stability and error estimates of local discontinuous galerkin methods with implicit explicit time marching for advection diffusion problems the main purpose of this paper is to analyze the stability and error estimates of the local discontinuous galerkin ldg methods coupled with carefully chosen implicit explicit imex runge kutta time discretization up to third order accuracy for solving one dimensional linear advection diffusion equations in the time discretization the advection term is treated explicitly and the diffusion term implicitly there are three highlights of this work the first is that we establish an important relationship between the gradient and interface jump of the numerical solution with the independent numerical solution of the gradient in the ldg methods the second is that by aid of the aforementioned relationship and the energy method we show that the imex ldg schemes are unconditionally stable for the linear problems in the sense that the time step tau is only required to be upper bounded by a constant which depends on the ratio of the diffusion and the square of the advection coefficients and is independent

advanced modularity specialized label propagation algorithm for detecting communities in networks abstract a modularity specialized label propagation algorithm lpam for detecting network communities was recently proposed this promising algorithm offers some desirable qualities however lpam favors community divisions where all communities are similar in total degree and thus it is prone to get stuck in poor local maxima in the modularity space to escape local maxima we employ a multistep greedy agglomerative algorithm msg that can merge multiple pairs of communities at a time combining lpam and msg we propose an advanced modularity specialized label propagation algorithm lpam experiments show that lpam successfully detects communities with higher modularity values than ever reported in two commonly used real world networks moreover lpam offers a fair compromise between accuracy and speed

vertex similarity in networks we consider methods for quantifying the similarity of vertices in networks we propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar this leads to a self consistent matrix formulation of similarity that can be evaluated iteratively using only a knowledge of the adjacency matrix of the network we test our similarity measure on computer generated networks for which the expected results are known and on a number of real world networks

mod 3 congruence and twisted signature of 24 dimensional string manifolds in this paper by combining modularity of the witten genus and the modular forms constructed by liu and wang we establish mod 3 congruence properties of certain twisted signatures of 24 dimensional string manifolds introduction let m be a 2n dimensional smooth closed oriented manifold let gtm be a riemmian metric on tm and tm the associated levi civita connection let v be a complex vector bundle over m with a hermitian metric hv and a unitary connection v let c t m be the complexified exterior algebra bundle of tm let c t m be the hermitian metric on c t m induced by gtm let dv be the riemannian volume form associated to gtm then m c t m has a hermitian metric such that for m c t m m c t m dv for x tm let c x be the clifford action on c t m defined by c x x ix where x t m corresponds to x via gtm let e1 e2 e2n be an oriented orthogonal basis of tm set 1 c e1 c e2n then one can show that is independent of the choice of the orthonormal basis and v 1 is a self adjoint element acting on c t m v such that v id c t m v let d be the exterior differentiation operator and d be the formal adjoint of d with respect to the hermitian metric the operator dsig d d 2n i 1 c ei c m ei m c t m m c t m is the signature operator and the more general twisted signature operator is defined as c f 6 dsig v 2n i 1 c ei c m v ei m c t m v m c t m v

finding community structure in networks using the eigenvectors of matrices we consider the problem of detecting communities or modules in networks groups of vertices with a higher than average density of edges connecting them previous work indicates that a robust approach to this problem is the maximization of the benefit function known as modularity over possible divisions of a network here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix which plays a role in community detection similar to that played by the graph laplacian in graph partitioning calculations this result leads us to a number of possible algorithms for detecting community structure as well as several other results including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong the algorithms and measures proposed are illustrated with applications to a variety of real world complex networks

optimizing the controllability of arbitrary networks with genetic algorithm abstract recently as the controllability of complex networks attracts much attention how to optimize networks controllability has become a common and urgent problem in this paper we develop an efficient genetic algorithm oriented optimization tool to optimize the controllability of arbitrary networks consisting of both state nodes and control nodes under popov belevitch hautus rank condition the experimental results on a number of benchmark networks show the effectiveness of this method and the evolution of network topology is captured furthermore we explore how network structure affects its controllability and find that the sparser a network is the more control nodes are needed to control it and the larger the differences between node degrees the more control nodes are needed to achieve the full control our framework provides an alternative to controllability optimization and can be applied to arbitrary networks without any limitations

