thresholds for epidemic spreading in networks we study the threshold of epidemic models in quenched networks with degree distribution given by a power law forthesusceptible infected susceptiblemodeltheactivitythresholdc vanishesinthelargesize limitonanynetworkwhosemaximumdegree kmax divergeswiththesystemsize atoddswithheterogeneous mean field hmf theory the vanishing of the threshold has nothing to do with the scale free nature of the networkbutstemsinsteadfromthelargesthubinthesystembeingactiveforanyspreadingrate 1 ffiffiffiffiffiffiffiffiffimax p and playing the role of a self sustained source that spreads the infection to the rest of the system the susceptible infected removedmodel displays insteadagreement with hmftheory and afinite threshold for scale rich networks we conjecture that on quenched scale rich networks the threshold of generic epidemic models is vanishing or finite depending on the presence or absence of a steady state

adaptive mixed finite element method for reissner mindlin plate abstract mixed finite element methods are designed to overcome shear locking phenomena observed in the numerical treatment of reissner mindlin plate models automatic adaptive mesh refining algorithms are an important tool to improve the approximation behavior of the finite element discretization in this paper a reliable and robust residual based a posteriori error estimate is derived which evaluates a t depending residual norm based on results in d arnold r falk r winther math modell numer anal 31 1997 517 557 the localized error indicators suggest an adaptive algorithm for automatic mesh refinement numerical examples prove that the new scheme is efficient

a new class of mixed finite element methods for reissner mindlin plates a new class of finite elements for the reissner mindlin plate problem is presented the family is based on a modified mixed formulation recently introduced by arnold and brezzi boundary value problems for partial differential equations and applications j l lions and c baiocchi eds masson paris 1993 a result of stability and convergence uniformly in the thickness is provided

residual based a posteriori error estimate for a mixed reiβner mindlin plate finite element method reliable and efficient residual based a posteriori error estimates are established for the stabilised locking free finite element methods for the reissner mindlin plate model the error is estimated by a computable error estimator from above and below up to multiplicative constants that do neither depend on the mesh size nor on the plate s thickness and are uniform for a wide range of stabilisation parameter the error is controlled in norms that are known to converge to zero in a quasi optimal way an adaptive algorithm is suggested and run for improving the convergence rates in three numerical examples for thicknesses 0 1 001 and 001

importance of small degree nodes in assortative networks with degree weight correlations it has been known that assortative network structure plays an important role in spreading dynamics for unweighted networks yet its influence on weighted networks is not clear in particular when weight is strongly correlated with the degrees of the nodes as we empirically observed in twitter here we use the self consistent probability method and revised nonperturbative heterogenous mean field theory method to investigate this influence on both susceptible infective recovered sir and susceptible infective susceptible sis spreading dynamics both our simulation and theoretical results show that while the critical threshold is not significantly influenced by the assortativity the prevalence in the supercritical regime shows a crossover under different degree weight correlations in particular unlike the case of random mixing networks in assortative networks the negative degree weight correlation leads to higher prevalence in their spreading beyond the critical transmissivity than that of the positively correlated in addition the previously observed inhibition effect on spreading velocity by assortative structure is not apparent in negatively degree weight correlated networks while it is enhanced for that of the positively correlated detailed investigation into the degree distribution of the infected nodes reveals that small degree nodes play essential roles in the supercritical phase of both sir and sis spreadings our results have direct implications in understanding viral information spreading over online social networks and epidemic spreading over contact networks

critical behavior of propagation on small world networks we report numerical evidence that an epidemiclike model which can be interpreted as the propagation of a rumor exhibits critical behavior at a finite randomness of the underlying small world network the transition occurs between a regime where the rumor dies in a small neighborhood of its origin and a regime where it spreads over a finite fraction of the whole population critical exponents are evaluated through finite size scaling analysis and the dependence of the critical randomness with the network connectivity is studied the behavior of this system as a function of the small network randomness bears noticeable similarities with an epidemiological model reported recently m kuperman and g abramson phys rev lett 86 2909 2001 in spite of substantial differences in the respective dynamical rules

