weighted network properties of chinese nature science basic research using the requisition papers of chinese nature science basic research in management and information department we construct the weighted network of research areas wnra in wnra two research areas which is represented by the subject codes are considered to be connected if they have been filled in one or more requisition papers the edge weight is defined as the number of requisition papers which have been filled in the same pairs of codes the node strength is defined as the number of requisition papers which have been filled in this code including the papers which have been filled in it alone here we study a variety of nonlocal statistics for wnra such as typical distance between research areas and measure of centrality such as betweenness these statistical characteristics can illuminate the global development trend of chinese scientific study it is also helpful to adjust the code system to reflect the real status more accurately finally we present a plausible model for the formation and structure of wnra with the observed properties

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

homoclinic solutions for a class of the second order hamiltonian systems abstract we study the existence of homoclinic orbits for the second order hamiltonian system q v q t q f t where q r n and v c 1 r r n r v t q k t q w t q is t periodic in t a map k satisfies the pinching condition b 1 q 2 k t q b 2 q 2 w is superlinear at the infinity and f is sufficiently small in l 2 r r n a homoclinic orbit is obtained as a limit of 2 kt periodic solutions of a certain sequence of the second order differential equations

existence of homoclinic orbits for second order hamiltonian systems without ar condition abstract the existence of homoclinic orbits is obtained for a class of the second order hamiltonian systems u t l t u t w t u t 0 t r by the local linking lemma where w t x is superquadratic and need not be nonnegative globally

temporal series analysis approach to spectra of complex networks the spacing of nearest levels of the spectrum of a complex network can be regarded as a time series joint use of the multifractal detrended fluctuation approach mf dfa and diffusion entropy de is employed to extract characteristics from this time series for the watts strogatz small world model there exists a critical point at rewiring probability p r 0 32 for a network generated in the range 0l p r l0 32 the correlation exponent is in the range of 1 0 char21 1 64 above this critical point all the networks behave similar to that at p r 1 for the erdos renyi model the time series behaves like fractional brownian motion noise at p text er 1 n for the growing random network grn model the values of the long range correlation exponent are in the range of 0 74 char21 0 83 for most of the grn networks the probability distribution function of a constructed time series obeys a gaussian form in the joint use of mf dfa and de the shuffling procedure in de is essential to obtain a reliable result

fast homoclinic solutions for some second order non autonomous systems abstract this paper is concerned with the existence of homoclinic solutions for the following second order non autonomous system fhs q c q u q t q 0 where q r n c 0 is a constant and u t q c 1 r r n r under some reasonable assumptions for the first time we introduce the concept of fast homoclinic solutions of fhs and establish some criteria to guarantee the existence of fast homoclinic solutions of fhs besides that in some particular case the uniqueness of homoclinic solutions of fhs is also obtained recent results in the literature are generalized and significantly improved

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

behaviors of susceptible infected epidemics on scale free networks with identical infectivity in this paper we propose a susceptible infected model with identical infectivity in which at every time step each node can only contact a constant number of neighbors we implemented this model on scale free networks and found that the infected population grows in an exponential form with the time scale proportional to the spreading rate furthermore by numerical simulation we demonstrated that the targeted immunization of the present model is much less efficient than that of the standard susceptible infected model finally we investigate a fast spreading strategy when only local information is available different from the extensively studied path finding strategy the strategy preferring small degree nodes is more efficient than that preferring large degree nodes our results indicate the existence of an essential relationship between network traffic and network epidemic on scale free networks

infinitely many homoclinic orbits for hamiltonian systems with indefinite sign subquadratic potentials abstract in this paper we deal with the existence and multiplicity of homoclinic solutions of the second order hamiltonian system u t l t u t w t u t 0 where l t and w t x are neither autonomous nor periodic in t under the assumption that w t x is indefinite sign and subquadratic as x and l t is a n n real symmetric positive definite matrices for all t r we establish some existence criteria to guarantee that the above system has at least one or infinitely many homoclinic solutions by using the genus properties in critical theory

assortative model for social networks in this brief report we present a version of a network growth model generalized in order to describe the behavior of social networks the case of study considered is the preprint archive at cul arxiv org each node corresponds to a scientist and a link is present whenever two authors wrote a paper together this graph is a nice example of degree assortative network that is to say a network where sites with similar degree are connected to each other the model presented is one of the few able to reproduce such behavior giving some insight on the microscopic dynamics at the basis of the graph structure