ten ways to generate the il in and related schemes abstract for one dimensional singularly perturbed boundary value problems there exist a remarkable variety of possibilities to generate uniformly convergent schemes we describe the basic ideas of ten different approaches and the advantages and disadvantages of several methods

community detection in complex networks using extremal optimization we propose a method to find the community structure in complex networks based on an extremal optimization of the value of modularity the method outperforms the optimal modularity found by the existing algorithms in the literature giving a better understanding of the community structure we present the results of the algorithm for computer simulated and real networks and compare them with other approaches the efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks

tmf0 3 characteristic classes for string bundles we compute the completed tmf 0 3 cohomology of the 7 connected cover bstring of bo we use cubical structures on line bundles over elliptic curves to construct an explicit class which together with the pontryagin classes freely generates the cohomology ring

link direction for link prediction abstract almost all previous studies on link prediction have focused on using the properties of the network to predict the existence of links between pairs of nodes unfortunately previous methods rarely consider the role of link direction for link prediction in fact many real world complex networks are directed and ignoring the link direction will mean overlooking important information in this study we propose a phase dynamic algorithm of the directed network nodes to analyse the role of link directions and demonstrate that the bi directional links and the one directional links have different roles in link prediction and network structure formation from this we propose new directional prediction methods and use six real networks to test our algorithms in real networks we find that compared to a pair of nodes which are connected by a one directional link a pair of nodes which are connected by a bi directional link always have higher probabilities to connect to the common neighbours with only bi directional links or conversely by one directional links we suggest that in the real networks the bi directional links will generally be more informative for link prediction and network structure formation in addition we propose a new directional randomized algorithm to demonstrate that the direction of the links plays a significant role in link prediction and network structure formation

eigenvectors of network complement reveal community structure more accurately abstract we propose a general spectral method to find communities of a network based on network complement and anti community concepts analytical and numerical results show that the eigenspace of matrices corresponding to a network complement reveals the community structure of a network more accurately than the eigenspace of matrices corresponding to the network itself it is shown that the laplacian eigenspace is the best candidate for spectral community detection especially in networks with a heterogeneous community structure the method is applied to some computer generated and real world networks with known community structures

fitness networks for real world systems via modified preferential attachment complex networks are virtually ubiquitous and the barabasi and albert model baba model has became an acknowledged standard for the modelling of these systems the so called baba model is a kind of preferential attachment growth model based on the intuitive premise that popularity is attractive however preferential attachment alone is insufficient to describe the diversity of complex networks observed in the real world in this paper we first use the accuracy of a link prediction method as a metric for network fitness the link prediction method predicts the occurrence of links consistent with preferential attachment the performance of this link prediction scheme is then a natural measure of the preferential attachment likeness of a given network we then propose several modification methods and modified baba models to construct networks which more accurately describe the fitness properties of real networks we find that all features assortativity degree distribution and rich club formation can play significant roles for the network construction and eventual structure moreover link sparsity and the size of a network are key factors for network reconstruction in addition we find that the structure of the network which is limited by geographic location nodes are embedded in a euclidean space and connectivity is correlated with distances differs from other typical networks in social networks we observe that the high school contact network has similar structure as the friends network and so we speculate that the contact behaviours can reflect real friendships

the degree related clustering coefficient and its application to link prediction abstract link prediction plays a significant role in explaining the evolution of networks however it is still a challenging problem that has been addressed only with topological information in recent years based on the belief that network nodes with a great number of common neighbors are more likely to be connected many similarity indices have achieved considerable accuracy and efficiency motivated by the natural assumption that the effect of missing links on the estimation of a node s clustering ability could be related to node degree in this paper we propose a degree related clustering coefficient index to quantify the clustering ability of nodes unlike the classical clustering coefficient our new coefficient is highly robust when the observed bias of links is considered furthermore we propose a degree related clustering ability path dcp index which applies the proposed coefficient to the link prediction problem experiments on 12 real world networks show that our proposed method is highly accurate and robust compared with four common neighbor based similarity indices common neighbors cn adamic adar aa resource allocation ra and preferential attachment pa and the recently introduced clustering ability ca index

