statistical analysis of airport network of china through the study of airport network of china anc composed of 128 airports nodes and 1165 flights edges we show the topological structure of anc conveys two characteristics of small worlds a short average path length 2 067 and a high degree of clustering 0 733 the cumulative degree distributions of both directed and undirected anc obey two regime power laws with different exponents i e the so called double pareto law in degrees and out degrees of each airport have positive correlations whereas the undirected degrees of adjacent airports have significant linear anticorrelations it is demonstrated both weekly and daily cumulative distributions of flight weights frequencies of anc have power law tails besides the weight of any given flight is proportional to the degrees of both airports at the two ends of that flight it is also shown the diameter of each subcluster consisting of an airport and all those airports to which it is linked is inversely proportional to its density of connectivity efficiency of anc and of its subclusters is measured through a simple definition in terms of that the efficiency of anc s subclusters increases as the density of connectivity does anc is found to have an efficiency of 0 484

nonlinear growth in weighted networks with neighborhood preferential attachment abstract we propose a nonlinear growing model for weighted networks with two significant characteristics i the new weights triggered by new edges at each time step grow nonlinearly with time and ii a neighborhood local world exists for local preferential attachment which is defined as one selected node and its neighbors global strength driven and local weight driven preferential attachment mechanisms are involved in our model we study the evolution process through both mathematical analysis and numerical simulation and find that the model exhibits a wide range power law distribution for node degree strength and weight in particular a nonlinear degree strength relationship is obtained this nonlinearity implies that accelerating growth of new weights plays a nontrivial role compared with accelerating growth of edges because of the specific local world model a small world property emerges and a significant hierarchical organization independent of the parameters is observed

discontinuous galerkin method based on peridynamic theory for linear elasticity modeling of discontinuities shock waves crack surfaces etc in solid mechanics is one of the major research areas in modeling the mechanical behavior of materials among the numerical methods the discontinuous galerkin method dgm poses some advantages in solving these problems in this study a novel formulation for dgm is derived for elastostatics based on the peridynamic theory derivation of the proposed formulation is presented numerical analyses are performed for different problems and the numerical results are compared to that of the known exact solutions of the problems the proposed weak formulation is stable and coercive peridynamic discontinuous galerkin formulation is found to be robust and successful in modeling elastostatic problems copyright 2011 john wiley sons ltd

mutual attraction model for both assortative and disassortative weighted networks for most complex networks the connection between a pair of nodes is the result of their mutual affinity and attachment in this letter we will propose a mutual attraction model to characterize weighted evolving networks by introducing the initial attractiveness a and the general mechanism of mutual attraction controlled by parameter m our model can naturally reproduce scale free distributions of degree weight and strength as found in many real systems also simulation results are consistent with theoretical predictions interestingly we obtain nontrivial clustering coefficient c and tunable degree assortativity r depending on the values of m and a our model appears as a more general one that unifies the characterization of both assortative and disassortative weighted networks

modeling the coevolution of topology and traffic on weighted technological networks for many technological networks the network structures and the traffic taking place on them mutually interact the demands of traffic increment spur the evolution and growth of the networks to maintain their normal and efficient functioning in parallel a change of the network structure leads to redistribution of the traffic in this paper we perform an extensive numerical and analytical study extending results of wang phys rev lett 94 188702 2005 by introducing a general strength coupling interaction driven by the traffic increment between any pair of vertices our model generates networks of scale free distributions of strength weight and degree in particular the obtained nonlinear correlation between vertex strength and degree and the disassortative property demonstrate that the model is capable of characterizing weighted technological networks moreover the generated graphs possess both dense clustering structures and an anticorrelation between vertex clustering and degree which are widely observed in real world networks the corresponding theoretical predictions are well consistent with simulation results

feature selection using a piecewise linear network we present an efficient feature selection algorithm for the general regression problem which utilizes a piecewise linear orthonormal least squares ols procedure the algorithm 1 determines an appropriate piecewise linear network pln model for the given data set 2 applies the ols procedure to the pln model and 3 searches for useful feature subsets using a floating search algorithm the floating search prevents the nesting effect the proposed algorithm is computationally very efficient because only one data pass is required several examples are given to demonstrate the effectiveness of the proposed algorithm

a quasi static discontinuous galerkin configurational force crack propagation method for brittle materials summary this paper presents a framework for r adaptive quasi static configurational force cf brittle crack propagation cast within a discontinuous galerkin dg symmetric interior penalty sipg finite element scheme cracks are propagated in discrete steps with a staggered algorithm along element interfaces which align themselves with the predicted crack propagation direction the key novelty of the work is the exploitation of the dg face stiffness terms existing along element interfaces to propagate a crack in a mesh independent r adaptive quasi static fashion driven by the cf at the crack tip this adds no new degrees of freedom to the data structure additionally as dg methods have element specific degrees of freedom a geometry driven p adaptive algorithm is also easily included allowing for more accurate solutions of the cf on a moving crack front further for non determinant systems we introduce an average boundary condition that restrains rigid body motion leading to a determinant system to the authors knowledge this is first time such a boundary condition has been described the proposed formulation is validated against single and multiple crack problems with single and mixed mode cracks demonstrating the predictive capabilities of the method this article is protected by copyright all rights reserved

