areawise significance tests for windowed recurrence network analysis many time series analysis techniques use sliding window approaches or are repeatedly applied over a continuous range of parameters when combined with a significance test intrinsic correlations among the pointwise analysis results can make falsely positive significant points appear as continuous patches rather than as isolated points to account for this effect we present an areawise significance test that identifies such false positive patches for this purpose we numerically estimate the decorrelation length of the statistic of interest by calculating correlation functions between the analysis results and require an areawise significant point to belong to a patch of pointwise significant points that is larger than this decorrelation length we apply our areawise test to results from windowed traditional and scale specific recurrence network analysis in order to identify dynamical anomalies in time series of a non stationary rossler system and tree ring width index values from eastern canada especially in the palaeoclimate context the areawise testing approach markedly reduces the number of points that are identified as significant and therefore highlights only the most relevant features in the data this provides a crucial step towards further establishing recurrence networks as a tool for palaeoclimate data analysis

interaction integrals for fracture analysis of functionally graded piezoelectric materials this paper presents domain form of the interaction integrals based on three independent formulations for computation of the stress intensity factors and electric displacement intensity factor for cracks in functionally graded piezoelectric materials conservation integrals of j type are derived based on the governing equations for piezoelectric media and the crack tip asymptotic fields of homogeneous piezoelectric medium as auxiliary fields each of the formulation differs in the way auxiliary fields are imposed in the evaluation of interaction integral and each of them results in a consistent form of the interaction integral in the sense that extra terms naturally appears in their derivation to compensate for the difference in the chosen crack tip asymptotic fields of homogeneous and functionally graded piezoelectric medium the additional terms play an important role of ensuring domain independence of the presented interaction integrals comparison of the numerically evaluated intensity factors through the three consistent formulations with those obtained using displacement extrapolation method is presented by means of two examples

a gromov hausdorff framework with diffusion geometry for topologically robust non rigid shape matching in this paper the problem of non rigid shape recognition is studied from the perspective of metric geometry in particular we explore the applicability of diffusion distances within the gromov hausdorff framework while the traditionally used geodesic distance exploits the shortest path between points on the surface the diffusion distance averages all paths connecting the points the diffusion distance constitutes an intrinsic metric which is robust in particular to topological changes such changes in the form of shortcuts holes and missing data may be a result of natural non rigid deformations as well as acquisition and representation noise due to inaccurate surface construction the presentation of the proposed framework is complemented with examples demonstrating that in addition to the relatively low complexity involved in the computation of the diffusion distances between surface points its recognition and matching performances favorably compare to the classical geodesic distances in the presence of topological changes between the non rigid shapes

multiple collinear cracks in a piezoelectric material abstract in this paper an exact solution of multiple collinear cracks in piezoelectric material is obtained the permittivity of air environment is considered two cases have been studied in the first case the permittivity of air is far less than that of piezoelectric material therefore the electric induction in the air is negligible in the second case the permittivity of air is comparable with that of piezoelectric material the problem is deduced into riemann hilbert problem and solved by the way the electric boundary conditions are discussed this result demonstrates that the consideration of air in crack gap reduces the stress intensity factor

mesh convolutional restricted boltzmann machines for unsupervised learning of features with structure preservation on 3 d meshes discriminative features of 3 d meshes are significant to many 3 d shape analysis tasks however handcrafted descriptors and traditional unsupervised 3 d feature learning methods suffer from several significant weaknesses 1 the extensive human intervention is involved 2 the local and global structure information of 3 d meshes cannot be preserved which is in fact an important source of discriminability 3 the irregular vertex topology and arbitrary resolution of 3 d meshes do not allow the direct application of the popular deep learning models 4 the orientation is ambiguous on the mesh surface and 5 the effect of rigid and nonrigid transformations on 3 d meshes cannot be eliminated as a remedy we propose a deep learning model with a novel irregular model structure called mesh convolutional restricted boltzmann machines mcrbms mcrbm aims to simultaneously learn structure preserving local and global features from a novel raw representation local function energy distribution in addition multiple mcrbms can be stacked into a deeper model called mesh convolutional deep belief networks mcdbns mcdbn employs a novel local structure preserving convolution lspc strategy to convolve the geometry and the local structure learned by the lower mcrbm to the upper mcrbm lspc facilitates resolving the challenging issue of the orientation ambiguity on the mesh surface in mcdbn experiments using the proposed mcrbm and mcdbn were conducted on three common aspects global shape retrieval partial shape retrieval and shape correspondence results show that the features learned by the proposed methods outperform the other state of the art 3 d shape features

