uniqueness and non degeneracy of positive radial solutions for quasilinear elliptic equations with exponential nonlinearity abstract we are concerned with the uniqueness and non degeneracy result of positive solutions for a class of quasilinear elliptic equations with exponential nonlinearity we convert a quasilinear elliptic equation into a semilinear one and study precise correspondences between two equations we show the uniqueness and the non degeneracy of positive solutions by analyzing the converted semilinear problem

random growth urban model with geographical fitness abstract this paper formulates a random growth urban model with a notion of geographical fitness using techniques of complex network theory we study our system as a type of preferential attachment model with fitness and we analyze its macro behavior to clarify the properties of the city size distributions it predicts first restricting the geographical fitness to take positive values and using a continuum approach we show that the city size distributions predicted by our model asymptotically approach pareto distributions with coefficients greater than unity then allowing the geographical fitness to take negative values we perform local coefficient analysis to show that the predicted city size distributions can deviate from pareto distributions as is often observed in actual city size distributions as a result the model we propose can generate a generic class of city size distributions including but not limited to pareto distributions for applications to city population projections our simple model requires randomness only when new cities are created not during their subsequent growth this property leads to smooth trajectories of city population growth in contrast to other models using gibrat s law in addition a discrete form of our dynamical equations can be used to estimate past city populations based on present day data this fact allows quantitative assessment of the performance of our model further study is needed to determine appropriate formulas for the geographical fitness

growth model for fractal scale free networks generated by a random walk abstract the diversity of networked systems with fractal structures suggests that knowing the underlying mechanism that generates the fractality is necessary for building a model of the development of complex networks in the present paper we propose a growth model of a network generated by a random walk and show that the evolving graph forms a fractal structure with various properties including the scale free property if the graph which provides a space where a random walk occurs by itself is formed by the random walk the proposed model is regulated by two parameters p v and p e which define the probability of either a roundabout path via a new vertex or a shortcut being formed by the random walk respectively the power law exponent describing the vertex degree distribution is determined by the ratio p e p v and is related to an internal factor f i via the relation 1 f i 1 where f i is a parameter that describes the local structure generated by the random walk a sufficiently small p v provides the small world property to the model network the small world property is usually considered to be incompatible with the fractal scaling property open m c l c d c where open m c is the average number of vertices which can be reached from a randomly chosen vertex in at most l c steps however we demonstrate that fractality can be reconciled with the small world property by introducing a size dependent fractal cluster dimension d c

soliton solutions for quasilinear schrodinger equations the critical exponential case abstract quasilinear elliptic equations in r 2 of second order with critical exponential growth are considered by using a change of variable the quasilinear equations are reduced to semilinear equations whose respective associated functionals are well defined in h 1 r 2 and satisfy the geometric hypotheses of the mountain pass theorem using this fact we obtain a cerami sequence converging weakly to a solution v in the proof that v is nontrivial the main tool is the concentration compactness principle p l lions the concentration compactness principle in the calculus of variations the locally compact case part i and ii ann inst h poincare anal non lineaire 1 1984 109 145 223 283 combined with test functions connected with optimal trudinger moser inequality

local world evolving networks with tunable clustering abstract we propose an extended local world evolving network model including a triad formation tf step in the process of network evolution random fluctuation in the number of new edges is involved we derive analytical expressions for degree distribution clustering coefficient and average path length our model can unify the generic properties of real life networks scale free degree distribution high clustering and small inter node separation moreover in our model the clustering coefficient is tunable simply by changing the expected number of tf steps after a single local preferential attachment step

pinning synchronization of delayed complex dynamical networks with nonlinear coupling abstract in this paper we find that complex networks with the watts strogatz or scale free ba random topological architecture can be synchronized more easily by pin controlling fewer nodes than regular systems theoretical analysis is included by means of lyapunov functions and linear matrix inequalities lmi to make all nodes reach complete synchronization numerical examples are also provided to illustrate the importance of our theoretical analysis which implies that there exists a gap between the theoretical prediction and numerical results about the minimum number of pinning controlled nodes

dynamics of directed graphs the world wide web we introduce and simulate a growth model of the world wide web based on the dynamics of outgoing links that is motivated by the conduct of the agents in the real web to update outgoing links re directing them towards constantly changing selected nodes emergent statistical correlation between the distributions of outgoing and incoming links is a key feature of the dynamics of the web the growth phase is characterized by temporal fractal structures which are manifested in the hierarchical organization of links we obtain quantitative agreement with the recent empirical data in the real web for the distributions of in and out links and for the size of the connected component in a fully grown network of n nodes we study the structure of connected clusters of nodes that are accessible along outgoing links from a randomly selected node the distributions of size and depth of the connected clusters with a giant component exhibit supercritical behavior by decreasing the control parameter average fraction of updated and added links per time step towards c n 10 the web can resume a critical structure with no giant component in it we find a different universality class when the updates of links are not allowed i e for 0 corresponding to the network of science citations

