the average amount of information lost in multiplication we show that if x and y are integers independently and uniformly distributed in the set 1 n then the information lost in forming their product which is given by the equivocation h x y xmiddoty is theta loglogn we also prove two extremal results regarding cases in which x and y are not necessarily independently or uniformly distributed first we note that the information lost in multiplication can of course be 0 we show that the condition h x y xmiddoty 0 implies 2log2n h x y omega loglogn furthermore if x and y are independent and uniformly distributed on disjoint sets of primes it is possible to have h x y xmiddoty 0 with log2n h x and log2n h y each o loglogn second we show that no matter how x and y are distributed h x y xmiddoty o logn loglogn furthermore there are distributions in which x and y are independent and uniformly distributed over sets of numbers having only small and distinct prime factors for which we have h x y xmiddoty omega logn loglogn

inequities in the shanks renyi prime number race an asymptotic formula for the densities chebyshev was the first to observe a bias in the distribution of primes in residue classes the general phenomenon is that if a is a nonsquare mod q and b is a square mod q then there tend to be more primes congruent to a mod q than b mod q in initial intervals of the positive integers more succinctly there is a tendency for p x q a to exceed p x q b rubinstein and sarnak defined d q a b to be the logarithmic density of the set of positive real numbers x for which this inequality holds intuitively d q a b is the probability that p x q a p x q b when x is chosen randomly in this paper we establish an asymptotic series for d q a b that can be instantiated with an error term smaller than any negative power of q this asymptotic formula is written in terms of a variance v q a b that is originally defined as an infinite sum over all nontrivial zeros of dirichlet l functions corresponding to characters mod q we show how v q a b can be evaluated exactly as a finite expression in addition to providing the exact rate at which d q a b converges to 1 2a sq grows these evaluations allow us to compare the various density values d q a b as a and b vary modulo q by analyzing the resulting formulas we can explain and predict which of these densities will be larger or smaller based on arithme tic properties of the residue classes a and b mod q for example we show that if a is a prime power and a 0 is not then d q a 1 d q a 0 1 for all but finitely many moduli q for which both a and a 0 are nonsquares finally we establish rigorous numerical bounds for these densities d q a b and report on extensive calculations of them including for ex ample the determination of all 117 density values that exceed 9 10

short effective intervals containing primes in arithmetic progressions and the seven cubes problem for any e 0 and any non exceptional modulus q 3 we prove that for x large enough x e log 2 q the interval e x e 3x e contains a prime p in any of the arithmetic progressions modulo q we apply this result to establish that every integer n larger than exp 71000 is a sum of seven cubes

forecasting interval time series using a fully complex valued rbf neural network with dpso and pso algorithms we propose a novel interval time series its forecasting approach a fully complex valued rbf neural network is extended to address its forecasting dpso pso are used to jointly optimize the structure and parameters of the model results on simulated and real world its data confirm the efficacy of the approach interval time series prediction is one of the most challenging research topics in the field of time series modeling and prediction in view of the remarkable function approximation capability of fully complex valued radial basis function neural networks fcrbfnns we set out to investigate the possibility of forecasting interval time series by denoting the lower and upper bounds of the interval as real and imaginary parts of a complex number respectively this results in a complex valued interval we then model the resulted complex valued interval time series via a fcrbfnn furthermore we propose to evolve the fcrbfnn by using particle swarm optimization pso and discrete pso for joint optimization of the structure and parameters finally the proposed interval time series prediction approach is tested with simulated interval time series data as well as real interval stock price time series data from the new york stock exchange our experimental results indicate that it is a promising alternative for interval time series forecasting

accuracy test for link prediction in terms of similarity index the case of ws and ba models abstract link prediction is a technique that uses the topological information in a given network to infer the missing links in it since past research on link prediction has primarily focused on enhancing performance for given empirical systems negligible attention has been devoted to link prediction with regard to network models in this paper we thus apply link prediction to two network models the watts strogatz ws model and barabasi albert ba model we attempt to gain a better understanding of the relation between accuracy and each network parameter mean degree the number of nodes and the rewiring probability in the ws model through network models six similarity indices are used with precision and area under the roc curve auc value as the accuracy metrics we observe a positive correlation between mean degree and accuracy and size independence of the auc value