computable elastic distances between shapes we dene distances between geometric curves by the square root of the minimal energy required to transform one curve into the other the energy is formally dened from a left invariant riemannian distance on an innite dimensional group acting on the curves which can be explicitly computed the obtained distance boils down to a variational problem for which an optimal matching between the curves has to be computed an analysis of the distance when the curves are polygonal leads to a numerical procedure for the solution of the variational problem which can eciently be implemented as illustrated by experiments 1 1 generalities the problem of matching two objects together is very impor tant in computer vision and shape recognition in many cases recognition is based on shapes outlines with the help of some suitably designed distance a general principle is to associate with any pair o1 o 2 of objects to be compared a measure of discrepancy d o1 o 2 the recognition of an observed object o may be done by nding from a dictionary of templates the previously recorded object otemp for which d o otemp is minimal clearly the denition of the distance is the crucial step of the method and much research has been done in this direction we shall not try here to provide a review of the huge literature existing on the subject see for example 17 but rather focus on methods related to deformable templates with which we are directly concerned instead of basing recognition on a nite collection of points of interest primitives taken from the outline of an object corners inflexion points etc which is a popular way of handling the problem our purpose is to base the comparison on the whole outline considered as a plane curve the distance we shall dene incorporates some deformation energy between the curves the approach as we will see turns out to be intrinsic and robust to usual euclidean transformations the method is related to the wide literature on snakes 14 7 21 etc in the way that our distance corresponds to some continuous process of deformation of one curve into another it is also related to papers on elastic matching such as 8 however we provide an elastic matching algorithm which is based on a true distance between intrinsic properties of the shapes taking into account possible invariance to scaling or euclidean transformations in the case they are required from this point of view our results are indebted to the seminal work of grenander on group theory applied to pattern recognition cf 10 and 11 in particular see also 1 2 12 another source of inspiration may come from mathematical physics since we are going to look to the path process of lowest energy which deforms one object into

dynamic analysis of traffic time series at different temporal scales a complex networks approach abstract the analysis of dynamics in traffic flow is an important step to achieve advanced traffic management and control in intelligent transportation system its complexity and periodicity are definitely two fundamental properties in traffic dynamics in this study we first measure the complexity of traffic flow data by lempel ziv algorithm at different temporal scales and the data are collected from loop detectors on freeway second to obtain more insight into the complexity and periodicity in traffic time series we then construct complex networks from traffic time series by considering each day as a cycle and each cycle as a single node the optimal threshold value of complex networks is estimated by the distribution of density and its derivative in addition the complex networks are subsequently analyzed in terms of some statistical properties such as average path length clustering coefficient density average degree and betweenness finally take 2 min aggregation data as example we use the correlation coefficient matrix adjacent matrix and closeness to exploit the periodicity of weekdays and weekends in traffic flow data the findings in this paper indicate that complex network is a practical tool for exploring dynamics in traffic time series

consistency and recovery in electroelasticity part i standard finite elements developing finite elements for electroelastic analysis requires a special care as the coupling in the discrete equations depends on the matching between the approximations assumed for mechanical and electrical variables to provide a formal basis to this intuitive remark a notion of consistency is established and a rigorous consistency analysis is presented for the standard finite element model based on assumed displacement and electric potential in this way specific analytical requirements are obtained which serve as a guide to select the interpolation functions for primary variables moreover the analysis shows that violating consistency can be reflected as spurious outcomes upsetting the local distributions of secondary variables indeed this undesirable effect is shown to be typical of the standard approach if stress and electric flux density are computed via the constitutive equations to cure the trouble an alternative recovery procedure is devised based on the consistency analysis the procedure is variationally correct and reconstitutes in a consistent manner the distributions of stress and electric flux density

analysis of stress and electric fields in a rectangular piezoelectric body with a center crack under anti plane shear loading abstract the singular stress and electric fields in a rectangular piezoelectric ceramic body containing a griffith center crack under anti plane shear loading are obtained by the theory of linear piezoelectricity fourier transforms and fourier sine series are used to reduce the problem to a pair of dual integral equations which is expressed to a fredholm integral equation of the second kind numerical values on the stress intensity factor and the energy release rate are obtained to show the influence of the electric field

infinite sequence of parallel cracks in an anisotropic piezoelectric solid in this paper the problem of an infinite sequence of parallel cracks in an infinite extended piezoelectric solid is analyzed a system of singular integral equations is formulated for general anisotropic piezoelectric materials of which the kernel functions developed are in complex form for commonly used transversely isotropic piezoelectric materials the kernel functions are given in real forms furthermore the obtained real kernel functions may be reduced respectively to those kernel functions for purely elastic and purely electric problems when the coupled mechanical and electric effects disappear the system of singular integral equations is solved numerically and the coupling effects of the mechanical and electric phenomena are presented by the generalized stress intensity factors

numerical inversion of srnf maps for elastic shape analysis of genus zero surfaces recent developments in elastic shape analysis esa are motivated by the fact that it provides a comprehensive framework for simultaneous registration deformation and comparison of shapes these methods achieve computational efficiency using certain square root representations that transform invariant elastic metrics into euclidean metrics allowing for the application of standard algorithms and statistical tools for analyzing shapes of embeddings of mathbf s 2 in mathbb r 3 jermyn et al 1 introduced square root normal fields srnfs which transform an elastic metric with desirable invariant properties into the mathbb l 2 metric these srnfs are essentially surface normals scaled by square roots of infinitesimal area elements a critical need in shape analysis is a method for inverting solutions deformations averages modes of variations etc computed in srnf space back to the original surface space for visualizations and inferences due to the lack of theory for understanding srnf maps and their inverses we take a numerical approach and derive an efficient multiresolution algorithm based on solving an optimization problem in the surface space that estimates surfaces corresponding to given srnfs this solution is found to be effective even for complex shapes that undergo significant deformations including bending and stretching e g human bodies and animals we use this inversion for computing elastic shape deformations transferring deformations summarizing shapes and for finding modes of variability in a given collection while simultaneously registering the surfaces we demonstrate the proposed algorithms using a statistical analysis of human body shapes classification of generic surfaces and analysis of brain structures

decoupled formulation of piezoelectric elasticity under generalized plane deformation and its application to wedge problems abstract this paper presents the formulation of piezoelectric elasticity under generalized plane deformation derived from the three dimensional theory there are four decoupled classes in the generalized plane deformation formulation i e when l 3 l 2 0 l 3 l 3 0 l 3 l 2 0 or l 3 l 3 l 2 0 only the inplane fields of the first class and the antiplane field of the second class include the piezoelectric effect several examples of wedge problem often encountered in smart structures such as sensors or actuators are studied to examine the stress singularity near the apex of the structure the bonded materials to the pzt 4 wedge are pzt 5 graphite epoxy or aluminum conductor the influencing factors on the singular behavior of the electro elastic fields include the wedge angle material type poling direction and the boundary and interface conditions the numerical results of the first case are compared with xu s graphs and some comments are made in detail in addition some new results regarding the antiplane stress singularity of the second class are obtained via the case study the coupled singularity solutions under generalized plane deformation are also investigated to seek the conditions of the weakest or vanishing singular stress fields

motif distributions in phase space networks for characterizing experimental two phase flow patterns with chaotic features the dynamics of two phase flows have been a challenging problem in nonlinear dynamics and fluid mechanics we propose a method to characterize and distinguish patterns from inclined water oil flow experiments based on the concept of network motifs that have found great usage in network science and systems biology in particular we construct from measured time series phase space complex networks and then calculate the distribution of a set of distinct network motifs to gain insight we first test the approach using time series from classical chaotic systems and find a universal feature motif distributions from different chaotic systems are generally highly heterogeneous our main finding is that the distributions from experimental two phase flows tend to be heterogeneous as well suggesting the underlying chaotic nature of the flow patterns calculation of the maximal lyapunov exponent provides further support for this motif distributions can thus be a feasible tool to understand the dynamics of realistic two phase flow patterns

finding metastable states in real world time series with recurrence networks in the framework of time series analysis with recurrence networks we introduce a self adaptive method that determines the elusive recurrence threshold and identifies metastable states in complex real world time series as initial step we introduce a way to set the embedding parameters used to reconstruct the state space from the time series we set them as the ones giving the maximum shannon entropy of the diagonal line length distribution for the first simultaneous minima of recurrence rate and shannon entropy to identify metastable states as well as the transitions between them we use a soft partitioning algorithm for module finding which is specifically developed for the case in which a system shows metastability we illustrate our method with a complex time series example finally we show the robustness of our method for identifying metastable states our results suggest that our method is robust for identifying metastable states in complex time series even when introducing considerable levels of noise and missing data points

efficient computation of isometry invariant distances between surfaces we present an efficient computational framework for isometry invariant comparison of smooth surfaces we formulate the gromov hausdorff distance as a multidimensional scaling like continuous optimization problem in order to construct an efficient optimization scheme we develop a numerical tool for interpolating geodesic distances on a sampled surface from precomputed geodesic distances between the samples for isometry invariant comparison of surfaces in the case of partially missing data we present the partial embedding distance which is computed using a similar scheme the main idea is finding a minimum distortion mapping from one surface to another while considering only relevant geodesic distances we discuss numerical implementation issues and present experimental results that demonstrate its accuracy and efficiency

3d shape matching via two layer coding view based 3d shape retrieval is a popular branch in 3d shape analysis owing to the high discriminative property of 2d views however many previous works do not scale up to large 3d shape databases we propose a two layer coding tlc framework to conduct shape matching much more efficiently the first layer coding is applied to pairs of views represented as depth images the spatial relationship of each view pair is captured with so called eigen angle which is the planar angle between the two views measured at the center of the 3d shape prior to the second layer coding the view pairs are divided into subsets according to their eigen angles consequently view pairs that differ significantly in their eigen angles are encoded with different codewords which implies that spatial arrangement of views is preserved in the second layer coding the final feature vector of a 3d shape is the concatenation of all the encoded features from different subsets which is used for efficient indexing directly tlc is not limited to encode the local features from 2d views but can be also applied to encoding 3d features exhaustive experimental results confirm that tlc achieves state of the art performance in both retrieval accuracy and efficiency

from the time series to the complex networks the parametric natural visibility graph abstract we present the modification of natural visibility graph nvg algorithm used for the mapping of the time series to the complex networks graphs we propose the parametric natural visibility graph pnvg algorithm the pnvg consists of nvg links which satisfy an additional constraint determined by a newly introduced continuous parameter the view angle the alteration of view angle modifies the pnvg and its properties such as the average node degree average link length of the graph as well as cluster quantity of built graph etc we calculated and analyzed different pnvg properties depending on the view angle for different types of the time series such as the random uncorrelated correlated and fractal and cardiac rhythm time series for healthy and ill patients investigation of different pnvg properties shows that the view angle gives a new approach to characterize the structure of the time series that are invisible in the conventional version of the algorithm it is also shown that the pnvg approach allows us to distinguish identify and describe in detail various time series