contribution of large scale biases in decoding of direction of motion from high resolution fmri data in human early visual cortex previous studies have demonstrated that the perceived direction of motion of a visual stimulus can be decoded from the pattern of functional magnetic resonance imaging fmri responses in occipital cortex using multivariate analysis methods kamitani and tong 2006 one possible mechanism for this is a difference in the sampling of direction selective cortical columns between voxels implying that information at a level smaller than the voxel size might be accessible with fmri alternatively multivariate analysis methods might be driven by the organization of neurons into clusters or even orderly maps at a much larger scale to assess the possible sources of the direction selectivity observed in fmri data we tested how classification accuracy varied across different visual areas and subsets of voxels for classification of motion direction to enable high spatial resolution functional mri measurements 1 5 mm isotropic voxels data were collected at 7 t to test whether information about the direction of motion is represented at the scale of retinotopic maps we looked at classification performance after combining data across different voxels within visual areas v1 3 and mt v5 before training the multivariate classifier a recent study has shown that orientation biases in v1 are both necessary and sufficient to explain classification of stimulus orientation freeman et al 2011 here we combined voxels with similar visual field preference as determined in separate retinotopy measurements and observed that classification accuracy was preserved when averaging in this retinotopically restricted way compared to random averaging of voxels this insensitivity to averaging of voxels with similar visual angle preference across substantial distances in cortical space suggests that there are large scale biases at the level of retinotopic maps underlying our ability to classify direction of motion

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

dynamics of rumor propagation on small world networks we study the dynamics of an epidemiclike model for the spread of a rumor on a small world network it has been shown that this model exhibits a transition between regimes of localization and propagation at a finite value of the network randomness here by numerical means we perform a quantitative characterization of the evolution in the two regimes the variant of dynamic small worlds where the quenched disorder of small world networks is replaced by randomly changing connections between individuals is also analyzed in detail and compared with a mean field approximation

generation of uncorrelated random scale free networks uncorrelated random scale free networks are useful null models to check the accuracy and the analytical solutions of dynamical processes defined on complex networks we propose and analyze a model capable of generating random uncorrelated scale free networks with no multiple and self connections the model is based on the classical configuration model with an additional restriction on the maximum possible degree of the vertices we check numerically that the proposed model indeed generates scale free networks with no two and three vertex correlations as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree k respectively complex networks constitute a general framework for the topological characterization of many natural and technological systems whose complexity prevents a more detailed microscopic description f1 3g within this framework these systems are represented in terms of networks or graphs f4g in which vertices stand for the units composing the system while edges among vertices represent the interactions or relations between pairs of units the focus is thus shift to the topological characterization of the representative network a task which is largely more feasible and yields nevertheless a noticeable amount of information on the structure and properties of the original system the empirical analysis of many real complex networks has unveiled the presence of several typical properties widely found in systems belonging to a large variety of realms one of the most relevant is given by the scale free nature of the degree distribution pskd f1 3 5g defined as the probability that a randomly chosen vertex has degree k si e it is connected to other k verticesd in mathematical terms the scale free property translates into a power law function of the form psk d k g

from the hu washizu formulation to the average nodal strain formulation abstract we present a stabilized finite element method for the hu washizu formulation of linear elasticity based on simplicial meshes leading to the stabilized nodal strain formulation or node based uniform strain elements we show that the finite element approximation converges uniformly to the exact solution for the nearly incompressible case

analysis of new augmented lagrangian formulations for mixed finite element schemes two new augmented lagrangian formulations for mixed finite element schemes are presented the methods lead in some cases to an improvement in the order of the approximation an error analysis is provided together with some interesting examples of applications

modelling rumors the no plane pentagon french hoax case abstract the recent astonishing wide adhesion of french people to the rumor claiming no plane did crash on the pentagon on september 11 is given a generic explanation in terms of a model of minority opinion spreading using a majority rule reaction diffusion dynamics a rumor is shown to invade for sure a social group provided it fulfills simultaneously two criteria first it must initiate with a support beyond some critical threshold which however turns out to be always very low then it has to be consistent with some larger collective social paradigm of the group otherwise it just dies out both conditions were satisfied in the french case with the associated book sold at more than 200 000 copies in just a few days the rumor was stopped by the firm stand of most newspaper editors stating it is nonsense such an incredible social dynamics is shown to result naturally from an open and free public debate among friends and colleagues each one searching for the truth sincerely on a free will basis and without individual biases the polarization process appears also to be very quick in agreement with reality it is a very strong anti democratic reversal of opinion although made quite democratically the model may apply to a large range of rumors