generating structured networks based on a weight dependent deactivation mechanism motivated by the degree dependent deactivation model generating networks with high clustering coefficient k klemm et al phys rev e 65 036123 2002 a weight dependent version is studied to model evolving networks the growth dynamics of the network is based on a naive weight driven deactivation mechanism which couples the establishment of new active vertices and the weights dynamical evolution both analytical solutions and numerical simulations show that the generated networks possess a high clustering coefficient larger than that for regular lattices of the same average connectivity weighted structured scale free networks are obtained as the deactivated vertex is target selected at each time step and weighted structured exponential networks are realized for the random selected case

generalized strength of weighted scale free networks an analysis to describe statistical properties of weighted complex networks is proposed effective structures of weighted networks depend on how strongly weights w are paid attention or which weights are relevant to the network problem defining the metaweight w q with a real parameter q we characterize systematically weighted complex networks depending on the level of importance of weights it is found that power law distribution functions r q s q of metastrengths s q defined by s i q summation operator j w ij q where i and j denote node indices for any q are characterized by only three exponents if the weight distribution is independent of network topology we also examine the validity of our analytical arguments and the meaning of power law forms of r q s q for different q values by illustrating some examples

nonlocal evolution of weighted scale free networks we introduce the notion of globally updating evolution for a class of weighted networks in which the weight of a link is characterized by the amount of data packet transport flowing through it by noting that the packet transport over the network is determined nonlocally this approach can explain the generic nonlinear scaling between the strength and the degree of a node we demonstrate by a simple model that the strength driven evolution scheme recently introduced can be generalized to a nonlinear preferential attachment rule generating the power law behaviors in degree and in strength simultaneously

local overfitting control via leverages we present a novel approach to dealing with overfitting in black box models it is based on the leverages of the samples that is on the influence that each observation has on the parameters of the model since overfitting is the consequence of the model specializing on specific data points during training we present a selection method for nonlinear models based on the estimation of leverages and confidence intervals it allows both the selection among various models of equivalent complexities corresponding to different minima of the cost function e g neural nets with the same number of hidden units and the selection among models having different complexities e g neural nets with different numbers of hidden units a complete model selection methodology is derived

quadrature free implementation of discontinuous galerkin method for hyperbolic equations a discontinuous galerkin formulation that avoids the use of discrete quadrature formulas is described and applied to linear and nonlinear test problems in one and two space dimensions this approach requires less computational time and storage than conventional implementations but preserves the compactness and robustness inherent in the discontinuous galerkin method test problems include the linear and nonlinear one dimensional scalar advection of smooth initial value problems that are discretized by using unstructured grids with varying degrees of smoothness and regularity and two dimensional linear euler solutions on unstructured grids

memory based snowdrift game on networks we present a memory based snowdrift game mbsg taking place on networks we found that when a lattice is taken to be the underlying structure the transition of spatial patterns at some critical values of the payoff parameter is observable for both four and eight neighbor lattices the transition points as well as the styles of spatial patterns can be explained by local stability analysis in sharp contrast to previously reported results cooperation is promoted by the spatial structure in the mbsg interestingly we found that the frequency of cooperation of the mbsg on a scale free network peaks at a specific value of the payoff parameter this phenomenon indicates that properly encouraging selfish behaviors can optimally enhance the cooperation the memory effects of individuals are discussed in detail and some nonmonotonous phenomena are observed on both lattices and scale free networks our work may shed some new light on the study of evolutionary games over networks

spacetime dimensional analysis and self similar solutions of linear elastodynamics and cohesive dynamic fracture we present a dimensional analysis and self similar solutions for linear elastodynamics with extensions to dynamic fracture models based on cohesive traction separation relations we formulate the problem using differential forms in spacetime and show that the scaling rules expressed in terms of forms are simpler and more uniform than those obtained for tensor representations of the solution in the extension to cohesive elastodynamic fracture we identify and study the influence of certain intrinsic cohesive scales on dynamic fracture behavior and describe a fundamental set of nondimensional groups that uniquely identifies families of self similar solutions we present numerical studies of the influence of selected nondimensional parameters on dynamic fracture response to verify the dimensional analysis including the identification of the fundamental set for cohesive fracture mechanics we show that distinct values of a widely used nondimensional quantity can produce self similar solutions therefore this quantity is not fundamental and it cannot parameterize dynamic cohesive fracture response

applying electromagnetism like mechanism for feature selection in recent years methods of feature selection have been increasingly emphasized as venues for reducing cost and shortening the length of time required for computation in data mining this study utilizes electromagnetism like mechanism as a wrapper approach to feature selection birbil and fang proposed em in 2003 em uses the attraction repulsion mechanism of the electromagnetism theory to ascertain the optimal solution although em has been applied to the topic of optimization in continuous space and a small number of studies on discrete problems it has not been applied to the subject of feature selection in this study em combined with 1 nearest neighbor 1nn was applied for feature selection and classification this study utilized the total force exerted on a particle and evaluated this force to determine which features are to be selected the most crucial features were selected according to the proposed method based on the minimum miss classification rate which was attained through 1nn an unknown datum was classified by 1nn based on the chosen reduced model to estimate the effectiveness of the proposed method a numerical experiment was conducted using several data sets with diverse sizes features separability and classes experimental results indicated that the proposed method outperformed other well known algorithms in not only balanced classification accuracy but also efficiency of feature selection lastly this study used an actual case concerning gestational diabetes mellitus to demonstrate the workability of the proposed method