horizontal visibility graphs transformed from fractional brownian motions topological properties versus the hurst index abstract nonlinear time series analysis aims at understanding the dynamics of stochastic or chaotic processes in recent years quite a few methods have been proposed to transform a single time series to a complex network so that the dynamics of the process can be understood by investigating the topological properties of the network we study the topological properties of horizontal visibility graphs constructed from fractional brownian motions with different hurst indexes h 0 1 special attention has been paid to the impact of the hurst index on topological properties it is found that the clustering coefficient c decreases when h increases we also found that the mean length l of the shortest paths increases exponentially with h for fixed length n of the original time series in addition l increases linearly with respect to n when h is close to 1 and in a logarithmic form when h is close to 0 although the occurrence of different motifs changes with h the motif rank pattern remains unchanged for different h adopting the node covering box counting method the horizontal visibility graphs are found to be fractals and the fractal dimension d b decreases with h furthermore the pearson coefficients of the networks are positive and the degree degree correlations increase with degree which indicate that the horizontal visibility graphs are assortative with the increase of h the pearson coefficient decreases first and then increases in which the turning point is around h 0 6 the presence of both fractality and assortativity in the horizontal visibility graphs converted from fractional brownian motions is different from many cases where fractal networks are usually disassortative

uniform framework for the recurrence network analysis of chaotic time series we propose a general method for the construction and analysis of unweighted e recurrence networks from chaotic time series the selection of the critical threshold e c in our scheme is done empirically and we show that its value is closely linked to the embedding dimension m in fact we are able to identify a small critical range e numerically that is approximately the same for the random and several standard chaotic time series for a fixed m this provides us a uniform framework for the nonsubjective comparison of the statistical measures of the recurrence networks constructed from various chaotic attractors we explicitly show that the degree distribution of the recurrence network constructed by our scheme is characteristic to the structure of the attractor and display statistical scale invariance with respect to increase in the number of nodes n we also present two practical applications of the scheme detection of transition between two dynamical regimes in a time delayed system and identification of the dimensionality of the underlying system from real world data with a limited number of points through recurrence network measures the merits limitations and the potential applications of the proposed method are also highlighted

a coupled electromechanical analysis of a piezoelectric layer bonded to an elastic substrate part ii numerical solution and applications this two part contribution presents a novel and efficient method to analyze the two dimensional 2 d electromechanical fields of a piezoelectric layer bonded to an elastic substrate which takes into account the fully coupled electric and mechanical behaviors in part i we have obtained a system of governing integro differential equations for the structure via a variational principle this part presents a numerical solution algorithm of the integro differential equations and the numerical results of some applications a numerical algorithm for solving the system of four integro differential equations with strongly singular kernels is developed the convergence of the numerical algorithm is discussed the numerical results suggest that the fully coupled electromechanical analysis is helpful for a better understanding of the performance of the piezoelectric sensor and actuator the interfacial normal stress is much higher than the interfacial shear stress suggesting that the interfacial normal stress causes a delamination initiation

an intrinsic framework for analysis of facial surfaces a statistical analysis of shapes of facial surfaces can play an important role in biometric authentication and other face related applications the main difficulty in developing such an analysis comes from the lack of a canonical system to represent and compare all facial surfaces this paper suggests a specific yet natural coordinate system on facial surfaces that enables comparisons of their shapes here a facial surface is represented as an indexed collection of closed curves called facial curves that are level curves of a surface distance function from the tip of the nose defining the space of all such representations of face this paper studies its differential geometry and endows it with a riemannian metric it presents numerical techniques for computing geodesic paths between facial surfaces in that space this riemannian framework is then used to i compute distances between faces to quantify differences in their shapes ii find optimal deformations between faces and iii define and compute average of a given set of faces experimental results generated using laser scanned faces are presented to demonstrate these ideas

penny shaped crack in a piezoelectric cylinder surrounded by an elastic medium subjected to combined in plane mechanical and electrical loads the fracture problem of a penny shaped crack in a piezoelectric ceramic cylinder surrounded by an infinite elastic medium under in plane normal mechanical and electrical loads is considered with the electric continuous boundary conditions on the crack surface by using the potential theory and hankel transform a system of dual integral equations is obtained and expressed to a fredholm integral equation of the second kind the mechanical and electrical field equations and all sorts of field intensity factors of mode i are obtained and the numerical values of various field intensity factors for pzt 6b piezoelectric ceramic surrounded by several different elastic media are graphically shown for a uniform load and a ring shaped load respectively and the effects of the size of the piezoelectric cylinder and the elastic material properties on various field intensity factors are obtained