vascular contributions to pattern analysis comparing gradient and spin echo fmri at 3t multivariate pattern analysis is often assumed to rely on signals that directly reflect differences in the distribution of particular neural populations the source of the signal used in these analyses remains unclear however and an alternative model suggests that signal from larger draining veins may play a significant role the current study was designed to investigate the vascular contribution to pattern analyses at 3t by comparing the results obtained from gradient and spin echo data classification analyses were carried out comparing line orientations in v1 tone frequencies in a1 and responses from different fingers in m1 in all cases classification accuracy in the spin echo data was not significantly different from chance in contrast classification accuracies in the gradient echo data were significantly above chance and significantly higher than the accuracies observed for the spin echo data these results suggest that at the field strength and spatial resolution used for the majority of fmri studies a considerable proportion of the signal used by pattern analysis originates in the vasculature

epidemic incidence in correlated complex networks a few years ago watts and strogatz 1 introduced a model able to produce networks with properties of both regu lar lattices and random graphs with small diameter their model soon led to a burst of activity in the field 2 3 further spurred by barabasi and co workers who found that many seemingly diverse systems share several topological proper ties such as a power law behavior in their connectivity dis tributions when represented as networks 4 these complex networks are formed by a set of many elements or nodes that are linked together through edges or links if they in teract directly empirical evidence supports that in notable networks such as metabolic or communication webs the probability p k that any node has k links to other nodes is distributed accordingly to a power law p k k 2g 5 7

nonperturbative heterogeneous mean field approach to epidemic spreading in complex networks since roughly a decade ago network science has focused among others on the problem of how the spreading of diseases depends on structural patterns here we contribute to further advance our understanding of epidemic spreading processes by proposing a nonperturbative formulation of the heterogeneous mean field approach that has been commonly used in the physics literature to deal with this kind of spreading phenomena the nonperturbative equations we propose have no assumption about the proximity of the system to the epidemic threshold nor any linear approximation of the dynamics in particular we first develop a probabilistic description at the node level of the epidemic propagation for the so called susceptible infected susceptible family of models and after we derive the corresponding heterogeneous mean field approach we propose to use the full extension of the approach instead of pruning the expansion to first order which leads to a nonperturbative formulation that can be solved by fixed point iteration and used with reliability far away from the epidemic threshold to assess the prevalence of the epidemics our results are in close agreement with monte carlo simulations thus enhancing the predictive power of the classical heterogeneous mean field approach while providing a more effective framework in terms of computational time

asymptotic properties of degree correlated scale free networks the possible correlation profiles of networks with a given scale free degree distribution are restricted and bounded by maximally correlated configurations dissortative networks consist of nested bilayers in which low degree vertices are connected to high degree vertices the number of these bilayers attains a constant value for large network size n assortative networks exhibit monolayers of low degree vertices the number of which grows monotonously with n analytical relations for the pearson correlation coefficient r of these extremal configurations are derived and shown to provide lower and upper bounds on the possible r values both bounds are found to vanish for large networks

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

epidemic dynamics and endemic states in complex networks we study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks in networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null on the contrary on a wide range of scale free networks we observe the absence of an epidemic threshold and its associated critical behavior this implies that scale free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess these results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks

infection dynamics on scale free networks we discuss properties of infection processes on scale free networks relating them to the node connectivity distribution that characterizes the network considering the epidemiologically important case of a disease that confers permanent immunity upon recovery we derive analytic expressions for the final size of an epidemic in an infinite closed population and for the dependence of infection probability on an individual s degree of connectivity within the population as in an earlier study r pastor satorras and a vesipignani phys rev lett 86 3200 2001 phys rev e 63 006117 2001 for an infection that did not confer immunity upon recovery the epidemic process in contrast with many traditional epidemiological models does not exhibit threshold behavior and we demonstrate that this is a consequence of the extreme heterogeneity in the connectivity distribution of a scale free network finally we discuss effects that arise from finite population sizes showing that networks of finite size do exhibit threshold effects infections cannot spread for arbitrarily low transmission probabilities

