower order pc the order of pc expansion is increased only after the first updation thus reducing computational complexities

average complexity of the jiang wang zhang pairwise tree alignment algorithm and of a rna secondary structure alignment algorithm we prove that the average complexity of the pairwise ordered tree alignment algorithm of jiang wang and zhang is in o nm where n and m stand for the sizes of the two trees respectively we show that the same result holds for the average complexity of pairwise comparison of rna secondary structures using a set of biologically relevant operations

a galerkin finite element technique for stochastic field problems a new finite element method is developed to analyse the structures with more than one parameter behaving in a stochastic manner the galerkin weighted residual method is used as a generalization this paper treats the random eigenvalue problems arising when the material property values of the structural systems are having stochastic fluctuations i e the measurement errors can be accounted for when probabilistic modelling is used the free vibration problem of a stochastic beam whose young s modulus and mass density are distributed stochastically is considered using galerkin s weighted residual procedure a stochastic finite element method is developed and implemented to arrive at a random algebraic eigenvalue problem the stochastic characteristics of eigensolutions are derived in terms of the stochastic material property variations numerical examples are given it is demonstrated that through this formulation the finite element discretization need not be dependent on the characteristics of stochastic fields describing the fluctuations in the material property values further calculation of covariances between stiffness elements mass elements etc is carried out in a relatively simple manner and is more general in nature

non conservatively loaded stochastic columns a new finite element method is developed to analyse non conservative structures with more than one parameter behaving in a stochastic manner as a generalization this paper treats the subsequent non self adjoint random eigenvalue problem that arises when the material property values of the non conservative structural system have stochastic fluctuations resulting from manufacturing and measurement errors the free vibration problems of stochastic beck s column and stochastic leipholz column whose young s modulus and mass density are distributed stochastically are considered the stochastic finite element method that is developed is implemented to arrive at a random non self adjoint algebraic eigenvalue problem the stochastic characteristics of eigensolutions are derived in terms of the stochastic material property variations numerical examples are given it is demonstrated that through this formulation the finite element discretization need not be dependent on the characteristics of stochastic processes of the fluctuations in material property value

stochastic free vibration of orthotropic plates using generalized polynomial chaos expansion this paper presents the theory and application of the generalized polynomial chaos expansion for the stochastic free vibration of orthotropic plates specifically the stochastic analysis of orthotropic plates under the uncertainties in elasticity moduli is investigated the uncertain moduli eigen frequencies and eigen modes of the plates are represented by truncated polynomial chaos expansions with arbitrary random basis the expansions are substituted in the governing differential equations to calculating the polynomial chaos coefficients of the eigen frequencies and the eigen modes distribution functions of the uncertain moduli are derived from experimental data where the pearson model is used to identify the type of density functions this realization then is employed to construct random orthogonal basis for each uncertain parameter because of available experimental modal analysis data this paper provides a useful practical example on the efficacy of polynomial chaos where the statistical moments and the probability distributions of modal responses are compared with experimental results

random field finite elements the probabilistic finite element method pfem is formulated for linear and non linear continua with inhomogeneous random fields analogous to the discretization of the displacement field in finite element methods the random field is also discretized the formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization furthermore it is shown that a reduced set of the uncorrelated variables is sufficient for the second moment analysis based on the linear formulation of the pfem the method is then extended to transient analysis in non linear continua the accuracy and efficiency of the method is demonstrated by application to a one dimensional elastic plastic wave propagation problem and a two dimensional plane stress beam bending problem the moments calculated compare favourably with those obtained by monte carlo simulation also the procedure is amenable to implementation in deterministic fem based computer programs