weighted scale free networks in euclidean space using local selection rule received 23 july 2005 revised manuscript received 21 july 2006 published 22 september 2006a spatial scale free network is introduced and studied whose motivation originated in the growing internetas well as airport networks we argue that in these real world networks a new node necessarily selects one ofits neighboring local nodes for connection and is not controlled by preferential attachment as in the barabasi albert ba model this observation is mimicked in our model where the nodes pop up at randomly locatedpositions in the euclidean space and are connected to one end of the nearest link in spite of this crucialdifference it is observed that the leading behavior of our network is like that of the ba model de ning the linkweight as an algebraic power of its euclidean length the weight distribution and the nonlinear dependence ofthe nodal strength on the degree are analytically calculated it is claimed that a power law decay of the linkweights with time ensures such nonlinear behavior switching off the euclidean space from the same modelyields a much simpler de nition of the ba model where numerical effort grows linearly with

the effect of weight on community structure of networks abstract the effect of weight on community structures is investigated in this paper we use weighted modularity q w to evaluate the partitions and weighted extremal optimization algorithm to detect communities starting from empirical and idealized weighted networks the matching between weights and edges are disturbed then using similarity function s to measure the difference between community structures it is found that the redistribution of weights does strongly affect the community structure especially in dense networks this indicates that the community structure in networks is a suitable property to reflect the role of weight

effects of accelerating growth on the evolution of weighted complex networks many real systems possess accelerating statistics where the total number of edges grows faster than the network size in this paper we propose a simple weighted network model with accelerating growth we derive analytical expressions for the evolutions and distributions for strength degree and weight which are relevant to accelerating growth we also find that accelerating growth determines the clustering coefficient of the networks interestingly the distributions for strength degree and weight display a transition from scale free to exponential form when the parameter with respect to accelerating growth increases from a small to large value all the theoretical predictions are successfully contrasted with numerical simulations

feature selection via coalitional game theory we present and study the contribution selection algorithm csa a novel algorithm for feature selection the algorithm is based on the multiperturbation shapley analysis msa a framework that relies on game theory to estimate usefulness the algorithm iteratively estimates the usefulness of features and selects them accordingly using either forward selection or backward elimination it can optimize various performance measures over unseen data such as accuracy balanced error rate and area under receiver operator characteristic curve empirical comparison with several other existing feature selection methods shows that the backward elimination variant of csa leads to the most accurate classification results on an array of data sets

maximal planar networks with large clustering coefficient and power law degree distribution in this article we propose a simple rule that generates scale free networks with very large clustering coefficient and very small average distance these networks are called random apollonian networks rans as they can be considered as a variation of apollonian networks we obtain the analytic results of power law exponent ensuremath gamma 3 and clustering coefficient c frac 46 3 ensuremath 36 phantom rule 0 2em 0ex mathrm ln phantom rule 0 2em 0ex frac 3 2 ensuremath approx 0 74 which agree with the simulation results very well we prove that the increasing tendency of average distance of rans is a little slower than the logarithm of the number of nodes in rans since most real life networks are both scale free and small world networks rans may perform well in mimicking the reality the rans possess hierarchical structure as c k ensuremath sim k ensuremath 1 that are in accord with the observations of many real life networks in addition we prove that rans are maximal planar networks which are of particular practicability for layout of printed circuits and so on the percolation and epidemic spreading process are also studied and the comparisons between rans and barab asi albert ba as well as newman watts nw networks are shown we find that when the network order n the total number of nodes is relatively small as n ensuremath sim 10 4 the performance of rans under intentional attack is not sensitive to n while that of ba networks is much affected by n and the diseases spread slower in rans than ba networks in the early stage of the suseptible infected process indicating that the large clustering coefficient may slow the spreading velocity especially in the outbreaks

a one field full discontinuous galerkin method for kirchhoff love shells applied to fracture mechanics abstract in order to model fracture the cohesive zone method can be coupled in a very efficient way with the finite element method nevertheless there are some drawbacks with the classical insertion of cohesive elements it is well known that on one the hand if these elements are present before fracture there is a modification of the structure stiffness and that on the other hand their insertion during the simulation requires very complex implementation especially with parallel codes these drawbacks can be avoided by combining the cohesive method with the use of a discontinuous galerkin formulation in such a formulation all the elements are discontinuous and the continuity is weakly ensured in a stable and consistent way by inserting extra terms on the boundary of elements the recourse to interface elements allows to substitute them by cohesive elements at the onset of fracture the purpose of this paper is to develop this formulation for kirchhoff love plates and shells it is achieved by the establishment of a full dg formulation of shell combined with a cohesive model which is adapted to the special thickness discretization of the shell formulation in fact this cohesive model is applied on resulting reduced stresses which are the basis of thin structures formulations finally numerical examples demonstrate the efficiency of the method