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

decelerated spreading in degree correlated networks while degree correlations are known to play a crucial role for spreading phenomena in networks their impact on the propagation speed has hardly been understood here we investigate a tunable spreading model on scale free networks and show that the propagation becomes slow in positively negatively correlated networks if nodes with a high connectivity locally accelerate decelerate the propagation examining the efficient paths offers a coherent explanation for this result while the k core decomposition reveals the dependence of the nodal spreading efficiency on the correlation our findings should open new pathways to delicately control real world spreading processes

structure of a large social network we study a social network consisting of over 10 4 individuals with a degree distribution exhibiting two power scaling regimes separated by a critical degree k mathrm crit and a power law relation between degree and local clustering we introduce a growing random model based on a local interaction mechanism that reproduces the observed scaling features and their exponents we suggest that the double power law originates from two very different kinds of networks that are simultaneously present in the human social network

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

a volume averaged nodal projection method for the reissner mindlin plate model abstract we introduce a novel meshfree galerkin method for the solution of reissner mindlin plate problems that is written in terms of the primitive variables only i e rotations and transverse displacement and is devoid of shear locking the proposed approach uses linear maximum entropy basis functions for field variables approximation and is built variationally on a two field potential energy functional wherein the shear strain written in terms of the primitive variables is computed via a volume averaged nodal projection operator that is constructed from the kirchhoff constraint of the three field mixed weak form the meshfree approximation is constructed over a set of scattered nodes that are obtained from an integration mesh of three node triangles on which the meshfree stiffness matrix and nodal force vector are numerically integrated the stability of the method is rendered by adding bubble like enrichment to the rotation degrees of freedom some benchmark problems are presented to demonstrate the accuracy and performance of the proposed method for a wide range of plate thicknesses

the confounding effect of response amplitude on mvpa performance measures multi voxel pattern analysis mvpa is proving very powerful in the analysis of fmri timeseries data yielding surprising sensitivity in many different contexts to the response characteristics of neurons in a given brain region however mvpa yields a metric classification performance that does not readily lend itself to quantitative comparisons across experimental conditions brain regions or people this is because performance is influenced by a number of factors other than the sensitivity of neurons to the experimental manipulation one such factor that varies widely but has been largely ignored in mvpa studies is the amplitude of the response being decoded in a noisy system it is expected that measured classification performance will decline with declining response amplitude even if the underlying neuronal specificity is constant we document the relationship between response amplitude and classification performance in the context of orientation decoding in the visual cortex flickering sine gratings were presented at each of two orthogonal orientations in a block design multivariate experiment or an event related design univariate experiment response amplitude was manipulated by varying stimulus contrast orientation classification performance in retinotopically defined occipital area v1 increased approximately linearly with the logarithm of stimulus contrast as expected univariate response amplitude also increased with contrast similar results were obtained in v2 v3 and v3a plotting classification performance against response amplitude gave a function with a compressive non linearity that was well fit by a power function knowledge of this function potentially allows adjustment of classification performance to take account of the effect of response size making comparisons across brain areas categories or people more meaningful

theory of rumour spreading in complex social networks we introduce a general stochastic model for the spread of rumours and derive mean field equations that describe the dynamics of the model on complex social networks in particular those mediated by the internet we use analytical and numerical solutions of these equations to examine the threshold behaviour and dynamics of the model on several models of such networks random graphs uncorrelated scale free networks and scale free networks with assortative degree correlations we show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumour spreading rate below which a rumour cannot propagate in the system in the case of scale free networks on the other hand this threshold becomes vanishingly small in the limit of infinite system size we find that the initial rate at which a rumour spreads is much higher in scale free networks than in random graphs and that the rate at which the spreading proceeds on scale free networks is further increased when assortative degree correlations are introduced the impact of degree correlations on the final fraction of nodes that ever hears a rumour however depends on the interplay between network topology and the rumour spreading rate our results show that scale free social networks are prone to the spreading of rumours just as they are to the spreading of infections they are relevant to the spreading dynamics of chain emails viral advertising and large scale information dissemination algorithms on the internet