scaling invariance in spectra of complex networks a diffusion factorial moment approach a new method called diffusion factorial moment is used to obtain scaling features embedded in the spectra of complex networks for an erdos renyi network with connecting probability p mathit er l1 n the scaling parameter is ensuremath delta 0 51 while for p mathit er ensuremath geqslant 1 n the scaling parameter deviates from it significantly for ws small world networks in the special region p r 0 05 0 2 typical scale invariance is found for growing random networks in the range of ensuremath theta 0 33 049 we have ensuremath delta 0 6 ifmmode pm else textpm fi 0 1 and the value of ensuremath delta oscillates around ensuremath delta 0 6 abruptly in the range of ensuremath theta 0 54 1 we have basically ensuremath delta g0 7 scale invariance is one of the common features of the three kinds of networks which can be employed as a global measurement of complex networks in a unified way

homoclinic solutions for ordinary p laplacian systems abstract a new result for the existence of homoclinic orbits is obtained for ordinary p laplacian system d dt u t p 2 u t v t u t f t where p 1 t r u r n and v c 1 r r n r v t x k t x w t x is t periodic with respect to t t 0 and f r r n is a continuous and bounded function this result generalizes and improves some known results in the previous literature

existence of homoclinic solutions for a class of second order hamiltonian systems abstract a new result for existence of homoclinic orbits is obtained for the second order hamiltonian systems under a class of new superquadratic conditions a homoclinic orbit is obtained as a limit of solutions of a certain sequence of boundary value problems which are obtained by the minimax methods

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

existence of homoclinic solutions for a class of time dependent hamiltonian systems n 1 n n 2 where q s q q g r w g c r r r and l t g c r r 1 n is a positive definite symmetric matrix for all t g r the case where l t and w t q are either periodic in t or independent of t were studied by several authors see for instance ambrosetti and w x w x bertotti 1 coti zelati ekeland and sere 4 coti zelati and rabinowitz w x w x w x 5 rabinowitz 15 17 sere 19 and their references in this kind of problem the function l t plays an important role for example if l t s ai where a 0 and i denotes the identity matrix n n w x felmer and silva 8 have showed the existence of homoclinic orbits as the limit of subharmonic solutions provided that hs is autonomous see also w x w x rabinowitz and tanaka 18 serra tarallo and terracini 20 using an w x w x approach introduced by 4 see also 19 treated the hs problem

recursive graphs with small world scale free properties we discuss a category of graphs recursive clique trees which have small world and scale free properties and allow a fine tuning of the clustering and the power law exponent of their discrete degree distribution we determine relevant characteristics of those graphs the diameter degree distribution and clustering parameter the graphs have also an interesting recursive property and generalize recent constructions with fixed degree distributions

brief suboptimal markovian smoothing estimates based on continuous curves of solutions of the algebraic riccati inequality based on a result on continuous dependence of solutions of an algebraic riccati equation on the data matrices we construct continuous curves of solutions of an algebraic riccati inequality and derive suboptimal markovian estimates for the steady state smoothing problem

infinitely many homoclinic orbits for the second order hamiltonian systems with general potentials abstract in this paper we study the following nonperiodic second order hamiltonian systems u t l t u t r t u t r where l t may not be uniformly positive definite for all t r under more general conditions on r u t u we prove that the above system has infinitely many homoclinic orbits provided r is even in u

homoclinic orbits for a class of hamiltonian systems consider the second order hamiltonian system where q n and v c 1 n is t periodic in t suppose v q t 0 0 0 is a local maximum for v t and v t x x under these and some additional technical assumptions we prove that hs has a homoclinic orbit q emanating from 0 the orbit q is obtained as the limit as k of 2 kt periodic solutions i e subharmonics q k of hs the subharmonics q k are obtained in turn via the mountain pass theorem

better synchronizability predicted by crossed double cycle in this brief report we propose a network model named crossed double cycles which are completely symmetrical and can be considered as the extensions of nearest neighboring lattices the synchronizability measured by eigenratio r can be sharply enhanced by adjusting the only parameter the crossed length m the eigenratio r is shown very sensitive to the average distance l and the smaller average distance will lead to better synchronizability furthermore we find that in a wide interval the eigenratio r approximately obeys a power law form as r approximately l 1 5