effects of degree biased transmission rate and nonlinear infectivity on rumor spreading in complex social networks we introduce a generalized rumor spreading model and analytically investigate the spreading of rumors on scale free sf networks in the standard rumor spreading model each node has an infectivity equal to its degree and connectivity is uniform across all links to generalize this model we introduce an infectivity function that determines the number of simultaneous contacts that a given node individual may establish with its connected neighbors and a connectivity strength function csf for the direct link between two connected nodes these lead to a degree biased propagation of rumors for nonlinear functions this generalization is reflected in the infectivity s exponent ensuremath alpha and the csf s exponent ensuremath beta we show that by adjusting exponents ensuremath alpha and ensuremath beta the epidemic threshold can be controlled this feature is absent in the standard rumor spreading model in addition we obtain a critical threshold we show that the critical threshold for our generalized model is greater than that of the standard model on a finite sf network theoretically we show that ensuremath beta ensuremath 1 leads to a maximum spreading of rumors and computation results on different networks verify our theoretical prediction also we show that a smaller ensuremath alpha leads to a larger spreading of rumors our results are interesting since we obtain these results regardless of the network topology and configuration

an efficient algorithm for link prediction in temporal uncertain social networks present a link prediction algorithm in temporal uncertain social networks we transform the link prediction in uncertain network to a random walk in a deterministic one we compute the similarity scores between a node and its neighbors within a subgraph instead of computations in the whole network present an o v 3 method to compute the similarity matrix instead of enumerating the 2 e possible worlds in the network we propose a method for integrating temporal and global topological information in temporal uncertain networks due to the inaccuracy incompleteness and noise in data from real applications uncertainty is a natural feature of real world networks in such networks each edge is associated with a probability value indicating its existence in the network predicting links in uncertain networks is computationally more challenging and differs semantically from predicting connections in deterministic networks this paper presents a method for link prediction in temporal uncertain networks in our method the predicting problem is formalized by designing a random walk in temporal uncertain networks the algorithm first transforms the link prediction problem in uncertain networks to a random walk in a deterministic network then the similarity scores between a node and its neighbors are computed within a sub graph around this node to reduce the computational time the proposed method integrates temporal and global topological information in temporal uncertain networks and can obtain more accurate results experimental results on real social networks show that our method can predict future links efficiently in temporal uncertain social networks and achieves higher quality results than other similar methods

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

generalized exponential operators in the continuation of the confluent hypergeometric functions abstract use of successive continuation procedures for the confluent hypergeometric functions is developed analyzed and then applied to the evaluation of bessel functions k 0 x k 1 x k iv x as well as fourier series n 1 cos nc k 0 nb a miller formula for k iv x and k iv x is also discussed

global convergence of a reaction diffusion predator prey model with stage structure and nonlocal delays in this paper a lotka volterra type reaction diffusion predator prey model with stage structure for the prey and nonlocal delays due to gestation of the predator is investigated in the case of a general domain sufficient conditions are obtained for the global convergence of positive solutions of the proposed problem by using the energy function method numerical simulations are carried out to illustrate the main results

conservation of integrals and symplectic structure in the integration of differential equations by multistep methods we consider the question of whether multistep methods inherit in some sense quadratic first integrals possessed by the differential system being integrated we also investigate whether in the integration of hamiltonian systems multistep methods conserve the symplectic structure of the phase space

on the relations between b2v ms and runge kutta collocation methods the principal aim of this paper is a rigorous analysis of the relations between block boundary value methods b 2v ms with minimal blocksize defined over a suitable nonuniform finer mesh and well known runge kutta collocation methods moreover a further aspect that will be briefly investigated is the construction of an extended finer mesh for building b 2v ms with nonminimal blocksize some advantages that may arise from the use of the so obtained methods will be also discussed