topological properties and fractal analysis of a recurrence network constructed from fractional brownian motions many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks in this work we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional brownian motions fbms first our results indicate that the constructed recurrence networks have exponential degree distributions the average degree exponent increases first and then decreases with the increase of hurst index h of the associated fbms the relationship between h and can be represented by a cubic polynomial function we next focus on the motif rank distribution of recurrence networks so that we can better understand networks at the local structure level we find the interesting superfamily phenomenon i e the recurrence networks with the same motif rank pattern being grouped into two superfamilies last we numerically analyze the fractal and multifractal properties of recurrence networks we find that the average fractal dimension db of recurrence networks decreases with the hurst index h of the associated fbms and their dependence approximately satisfies the linear formula db 2 h which means that the fractal dimension of the associated recurrence network is close to that of the graph of the fbm moreover our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks and the multifractality of these networks becomes stronger at first and then weaker when the hurst index of the associated time series becomes larger from 0 4 to 0 95 in particular the recurrence network with the hurst index h 0 5 possesses the strongest multifractality in addition the dependence relationships of the average information dimension d 1 and the average correlation dimension d 2 on the hurst index h can also be fitted well with linear functions our results strongly suggest that the recurrence network inherits the basic characteristic and the fractal nature of the associated fbm series

the general solution of three dimensional problems in piezoelectric media abstract the governing equations of three dimensional problems in transversely isotropic piezo electric material are composed of four second order partial differential equations in which the displacement components and electric potential functions are the essential unknowns in this paper the so called general solutions of these equations are obtained with the aid of a set of new potential functions which are used to express the components of displacements and the electric potential functions as an application of the general solution the problem of a half space piezoelectrics acted by a concentrated lateral shear force is solved

shape vocabulary a robust and efficient shape representation for shape matching in this paper a learning based shape descriptor for shape matching is demonstrated formulated in a bag of words like framework the proposed method summarizes the local features extracted from certain shape to generate a integrated representation it contributes to the speed up of shape matching since the distance metric in the vector space analysis can be directly applied to compare the constructed global descriptors eliminating the time consuming stage of local feature matching similar to the philosophy in spatial pyramid matching a strategy for feature division is applied in the phase of encoded feature pooling and vocabulary learning which helps to construct a more discriminative descriptor incorporating both global and local information also a local contour based feature extraction method is designed for 2d shapes while significant properties of the local contours are inspected for the design of feature division rules the designed local feature extraction method and the feature division rules manage to reduce the variances of shape representation due to the changes in rotation in addition to 2d shape we also present a simple and natural method to extend the proposed method to the scenario of 3d shape representation the proposed shape descriptor is validated on several benchmark data sets for evaluating 2d and 3d shape matching algorithms and it is observed that the investigated shape descriptor maintains superior discriminative power as well as high time efficiency

plane problems in piezoelectric media with defects abstract a two dimensional electroelastic analysis is performed on a transversely isotropic piezoelectric material containing defects a general solution is provided in terms of complex potentials with emphasis being placed on stress concentrations that arise in the vicinity of circular and elliptical holes it is shown that for this genre of problem both mechanical and electrical variables are responsible for the peak stresses

a new 3d matching method of nonrigid and partially similar models using curve analysis the 3d shape matching problem plays a crucial role in many applications such as indexing or modeling by example here we present a novel approach to matching 3d objects in the presence of nonrigid transformation and partially similar models in this paper we use the representation of surfaces by 3d curves extracted around feature points indeed surfaces are represented with a collection of closed curves and tools from shape analysis of curves are applied to analyze and to compare curves the belief functions are used to define a global distance between 3d objects the experimental results obtained on the tosca and the shrec07 data sets show that the system performs efficiently in retrieving similar 3d models

partial similarity of objects or how to compare a centaur to a horse similarity is one of the most important abstract concepts in human perception of the world in computer vision numerous applications deal with comparing objects observed in a scene with some a priori known patterns often it happens that while two objects are not similar they have large similar parts that is they are partially similar here we present a novel approach to quantify partial similarity using the notion of pareto optimality we exemplify our approach on the problems of recognizing non rigid geometric objects images and analyzing text sequences

sparse contextual activation for efficient visual re ranking in this paper we propose an extremely efficient algorithm for visual re ranking by considering the original pairwise distance in the contextual space we develop a feature vector called sparse contextual activation sca that encodes the local distribution of an image hence re ranking task can be simply accomplished by vector comparison under the generalized jaccard metric which has its theoretical meaning in the fuzzy set theory in order to improve the time efficiency of re ranking procedure inverted index is successfully introduced to speed up the computation of generalized jaccard metric as a result the average time cost of re ranking for a certain query can be controlled within 1 ms furthermore inspired by query expansion we also develop an additional method called local consistency enhancement on the proposed sca to improve the retrieval performance in an unsupervised manner on the other hand the retrieval performance using a single feature may not be satisfactory enough which inspires us to fuse multiple complementary features for accurate retrieval based on sca a robust feature fusion algorithm is exploited that also preserves the characteristic of high time efficiency we assess our proposed method in various visual re ranking tasks experimental results on princeton shape benchmark 3d object wm srhec07 3d competition yael data set b face mpeg 7 data set shape and ukbench data set image manifest the effectiveness and efficiency of sca