stochastic boundary elements for two dimensional potential flow in non homogeneous media abstract a stochastic boundary element formulation is presented for the treatment of two dimensional problems of steady state potential flow in non homogeneous media that involve a random operator in the governing differential equation the randomness is introduced through the material parameter of the domain which is described as a non homogeneous random field the random field is discretized into a set of correlated random variables and a perturbation is applied to the differential equation of the problem this leads to differential equations for the unknown potential and its first and second order derivatives respectively evaluated at the mathematical expectations of the random variables resulting from the discretization of the random field an approximate method is applied for the solution of these equations by expressing the potential and its derivatives as a sum of functions of descending order these solutions are introduced into the differential equations and upon equating similar order terms a sequence of poisson s equations is obtained for each order a transformation of the correlated random variables into an uncorrelated set is performed to reduce the number of numerical operations by retaining a small number of transformed random variables the resulting equations are solved using the boundary element method to obtain the unknown boundary values of the potentials and their respective first and second order derivatives which are then used to compute the desired response statistics quadratic conforming boundary elements are used in the boundary integration and four node quadrilateral cells are used in the domain integration strongly singular terms of the boundary element matrices are obtained indirectly by applying a state of uniform unit potential over the entire contour of the object the singular domain integrals are calculated analytically direct solution techniques are used to calculate the response variables and their derivatives respectively a number of example problems are presented and the results are compared with those obtained from monte carlo simulations a good agreement of the results is observed

a perturbation method for stochastic meshless analysis in elastostatics a stochastic meshless method is presented for solving boundary value problems in linear elasticity that involves random material properties the material property was modelled as a homogeneous random field a meshless formulation was developed to predict stochastic structural response unlike the finite element method the meshless method requires no structured mesh since only a scattered set of nodal points is required in the domain of interest there is no need for fixed connectivities between nodes in conjunction with the meshless equations classical perturbation expansions were derived to predict second moment characteristics of response numerical examples based on one and two dimensional problems are presented to examine the accuracy and convergence of the stochastic meshless method a good agreement is obtained between the results of the proposed method and monte carlo simulation since mesh generation of complex structures can be a far more time consuming and costly effort than the solution of a discrete set of equations the meshless method provides an attractive alternative to finite element method for solving stochastic mechanics problems copyright 2001 john wiley sons ltd

a generalized dimension reduction method for multidimensional integration in stochastic mechanics summary a new generalized multivariate dimension reduction method is presented for calculating statistical moments of the response of mechanical systems subject to uncertainties in loads material properties and geometry the method involves an additive decomposition of an n dimensional response function into at most s dimensional functions where s n an approximation of response moments by moments of input random variables and a moment based quadrature rule for numerical integration a new theorem is presented which provides a convenient means to represent the taylor series up to a specific dimension without involving any partial derivatives a complete proof of the theorem is given using two lemmas also proved in this paper the proposed method requires neither the calculation of partial derivatives of response as in commonly used taylor expansion perturbation methods nor the inversion of random matrices as in the neumann expansion method eight numerical examples involving elementary mathematical functions and solid mechanics problems illustrate the proposed method results indicate that the multivariate dimension reduction method generates convergent solutions and provides more accurate estimates of statistical moments or multidimensional integration than existing methods such as first and second order taylor expansion methods statistically equivalent solutions quasi monte carlo simulation and the fully symmetric interpolatory rule while the accuracy of the dimension reduction method is comparable to that of the fourth order neumann expansion method a comparison of cpu time suggests that the former is computationally far more efficient than the latter copyright 2004 john wiley sons ltd

stochastic isogeometric analysis of free vibration of functionally graded plates considering material randomness abstract the paper is to develop stochastic isogeometric analysis for the free vibration of functionally graded plates with spatially varying random material properties the isogeometric analysis method is employed in the new stochastic analysis scheme which is called stochastic isogeometric analysis siga the elastic modulus and mass density are modeled as homogeneous gaussian random fields along the plane of structure the governing equation of stochastic isogeometric analysis for free vibration of functionally graded plates is derived in conjunction with perturbation expansions to predict the first and second moments of eigenvalues in order to verify proposed method the brute force monte carlo simulation is employed the mean variance and cov coefficient of variation predicted by siga and those predicted by monte carlo simulation show good agreement the numerical examples demonstrate that the randomness of material properties affects significantly the structural responses of the functionally graded plates the correlation between elastic modulus and mass density is also observed to have significant effect on the response cov of eigenvalue

beyond the limitations of perturbation methods for real random eigenvalue problems using exceptional points and analytic continuation a numerical method is proposed to approximate the solution of parametric eigenvalue problem when the variability of the parameters exceed the radius of convergence of low order perturbation methods the radius of convergence of eigenvalue perturbation methods based on taylor series is known to decrease when eigenvalues are getting closer to each other this phenomenon knwon as veering in structural dynamics is a direct consequence of the existence of branch point singularity in the complex plane of the varying parameters where some eigenvalues are defective when this degeneracy referred to as exceptional point ep is close to the real axis the veering becomes stronger the main idea of the proposed approach is to combined a pair of eigenvalues to remove this singularity to do so two analytic auxiliary functions are introduced and are computed through high order derivatives of the eigenvalue pair with respect to the parameter this yields a new robust eigenvalue reconstruction scheme which is compared to taylor and puiseux series in all cases theoretical bounds are established and all approximations are compared numerically on a three degrees of freedom toy model this system illustrate the ability of the method to handle the vibrations of a structure with a randomly varying parameter computationally efficient the proposed algorithm could also be relevant for actual numerical models of large size arising from other applications involving parametric eigenvalue problems e g waveguides rotating machinery or instability problems such as squeal or flutter

parametric instability of stochastic columns columns which have stochastically distributed young s modulus and mass density and are subjected to deterministic periodic axial loadings are considered the general case of a column supported on a winkler elastic foundation of random stiffness and also on discrete elastic supports which are also random is considered material property fluctuations are modeled as independent one dimensional univariate homogeneous real random fields in space in addition to autocorrelation functions or their equivalent power spectral density functions the input random fields are characterized by scale of fluctuations or variance functions for their second order properties the foundation stiffness coefficient and the stiffnesses of discrete elastic supports are treated to constitute independent random variables the system equations of boundary frequencies are obtained using bolotin s method for deterministic systems stochastic fem is used to obtain the discrete system with random as well as periodic coefficients statistical properties of boundary frequencies are derived in terms of input parameter statistics a complete covariance structure is obtained the equations developed are illustrated using a numerical example employing a practical correlation structure

alignment distance of regular tree languages abstract we consider the tree alignment distance problem between a tree and a regular tree language the tree alignment distance is an alternative of the tree edit distance in which we construct an optimal alignment between two trees and compute its cost instead of directly computing the minimum cost of tree edits the alignment distance is crucial for understanding the structural similarity between trees we in particular consider the following problem given a tree t and a tree automaton recognizing a regular tree language l find the most similar tree from l with respect to t under the tree alignment metric regular tree languages are commonly used in practice such as xml schema or bioinformatics we propose an o m n time algorithm for computing the ordered alignment distance between t and l when the maximum degree of t and trees in l is bounded by a constant and o m n 2 time algorithm when the maximum degree of trees in l is not bounded where m is the size of t and n is the size of a finite tree automaton for l we also study the case where a tree is not necessarily ordered and show that the time complexity remains o m n if the maximum degree is bounded and max snp hard otherwise

an algebraic view of the relation between largest common subtrees and smallest common supertrees the relationship between two important problems in tree pattern matching the largest common subtree and the smallest common supertree problems is established by means of simple constructions which allow one to obtain a largest common subtree of two trees from a smallest common supertree of them and vice versa these constructions are the same for isomorphic homeomorphic topological and minor embeddings they take only time linear in the size of the trees and they turn out to have a clear algebraic meaning

nonlinear free vibration analysis of composite plates with material uncertainties a monte carlo simulation approach abstract in this paper the effects of dispersion in material properties on free vibration response of composite plates with geometric nonlinearity in von karman sense are investigated the higher order shear deformation theory is employed for the study reported here an efficient c0 finite element formulation is developed for the analysis using monte carlo simulation the second order statistics i e mean and standard deviation of the nonlinear free vibration response of the composite laminates are obtained for different thickness and amplitude ratios the input statistics mean and variance of the material property are assumed to be known as a priori the computed results demonstrate the influence of the variations in the material properties and amplitudes on the nonlinear free vibration response of the composite plates the results are compared with those available in the literature

identifying consensus of trees through alignment abstract in this paper we present a dynamic programming algorithm for identifying the similar consensus sc or the largest approximately common substructures of two ordered labeled trees based on the alignment distance we consider a substructure of a tree t to be a connected subgraph of t given two trees t 1 t 2 and an integer d the sc problem is to find a substructure u 1 of t 1 and a substructure u 2 of t 2 such that u 1 is within distance d of u 2 and where there does not exist any other substructure v 1 of t 1 and v 2 of t 2 such that v 1 and v 2 satisfy the distance constraint and the sum of the sizes of v 1 and v 2 is greater than the sum of the sizes of u 1 and u 2 the proposed algorithm solves the sc problem in time o d 2 t 1 t 2 g 1 g 2 2 where t i i 1 2 is the size of tree t i and g i is the maximum degree of t i this is as fast as the best known algorithm for aligning two ordered labeled trees when the distance allowed in the common substructures is a constant independent of the input trees to demonstrate the utility of our algorithm we discuss its application to characterizing the conformation space of rna sequences pertaining to the poliovirus human rhinovirus and coxsackievirus where the rna structures are represented by ordered labeled trees

stochastic galerkin methods for elliptic interface problems with random input in this work we consider random elliptic interface problems namely the media in elliptic equations have both randomness and interfaces a galerkin method using bi orthogonal polynomials is used to convert the random problem into an uncoupled system of deterministic interface problems a principle on how to choose the orders of the approximated polynomial spaces is given based on the sensitivity analysis in random spaces with which the total degree of freedom can be significantly reduced then immersed finite element methods are introduced to solve the resulting system convergence results are given both theoretically and numerically

interval field model and interval finite element analysis uncertain parameters with inherent spatial variability are commonly encountered in engineering modeling of this kind of spatial uncertainty plays a fundamental role in structural uncertainty analysis which provides a necessary basis for subsequent uncertainty propagation through the system an interval field model for quantification of spatial uncertain parameters is proposed by which only the upper and lower bounds of the spatial uncertain parameters rather than their precise probability distributions are required the dependency can be fully considered by the proposed interval field model with the information of dependency an interval k l expansion is presented as a combination of deterministic functions with uncorrelated standard interval variables through which the continuous spatial interval field with dependency can be expressed only by very limited intervals necessary mathematical illustrations are provided for the proposed interval field model and the interval k l expansion the sampling method for the interval field model is given providing a robust numerical analysis basis for subsequent structural uncertainty analysis when the interval field model is applied in finite element analysis of structures with spatial uncertain parameters the non deterministic equilibrium equations with interval factors is then formulated the mcs method and the perturbation method are developed for solution of the derived interval equilibrium equations the feasibility and validity of the proposed interval field model and corresponding interval finite element methods are verified by numerical examples where the upper and lower bounds of the responses such as the displacements and the stresses of structures with spatial uncertain parameters are computed and compared

harnack inequalities for supersolutions of fully nonlinear elliptic difference and differential equations abstract we present a new harnack inequality for non negative discrete supersolutions of fully nonlinear uniformly elliptic difference equations on rectangular lattices this estimate applies to all supersolutions and has the harnack constant depending on the graph distance on lattices for the proof we modify the proof of the weak harnack inequality applying the same idea to elliptic equations in a euclidean space we also derive a harnack type inequality for non negative viscosity supersolutions

a similarity measure for graphs with low computational complexity we present and analyze an algorithm to measure the structural similarity of generalized trees a new graph class which includes rooted trees for this we represent structural properties of graphs as strings and define the similarity of two graphs as optimal alignments of the corresponding property stings we prove that the obtained graph similarity measures are so called backward similarity measures from this we find that the time complexity of our algorithm is polynomial and hence significantly better than the time complexity of classical graph similarity methods based on isomorphic relations

forest alignment with affine gaps and anchors applied in rna structure comparison we present two enhancements to jiang s tree alignment algorithm motivated by experience with its use for rna structure alignment one enhancement is the introduction of an affine gap model which can be accommodated with a runtime increase by a constant factor the second enhancement is a speed up of the alignment algorithm when certain nodes in the trees are pre aligned by a so called anchoring both enhancements are included in a new implementation of the tool rnaforester we evaluate the new algorithm with two applications related to rna secondary structure analysis based on our experience we suggest a new formulation of the tree alignment model based on regular tree languages and rewrite rules

numerical methods for second order shape sensitivity analysis with applications to heat conduction problems in this paper two finite element based schemes for second order shape sensitivity analysis are presented in the first formulation the av dd method the first order shape sensitivity equation is derived and expressed in terms of state and adjoint variables the resultant equation is then directly differentiated to obtain the second order shape sensitivity equation in the second formulation the dd av method the functional of concern is differentiated twice to yield the second order sensitivity equation in which the second order shape derivatives can be eliminated by introducing a proper adjoint equation a thermal fin problem and a thermal insulation layer problem have been studied to validate the proposed schemes it is shown that both methods yield identical results though the dd av method is computationally more efficient

selected tree classifier combination based on both accuracy and error diversity this paper proposes a method for combining multiple tree classifiers based on both classifier ensemble bagging and dynamic classifier selection schemes dcs the proposed method is composed of the following procedures 1 building individual tree classifiers based on bootstrap samples 2 calculating the distance between all possible two trees 3 clustering the trees based on single linkage clustering 4 selecting two clusters by local region in terms of accuracy and error diversity and 5 voting the results of tree classifiers selected in the two clusters empirical evaluation using publicly available data sets confirms the superiority of our proposed approach over other classifier combining methods

robust design of structures using optimization methods the robust design of structures with stochastic parameters is studied using optimization techniques the first two statistical moments of the stochastic parameters including design variables are considered in conjunction with the second order perturbation method for the approximation of mean value and variance of the structural response in this framework the sensitivities of the mean values and variances of the structural performance function with respect to the design variables are calculated for use in the optimization task the robust design of structures is formulated as a multi criteria optimization problem in which both the expected value and the standard deviation of the objective function are to be minimized the robustness of the feasibility is also taken into account by involving the variability of the structural response in the constraints the two criteria optimization problem is converted into a scalar one and is then solved by a gradient based optimization algorithm to demonstrate the applicability of the presented method numerical examples are given involving static and dynamic response

approximation and parameterized algorithms for common subtrees and edit distance between unordered trees given two rooted labeled unordered trees the common subtree problem is to find a bijective matching between subsets of nodes of the trees of maximum cardinality which preserves labels and ancestry relationship the tree edit distance problem is to determine the least cost sequence of insertions deletions and substitutions that converts a tree into another given tree both problems are known to be hard to approximate within some constant factor in general we tackle these problems from two perspectives giving exact algorithms either for special cases or in terms of some parameters and approximation algorithms and hardness of approximation we present a parameterized algorithm in terms of the number of branching nodes that solves both problems and yields polynomial algorithms for several special classes of trees this is complemented with a tighter apx hardness proof that holds when the trees are of height one and two respectively furthermore we present the first approximation algorithms for both problems in particular for the common subtree problem for t trees we present an algorithm achieving a tlog 2 b o p t 1 ratio where b o p t is the number of branching nodes in the optimal solution we also present constant factor approximation algorithms for both problems in the case of bounded height trees

stability analysis of stochastically parametered nonconservative columns nonconservatively loaded columns which have stochastically distributed material property values and stochastic loadings in space are considered young s modulus and mass density are treated to constitute random fields the support stiffness coefficient and tip follower load are considered to be random variables the fluctuations of external and distributed loadings are considered to constitute a random field the variational formulation is adopted to get the differential equation and boundary conditions the non self adjoint operators are used at the boundary of the regularity domain the statistics of vibration frequencies and modes are obtained using the standard perturbation method by treating the fluctuations to be stochastic perturbations linear dependence of vibration and stability parameters over property value fluctuations and loading fluctuations are assumed bounds for the statistics of vibration frequencies are obtained the critical load is first evaluated for the averaged problem and the corresponding eigenvalue statistics are sought then the frequency equation is employed to transform the eigenvalue statistics to critical load statistics specialization of the general procedure to beck leipholz and pfluger columns is carried out for pfluger column nonlinear transformations are avoided by directly expressing the critical load statistics in terms of input variable statistics

a metric for rooted trees with unlabeled vertices based on nested parentheses in this paper we propose a new metric for rooted trees with unlabeled vertices based on alignments of nested parenthesis strings we prove that the time complexity for computing this metric is np hard and present a 1 5 approximation algorithm for it

karhunen loeve decomposition of random fields based on a hierarchical matrix approach summary the simulation of the behavior of structures with uncertain properties is a challenging issue because it requires suitable probabilistic models and adequate numerical tools nowadays it is possible to perform probabilistic investigations of the structural performance which take into account a space variant uncertainty characterization of the structures given a structural solver and the probabilistic models the reliability analysis of the structural response depends on the continuous random fields approximation which is carried out by means of a finite set of random variables the paper analyzes the main aspects of discretization in the case of 2d problems the combination of the well known karhunen loeve series expansion the finite element method and the hierarchical matrices approach is proposed in the paper copyright 2013 john wiley sons ltd

probabilistic analysis of non self adjoint mechanical systems with uncertain parameters a new approach to analyze mechanical systems that have an uncertain distribution of material properties and loadings for the variability of their dynamic response parameters is developed the methodology is demonstrated through solving for the probabilistic moments of eigenvalues of a non self adjoint structural system material properties are modelled using random fields and uncertain loadings are modelled using random variables by treating the random fluctuations of vibratory response to be the stochastic perturbations to mean response second order moments of eigenvalues are obtained to circumvent the practical difficulty of obtaining the exact correlation models for parameter variability second order moments of eigenvalues are evaluated in terms of variance functions both the sensitivity of eigenvalues to the variability in system parameters and the effects on the eigenvalue variability of correlation properties of uncertain parameters are demonstrated

an efficient 3d stochastic finite element method real life structural systems are characterized by their inherent or externally induced uncertainties in the design parameters this study proposes a stochastic finite element tool efficient to take account of these uncertainties here uncertain structural parameter is modeled as homogeneous gaussian stochastic field and commonly used two dimensional 2d local averaging technique is extended and generalized for 3d random field this is followed by cholesky decomposition of respective covariance matrix for digital simulation by expanding uncertain stiffness matrix about its reference value the neumann expansion method is introduced blended with direct monte carlo simulation this approach involves decomposition of stiffness matrix only once for the entire simulated structure thus substantial saving of cpu time and also the scope of tackling several stochastic fields simultaneously are the basic advantages of the proposed algorithm accuracy and efficiency of this method with reference to example problem is also studied here and numerical results validate its superiority over direct simulation method or first order perturbation approach

stress based topology optimization of continuum structures under uncertainties abstract this work addresses the use of the topology optimization approach to the design of continuum structures with failure constraints under the hypothesis of uncertainties in the spatial distribution of young s modulus to this end the first order perturbation approach is used to model the response of the structure and the midpoint discretization technique is used to represent the random field the objective is the minimization of the amount of material used in the design subjected to local stress constraints under uncertainties the probability of failure is bounded by the one sided chebychev inequality since the exact probability distribution function of the stress constraints is not known in advance the effective probability of failure of the obtained optimal designs is validated with the use of the monte carlo simulation approach indicating that the probability of failures of the topologies obtained with the stochastic approach is within the bounds provided by the one sided chebychev inequality the optimization problem is solved by means of the augmented lagrangian method in order to address the large number of constraints associated to this kind of formulation it is shown that the correlation length and the number of standard deviations considered in the formulation play an important role in both the obtained topology and effective probability of failure

alignment of trees an alternative to tree edit abstract in this paper we propose the alignment of trees as a measure of the similarity between two labeled trees both ordered and unordered trees are considered an algorithm is designed for ordered trees the time complexity of this algorithm is o t 1 t 2 deg t 1 deg t 2 2 where t 1 is the number of nodes in t 1 and deg t 1 is the degree of t 1 i 1 2 the algorithm is faster than the best known algorithm for tree edit when deg t 1 and deg t 2 are smaller than the depths of t 1 and t 2 for unordered trees we show that the alignment problem can be solved in polynomial time if the trees have a bounded degree and becomes max snp hard if one of the trees is allowed to have an arbitrary degree in contrast the edit problem for unordered trees is max snp hard even if both trees have a bounded degree zhang and jiang 1994 finally multiple alignment of trees is discussed

an iterative polynomial chaos approach for solution of structural mechanics problem with gaussian material property abstract a new approach for solution of stochastic structural mechanics problem with random coefficient in the framework of polynomial chaos pc expansion is proposed the basic strategy of the proposed method is to iteratively construct a pc expansion with reduced numbers of unknown coefficients the method is based on orthogonal expansion of stochastic responses and generation of an iterative pc based on the responses of the previous iteration the polynomials are evaluated using gram schmidt orthogonalization process the number of random variables in pc expansion is reduced by considering only the dominant components of the response characteristics which is evaluated using karhunen loeve kl expansion in case of random material field problem kl expansion is used to discretize the random field the usefulness of the proposed method in terms of accuracy and computational efficiency is examined the results of linear static structural mechanics problems are compared with mcs and pc method the proposed method is observed to be computationally more efficient and accurate than pc method