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

complex dynamic behavior of a rumor propagation model with spatial temporal diffusion terms a spatial temporal rumor propagation model with discrete and non local delays is regarded stability and hopf bifurcation are proved in a strict mathematical way sensitivity analysis is applied to search active parameters hopf bifurcation causes an oscillation phenomenon in this model numerical simulations provide a new insight into rumor spreading in online social networks rumor propagation as a typical form of social communication in online social networks has had a significant negative impact on a harmonious and stable society with the rapid development of mobile communication equipments traditional rumor propagation models which depend on ordinary differential equations ode may not be suitable for describing rumor propagation in an online social network in this paper based on reaction diffusion equations we propose a novel epidemic like model with both discrete and nonlocal delays for investigating the spatial temporal dynamics of rumor propagation by analyzing the corresponding characteristic equations of this model the local stability conditions of a boundary equilibrium point and a positive equilibrium point are established by applying the linear approximation method of nonlinear systems sufficient conditions are derived for the existence of hopf bifurcation at the above two kinds of equilibrium points moreover a sensitivity analysis method based on the density of spreading users is proposed and then in theoretical and experimental aspect we identify some sensitive parameters in the process of rumor propagation finally numerical simulations are performed to illustrate the theoretical results

numerical computations concerning the erh this paper describes a computation which established the erh to height 10000 for all primitive dirichlet l series with conductor q 13 and to height 2500 for all q 72 all composite q 112 and other moduli the computations were based on euler maclaurin summation care was taken to obtain mathematically rigorous results the zeros were first located within 10 12 then rigorously separated using an interval arithmetic package a generalized turing criterion was used to show there were no zeros off the critical line statistics about the spacings between zeros were compiled to test the pair correlation conjecture and gue hypothesis

maximizing the spread of influence ranking in social networks abstract information flows in a network where individuals influence each other in this paper we study the influence maximization problem of finding a small subset of nodes in a social network that could maximize the spread of influence we propose a novel information diffusion model ctmc icm which introduces the theory of continuous time markov chain ctmc into the independent cascade model icm furthermore we propose a new ranking metric named spreadrank generalized by the new information propagation model ctmc icm we experimentally demonstrate the new ranking method that can in general extract nontrivial nodes as an influential node set that maximizes the spread of information in a social network and is more efficient than a distance based centrality

link prediction in multi relational networks based on relational similarity presented a belief propagation method to calculate the belief of each node in a network proposed a measurement of influence between different types of relations using belief vectors presented a nonnegative matrix factorization based algorithm for link prediction in multi relational networks theoretically proved the convergence and correctness of the proposed algorithm empirically demonstrated the proposed algorithm can achieve higher quality prediction results many real world networks contain multiple types of interactions and relations link prediction in such multi relational networks has become an important area in network analysis for link prediction in multi relational networks we should consider the similarity and influence between different types of relations in this paper we propose a link prediction algorithm in multi relational networks based on relational similarity in the algorithm a belief propagation method is presented to calculate the belief of each node and to construct the belief vector for each type of link we use the similarity between belief vectors to measure the influence between different types of relations based on the influence between different relations we present a nonnegative matrix factorization based method for link prediction in multi relational networks the convergence and correctness of the presented method are proved our experimental results show that our method can achieve higher quality prediction results than other similar algorithms

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

the exponentiated generalized birnbaum saunders distribution a new distribution called the exponentiated generalized birnbaum saunders distribution is proposed and studied the new distribution is quite flexible to model survival data reliability problems fatigue life studies and hydrological data it can have decreasing increasing upside down bathtub bathtub shaped increasing decreasing increasing and decreasing increasing decreasing hazard rate functions we provide a comprehensive account of the mathematical properties of the new distribution and various structural quantities are derived we discuss maximum likelihood estimation of the model parameters for uncensored and censored data two empirical applications of the new model to real data are presented for illustrative purposes

a rumor spreading model with variable forgetting rate abstract a rumor spreading model with the consideration of forgetting rate changing over time is examined in small world networks the mean field equations are derived to describe the dynamics of rumor spreading in small world networks further numerical solutions are conducted on livejournal an online social blogging platform to better understand the performance of the model results show that the forgetting rate has a significant impact on the final size of rumor spreading the larger the initial forgetting rate or the faster the forgetting speed the smaller the final size of the rumor spreading numerical solutions also show that the final size of rumor spreading is much larger under a variable forgetting rate compared to that under a constant forgetting rate

numerical integrators that preserve symmetries and reversing symmetries we consider properties of flows the relationships between them and whether numerical integrators can be made to preserve these properties this is done in the context of automorphisms and antiautomorphisms of a certain group generated by maps associated to vector fields this new framework unifies several known constructions we also use the concept of covariance of a numerical method with respect to a group of coordinate transformations the main application is to explore the relationship between spatial symmetries reversing symmetries and time symmetry of flows and numerical integrators

on the zeros of the riemann zeta function in the critical strip iv etude de la localisation des zeros complexes de la fonction zeta de riemann verification numerique de l hypothese de riemann pour les 1 500 000 001 premiers zeros de la forme it dans la bande critique avec 0 t 545 439 823 215 tous ces zeros ayant pour partie reelle 1 2

block boundary value methods for linear hamiltonian systems the problem of characterizing multistep methods suitable to efficiently approximate the solutions of linear hamiltonian systems is discussed showing that the appropriate methods should belong to the class of discrete boundary value methods bvms three families of such methods are proposed the presented methods have infinite regions of absolute stability and can be of any order in fact for every odd k there are k step methods of order up to 2k which is the maximum order reachable by a k step formula

values of the euler phi function not divisible by a given odd prime and the distribution of euler kronecker constants for cyclotomic fields let denote euler s phi function for a fixed odd prime q we investigate the first and second order terms of the asymptotic series expansion for the number of n 6 x such that q n part of the analysis involves a careful study of the euler kronecker constants for cyclotomic fields in particular we show that the extended riemann hypothesis the prime k tuples conjecture and a conjecture of ihara about the distribution of these euler kronecker constants cannot be all true

revealing the efficiency of information diffusion in online social networks of microblog abstract online social networks osns such as microblogs enable people to simultaneously share information with a large number of peers and revealing the properties of the formed network structure and the corresponding impacts on information diffusion are important in this article we empirically study 10 millions user profiles from the largest chinese mircoblog sina weibo and 41 7 millions profiles from twitter by studying followers topology we find an invariant characteristic that the followers count of users obeys a power law distribution with exponent near 2 we then investigate the reason from the theoretical view and find this network structure achieves the optimal information diffusion in terms of inducing a minimal propagation times our study thus reveals the efficiency of information diffusion in osns of microblogs which is validated by experimental examination theoretical analysis and numerical simulation

three dimensional gabor feature extraction for hyperspectral imagery classification using a memetic framework feature extraction based on three dimensional 3d wavelet transform is capable of improving the classification accuracy of hyperspectral imagery data by simultaneously capturing the geometrical and statistical spectral spatial structure of the data nevertheless the design of wavelets is always proceeded with empirical parameters which tends to involve a large number of irrelevant and redundant spectral spatial features and results in suboptimal configuration this paper proposes a 3d gabor wavelet feature extraction in a memetic framework named m3dgfe for hyperspectral imagery classification particularly the parameter setting of 3d gabor wavelet feature extraction is optimized using memetic algorithm so that discriminative and parsimonious feature set is acquired for accurate classification m3dgfe is characterized by an efficient fitness evaluation function and a pruning local search in the fitness evaluation function a new concept of redundancy free relevance based on conditional mutual information is proposed to measure the goodness of the extracted candidate features the pruning local search is specially designed to eliminate both irrelevant and redundant features without sacrificing the discriminability of the obtained feature subset m3dgfe is tested on both pixel level and image level classification using real world hyperspectral remote sensing data and hyperspectral face data respectively the experimental results show that m3dgfe achieves promising classification accuracy with parsimonious feature subset