topological transition features and synchronizability of a weighted hybrid preferential network abstract in this work we propose a weighted hybrid preferential network model by introducing a hybrid preferential attachment mechanism to a weighted network model proposed by barrat barthelemy and vespignani phys rev e 70 2004 066149 the new model is called hybrid preferential bbv hp bbv model topological properties and synchronizability of the hp bbv model are investigated we find that as the hybrid ratio of determinate to random preferential attachment increases the average clustering coefficient increases the average path length and the assortative coefficient decrease the synchronizability of type i hp bbv network is enhanced but the synchronizability of type ii hp bbv network is weakened

feature selection with ensembles artificial variables and redundancy elimination predictive models benefit from a compact non redundant subset of features that improves interpretability and generalization modern data sets are wide dirty mixed with both numerical and categorical predictors and may contain interactive effects that require complex models this is a challenge for filters wrappers and embedded feature selection methods we describe details of an algorithm using tree based ensembles to generate a compact subset of non redundant features parallel and serial ensembles of trees are combined into a mixed method that can uncover masking and detect features of secondary effect simulated and actual examples illustrate the effectiveness of the approach

universal robustness characteristic of weighted networks against cascading failure we investigate the cascading failure on weighted complex networks by adopting a local weighted flow redistribution rule where the weight of an edge is k i k j theta with k i and k j being the degrees of the nodes connected by the edge assume that a failed edge leads only to a redistribution of the flow passing through it to its neighboring edges we found that the weighted complex network reaches the strongest robustness level when the weight parameter theta 1 where the robustness is quantified by a transition from normal state to collapse we determined that this is a universal phenomenon for all typical network models such as small world and scale free networks we then confirm by theoretical predictions this universal robustness characteristic observed in simulations we furthermore explore the statistical characteristics of the avalanche size of a network thus obtaining a power law avalanche size distribution together with a tunable exponent by varying theta our findings have great generality for characterizing cascading failure induced disasters in nature

model selection and validation methods for non linear systems the theory of hypothesis testing is used to select a model with the correct structure and the relation of such a method to the aic and fpe criteria is investigated parametric validation and correlation validation methods are developed for non non linear difference equation models several shortcomings of traditional methods especially when applied to non linear systems are described

the effect of generalized deactivation mechanism in weighted networks abstract in this paper we propose a generalized deactivation model to characterize weighted networks by introducing the special aging mechanism the model can produce power law distributions of degree strength and weight as confirmed in many real networks we also characterize the clustering and correlation properties of this class of networks a scaling behavior of clustering coefficient c 1 m is observed where m refers to the number of active nodes the generated network simultaneously exhibits hierarchical organization and disassortative degree correlation all of these structural properties are confirmed by present empirical evidence

fingerprinting networks correlations of local and global network properties in complex networks a common task is to identify the most important or central nodes there are several definitions often called centrality measures which often lead to different results here we introduce fingerprints of networks which we define as correlation plots of local and global network properties we show that these fingerprints are suitable tools for characterizing networks beyond single quantity distributions in particular we study the correlations between four local and global measures namely the degree the shortest path betweenness the random walk betweenness and the subgraph centrality on different random network models like erd s renyi small world and barabasi albert as well as on different real networks like metabolic pathways social collaborations and computer networks and compare those fingerprints to determine the quality of those basic models the correlation fingerprints are quite different between the real networks and the model networks questioning whether the models really reflect all important properties of the real world

age based model for weighted network with general assortative mixing abstract in this paper we propose an evolutionary model for weighted networks by introducing an age based mutual selection mechanism our model generates power law distributions of degree weight and strength which are confirmed by analytical predictions and are consistent with real observations the investigation of the relationship between clustering and the connectivity of nodes suggests hierarchical organization in the weighted networks furthermore both assortative and disassortative properties can be naturally obtained by tuning a parameter which controls the strength of age based preferential attachments since the age information of nodes is easier to acquire than the degree and strength of nodes and almost all empirically observed structural and weighted properties can be reproduced by the simple evolutionary regulation our model may reveal some underlying mechanisms that are key for the evolution of weighted complex networks

the generalized finite element method this paper describes a pilot design and implementation of the generalized finite element method gfem as a direct extension of the standard finite element method sfem or fem which makes possible the accurate solution of engineering problems in complex domains which may be practically impossible to solve using the fem the development of the gfem is illustrated for the laplacian in two space dimensions in domains which may include several hundreds of voids and or cracks for which the construction of meshes used by the fem is practically impossible the two main capabilities are 1 it can construct the approximation using meshes which may overlap part or all of the domain boundary 2 it can incorporate into the approximation handbook functions which are known analytically or are generated numerically and approximate well the solution of the boundary value problem in the neighborhood of corner points voids cracks etc the main tool is a special integration algorithm which we call the fast remeshing approach which is robust and works for any domain with arbitrary complexity the incorporation of the handbook functions into the gfem is done by employing the partition of unity method pum the presented formulations and implementations can be easily extended to the multi material medium where the voids are replaced by inclusions of various shapes and sizes and to the case of the elasticity problem this work can also be understood as a pilot study for the feasibility and demonstration of the capabilities of the gfem which is needed before analogous implementations are attempted in the three dmensional and nonlinear cases which are the cases of main interest for future work