existence of even homoclinic orbits for second order hamiltonian systems some existence theorems for even homoclinic orbits are obtained for a class of second order nonautonomous hamiltonian systems with symmetric potentials under a class of new superquadratic conditions a homoclinic orbit is obtained as a limit of solutions of a certain sequence of nil boundary value problems which are obtained by the minimax methods

growing network with local rules preferential attachment clustering hierarchy and degree correlations the linear preferential attachment hypothesis has been shown to be quite successful in explaining the existence of networks with power law degree distributions it is then quite important to determine if this mechanism is the consequence of a general principle based on local rules in this work it is claimed that an effective linear preferential attachment is the natural outcome of growing network models based on local rules it is also shown that the local models offer an explanation for other properties like the clustering hierarchy and degree correlations recently observed in complex networks these conclusions are based on both analytical and numerical results for different local rules including some models already proposed in the literature

complex network properties of chinese natural science basic research in this paper we studied the research areas of chinese natural science basic research from a point view of complex network two research areas are considered to be connected if they appear in one fund proposal the explicit network of such connections using data from 1999 to 2004 is constructed the analysis of the real data shows that the degree distribution of the bf research areas network ran may be better fitted by the exponential distribution it displays small world effect in which randomly chosen pairs of research areas are typically separated by only a short path of intermediate research areas the average distance of ran decreases with time while the average clustering coefficient increases with time which indicates that the scientific study would like to be integrated together in terms of the studied areas the relationship between the clustering coefficient c k and the degree k indicates that there is no hierarchical organization in ran

existence of homoclinic solution for the second order hamiltonian systems abstract an existence theorem of homoclinic solution is obtained for a class of the nonautonomous second order hamiltonian systems u t l t u t w t u t 0 t r by the minimax methods in the critical point theory specially the generalized mountain pass theorem where l t is unnecessary uniformly positively definite for all t r and w t x satisfies the superquadratic condition w t x x 2 as x uniformly in t and need not satisfy the global ambrosetti rabinowitz condition

a unified proof on existence of homoclinic orbits for some semilinear ordinary differential equations with periodic potentials abstract this paper gives a direct short and unified proof of rabinowitz s theorem grossinho minhos tersian s theorem and tersian chaparova s theorems on existence of homoclinic orbits for second order periodic hamiltonian systems fourth and sixth order periodic ordinary differential equations respectively by brezis nirenberg type mountain pass lemma

symmetrically homoclinic orbits for symmetric hamiltonian systems in this paper we study the existence of symmetric homoclinic orbits for first order and second order hamiltonian systems with some symmetric hamiltonian functions

homoclinic solutions of some second order non autonomous systems abstract in this paper we investigate the existence of homoclinic solutions for the following second order non autonomous system q a q l t q w q t q 0 ds where a is an antisymmetric constant matrix l c r r n 2 is a symmetric and positive definite matrix for all t r w t q a t v q such that a r r is a continuous function and v c 1 r n r assuming that v q is subquadratic as q and some technical assumptions on a and l we establish two existence criteria to guarantee that ds has at least one nontrivial homoclinic solution by using a standard minimizing argument besides that in some particular case for the first time the uniqueness of homoclinic solutions of ds is also obtained recent results in the literature are generalized and significantly improved

fast homoclinic solutions for a class of damped vibration problems in this paper we deal with the existence and multiplicity of homoclinic solutions of the following damped vibration problemsu t q t u t l t u t w t u t 0 where l t and w t x are neither autonomous nor periodic in t our approach is variational and it is based on the critical point theory we prove existence and multiplicity results of fast homoclinic solutions under general growth conditions on the potential function moreover some open problems proposed by zhang and ruan are resolved our theorems appear to be the first such result

homoclinic solutions for a class of nonperiodic and noneven second order hamiltonian systems abstract the existence of homoclinic solutions is obtained for second order hamiltonian systems u t l t u t w t u t f t as the limit of the solutions of a sequence of nil boundary value problems which are obtained by the mountain pass theorem when l t and w t x are neither periodic nor even with respect to t

homoclinic solutions for a class of non autonomous subquadratic second order hamiltonian systems abstract in this paper we consider the existence of homoclinic solutions for the following second order non autonomous hamiltonian system hs q l t q w q t q 0 where l t c r r n 2 is a symmetric and positive definite matrix for all t r w t q a t q with a t r r is a positive continuous function and 1 2 is a constant adopting some other reasonable assumptions for l and w we obtain a new criterion for guaranteeing that hs has one nontrivial homoclinic solution by use of a standard minimizing argument in critical point theory recent results from the literature are generalized and significantly improved