a finite element method for a three field formulation of linear elasticity based on biorthogonal systems abstract we consider a mixed finite element method based on simplicial triangulations for a three field formulation of linear elasticity the three field formulation is based on three unknowns displacement stress and strain in order to obtain an efficient discretization scheme we use a pair of finite element bases forming a biorthogonal system for the strain and stress the biorthogonality relation allows us to statically condense out the strain and stress from the saddle point system leading to a symmetric and positive definite system the strain and stress can be recovered in a post processing step simply by inverting a diagonal matrix moreover we show a uniform convergence of the finite element approximation in the incompressible limit numerical experiments are presented to support the theoretical results

iterative schemes for mixed finite element methods with applications to elasticity and compressible flow problems iterative schemes for mixed finite element methods are proposed and analyzed in two abstract formulations the first one has applications to elliptic equations and incompressible fluid flow problems while the second has applications to linear elasticity and compressible stokes problems these schemes are constructed through iteratively penalizing the mixed finite element scheme of which iterated penalty method and augmented lagrangian method are special cases convergence theorems are demonstrated in abstract formulations in hilbert spaces and applications to individual physical problems are considered as examples theoretical analysis and computational experiments both show that the proposed schemes have very fast convergence a few iterations are normally enough to reduce the iterative error to a prescribed precision numerical examples with continuous and discontinuous coefficients are presented

on gradient type optimization method utilizing mixed finite element approximation for optimal boundary control problem governed by bi harmonic equation in this paper a numerical method based on mixed finite element method for optimal boundary control problem governed by bi harmonic equation is presented the system of optimality equations consisting of state and costate function is derived based on the system a gradient type optimization method using a mixed finite approximation for solving the optimal boundary control is developed in our algorithm the trace of vortex function of costate equation on boundary plays a key role finally a local error analysis at every iteration for this gradient type optimization method is given

a stabilized mixed finite element method for the biharmonic equation based on biorthogonal systems abstract we propose a stabilized finite element method for the approximation of the biharmonic equation with a clamped boundary condition the mixed formulation of the biharmonic equation is obtained by introducing the gradient of the solution and a lagrange multiplier as new unknowns working with a pair of bases forming a biorthogonal system we can easily eliminate the gradient of the solution and the lagrange multiplier from the saddle point system leading to a positive definite formulation using a superconvergence property of a gradient recovery operator we prove an optimal a priori estimate for the finite element discretization for a class of meshes

an energetic formulation of a gradient damage model for concrete and its numerical implementation abstract the energetic formulation of a rate independent system assumes that the evolution of the system is driven by two scalar valued functions the storage energy functional and the dissipation pseudo potential the evolution of the material system is then characterized by two energetic principles the global stability condition and the energy balance between stored and dissipated energies with the work of external loading rate independent generalized standard materials are endowed with such structure whereas the existence of such energetic structure is not so apparent in materials with non associated flow rule in this paper we consider a rate independent gradient damage model for concrete where the evolution of the damage does not follow the normality rule we will show that such model can be nevertheless derived by a dissipation potential at the expense of having a state variable dependent potential and therefore the energetic formulation can be obtained also in this case after introducing the incremental minimization problem consistent with such formulation we obtain a discrete version of the stability condition and establish lower and upper a priori energy bounds met by the energetic solution these are fundamental results for the analysis of the formulation the actual numerical solution of the incremental minimization problem is realized by considering first a variable splitting in order to treat the gradient of the damage field as an independent variable and then by applying the augmented lagrangian method to tackle with the resulting constrained optimization problem we solve the first order stationarity conditions of the augmented lagrangian functional by a path following newton s method based on the energy dissipation rate control we show that we are able to describe highly non linear responses of the material such as softening branches and snap back responses several numerical tests are performed to verify the objectivity of the formulation and of the proposed numerical method details of the numerical implementation are also given