adaptive spacetime discontinuous galerkin method for hyperbolic advection diffusion with a non negativity constraint summary applications where the diffusive and advective time scales are of similar order give rise to advection diffusion phenomena that are inconsistent with the predictions of parabolic fickian diffusion models non fickian diffusion relations can capture these phenomena and remedy the paradox of infinite propagation speeds in fickian models in this work we implement a modified frame invariant form of cattaneo s hyperbolic diffusion relation within a spacetime discontinuous galerkin advection diffusion model an h adaptive spacetime meshing procedure supports an asynchronous patch by patch solution procedure with linear computational complexity in the number of spacetime elements this localized solver enables the selective application of optimization algorithms in only those patches that require inequality constraints to ensure a non negative concentration solution in contrast to some previous methods we do not modify the numerical fluxes to enforce non negative concentrations thus the element wise conservation properties that are intrinsic to discontinuous galerkin models are defined with respect to physically meaningful riemann fluxes on the element boundaries we present numerical examples that demonstrate the effectiveness of the proposed model and we explore the distinct features of hyperbolic advection diffusion response in subcritical and supercritical flows copyright 2015 john wiley sons ltd

an optimal network for passenger traffic abstract the optimal solution of an inter city passenger transport network has been studied using zipf s law for the city populations and the gravity law describing the fluxes of inter city passenger traffic assuming a fixed value for the cost of transport per person per kilometer we observe that while the total traffic cost decreases the total wiring cost increases with the density of links as a result the total cost to maintain the traffic distribution is optimal at a certain link density which vanishes on increasing the network size at a finite link density the network is scale free using this model the air route network of india has been generated and an one to one comparison of the nodal degree values with the real network has been made

statistics of weighted treelike networks we study the statistics of growing networks with a tree topology in which each link carries a weight k i k j theta where k i and k j are the node degrees at the end points of link ij network growth is governed by preferential attachment in which a newly added node attaches to a node of degree k with rate a k k lambda for general values of theta and lambda we compute the total weight of a network as a function of the number of nodes n and the distribution of link weights generically the total weight grows as n for lambda theta 1 and superlinearly otherwise the link weight distribution is predicted to have a power law form that is modified by a logarithmic correction for the case lambda 0 we also determine the node strength defined as the sum of the weights of the links that attach to the node as function of k using known results for degree correlations we deduce the scaling of the node strength on k and n

organization of growing random networks the organizational development of growing random networks is investigated these growing networks are built by adding nodes successively and linking each to an earlier node of degree k with an attachment probability a k when a k grows more slowly than linearly with k the number of nodes with k links n k t decays faster than a power law in k while for a k growing faster than linearly in k a single node emerges which connects to nearly all other nodes when a k is asymptotically linear n k t ensuremath sim mathrm tk ensuremath ensuremath nu with ensuremath nu dependent on details of the attachment probability but in the range 2l ensuremath nu l ensuremath infty the combined age and degree distribution of nodes shows that old nodes typically have a large degree there is also a significant correlation in the degrees of neighboring nodes so that nodes of similar degree are more likely to be connected the size distributions of the in and out components of the network with respect to a given node namely its descendants and ancestors are also determined the in component exhibits a robust s ensuremath 2 power law tail where s is the component size the out component has a typical size of order mathrm ln t and it provides basic insights into the genealogy of the network

the design and analysis of the generalized finite element method abstract in this paper we introduce the generalized finite element method gfem as a combination of the classical finite element method fem and the partition of unity method pum the standard finite element spaces are augmented by adding special functions which reflect the known information about the boundary value problem and the input data e g the singular functions obtained from the local asymptotic expansion of the exact solution in the neighborhood of a corner point etc the special functions are multiplied with the partition of unity corresponding to the standard linear vertex shape functions and pasted together with the existing finite element basis to construct an augmented conforming finite element space in this way the local approximability afforded by the special functions is included in the approximation while maintaining the existing infrastructure of finite element codes the major features of the gfem are 1 the essential boundary conditions can be imposed exactly as in the standard fem unlike other partition of unity based methods where this is a major issue 2 the accuracy of the numerical integration of the entries of the stiffness matrix and load vector is controlled adaptively so that the errors in integration of the special functions do not affect the accuracy of the constructed approximation this issue also has not been sufficiently addressed in other implementations of partition of unity or meshless methods and 3 linear dependencies in the system of equations are resolved by employing an easy modification of the direct linear solver the power of the gfem for solving problems in domains with complex geometry with less error and less computer resources than the standard fem is illustrated by numerical examples

riemann solutions and spacetime discontinuous galerkin method for linear elastodynamic contact abstract we derive riemann solutions for stick slip and separation contact modes in a linear elastic material with an isotropic coulomb friction relation and explore their numerical implementation the riemann solutions preserve the characteristic structure of the underlying elastodynamic system and imply dynamic contact conditions that are distinct from the quasi static conditions used in some numerical models nonphysical discontinuities in the standard coulomb model at stick slip transitions can cause contact mode chatter in numerical simulations we restate the coulomb relation to remove these artificial discontinuities and eliminate the need for algorithmic remedies discontinuous response at abrupt separation to contact transitions is physically reasonable and we propose a regularization scheme to address this case we implement the riemann contact solutions within an adaptive spacetime discontinuous galerkin sdg code and report numerical results that demonstrate the model s efficacy