bertrand s postulate for primes in arithmetical progressions abstract bertrand s postulate is the theorem that the interval x 2 x contains at least one prime for x 2 1 we prove building on work of erd os analogues of this result in which the interval is of the form x zx and there are at least m primes a mod d required to be contained in this interval and where z a and d have to satisfy some conditions for the case m 1 the results are worked out using a computer they can be found in table 1

a fast algorithm for predicting links to nodes of interest present a fast method to predict the links to nodes of interest the method computes the similarity scores of potential links connecting to a given node in a sub graph instead of in the whole network present an approach to construct the sub graph for the given node so that the errors of the similarities estimated are lower than a given threshold present a quasi global index based method to compute the similarities in the network in o n time while other similar methods require o n3 time experimental results show that the methods presented can obtain high precision results in less time than other methods the problem of link prediction has recently attracted considerable attention in various domains such as sociology anthropology information science and computer science in many real world applications we must predict similarity scores only between pairs of vertices in which users are interested rather than predicting the scores of all pairs of vertices in the network in this paper we propose a fast similarity based method to predict links related to nodes of interest in the method we first construct a sub graph centered at the node of interest by choosing the proper size for such a sub graph we can restrict the error of the estimated similarities within a given threshold because the similarity score is computed within a small sub graph the algorithm can greatly reduce computation time the method is also extended to predict potential links in the whole network to achieve high process speed and accuracy experimental results on real networks demonstrate that our algorithm can obtain high accuracy results in less time than other methods can

incomplete bessel generalized incomplete gamma or leaky aquifer functions functions characterized by the alternative appelations in the title hereof have application in areas as diverse as heat conduction probability theory electronic structure in periodic systems and hydrology these functions are regarded as difficult to evaluate and have been given attention by a number of investigators in all these fields this communication ties together the previously disjoint literature and presents several new expansions of these functions that are in various parameter ranges computationally more efficient than any of the previously proposed methods of evaluation a new formula for computation of these functions from nearby tabulated values is also reported the computational advantages of the new procedures are illustrated with examples

an improved upper bound for the error in the zero counting formulae for dirichlet l functions and dedekind zeta functions this paper contains new explicit upper bounds for the number of zeroes of dirichlet l functions and dedekind zeta functions in rectangles

energy conservation issues in the numerical solution of the semilinear wave equation in this paper we discuss energy conservation issues related to the numerical solution of the semilinear wave equation as is well known this problem can be cast as a hamiltonian system that may be autonomous or not depending on the prescribed boundary conditions we relate the conservation properties of the original problem to those of its semi discrete version obtained by the method of lines subsequently we show that the very same properties can be transferred to the solutions of the fully discretized problem obtained by using energy conserving methods in the hbvms hamiltonian boundary value methods class similar arguments hold true for different types of hamiltonian partial differential equations e g the nonlinear schrodinger equation

identifying influential nodes in complex networks abstract identifying influential nodes that lead to faster and wider spreading in complex networks is of theoretical and practical significance the degree centrality method is very simple but of little relevance global metrics such as betweenness centrality and closeness centrality can better identify influential nodes but are incapable to be applied in large scale networks due to the computational complexity in order to design an effective ranking method we proposed a semi local centrality measure as a tradeoff between the low relevant degree centrality and other time consuming measures we use the susceptible infected recovered sir model to evaluate the performance by using the spreading rate and the number of infected nodes simulations on four real networks show that our method can well identify influential nodes

explicit zero density estimate for the riemann zeta function near the critical line abstract in 1946 a selberg proved n t t 1 1 4 1 2 log t where n t is the number of nontrivial zeros of the riemann zeta function with and 0 t we provide an explicit version of this estimate together with an explicit approximate functional equation and an explicit upper bound for the second power moment of the zeta function on the critical line