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

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

weighted networks of scientific communication the measurement and topological role of weight abstract in order to take the weight of connection into consideration and to find a natural measurement of weight we have collected papers in econophysics and constructed a network of scientific communication to integrate idea transportation among econophysicists by collaboration citation and personal discussion some basic statistics such as weight per degree are discussed in fan et al j mod phys b 17 19 2004 2505 in this paper by including the papers published recently further statistical results for the network are reported clustering coefficient of weighted networks is introduced and empirically studied in this network we also compare the typical statistics on this network under different weight assignments including random and inverse weight the conclusion from weight redistributed network is helpful to the investigation of the topological role of weight

some results on connecting orbits for a class of hamiltonian systems abstract the existence of various kinds of connecting orbits is established for a certain hamiltonian system as well as its time dependent analogue for the autonomous case our main assumption is that v has a global maximum e g at x o and we find a various kinds of orbits terminating at o for the time dependent case v has a local but not global maximum at x o and we find a homoclinic orbit emanating from and terminating at o keywords periodic solution

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

existence and multiplicity of homoclinic orbits for the second order hamiltonian systems in this paper we study the following nonperiodic second order hamiltonian system u t l t u t ur t u t r where l t may not be uniformly positive definite for all t r and r t u is asymptotically quadratic in u as u by applying a generalized linking theorem in bartsch and ding 2006 8 we obtain the existence and multiplicity of homoclinic orbits for the above system

information filtering via weighted heat conduction algorithm abstract in this paper by taking into account effects of the user and object correlations on a heat conduction hc algorithm a weighted heat conduction whc algorithm is presented we argue that the edge weight of the user object bipartite network should be embedded into the hc algorithm to measure the object similarity the numerical results indicate that both the accuracy and diversity could be improved greatly compared with the standard hc algorithm and the optimal values reached simultaneously on the movielens and netflix datasets the algorithmic accuracy measured by the average ranking score can be improved by 39 7 and 56 1 in the optimal case respectively and the diversity could reach 0 9587 and 0 9317 when the recommendation list equals to 5 further statistical analysis indicates that in the optimal case the distributions of the edge weight are changed to the poisson form which may be the reason why hc algorithm performance could be improved this work highlights the effect of edge weight on a personalized recommendation study which maybe an important factor affecting personalized recommendation performance

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

why social networks are different from other types of networks we argue that social networks differ from most other types of networks including technological and biological networks in two important ways first they have nontrivial clustering or network transitivity and second they show positive correlations also called assortative mixing between the degrees of adjacent vertices social networks are often divided into groups or communities and it has recently been suggested that this division could account for the observed clustering we demonstrate that group structure in networks can also account for degree correlations we show using a simple model that we should expect assortative mixing in such networks whenever there is variation in the sizes of the groups and that the predicted level of assortative mixing compares well with that observed in real world networks

enhanced synchronizability by structural perturbations in this brief report we investigate the collective synchronization of a system of coupled oscillators on a barab asi albert scale free network we propose an approach of structural perturbations aiming at those nodes with maximal betweenness this method can markedly enhance the network synchronizability and is easy to realize the simulation results show that the eigenratio will sharply decrease by one half when only 0 6 of those hub nodes occur under three division processes when the network size n 2000 in addition the present study also provides numerical evidence that the maximal betweenness plays a major role in network synchronization

homoclinic orbits for superquadratic hamiltonian systems without a periodicity assumption abstract in this paper we consider the second order hamiltonian system q t v t q t f t where v t q k t q w t q under suitable conditions on the growth of w and k we establish the existence of a nontrivial homoclinic orbit without any assumption of periodicity on v this homoclinic orbit is obtained as a limit of solutions of a certain sequence of nil boundary value problems which are obtained by the minimax methods