uniform synchronous criticality of diversely random complex networks abstract we investigate collective synchronous behaviors in random complex networks of limit cycle oscillators with the non identical asymmetric coupling scheme and find a uniform coupling criticality of collective synchronization which is independent of complexity of network topologies numerical simulations on categories of random complex networks have verified this conclusion

projective cluster synchronization in drive response dynamical networks abstract in this paper we study the projective cluster synchronization in a drive response dynamical network with 1 n coupled partially linear chaotic systems because the scaling factors characterizing the dynamics of projective synchronization remain unpredictable pinning control ideas are adopted to direct the different scaling factors onto the desired values it is also shown that the projection cluster synchronization can be realized by controlling only one node in each cluster numerical simulations on the chaotic lorenz system are illustrated to verify the theoretical results

effect of node deleting on network structure abstract the ever increasing knowledge of the structure of various real world networks has uncovered their complex multi mechanism governed evolution processes therefore a better understanding of the structure and evolution of these networked complex systems requires us to describe such processes in a more detailed and realistic manner in this paper we introduce a new type of network growth rule which comprises addition and deletion of nodes and propose an evolving network model to investigate the effect of node deleting on network structure it is found that with the introduction of node deleting network structure is significantly transformed in particular degree distribution of the network undergoes a transition from scale free to exponential forms as the intensity of node deleting increases at the same time nontrivial disassortative degree correlation develops spontaneously as a natural result of network evolution in the model we also demonstrate that node deleting introduced in the model does not destroy the connectedness of a growing network so long as the increasing rate of edges is not excessively small in addition it is found that node deleting will weaken but not eliminate the small world effect of a growing network and generally it will decrease the clustering coefficient in a network

oscillatory epidemic prevalence in growing scale free networks we study the persistent epidemic prevalence with oscillatory behavior and the extinction of computer viruses via e mails on a contact relational network growing with new users for which scale free structure is estimated from real data typical oscillatory phenomenon is simulated in a stochastic model for the execution and detection of viruses the conditions of extinction by random and targeted immunizations for hubs are derived through bifurcation analysis for simpler deterministic models by using a mean field approximation without the connectivity correlations we can qualitatively understand the mechanisms of the spread in linearly growing scale free networks

how much information is needed to be the majority during the binary state opinion formation abstract in this paper we try to propose a toy model which follows the majority rule with the fermi function to uncover the role of the heterogeneous interaction between individuals in opinion formation in order to do this we define the impact factor i f i says individual i as the exponential function of its connectivity k i with the tunable parameter also shows the public information that can be collected by individuals in the system we realize our model in scale free networks with mean connectivity k we find that much more public information 2 and less public information 1 cannot let either of the two opinions be the majority during the opinion formation furthermore 1 is a constant and equal to 0 76 0 04 and 2 decreases as a power law function of the mean connectivity k of the network our work can provide some perspectives and tools to understand the diversity of opinion in social networks

soliton solutions for quasilinear schrodinger equations ii abstract for a class of quasilinear schrodinger equations we establish the existence of ground states of soliton type solutions by a variational method

epidemic dynamics behavior in some bus transport networks abstract we abstract bus transport networks btns to complex networks using the space p approach first we select three actual btns in three major cities in china namely beijing shanghai and hangzhou using the sis model we simulate and study the epidemic spreading in the three btns we obtain the density of infected vertices varying with time and the stationary density of infected vertices varying with infection rate second we simulate and study the epidemic spreading in a recently introduced btn evolution model the network properties of which correspond well with those of actual btns third we use mean field theory to analyze the epidemic dynamics behavior of the btn evolution model and obtain the theoretical epidemic threshold of this model the theoretical value agrees well with the simulation results based on the work in this paper we provide the following possible forecasts for epidemic dynamics in actual btns an actual btn should have a finite positive epidemic threshold if the effective infection rate is above this threshold the epidemic spread in the network and the density of infected vertices finally stabilizes in a balanced state below this threshold the number of infected vertices decays exponentially fast and the epidemic cannot spread on a large scale

equilibrium distributions in entropy driven balanced processes abstract for entropy driven balanced processes we obtain final states with poisson bernoulli negative binomial and polya distributions we apply this both for complex networks and particle production for random networks we follow the evolution of the degree distribution p n in a system where a node can activate k fixed connections from k possible partnerships among all nodes the total number of connections n is also fixed for particle physics problems p n is the probability of having n particles or other quanta distributed among k states phase space cells while altogether a fixed number of n particles reside on k states

structure of n clique networks embedded in a complex network we propose the n clique network as a powerful tool for understanding global structures of combined highly interconnected subgraphs and provide theoretical predictions for statistical properties of the n clique networks embedded in a complex network using the degree distribution and the clustering spectrum furthermore using our theoretical predictions we find that the statistical properties are invariant between 3 clique networks and original networks for several observable real world networks with the scale free connectivity and the hierarchical modularity the result implies that structural properties are identical between the 3 clique networks and the original networks

asymptotic uniqueness of ground states for a class of quasilinear schrodinger equations with h 1 supercritical exponent in this paper we obtain the asymptotic uniqueness of ground states for a class of quasilinear schrodinger equations with h1 supercritical exponent to this aim the uniqueness and the non degeneracy of positive solutions of the corresponding limit equation which is a zero mass problem play important roles thus we also show the uniqueness and non degeneracy result for a class of zero mass problems by applying ode techniques