symmetric schemes time reversal symmetry and conservative methods for hamiltonian systems it is important when integrating numerically hamiltonian problems that the numerical methods retain some properties of the continuous problem such as the constants of motion and the time reversal symmetry this may be a difficult task for multistep numerical methods in the present paper we discuss the problem in the case of linear autonomous hamiltonian systems and we show the equivalence among the symmetry of the numerical methods and the above mentioned requirements in particular the analysis is carried out for the class of methods known as boundary value methods bvms brugnano trigiante solving differential problems by multistep initial and boundary value methods gordon and breach science publishers amsterdam 1998

stability and hopf bifurcation analysis of an eco epidemic model with a stage structure abstract in this paper an eco epidemiological model with a stage structure is considered the asymptotical stability of the five equilibria the existence of stability switches about positive equilibrium is investigated it is found that hopf bifurcation occurs when the delay passes though a critical value some explicit formulae determining the stability and the direction of the hopf bifurcation periodic solutions bifurcating from hopf bifurcations are obtained by using the normal form theory and center manifold theory some numerical simulations for justifying the theoretical analysis are also provided finally biological explanations and main conclusions are given

deprecation based greedy strategy for target set selection in large scale social networks the problem of target set selection for large scale social networks is addressed in the paper we describe a novel deprecation based greedy strategy to be applied over a pre ordered as obtained with any heuristic influence function set of nodes the proposed algorithm runs in iteration and has two stages i estimation where the performance of each node is evaluated and ii marking where the nodes to be deprecated in later iterations are marked we have theoretically proved that for any monotonic and sub modular influence function the algorithm correctly identifies the nodes to be deprecated for any finite set of input nodes it is shown that the algorithm can meet the ending criteria the worst case performance of the algorithm both in terms of time and performance is also analyzed experimental results on seven un weighted as well as weighted social networks show that the proposed strategy improves the ranking of the input seeds in terms of the total number of nodes influenced

greedy discrete particle swarm optimization for large scale social network clustering social computing is a new paradigm for information and communication technology social network analysis is one of the theoretical underpinnings of social computing community structure detection is believed to be an effective tool for social network analysis uncovering community structures in social networks can be regarded as clustering optimization problems because social networks are characterized by dynamics and huge volumes of data conventional nature inspired optimization algorithms encounter serious challenges when applied to solving large scale social network clustering optimization problems in this study we put forward a novel particle swarm optimization algorithm to reveal community structures in social networks the particle statuses are redefined under a discrete scenario the status updating rules are reconsidered based on the network topology a greedy strategy is designed to drive particles to a promising region to this end a greedy discrete particle swarm optimization framework for large scale social network clustering is suggested to determine the performance of the algorithm extensive experiments on both synthetic and real world social networks are carried out we also compare the proposed algorithm with several state of the art network community clustering methods the experimental results demonstrate that the proposed method is effective and promising for social network clustering

primes in arithmetic progressions strengthening work of rosser schoenfeld and mccurley we establish explicit chebyshev type estimates in the prime number theorem for arithmetic progressions for all moduli k 72 and other small moduli

partial differential equation modeling of malware propagation in social networks with mixed delays abstract with the wide applications of social networks government and individuals increasingly emphasize information networks security this paper is devoted to investigating a reaction diffusion malware propagation model with mixed delays to describe the process of social networks applying matrix theory for characteristic values we establish the local stability conditions of a positive equilibrium point based on the linear approximation method of nonlinear systems the hopf bifurcation at the positive equilibrium point is considered additionally we identify some sensitive parameters in the process of malware propagation that are significant for control theory finally numerical simulations are performed to illustrate the theoretical results

on sums of seven cubes we show that every integer between 1290741 and 3 375 10 12 is a sum of 5 non negative cubes from which we deduce that every integer which is a cubic residue modulo 9 and an invertible cubic residue modulo 37 is a sum of 7 non negative cubes

predicting link directions using local directed path abstract link prediction in directed network is attracting growing interest among many network scientists compared with predicting the existence of a link determining its direction is more complicated in this paper we propose an efficient solution named local directed path to predict link direction by adding an extra ground node to the network we solve the information loss problem in sparse network which makes our method effective and robust as a quasi local method our method can deal with large scale networks in a reasonable time empirical analysis on real networks shows that our method can correctly predict link directions which outperforms some local and global methods