network ensemble comparisons with stochastic rewiring and von neumann entropy assessing whether a given network is typical or atypical for a random network ensemble i e network ensemble comparison has widespread applications ranging from null model selection and hypothesis testing to clustering and classifying networks we develop a framework for network ensemble comparison by subjecting the network to stochastic rewiring we study two rewiring processes uniform and degree preserved rewiring which yield random network ensembles that converge to the erdos renyi and configuration model ensembles respectively we study convergence through von neumann entropy vne a network summary statistic measuring information content based on the spectra of a laplacian matrix and develop a perturbation analysis for the expected effect of rewiring on vne our analysis yields an estimate for how many rewires are required for a given network to resemble a typical network from an ensemble offering a computationally efficient quantity for network ensemble comparison that does not require

topological modular forms with level structure the cohomology theory known as mathrm tmf for topological modular forms is a universal object mapping out to elliptic cohomology theories and its coefficient ring is closely connected to the classical ring of modular forms we extend this to a functorial family of objects corresponding to elliptic curves with level structure and modular forms on them along the way we produce a natural way to restrict to the cusps providing multiplicative maps from mathrm tmf with level structure to forms of k theory in particular this allows us to construct a connective spectrum mathrm tmf 0 3 consistent with properties suggested by mahowald and rezk this is accomplished using the machinery of logarithmic structures we construct a presheaf of locally even periodic elliptic cohomology theories equipped with highly structured multiplication on the log etale site of the moduli of elliptic curves evaluating this presheaf on modular curves produces mathrm tmf with level structure

implicit explicit methods for time dependent partial differential equations implicit explicit imex schemes have been widely used especially in conjunction with spectral methods for the time integration of spatially discretized partial differential equations pdes of diffusion convection type typically an implicit scheme is used for the diffusion term and an explicit scheme is used for the convection term reaction diffusion problems can also be approximated in this manner in this work we systematically analyze the performance of such schemes propose improved new schemes and pay particular attention to their relative performance in the context of fast multigrid algorithms and of aliasing reduction for spectral methods for the prototype linear advection diffusion equation a stability analysis for first second third and fourth order multistep imex schemes is performed stable schemes permitting large time steps for a wide variety of problems and yielding appropriate decay of high frequency error modes are identified numerical experiments demonstrate that weak decay

community mining with new node similarity by incorporating both global and local topological knowledge in a constrained random walk abstract detection of community is a crucial step to understand the structure and dynamics of complex networks most of conventional community detection methods focus on optimizing a certain objective function or on clustering nodes based on their similarities which leads to a phenomenon that they have preference for specific types of networks but are not general using constrained random walk we exploit global and local topology structures of network to propose a modified transition matrix and further to define a new similarity metric named isim between two nodes in contrast to the existing similarities isim does not work directly on the observed data but in a convergent stable space this feature makes isim robust to the observed noisy data in real world networks isim not only measures node s distance but also captures node s topology structure in network experiments on synthetic and real world networks demonstrate that isim can be successfully applied to community detection in broader types of networks and outperforms other community detection methods

partition of networks into basins of attraction we study partition of networks into basins of attraction based on a steepest ascent search for the node of highest degree each node is associated with or attracted to its neighbor of maximal degree as long as the degree is increasing a node that has no neighbors of higher degree is a peak attracting all the nodes in its basin maximally random scale free networks exhibit different behavior based on their degree distribution exponent gamma for small gamma broad distribution networks are dominated by a giant basin whereas for large gamma narrow distribution there are numerous basins with peaks attracting mainly their nearest neighbors we derive expressions for the first two moments of the number of basins we also obtain the complete distribution of basin sizes for a class of hierarchical deterministic scale free networks that resemble random nets finally we generalize the problem to regular networks and lattices where all degrees are equal and thus the attractiveness of a node must be determined by an assigned weight rather than the degree we derive the complete distribution of basins of attraction resulting from randomly assigned weights in one dimensional chains