simple fast algorithms for the editing distance between trees and related problems ordered labeled trees are trees in which the left to right order among siblings is significant the distance between two ordered trees is considered to be the weighted number of edit operations insert delete and modify to transform one tree to another the problem of approximate tree matching is also considered specifically algorithms are designed to answer the following kinds of questions 1 what is the distance between two trees 2 what is the minimum distance between t 1 and t 2 when zero or more subtrees can be removed from t 2 3 let the pruning of a tree at node n mean removing all the descendants of node n the analogous question for prunings as for subtrees is answered a dynamic programming algorithm is presented to solve the three questions in sequential time o t 1 times t 2 times min textit depth t 1 textit leaves t 1 times min textit depth t 2 textit leaves t 2 and space o t 1 times t 2 compared with o t 1 times t 2 t

a survey on tree edit distance and related problems we survey the problem of comparing labeled trees based on simple local operations of deleting inserting and relabeling nodes these operations lead to the tree edit distance alignment distance and inclusion problem for each problem we review the results available and present in detail one or more of the central algorithms for solving the problem

explicit solution to the stochastic system of linear algebraic equations α1a1 α2a2 αmam x b abstract this paper presents a novel solution strategy to the stochastic system of linear algebraic equations 1 a 1 2 a 2 m a m x b arising from stochastic finite element modelling in computational mechanics in which i i 1 m denote random variables a i i 1 m real symmetric deterministic matrices b a deterministic random vector and x the unknown random vector to be solved the system is first decoupled by simultaneously diagonalizing all the matrices a i via a similarity transformation and then it is trivial to invert the sum of the diagonalized stochastic matrices to obtain the explicit solution of the stochastic equation system unless all the matrices a i share exactly the same eigen structure the joint diagonalization can only be approximately achieved hence the solution is approximate and corresponds to a particular average eigen structure of the matrix family specifically the classical jacobi algorithm for the computation of eigenvalues of a single matrix is modified to accommodate multiple matrices and the resulting jacobi like joint diagonalization algorithm preserves the fundamental properties of the original version including its convergence and an explicit solution for the optimal givens rotation angle three numerical examples are provided to illustrate the performance of the method

stochastic finite elements of discretely parameterized random systems on domains with boundary uncertainty the problem of representing random fields describing the material and boundary properties of the physical system at discrete points of the spatial domain is studied in the context of linear stochastic finite element method a randomly parameterized diffusion system with a set of independent identically distributed stochastic variables is considered the discretized parametric fields are interpolated within each element with multidimensional lagrange polynomials and integrated into the weak formulation the proposed discretized random field representation has been utilized to express the random fluctuations of the domain boundary with nodal position coordinates and a set of random variables the description of the boundary perturbation has been incorporated into the weak stochastic finite element formulation using a stochastic isoparametric mapping of the random domain to a deterministic master domain a method for obtaining the linear system of equations under the proposed mapping using generic finite element weak formulation and the stochastic spectral galerkin framework is studied in detail the treatment presents a unified way of handling the parametric uncertainty and random boundary fluctuations for dynamic systems the convergence behavior of the proposed methodologies has been demonstrated with numerical examples to establish the validity of the numerical scheme

free vibration of laminated spherical panels with random material properties randomness in the material properties is inherent in all engineering materials composites exhibit a greater scatter compared to conventional materials because of the larger number of parameters associated with its fabrication and manufacturing for accurate prediction of its behavior the composite material properties have been modelled as random variables in the present study higher order shear deformation theory including rotatory inertia effects has been employed in developing the system equations and first order perturbation technique has been adopted for the solution an approach has been presented for obtaining the analytical solution for generalized eigenvalue problem associated with free vibrations mean and variance of the natural frequency have been obtained for cross ply spherical laminates projected in rectangular plan form with different boundary conditions

computational uncertainty analysis in multiresolution materials via stochastic constitutive theory abstract a stochastic constitutive theory is proposed in this work to propagate microstructure uncertainties in computational multiscale continuum models to bulk multiresolution material behavior ubiquitous fine resolution uncertainty sources influencing prediction of material properties based on their structures are categorized in detail and this research transmits these uncertainties to coarser material resolutions by introducing a stochastic constitutive theory deduced from volume element simulations to implement the stochastic upscaling process two advanced uncertainty quantification methods are examined statistical copula functions and random process polynomial chaos expansion both methods confront the mathematical difficulty in randomizing constitutive laws by capturing the marked correlation among constitutive parameters seen in complex materials thus the results proffer a more accurate probabilistic estimation of constitutive material behavior the contribution of this work is twofold uncertainty is propagated from heterogeneous material structure to material property via the stochastic constitutive theory and rigorous data driven mathematics are formalized to represent complicated dependence structures in multivariate statistical distributions to the authors knowledge this is the first work in multiresolution mechanics that presents an approach to computationally derive correlation functions from numerical experiments as opposed for instance to assuming one a priori the method put forth in this research though quite general is applied to a mathematical example and plastic high strength steel alloy for demonstration results include stochastic constitutive curve confidence intervals for the material stress strain response and qualitative comparisons of the two stochastic methods detailed herein

random eigenvalue problems in structural dynamics experimental investigations an experimental investigation of uncertainty in natural frequencies of linear structures estimated from measured frequency response function frf under dynamic loading is presented experiments were conducted on one hundred nominally identical realizations of a fixed fixed beam each realisation was obtained by placin g twelve identical masses at random spatial locations generated by a computer along the length of the beam the total random mass is about 2 of the total mass of the beam these experiments contain parametric uncertainty in the mass matrix and hence may be useful for the validation of many random eigenvalue analysis and prediction methods currently available to structural dynamicist predictions from monte carlo simulation of deterministic finite elements model are compared with experiments it is co ncluded that the method of estimation of natural frequencies from frfs and the spatial location of the measurements has significant influence upon the first two moments mean and standard deviation of the natural frequency ensemble furthermore whilst the monte carlo simulation estimates of the mean and standard deviation are in reasonable agreement with experiments at higher frequencies the probability density function differ appreciably within the limits of the sample size investigated in this study

an algorithm for finding the largest approximately common substructures of two trees ordered labeled trees are trees in which each node has a label and the left to right order of its children if it has any is fixed such trees have many applications in vision pattern recognition molecular biology and natural language processing we consider a substructure of an ordered labeled tree t to be a connected subgraph of t given two ordered labeled trees t sub 1 and t sub 2 and an integer d the largest approximately common substructure problem is to find a substructure u sub 1 of t sub 1 and a substructure u sub 2 of t sub 2 such that u sub 1 is within edit distance d of u sub 2 and where there does not exist any other substructure v sub 1 of t sub 1 and v sub 2 of t sub 2 such that v sub 1 and v sub 2 satisfy the distance constraint and the sum of the sizes of v sub 1 and v sub 2 is greater than the sum of the sizes of u sub 1 and u sub 2 we present a dynamic programming algorithm to solve this problem which runs as fast as the fastest known algorithm for computing the edit distance of two trees when the distance allowed in the common substructures is a constant independent of the input trees to demonstrate the utility of our algorithm we discuss its application to discovering motifs in multiple rna secondary structures which are ordered labeled trees

a new algorithm for aligning nested arc annotated sequences under arbitrary weight schemes in this paper we propose a new algorithm for the alignment of nested arc annotated sequences having applications in the comparison of rna secondary structures without pseudo knots we use a general edit distance model between arc annotated sequences that considers classical sequences of edit operations and structural edit operations on arcs in this model the general edit distance problem under a non constrained weight scheme is np hard recently a hierarchy of arc annotated sequence alignment problems that highlights less general but tractable problems was introduced we refine this hierarchy of alignment problems and extend the class of tractable alignment problems up to date the alignment problem we solve is the most general one that is known to be tractable in the considered edit distance model and under arbitrary weight schemes this algorithm is efficient as its asymptotic time and space complexities are the same as the complexities of the best previously published algorithm