large scale topological and dynamical properties of the internet we study the large scale topological and dynamical properties of real internet maps at the autonomous system level collected in a 3 yr time interval we find that the connectivity structure of the internet presents statistical distributions settled in a well defined stationary state the large scale properties are characterized by a scale free topology consistent with previous observations correlation functions and clustering coefficients exhibit a remarkable structure due to the underlying hierarchical organization of the internet the study of the internet time evolution shows a growth dynamics with aging features typical of recently proposed growing network models we compare the properties of growing network models with the present real internet data analysis

theory and numerics for finite deformation fracture modelling using strong discontinuities a general finite element approach for the modelling of fracture is presented for the geometrically non linear case the kinematical representation is based on a strong discontinuity formulation in line with the concept of partition of unity for finite elements thus the deformation map is defined in terms of one continuous and one discontinuous portion considered as mutually independent giving rise to a weak formulation of the equilibrium consisting of two coupled equations in addition two different fracture criteria are considered firstly a principle stress criterion in terms of the material mandel stress in conjunction with a material cohesive zone law relating the cohesive mandel traction to a material displacement jump associated with the direct discontinuity secondly a criterion of griffith type is formulated in terms of the material crack driving force mcdf with the crack propagation direction determined by the direction of the force corresponding to the direction of maximum energy release apart from the material modelling the numerical treatment and aspects of computational implementation of the proposed approach is also thoroughly discussed and the paper is concluded with a few numerical examples illustrating the capabilities of the proposed approach and the connection between the two fracture criteria copyright 2005 john wiley sons ltd

geographical networks evolving with an optimal policy in this article we propose a growing network model based on an optimal policy involving both topological and geographical measures in this model at each time step a new node having randomly assigned coordinates in a 1 1 square is added and connected to a previously existing node i which minimizes the quantity r 2 k where ri is the geographical distance ki the degree and a free parameter the degree distribution obeys a power law form when 1 and an exponential

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

on the relevance of linear discriminative features linear discriminant analysis lda has been widely used to extract linear features for classification in real applications the usefulness of the extracted features usually needs to be confirmed using an error rate of classification embedded in a classifier little attention has been paid to whether and how discriminative features themselves can be interpreted as indicators of usefulness we refer to this as relevance i e the capability of discriminative features to characterize the contribution of the original variables to classification we approach the relevance by considering how it could be lost while extracting optimal discriminative features then the discrepancy between the relevance and optimality of discriminative features is shown to originate from the angle between the space spanned by eigenvectors of the within class scattering matrix and the primary space in which the original variables reside in particular for a given dataset the larger the angle the less evident is the relevance discovered from optimal discriminative features furthermore the relevance and optimality are regarded as two constraint conditions or a tradeoff in order to extract relevant discriminative features at last a simulated experiment is used to show how the relevance is lost when the angle is changed experimental results based on both usps handwritten digitals and pie face databases show that a maximum margin criterion is a reasonable compromise between the relevance and optimality since it approximates the averaged class margin using euclidean distance measured in the primary space

modeling the evolution of weighted networks we present a general model for the growth of weighted networks in which the structural growth is coupled with the edges weight dynamical evolution the model is based on a simple weight driven dynamics and a weights reinforcement mechanism coupled to the local network growth that coupling can be generalized in order to include the effect of additional randomness and nonlinearities which can be present in real world networks the model generates weighted graphs exhibiting the statistical properties observed in several real world systems in particular the model yields a nontrivial time evolution of vertices properties and scale free behavior with exponents depending on the microscopic parameters characterizing the coupling rules very interestingly the generated graphs spontaneously achieve a complex hierarchical architecture characterized by clustering and connectivity correlations varying as a function of the vertices degree

a space time discontinuous galerkin method for linearized elastodynamics with element wise momentum balance abstract we present a new space time discontinuous galerkin finite element method for linearized elastodynamics that delivers exact balance of linear and angular momentum over every space time element the method is formulated for use with fully unstructured space time grids and uses displacement basis functions that are discontinuous across all inter element boundaries we introduce a new space time formulation of continuum elastodynamics that uses differential forms and the exterior calculus on manifolds to generate a system of space time field equations and jump conditions then we invoke a bubnov galerkin weighted residuals procedure to formulate the finite element method we describe an implementation on patch wise causal meshes that features linear complexity in the number of elements and special per pixel accurate visualization numerical examples confirm an a priori error estimate and demonstrate the method s shock capturing capabilities

transport on weighted networks when the correlations are independent of the degree most real world networks are weighted graphs with the weight of the edges reflecting the relative importance of the connections in this work we study nondegree dependent correlations between edge weights generalizing thus the correlations beyond the degree dependent case we propose a simple method to introduce weight weight correlations in topologically uncorrelated graphs this allows us to test different measures to discriminate between the different correlation types and to quantify their intensity we also discuss here the effect of weight correlations on the transport properties of the networks showing that positive correlations dramatically improve transport finally we give two examples of real world networks social and transport graphs in which weight weight correlations are present