an improved upper bound for the argument of the riemann zeta function on the critical line this paper concerns the function s t the argument of the rie mann zeta function along the critical line the main result is that s t 0 111logt 0 275 log logt 2 450 which holds for all te

a multi objective memetic algorithm based on locality sensitive hashing for one to many to one dynamic pickup and delivery problem this paper presents an early attempt to solve one to many to one dynamic pickup and delivery problem dpdp by proposing a multi objective memetic algorithm called lsh moma which is a synergy of multi objective evolutionary algorithm and locality sensitive hashing lsh based local search three objectives namely route length response time and workload are optimized simultaneously in an evolutionary framework in each generation of lsh moma lsh based rectification and local search are imposed to repair and improve the individual solutions lsh moma is evaluated on four benchmark dpdps and the experimental results show that lsh moma is efficient in obtaining optimal tradeoff solutions of the three objectives

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

explicit zero density for the riemann zeta function abstract let n t denote the number of nontrivial zeros of the riemann zeta function with real part greater than and imaginary part between 0 and t we provide explicit upper bounds for n t commonly referred to as a zero density result in 1937 ingham showed the following asymptotic result n t o t 8 3 1 log t 5 ramare recently proved an explicit version of this estimate we discuss a generalization of the method used in these two results which yields an explicit bound of a similar shape while also improving the constants

scaling fields in the two dimensional abelian sandpile model we consider the unoriented two dimensional abelian sandpile model from a perspective based on two dimensional conformal field theory we compute lattice correlation functions for various cluster variables at and off criticality from which we infer the field theoretic description in the scaling limit we find perfect agreement with the predictions of a c 2 conformal field theory and its massive perturbation thereby providing direct evidence for conformal invariance and more generally for a description in terms of a local field theory the question of the height 2 variable is also addressed with however no definite conclusion yet

super mediator a new centrality measure of node importance for information diffusion over social network we propose an efficient method to discover a new type of influential nodes in a social network which we name super mediators i e those nodes which if removed decrease information spread it is formulated mathematically as a problem of difference maximization of the average influence degree with respect to removal of a node i e a node that contributes to making the difference large is influential this definition requires use of information diffusion model for their identification and thus is model driven the other definition which is more empirical is that super mediators are those nodes that appear frequently in long diffusion sequences but much less frequently in short diffusion sequences this definition does not require any model but does require abundant information diffusion data and thus is data driven we attempt to characterize the property of super mediators from various angles how the resulting super mediators are different between these two definitions and which is more reasonable how super mediators are compared with nodes identified by other centralities e g betweenness degree closeness etc how super mediators are different from the solution of well studied influence maximization problem i e nodes capable of widely spreading information to other recipient nodes and the solution of reverse influence maximization problem i e nodes capable of widely receiving information from other information source nodes we conducted extensive experiments using three real world social networks the major findings are 1 model driven super mediator degree has the best discrimination capability while influence degree reverse influence degree and data driven super mediator degree are much less discriminative all flat for high ranked nodes 2 model driven super mediators have high scores for either influence degree or reverse influence degree while data driven super mediators have high scores for both and 3 model driven super mediators are closely correlated with betweenness centrality but the strength of the correlation depends on the value of diffusion probability

influence maximization in social networks based on discrete particle swarm optimization influence maximization in social networks aims to find a small group of individuals which have maximal influence cascades in this study an optimization model based on a local influence criterion is established for the influence maximization problem the local influence criterion can provide a reliable estimation for the influence propagations in independent and weighted cascade models a discrete particle swarm optimization algorithm is then proposed to optimize the local influence criterion the representations and update rules for the particles are redefined in the proposed algorithm moreover a degree based heuristic initialization strategy and a network specific local search strategy are introduced to speed up the convergence experimental results on four real world social networks demonstrate the effectiveness and efficiency of the proposed algorithm for influence maximization