two dimensional piezoelectricity part ii general solution green s function and interface cracks abstract the complete solution space of a piezoelectric material is the direct sum of several orthogonal eigenspaces one for each distinct eigenvalue each one of the 14 different classes of piezoelectric materials has a distinct form of the general solution expressed in terms of the eigenvectors of the zeroth and higher orders and a kernel matrix containing analytic functions when these functions are chosen to be logarithmic one obtains in a unified way green s function of the infinite space as a single 8 8 matrix function g for the various load cases of concentrated line forces dislocations and a line charge this expression of green s function is valid for all classes of nondegenerate and degenerate materials with an appropriate choice of the parameters it reduces to the solution of a half space with concentrated line forces at a boundary point and with dislocations in the displacements as another application eigenvalues and eigensolutions are obtained for the bimaterial interface crack problem

an exact correspondence between plane piezoelectricity and generalized plane strain in elasticity we consider an anisotropic body bounded by a cylindrical surface which is infinitely long in the axial direction suppose the body is loaded in such a way that the field variables do not vary along the generators an exact correspondence is established between the plane piezoelectric equations and those of generalized plane strain in elasticity in particular we show that by setting a linkage between the two sets of material constants any problem of a plane deformation in piezoelectricity may be solved as a generalized plane strain in elasticity and vice versa the assertation is true for rectilinearly as well as for cylindrically anisotropic solids the equivalence is found for the most general anisotropic case which links the fields between a monoclinic piezoelectric body of class m and a fully anisotropic triclinic elastic solid a few degenerate systems are also identified in addition these correspondences can be extended to inhomogeneous media applied to composite materials or polycrystalline aggregates they imply that results for effective elastic tensors immediately give the formulae for the effective electroelastic tensors and vice versa we also demonstrate that the connection can be used to extend the scope of the invariant stress theorem proved by cherkaev lurie and milton in illustration we present solutions for the plane problem of an elliptical inhomogeneity in an unbounded piezoelectric medium subjected to a uniform loading at infinity lekhnitskii9s complex potential approach together with the conformal mapping technique are employed general solutions of the fields inside the inhomogeneity and the matrix are obtained the results are analytically proven to be identical with the existing solutions of the corresponding purely elastic boundary value problem

ambiguities in recurrence based complex network representations of time series recently different approaches have been proposed for studying basic properties of time series from a complex network perspective in this work the corresponding potentials and limitations of networks based on recurrences in phase space are investigated in some detail we discuss the main requirements that permit a feasible system theoretic interpretation of network topology in terms of dynamically invariant phase space properties possible artifacts induced by disregarding these requirements are pointed out and systematically studied finally a rigorous interpretation of the clustering coefficient and the betweenness centrality in terms of invariant objects is proposed

on chaotic graphs a different approach for characterizing aperiodic dynamics fractal worlds with limited connectivity are the topological result of growing graphs from chaotic series we show how this model presents original characteristics which cannot be detected by means of the standard network descriptors in detail intrinsic inaccessibility to the fully connected configuration is demonstrated to be a universal feature associated with this family of graphs and strictly related to the fractality of a specific chaotic source here we discuss the potential of our model to be a generator of fractal graphs and also a self consistent tool for differentiating chaotic dynamics from stochastic processes

euclidean distance based canonical forms for non rigid 3d shape retrieval retrieval of 3d shapes is a challenging problem especially for non rigid shapes one approach giving favourable results uses multidimensional scaling mds to compute a canonical form for each mesh after which rigid shape matching can be applied however a drawback of this method is that it requires geodesic distances to be computed between all pairs of mesh vertices due to the super quadratic computational complexity canonical forms can only be computed for low resolution meshes we suggest a linear time complexity method for computing a canonical form using euclidean distances between pairs of a small subset of vertices this approach has comparable retrieval accuracy but lower time complexity than using global geodesic distances allowing it to be used on higher resolution meshes or for more meshes to be considered within a time budget highlightsour method computes canonical forms of 3d meshes without using geodesic distances our method maximises the euclidean distance between a small set of feature points our method has a lower time complexity than other approaches yet provides comparable retrieval results

integral representation and green s functions for 3d time dependent thermo piezoelectricity abstract a boundary integral method is developed for 3d time dependent quasistatic thermo piezoelectricity this time domain formulation involves only surface quantities as a result volume discretization is completely avoided green s functions are derived by resorting to radon transform and presented in integral form reductions to the case of isotropic dielectric solid have been worked out in detail and its corresponding solutions expressed in explicit form are consistent with the existing solutions

signatures of chaotic and stochastic dynamics uncovered with recurrence networks an old and important problem in the field of nonlinear time series analysis entails the distinction between chaotic and stochastic dynamics recently recurrence networks have been proposed as a t

the transferable belief model abstract we describe the transferable belief model a model for representing quantified beliefs based on belief functions beliefs can be held at two levels 1 a credal level where beliefs are entertained and quantified by belief functions 2 a pignistic level where beliefs can be used to make decisions and are quantified by probability functions the relation between the belief function and the probability function when decisions must be made is derived and justified four paradigms are analyzed in order to compare bayesian upper and lower probability and the transferable belief approaches

universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices the investigations of financial markets from a complex network perspective have unveiled many phenomenological properties in which the majority of these studies map the financial markets into one complex network in this work we investigate 30 world stock market indices through their visibility graphs by adopting the visibility algorithm to convert each single stock index into one visibility graph a universal allometric scaling law is uncovered in the minimal spanning trees whose scaling exponent is independent of the stock market and the length of the stock index in contrast the maximal spanning trees and the random spanning trees do not exhibit universal allometric scaling behaviors there are marked discrepancies in the allometric scaling behaviors between the stock indices and the brownian motions using surrogate time series we find that these discrepancies are caused by the fat tailedness of the return distribution and the nonlinear long term correlation

three dimensional eigenfunction analysis of a crack in a piezoelectric material abstract a three dimensional analysis of a semi infinite crack embedded in a transversely isotropic piezoelectric material was performed by means of the eigenfunction expansions method the results show the characteristic 1 r singular behavior of the stress tensor in the vicinity of the crack a similar behavior is also revealed for the electric field in addition the study demonstrates that coupling or decoupling of the mechanical and electrical variables is a function of the distance to the crack tip as well as of the crack orientation

unsupervised 3d local feature learning by circle convolutional restricted boltzmann machine extracting local features from 3d shapes is an important and challenging task that usually requires carefully designed 3d shape descriptors however these descriptors are hand crafted and require intensive human intervention with prior knowledge to tackle this issue we propose a novel deep learning model namely circle convolutional restricted boltzmann machine ccrbm for unsupervised 3d local feature learning ccrbm is specially designed to learn from raw 3d representations it effectively overcomes obstacles such as irregular vertex topology orientation ambiguity on the 3d surface and rigid or slightly non rigid transformation invariance in the hierarchical learning of 3d data that cannot be resolved by the existing deep learning models specifically by introducing the novel circle convolution ccrbm holds a novel ring like multi layer structure to learn 3d local features in a structure preserving manner circle convolution convolves across 3d local regions via rotating a novel circular sector convolution window in a consistent circular direction in the process of circle convolution extra points are sampled in each 3d local region and projected onto the tangent plane of the center of the region in this way the projection distances in each sector window are employed to constitute a novel local raw 3d representation called projection distance distribution pdd in addition to eliminate the initial location ambiguity of a sector window the fourier transform modulus is used to transform the pdd into the fourier domain which is then conveyed to ccrbm experiments using the learned local features are conducted on three aspects global shape retrieval partial shape retrieval and shape correspondence the experimental results show that the learned local features outperform other state of the art 3d shape descriptors

exploring dynamic property of traffic flow time series in multi states based on complex networks phase space reconstruction versus visibility graph abstract a new method based on complex network theory is proposed to analyze traffic flow time series in different states we use the data collected from loop detectors on freeway to establish traffic flow model and classify the flow into three states based on k means method we then introduced two widely used methods to convert time series into networks phase space reconstruction and visibility graph furthermore in phase space reconstruction we discuss how to determine delay time constant and embedding dimension and how to select optimal critical threshold in terms of cumulative degree distribution in the visibility graph we design a method to construct network from multi variables time series based on logical or finally we study and compare the statistic features of the networks converted from original traffic time series in three states based on phase space and visibility by using the degree distribution network structure correlation of the cluster coefficient to betweenness and degree degree correlation

electroelastic analysis of an anti plane shear crack in a piezoelectric ceramic strip the electroelastic analysis of a piezoelectric strip with an anti plane shear crack whose surfaces are parallel to the strip boundaries is made four cases of combined electromechanical loadings applied at the strip boundaries are considered for the case of a crack lying at the center of a strip the electroelastic field field intensity factors and energy release rate can be determined in explicit form via solving a resulting singular integral equation for other cases they can be given in terms of an auxiliary function which is obtained as a power series of via solving a resulting fredholm integral equation using the iterative method 2 being the ratio of the crack length over the strip width some numerical results are presented graphically to show the influence of crack length and crack position on the normalized energy release rate

boscc bag of spatial context correlations for spatially enhanced 3d shape representation highly discriminative 3d shape representations can be formed by encoding the spatial relationship among virtual words into the bag of words bow method to achieve this challenging task several unresolved issues in the encoding procedure must be overcome for 3d shapes including 1 arbitrary mesh resolution 2 irregular vertex topology 3 orientation ambiguity on the 3d surface and 4 invariance to rigid and non rigid shape transformations in this paper a novel spatially enhanced 3d shape representation called bag of spatial context correlations bosccs is proposed to address all these issues adopting a novel local perspective boscc is able to describe a 3d shape by an occurrence frequency histogram of spatial context correlation patterns which makes boscc become more compact and discriminative than previous global perspective based methods specifically the spatial context correlation is proposed to simultaneously encode the geometric and spatial information of a 3d local region by the correlation among spatial contexts of vertices in that region which effectively resolves the aforementioned issues the spatial context of each vertex is modeled by markov chains in a multi scale manner which thoroughly captures the spatial relationship by the transition probabilities of intra virtual words and the ones of inter virtual words the high discriminability and compactness of boscc are effective for classification and retrieval especially in the scenarios of limited samples and partial shape retrieval experimental results show that boscc outperforms the state of the art spatially enhanced bow methods in three common applications global shape retrieval shape classification and partial shape retrieval