exponentially fitted imex methods for advection diffusion problems the paper is devoted to the numerical solution of advection diffusion problems of boussinesq type by means of adapted numerical methods the adaptation occurs at two levels along space by suitably semidiscretizing the spatial derivatives through finite differences based on exponential fitting along time integration through an adapted imex method based on exponential fitting itself stability analysis is provided and numerical examples showing the effectiveness of the approach also in comparison with the classical one are given

numerical solution of reaction diffusion systems of λ ω type by trigonometrically fitted methods the numerical solution of reaction diffusion equations of type which are known to possess a one parameter family of periodic plane wave solutions is object of this paper due to the periodic character of such solutions a special purpose numerical integration is here proposed based on adapted finite differences the adaptation occurs at the level of the problem by a suitable spatial semi discretization based on trigonometrically fitted finite differences numerical experiments confirming the effectiveness of the approach are given

an e splitting of spin bordism the work determines the e structure of the k 1 local spin bordism spectrum by giving a multiplicative splitting into e cells the splitting leads to a cellular decomposition of the a map and creates new isomorphisms of conner floyd type introduction and statement of results one of the most important results on spin bordism goes back to anderson brown and peterson abp they showed that two spin manifolds are spin bordant if and only if all stiefel whitney and ko characteristic numbers coincide moreover the spin bordism groups can be computed from the additive 2 local splitting mspin

detecting community structure in complex networks based on a measure of information discrepancy abstract properties of complex networks such as small world property power law degree distribution network transitivity and network community structure which seem to be common to many real world networks have attracted great interest among researchers in this study global information of the networks is considered by defining the profile of any node based on the shortest paths between it and all the other nodes in the network then a useful iterative procedure for community detection based on a measure of information discrepancy and the popular modular function q is presented the new iterative method does not need any prior knowledge about the community structure and can detect an appropriate number of communities which can be hub communities or non hub communities the computational results of the method on real networks confirm its capability

clustering coefficients of large networks abstract let g be a network with n nodes and eigenvalues 1 2 n then g is called an n d network if it is d regular and max 2 3 n it is shown that if g is an n d network and o d the average clustering coefficient c g of g satisfies c g d n for large d we show that this description also holds for strongly regular graphs and erd s renyi graphs although most real world networks are not constructed theoretically we find that many of them have c g close to d n and many close to 1 2 n d 1 d d 1 where d is the average degree of g and 2 is the average of the numbers of common neighbors over all non adjacent pairs of nodes

exponentially fitted methods applied to fourth order boundary value problems fourth order boundary value problems are solved by means of exponentially fitted methods of different orders these methods which depend on a parameter can be constructed following a six step flow chart of ixaru and vanden berghe special attention is paid to the expression for the error term and to the choice of the parameter in order to make the error as small as possible some numerical examples are given to illustrate the practical implementation issues of these methods

identifying overlapping communities in networks using evolutionary method abstract community structure is a typical property of real world networks and has been recognized as a key to understand the dynamics of the networked systems in most of the networks overwhelming nodes apparently live in a community while there often exists a few nodes straddling several communities hence an ideal algorithm for community detection is that which can identify the overlapping communities in these networks we present an evolutionary method for detecting overlapping community structure in the network to represent an overlapping division of a network we develop an encoding scheme composed of two segments the first one represents a disjoint partition and the second one represents an extension of the partition that allows of multiple memberships we give two measures for the informativeness of a node and present a coevolutionary scheme between two segments over the population for solving the overlapping partition of the network experimental results show this method can give a better solution to a network it is also revealed that a best overlapping partition of the network might not be rooted from a best disjoint partition

exponentially fitted two step runge kutta methods construction and parameter selection abstract we derive exponentially fitted two step runge kutta methods for the numerical solution of y f x y specially tuned to the behaviour of the solution such methods have nonconstant coefficients which depend on a parameter to be suitably estimated the construction of the methods is shown and a strategy of parameter selection is presented some numerical experiments are provided to confirm the theoretical expectations

k 1 local topological modular forms we construct the witten orientation of the topological modular forms spectrum tmf in the k 1 local setting by attaching e cells to the bordism theory mo we also identify the ko homology of tmf with the ring of divided congruences