explicit estimates for the error term in the prime number theorem for arithmetic progressions we give explicit numerical estimates for the chebyshev functions 4 x k l and g x k l for certain nonexceptional moduli k for values of e and b a constant c is tabulated such that 14 x k l x 9p k l exp c log2 k and k 10b the methods are similar to those used by rosser and schoenfeld in the case k 1 but are based on explicit estimates of n t x and an explicit zero free region for dirichlet l functions

minimizing the expected complete influence time of a social network complete influence time specifies how long it takes to influence all individuals in a social network which plays an important role in many real life applications in this paper we study the problem of minimizing the expected complete influence time of social networks we propose the incremental chance model to characterize the diffusion of influence which is progressive and able to achieve complete influence theoretical properties of the expected complete influence time under the incremental chance model are presented in order to trade off between optimality and complexity we design a framework of greedy algorithms finally we carry out experiments to show the effectiveness of the proposed algorithms

stability and hopf bifurcation analysis on a ring of four neurons with delays we consider a four neuron ring with self feedback and delays by analyzing the associated characteristic equation linear stability is investigated and hopf bifurcations are demonstrated as well as the stability and direction of the hopf bifurcation are determined by employing the normal form method and the center manifold reduction numerical simulations are presented to illustrate the results

niching particle swarm optimization with local search for multi modal optimization multimodal optimization is still one of the most challenging tasks for evolutionary computation in recent years many evolutionary multi modal optimization algorithms have been developed all these algorithms must tackle two issues in order to successfully solve a multi modal problem how to identify multiple global local optima and how to maintain the identified optima till the end of the search for most of the multi modal optimization algorithms the fine local search capabilities are not effective if the required accuracy is high these algorithms fail to find the desired optima even after converging near them to overcome this problem this paper integrates a novel local search technique with some existing pso based multimodal optimization algorithms to enhance their local search ability the algorithms are tested on 14 commonly used multi modal optimization problems and the experimental results suggest that the proposed technique not only increases the probability of finding both global and local optima but also reduces the average number of function evaluations

discrete particle swarm optimization for high order graph matching high order graph matching aims at establishing correspondences between two sets of feature points using high order constraints it is usually formulated as an np hard problem of maximizing an objective function this paper introduces a discrete particle swarm optimization algorithm for resolving high order graph matching problems which incorporates several re defined operations a problem specific initialization method based on heuristic information and a problem specific local search procedure the proposed algorithm is evaluated on both synthetic and real world datasets its outstanding performance is validated in comparison with three state of the art approaches

effective irrationality measure for certain algebraic numbers a result of chudnovsky concerning rational approximation to certain algebraic numbers is reworked to provide a quantitative result in which all constants are explicitly given more particularly pade approximants to the function 1 x 113 are employed to show for certain integers a and b that j a b 1 3 p q cq k when q 0 here c and k are given as functions of a and b only in 1964 baker 1 improving a technique used by siegel 8 was able to obtain effective irrationality measures for the function 1 x m n evaluated at certain rational points in particular he was able to show that for integers p q we have 1 121 3 p q 10 6q 2955 when q 0 the technique was further refined by chudnovsky 2 whose results when applied to 21 3 imply that for any 0 there exists a positive integer qo c such that for integers p q we have 2 121 3 p qi q 2 429 e when q q0 chudnovsky s result is effective in the sense that it is possible in principle to work through the proof and compute for any particular value of a qo c for which 2 holds however chudnovsky does not undertake such computations in this article we rework baker s proof using chudnovsky s refinement together with a chebyshev type result for primes in arithmetical progressions due to mccurley 6 and obtain the following quantitative result theorem let a b be integers with 0 b a define d by 0 if 3 4 a b 3 d i1 if 311 a b 13 2 otherwise further define a k c and q0 by 4 x 2328 3d al1 2 b1 2 2 received may 9 1985 1980 mathematics subject classification primary iof25 1986 american mathematical society 0025 5718 86 1 00 25 per page 613 this content downloaded from 207 46 13 124 on wed 22 jun 2016 05 36 01 utc all use subject to http about jstor org terms