a scalable 3d fracture and fragmentation algorithm based on a hybrid discontinuous galerkin cohesive element method abstract a scalable algorithm for modeling dynamic fracture and fragmentation of solids in three dimensions is presented the method is based on a combination of a discontinuous galerkin dg formulation of the continuum problem and cohesive zone models czm of fracture prior to fracture the flux and stabilization terms arising from the dg formulation at interelement boundaries are enforced via interface elements much like in the conventional intrinsic cohesive element approach albeit in a way that guarantees consistency and stability upon the onset of fracture the traction separation law tsl governing the fracture process becomes operative without the need to insert a new cohesive element upon crack closure the reinstatement of the dg terms guarantee the proper description of compressive waves across closed crack surfaces the main advantage of the method is that it avoids the need to propagate topological changes in the mesh as cracks and fragments develop which enables the indistinctive treatment of crack propagation across processor boundaries and thus the scalability in parallel computations another advantage of the method is that it preserves consistency and stability in the uncracked interfaces thus avoiding issues with wave propagation typical of intrinsic cohesive element approaches a simple problem of wave propagation in a bar leading to spall at its center is used to show that the method does not affect wave characteristics and as a consequence properly captures the spall process we also demonstrate the ability of the method to capture intricate patterns of radial and conical cracks arising in the impact of ceramic plates which propagate in the mesh impassive to the presence of processor boundaries

reshuffling scale free networks from random to assortative to analyze the role of assortativity in networks we introduce an algorithm which produces assortative mixing to a desired degree this degree is governed by one parameter p changing this parameter one can construct networks ranging from fully random p 0 to totally assortative p 1 we apply the algorithm to a barabasi albert scale free network and show that the degree of assortativity is an important parameter governing the geometrical and transport properties of networks thus the average path length of the network increases dramatically with the degree of assortativity moreover the concentration dependences of the size of the giant component in the node percolation problem for uncorrelated and assortative networks are strongly different the behavior of the clustering coefficient is also discussed

branching process in a stochastic extremal model we considered a stochastic version of the bak sneppen model sbsm of ecological evolution where the number m of sites mutated in a mutation event is restricted to only two here the mutation zone consists of only one site and this site is randomly selected from the neighboring sites at every mutation event in an annealed fashion the critical behavior of the sbsm is found to be the same as the bs model in dimensions d 1 and 2 however on the scale free graphs the critical fitness value is nonzero even in the thermodynamic limit but the critical behavior is mean field like finally m has been made even smaller than two by probabilistically updating the mutation zone which also shows the original bs model behavior we conjecture that a sbsm on any arbitrary graph with any small branching factor greater than unity will lead to a self organized critical state

dimensionality reduction via sparse support vector machines we describe a methodology for performing variable ranking and selection using support vector machines svms the method constructs a series of sparse linear svms to generate linear models that can generalize well and uses a subset of nonzero weighted variables found by the linear models to produce a final nonlinear model the method exploits the fact that a linear svm no kernels with l1 norm regularization inherently performs variable selection as a side effect of minimizing capacity of the svm model the distribution of the linear model weights provides a mechanism for ranking and interpreting the effects of variables starplots are used to visualize the magnitude and variance of the weights for each variable we illustrate the effectiveness of the methodology on synthetic data benchmark problems and challenging regression problems in drug design this method can dramatically reduce the number of variables and outperforms svms trained using all attributes and using the attributes selected according to correlation coefficients the visualization of the resulting models is useful for understanding the role of underlying variables

asymmetry between odd and even node weight in complex networks abstract phenomenon of asymmetry between odd and even node weight distribution in some complex networks such as public transportation networks and internet is presented reasons related to this phenomenon are summarized i e 1 edges are solid connections between nodes which are embedded in real geometric background and 2 preferential mechanism during the process of network formation incorporating these two points complex networks are constructed by self avoiding random walk on 2d grid and the simulation results are consistent well with that of empirical researches

ranking a random feature for variable and feature selection we describe a feature selection method that can be applied directly to models that are linear with respect to their parameters and indirectly to others it is independent of the target machine it is closely related to classical statistical hypothesis tests but it is more intuitive hence more suitable for use by engineers who are not statistics experts furthermore some assumptions of classical tests are relaxed the method has been used successfully in a number of applications that are briefly described

orthogonal least squares learning algorithm for radial basis function networks the radial basis function network offers a viable alternative to the two layer neural network in many applications of signal processing a common learning algorithm for radial basis function networks is based on first choosing randomly some data points as radial basis function centers and then using singular value decomposition to solve for the weights of the network such a procedure has several drawbacks and in particular an arbitrary selection of centers is clearly unsatisfactory the authors propose an alternative learning procedure based on the orthogonal least squares method the procedure chooses radial basis function centers one by one in a rational way until an adequate network has been constructed in the algorithm each selected center maximizes the increment to the explained variance or energy of the desired output and does not suffer numerical ill conditioning problems the orthogonal least squares learning strategy provides a simple and efficient means for fitting radial basis function networks this is illustrated using examples taken from two different signal processing applications