information filtering based on transferring similarity in this brief report we propose an index of user similarity namely the transferring similarity which involves all high order similarities between users accordingly we design a modified collaborative filtering algorithm which provides remarkably higher accurate predictions than the standard collaborative filtering more interestingly we find that the algorithmic performance will approach its optimal value when the parameter contained in the definition of transferring similarity gets close to its critical value before which the series expansion of transferring similarity is convergent and after which it is divergent our study is complementary to the one reported in e a leicht p holme and m e j newman phys rev e 73 026120 2006 and is relevant to the missing link prediction problem

quantum behaved discrete multi objective particle swarm optimization for complex network clustering abstract complex network research has attracted lots of attention in both academic community and various application fields complex network clustering as one of the key issues in complex network explores the internal organization of the nodes in a complex network the discrete particle swarm optimization strategy has been successfully proposed for network clustering while the existing method works with weak robust in this paper we model the task of complex network clustering as a multi objective optimization problem and solve the problem with the quantum mechanism based particle swarm optimization algorithm which is a parallel algorithm to our knowledge this is the first attempt to apply the quantum mechanism based discrete particle swarm optimization algorithm into network clustering in addition the non dominant sorting selection operation is employed for individual replacement consequently a quantum behaved discrete multi objective particle swarm optimization algorithm is proposed for complex network clustering the experimental results demonstrate that the proposed algorithm performs effectively and achieves competitive performance with the state of the art approaches on the extension of girvan and newman benchmarks and real world networks especially on large scale networks

an evidential link prediction method and link predictability based on shannon entropy abstract predicting missing links is of both theoretical value and practical interest in network science in this paper we empirically investigate a new link prediction method base on similarity and compare nine well known local similarity measures on nine real networks most of the previous studies focus on the accuracy however it is crucial to consider the link predictability as an initial property of networks itself hence this paper has proposed a new link prediction approach called evidential measure em based on dempster shafer theory moreover this paper proposed a new method to measure link predictability via local information and shannon entropy

parameterized centrality metric for network analysis a variety of metrics have been proposed to measure the relative importance of nodes in a network one of these alpha centrality p bonacich am j sociol 92 1170 1987 measures the number of attenuated paths that exist between nodes we introduce a normalized version of this metric and use it to study network structure for example to rank nodes and find community structure of the network specifically we extend the modularity maximization method for community detection to use this metric as the measure of node connectivity normalized alpha centrality is a powerful tool for network analysis since it contains a tunable parameter that sets the length scale of interactions studying how rankings and discovered communities change when this parameter is varied allows us to identify locally and globally important nodes and structures we apply the proposed metric to several benchmark networks and show that it leads to better insights into network structure than alternative metrics

error analysis of imex runge kutta methods derived from differential algebraic systems in this paper we present an error analysis of the imex runge kutta methods when applied to stiff problems containing a nonstiff term and a stiff term characterized by a small stiffness parameter varepsilon in this analysis we expand the global error in powers of varepsilon and show that the coefficients of the error are the global errors of the imex runge kutta method applied to a differential algebraic system interesting convergence results of these errors and of the remainder of the expansion allow us to determine sharp error bounds for stiff problems as a representative example of stiff problems we have chosen the van der pol equation we illustrate that the theoretical prediction is confirmed by the numerical test specifically an order reduction phenomenon is observed when the problem becomes increasingly stiff in particular making several assumptions we try to improve global error estimates of several imex runge kutta methods existing in the literature

modular invariance and twisted cancellations of characteristic numbers by studying modular invariance properties of some characteristic forms which are related to elliptic genera we obtain twisted cancellation formulas for characteristic forms we apply these twisted cancellation formulas to study divisibilities on spin manifolds and congruences on spin c manifolds in particular we obtain twisted rokhlin congruences for 8k 4 dimensional spin c manifolds

power operations in elliptic cohomology and representations of loop groups the first part describes power operations in elliptic cohomology in terms of isogenies of the underlying elliptic curve the second part discusses a relationship between equivariant elliptic cohomology and representations of loop groups the third part investigates the representation theoretic considerations which give rise to the power operations discussed in the first part