analytical framework for recurrence network analysis of time series recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems while there are already many successful applications ranging from medicine to paleoclimatology a solid theoretical foundation of the method has still been missing so far here we interpret an ensuremath varepsilon recurrence network as a discrete subnetwork of a continuous graph with uncountably many vertices and edges corresponding to the system s attractor this step allows us to show that various statistical measures commonly used in complex network analysis can be seen as discrete estimators of newly defined continuous measures of certain complex geometric properties of the attractor on the scale given by ensuremath varepsilon in particular we introduce local measures such as the ensuremath varepsilon clustering coefficient mesoscopic measures such as ensuremath varepsilon motif density path based measures such as ensuremath varepsilon betweennesses and global measures such as ensuremath varepsilon efficiency this new analytical basis for the so far heuristically motivated network measures also provides an objective criterion for the choice of ensuremath varepsilon via a percolation threshold and it shows that estimation can be improved by so called node splitting invariant versions of the measures we finally illustrate the framework for a number of archetypical chaotic attractors such as those of the bernoulli and logistic maps periodic and two dimensional quasiperiodic motions and for hyperballs and hypercubes by deriving analytical expressions for the novel measures and comparing them with data from numerical experiments more generally the theoretical framework put forward in this work describes random geometric graphs and other networks with spatial constraints which appear frequently in disciplines ranging from biology to climate science

the boundary contour method for piezoelectric media with linear boundary elements this paper presents a development of the boundary contour method bcm for piezoelectric media first the divergence free property of the integrand of the piezoelectric boundary element is proved secondly the boundary contour method formulation is derived and potential functions are obtained by introducing linear shape functions and green s functions computer methods in applied mechanics and engineering 1998 158 65 for piezoelectric media the bcm is applied to the problem of piezoelectric media finally numerical solutions for illustrative examples are compared with exact ones and those of the conventional boundary element method bem the numerical results of the bcm coincide very well with the exact solution and the feasibility and efficiency of the method are verified copyright 2003 john wiley sons ltd

new developments concerning piezoelectric materials with defects abstract the problem of a piezoelectric body with an elliptic cavity is revisited within the frame work of two dimensional electro elasticity in contrast to our previous formulation the present analysis is based on the use of exact electric boundary conditions at the rim of the hole thus avoiding the common assumption of electric impermeability expressions for the elastic and electric variables induced inside and outside the cavity are derived in closed form in terms of complex potentials comparisons between present exact and previous approximate models are effected to establish the limitations associated with the assumption of the impermeable hole in particular when it becomes a slit crack

analysis of a central crack normal to a piezoelectric orthotropic interface this study is concerned with the general solution of the field intensity factors and energy release rate for a griffith crack normal to the interface between a rectangular piezoelectric ceramic and two same rectangular orthotropic materials of finite length under combined in plane electrical and anti plane mechanical loading both electrically continuous and impermeable crack surface conditions are considered employing fourier transforms and fourier series the problem is reduced to dual integral forms the solution to the resulting expressions is expressed in terms of fredholm integral equation of the second kind analytical solutions are provided for a number of cases to study the influence of material combinations geometry crack surface boundary and loading conditions the work also examines the influence of the crack boundary conditions on the results of the stress intensity factors and the energy release rate

fractal and complex network analyses of protein molecular dynamics based on protein molecular dynamics we investigate the fractal properties of energy pressure and volume time series using the multifractal detrended fluctuation analysis mf dfa and the topological and fractal properties of their converted horizontal visibility graphs hvgs the energy parameters of protein dynamics we considered are bonded potential angle potential dihedral potential improper potential kinetic energy van der waals potential electrostatic potential total energy and potential energy the shape of the h q h q curves from mf dfa indicates that these time series are multifractal the numerical values of the exponent h 2 h 2 of mf dfa show that the series of total energy and potential energy are non stationary and anti persistent the other time series are stationary and persistent apart from series of pressure with h 0 5h 0 5 indicating the absence of long range correlation the degree distributions of their converted hvgs show that these networks are exponential the results of fractal analysis show that fractality exists in these converted hvgs for each energy pressure or volume parameter it is found that the values of h 2 h 2 of mf dfa on the time series exponent of the exponential degree distribution and fractal dimension dbdb of their converted hvgs do not change much for different proteins indicating some universality we also found that after taking average over all proteins there is a linear relationship between h 2 h 2 from mf dfa on time series and db db of the converted hvgs for different energy pressure and volume

an eccentric crack in a piezoelectric strip under anti plane shear impact loading we consider the problem of determining the singular stress and electric fields in a piezoelectric ceramic strip containing a griffith eccentric crack off the center line under anti plane shear impact loading with the theory of linear piezoelectricity laplace transform and fourier transforms are used to reduce the problem to a pair of dual integral equations which are expressed to a fredholm integral equation of the second kind numerical values on the dynamic stress intensity factor and the dynamic energy release rate are obtained