the architecture of complex weighted networks networked structures arise in a wide array of different contexts such as technological and transportation infrastructures social phenomena and biological systems these highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity along with a complex topological structure real networks display a large heterogeneity in the capacity and intensity of the connections these features however have mainly not been considered in past studies where links are usually represented as binary states i e either present or absent here we study the scientific collaboration network and the world wide air transportation network which are representative examples of social and large infrastructure systems respectively in both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network we define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices this information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network these results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks

pseudofractal scale free web we find that scale free random networks are excellently modeled by simple deterministic graphs our graph has a discrete degree distribution degree is the number of connections of a vertex which is characterized by a power law with exponent gamma 1 ln 3 ln 2 properties of this compact structure are surprisingly close to those of growing random scale free networks with gamma in the most interesting region between 2 and 3 we succeed to find exactly and numerically with high precision all main characteristics of the graph in particular we obtain the exact shortest path length distribution for a large network ln n 1 the distribution tends to a gaussian of width approximately sqrt ln n centered at l approximately ln n we show that the eigenvalue spectrum of the adjacency matrix of the graph has a power law tail with exponent 2 gamma

self organization versus hierarchy in open source social networks complex networks emerge under different conditions including design i e top down decisions through simple rules of growth and evolution such rules are typically local when dealing with biological systems and most social webs an important deviation from such a scenario is provided by groups collectives of agents engaged in technology development such as open source communities here we analyze their network structure showing that it defines a complex weighted network with scaling laws at different levels as measured by looking at e mail exchanges we also present a simple model of network growth involving nonlocal rules based on betweenness centrality our weighted network analysis suggests that a well defined interplay between the overall goals of the community and the underlying hierarchical organization play a key role in shaping its dynamics

unified model for network dynamics exhibiting nonextensive statistics we introduce a dynamical network model which unifies a number of network families which are individually known to exhibit q exponential degree distributions the present model dynamics incorporates static nongrowing self organizing networks preferentially growing networks and preferentially rewiring networks further it exhibits a natural random graph limit the proposed model generalizes network dynamics to rewiring and growth modes which depend on internal topology as well as on a metric imposed by the space they are embedded in in all of the networks emerging from the presented model we find q exponential degree distributions over a large parameter space we comment on the parameter dependence of the corresponding entropic index q for the degree distributions and on the behavior of the clustering coefficients and neighboring connectivity distributions

an adaptive spacetime discontinuous galerkin method for cohesive models of elastodynamic fracture this paper describes an adaptive numerical framework for cohesive fracture models based on a spacetime discontinuous galerkin sdg method for elastodynamics with elementwise momentum balance discontinuous basis functions and jump conditions written with respect to target traction values simplify the implementation of cohesive traction separation laws in the sdg framework no special cohesive elements or other algorithmic devices are required we use unstructured spacetime grids in a h adaptive implementation to adjust simultaneously the spatial and temporal resolutions two independent error indicators drive the adaptive refinement one is a dissipation based indicator that controls the accuracy of the solution in the bulk material the second ensures the accuracy of the discrete rendering of the cohesive law applications of the sdg cohesive model to elastodynamic fracture demonstrate the effectiveness of the proposed method and reveal a new solution feature an unexpected quasi singular structure in the velocity response numerical examples demonstrate the use of adaptive analysis methods in resolving this structure as well as its importance in reliable predictions of fracture kinetics copyright 2009 john wiley sons ltd

mutual selection model for weighted networks for most networks the connection between two nodes is the result of their mutual affinity and attachment in this paper we propose a mutual selection model to characterize the weighted networks by introducing a general mechanism of mutual selection the model can produce power law distributions of degree weight and strength as confirmed in many real networks moreover we also obtained the nontrivial clustering coefficient c degree assortativity coefficient r and degree strength correlation depending on a single parameter m these results are supported by present empirical evidence studying the degree dependent average clustering coefficient c k and the degree dependent average nearest neighbors degree k nn k also provide us with a better description of the hierarchies and organizational architecture of weighted networks

mixing patterns in networks we study assortative mixing in networks the tendency for vertices in networks to be connected to other vertices that are like or unlike them in some way we consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age as a special example of the latter we consider mixing according to vertex degree i e according to the number of connections vertices have to other vertices do gregarious people tend to associate with other gregarious people we propose a number of measures of assortative mixing appropriate to the various mixing types and apply them to a variety of real world networks showing that assortative mixing is a pervasive phenomenon found in many networks we also propose several models of assortatively mixed networks both analytic ones based on generating function methods and numerical ones based on monte carlo graph generation techniques we use these models to probe the properties of networks as their level of assortativity is varied in the particular case of mixing by degree we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices

modulated scale free network in euclidean space a random network is grown by introducing at unit rate randomly selected nodes on the euclidean space a node is randomly connected to its ith predecessor of degree k i with a directed link of length l using a probability proportional to k i l alpha our numerical study indicates that the network is scale free for all values of alpha alpha c and the degree distribution decays stretched exponentially for the other values of alpha the link length distribution follows a power law d l approximately l delta where delta is calculated exactly for the whole range of values of alpha