random boolean network model exhibiting deterministic chaos this paper considers a simple boolean network with n nodes each node s state at time t being determined by a certain number of parent nodes which may vary from one node to another this is an extension of a model studied by andrecut and ali int j mod phys b 15 17 2001 who consider the same number of parents for all nodes we make use of the same boolean rule as andrecut and ali provide a generalization of the formula for the probability of finding a node in state 1 at a time t and use simulation methods to generate consecutive states of the network for both the real system and the model the results match well we study the dynamics of the model through sensitivity of the orbits to initial values bifurcation diagrams and fixed point analysis we show that the route to chaos is due to a cascade of period doubling bifurcations which turn into reversed period halving bifurcations for certain combinations of parameter values

bayesian canonical correlation analysis canonical correlation analysis cca is a classical method for seeking correlations between two multivariate data sets during the last ten years it has received more and more attention in the machine learning community in the form of novel computational formulations and a plethora of applications we review recent developments in bayesian models and inference methods for cca which are attractive for their potential in hierarchical extensions and for coping with the combination of large dimensionalities and small sample sizes the existing methods have not been particularly successful in fulfilling the promise yet we introduce a novel efficient solution that imposes group wise sparsity to estimate the posterior of an extended model which not only extracts the statistical dependencies correlations between data sets but also decomposes the data into shared and data set specific components in statistics literature the model is known as inter battery factor analysis ibfa for which we now provide a bayesian treatment

growing networks with mixed attachment mechanisms networks grow and evolve when new nodes and links are added in there are two methods to add the links uniform attachment and preferential attachment we take account of the addition of links with mixed attachment between uniform attachment and preferential attachment in proportion by using numerical simulations and analysis based on a continuum theory we obtain that the degree distribution p k has an extended power law form p k k k0 when the number of edges k of a node is much larger than a certain value k0 the degree distribution reduces to the power law form p k k and when k is much smaller than k0 the degree distribution degenerates into the exponential form it has been found that degree distribution possesses this extended power law form for many real networks such as the movie actor network the citation network of scientific papers and diverse protein interaction networks

lobby index in networks abstract we propose a new node centrality measure in networks the lobby index which is inspired by hirsch s h index it is shown that in scale free networks with exponent the distribution of the l index has power tail with exponent 1 properties of the l index and extensions are discussed

weighted scale free networks with stochastic weight assignments we propose a model of weighted scale free networks incorporating a stochastic scheme for weight assignments to the links taking into account both the popularity and fitness of a node as the network grows the weights of links are driven either by the connectivity with probability p or by the fitness with probability 1 ensuremath p numerical results show that the total weight exhibits a power law distribution with an exponent ensuremath sigma that depends on the probability p the exponent ensuremath sigma decreases continuously as p increases for p 0 the scaling behavior is the same as that of the connectivity distribution an analytical expression for the total weight is derived so as to explain the features observed in the numerical results numerical results are also presented for a generalized model with a fitness dependent link formation mechanism

uniqueness of the ground state solutions of quasilinear schrodinger equations abstract we are concerned with the uniqueness result of positive solutions for a class of quasilinear elliptic equation arising from plasma physics we convert a quasilinear elliptic equation into a semilinear one and show the unique existence of positive radial solution for original equation under the suitable conditions on the power of nonlinearity and quasilinearity we also investigate the non degeneracy of a positive radial solution for a converted semilinear elliptic equation

solutions for a quasilinear schrodinger equation a dual approach abstract we consider quasilinear stationary schrodinger equations of the form 1 u u 2 u g x u x r n introducing a change of unknown we transform the search of solutions u x of 1 into the search of solutions v x of the semilinear equation 2 v 1 1 2f 2 v g x f v x r n where f is suitably chosen if v is a classical solution of 2 then u f v is a classical solution of 1 variational methods are then used to obtain various existence results

multiple solutions for n kirchhoff type problems with critical exponential growth in rn abstract in this paper we consider a class of nonlocal n kirchhoff type problems involving a nonlinearity term having critical exponential growth by applying variational methods together with trudinger moser inequality in whole r n we obtain the existence of at least two positive solutions

stochastic resonance in coupled threshold elements on a barabasi albert network abstract stochastic resonance is investigated in a system of threshold elements located at nodes and coupled along edges of a barabasi albert network driven by a common subthreshold periodic signal and independent noises array enhanced stochastic resonance is observed i e increase of the spectral power amplification evaluated from the mean output of the network due to proper coupling this enhancement occurs though the response of individual threshold elements to the periodic signal is very diverse due to a power law distribution of their connectivity numerical results are qualitatively explained using simple linear response theory in the mean field approximation

cluster growth in two growing network models we analyse a simple model for growing tree networks and find that although it never percolates there is an anomalously large cluster at finite size we study the growth of both the maximal cluster and the cluster containing the original vertex and find that they obey power laws this property is also observed through simulations in a nonlinear model with loops and a true percolating phase

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved