oscillation caused by impulses the present paper is devoted to the investigation of the oscillation of a kind of very extensively studied second order nonlinear delay differential equations with impulses some interesting results are obtained which illustrate that impulses play a very important role in giving rise to the oscillations of equations

a survey on oscillation of impulsive delay differential equations this paper presents a systematic development of the oscillatory results for the linear and nonlinear impulsive delay differential equations we also discuss linearized oscillation theory and give some applications to mathematical biology

oscillation for solutions of nonlinear neutral differential equations with impulses abstract this paper is concerned with nonlinear neutral differential equations with impulses of the form some oscillation criteria for solutions of this equation are established an interesting example is also given which illustrates that impulses play an important role in giving rise to the oscillation of equations

the persistence of nonoscillatory solutions of difference equations under impulsive perturbations we obtain a sufficient condition for the persistence of nonoscillatory solutions of the difference equation with continuous variable x t t x t i 1mp i t x t c i t 0 under the impulsive perturbations x t k t x t k i k x t k k n 1

on delay differential equations with impulses abstract sufficient conditions are obtained respectively for the asymptotic stability of the trivial solution of x t ax t j 1 bjx tj t tj t tj and for the existence of a nonoscillatory solution conditions are also obtained for all solutions to be oscillatory the asymptotic behaviour of an impulsively perturbed delay logistic equation is investigated as an extension to a nonlinear equation

examples of pleating varieties for twice punctured tori we give an explicit description of some pleating varieties sets with a fixed set of bending lines in the convex hull boundary in the quasi fuchsian space of the twice punctured torus in accordance with a conjecture of the second author we show that their closures intersect fuchsian space in the simplices of minima introduced by kerckhoff all computations are done using complex fenchel nielsen coordinates for quasi fuchsian space referred to a maximal system of curves

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

linearized oscillation of nonlinear impulsive delay differential equations abstract the main result of this paper is to show oscillations of nonlinear impulsive delay differential equations are equivalent to those of corresponding linear impulsive delay differential equations the results of this paper generalize some well known results in the literature

statistical mechanics of community detection starting from a general ansatz we show how community detection can be interpreted as finding the ground state of an infinite range spin glass our approach applies to weighted and directed networks alike it contains the ad hoc introduced quality function from j reichardt and s bornholdt phys rev lett 93 218701 2004 and the modularity q as defined by newman and girvan phys rev e 69 026113 2004 as special cases the community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices we elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study further we show how hierarchies and overlap in the community structure can be detected computationally efficient local update rules for optimization procedures to find the ground state are given we show how the ansatz may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension finally we give expectation values for the modularity of random graphs which can be used in the assessment of statistical significance of community structure

comparing connectomes across subjects and populations at different scales brain connectivity can be represented by a network that enables the comparison of the different patterns of structural and functional connectivity among individuals in the literature two levels of statistical analysis have been considered in comparing brain connectivity across groups and subjects 1 the global comparison where a single measure that summarizes the information of each brain is used in a statistical test 2 the local analysis where a single test is performed either for each node connection which implies a multiplicity correction or for each group of nodes connections where each subset is summarized by one single test in order to reduce the number of tests to avoid a penalizing multiplicity correction we comment on the different levels of analysis and present some methods that have been proposed at each scale we highlight as well the possible factors that could influence the statistical results and the questions that have to be addressed in such an analysis

community detection in networks with positive and negative links detecting communities in complex networks accurately is a prime challenge preceding further analyses of network characteristics and dynamics until now community detection took into account only positively valued links while many actual networks also feature negative links we extend an existing potts model to incorporate negative links as well resulting in a method similar to the clustering of signed graphs as dealt with in social balance theory but more general to illustrate our method we applied it to a network of international alliances and disputes using data from 1993 2001 it turns out that the world can be divided into six power blocs similar to huntington s civilizations with some notable exceptions

positive solutions and asymptotic behavior of delay differential equations with nonlinear impulses abstract consider the delay differential equation dde with nonlinear impulses x t i 1 n p i t x t i 0 t t j t t 0 x t j x t j i j x t j j 1 2 wherepi c t0 r i 0 fori 1 2 n andij c r r forj 1 2 the purpose of this paper is to obtain a necessary and sufficient condition for the existence of positive solutions of dde without impulses and to establish a kind of order persistence of solutions of eq and criteria of the asymptotic behavior of eq which can be used to improve and develop some of the known results in the literature

uniform stability theorems for delay differential equations with impulses abstract in the paper we obtain sufficient conditions for the uniform stability of the zero solution of the delay differential equation with impulses x t h t x t f t x t t t 0 t t k x t k x t k i k x t k k n

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

oscillation properties of a second order impulsive delay differential equation abstract for the second order delay differential equation y t a t y t i 1 n p i t y g i t 0 t 0 t t k with impulsive conditions y t y t b y t y t y t b y t an explicit necessary and sufficient condition for all bounded solutions to be oscillatory is obtained by the comparison theorem on bounded oscillation of the impulsive differential equation with the corresponding nonimpulsive differential equation

the nonoscillatory solutions of delay differential equations with impulses abstract we obtain a sufficient condition for the impulsive delay differential equation t i 1 n p i t r i t t t k t k t k i k t k k n to have a nonoscillatory solution

benchmark graphs for testing community detection algorithms community structure is one of the most important features of real networks and reveals the internal organization of the nodes many algorithms have been proposed but the crucial issue of testing i e the question of how good an algorithm is with respect to others is still open standard tests include the analysis of simple artificial graphs with a built in community structure that the algorithm has to recover however the special graphs adopted in actual tests have a structure that does not reflect the real properties of nodes and communities found in real networks here we introduce a class of benchmark graphs that account for the heterogeneity in the distributions of node degrees and of community sizes we use this benchmark to test two popular methods of community detection modularity optimization and potts model clustering the results show that the benchmark poses a much more severe test to algorithms than standard benchmarks revealing limits that may not be apparent at a first analysis

fixed points of compositions of earthquakes let s be a closed surface of genus at least 2 and consider two measured geodesic laminations that fill s right earthquakes along these laminations are diffeomorphisms of the teichmuller space of s we prove that the composition of these earthquakes has a fixed point in the teichmuller space another way to state this result is that it is possible to prescribe any two measured laminations that fill a surface as the upper and lower measured bending laminations of the convex core of a globally hyperbolic ads manifold the proof uses some estimates from the geometry of those ads manifolds

polyhedra inscribed in a quadric we study convex polyhedra in three space that are inscribed in a quadric surface up to projective transformations there are three such surfaces the sphere the hyperboloid and the cylinder our main result is that a planar graph gamma is realized as the 1 skeleton of a polyhedron inscribed in the hyperboloid or cylinder if and only if gamma is realized as the 1 skeleton of a polyhedron inscribed in the sphere and gamma admits a hamiltonian cycle this answers a question asked by steiner in 1832 rivin characterized convex polyhedra inscribed in the sphere by studying the geometry of ideal polyhedra in hyperbolic space we study the case of the hyperboloid and the cylinder by parameterizing the space of convex ideal polyhedra in anti de sitter geometry and in half pipe geometry just as the cylinder can be seen as a degeneration of the sphere and the hyperboloid half pipe geometry is naturally a limit of both hyperbolic and anti de sitter geometry we promote a unified point of view to the study of the three cases throughout

partition signed social networks via clustering dynamics abstract inspired by the dynamics phenomenon occurred in social networks the wjjlgs model is modified to imitate the clustering dynamics of signed social networks analyses show that the clustering dynamics of the model can be applied to partition signed social networks traditionally blockmodel is applied to partition signed networks in this paper a detailed dynamics based algorithm for signed social networks dbas is presented simulations on several typical real world and illustrative networks that have been analyzed by the blockmodel verify the correctness of the proposed algorithm the efficiency of the algorithm is verified on large scale synthetic networks

oscillation criteria for second order nonlinear differential equations with impulses abstract the present paper is devoted to the investigation of the oscillatory behavior of a kind of extensively studied second order nonlinear delay differential equations with impulses some interesting results are obtained which illustrate that impulses play a very important role in giving rise to the oscillations of equations

oscillation of solutions of impulsive delay differential equations the oscillatory and asymptotic behaviour of first order impulsive delay differential equations and inequalities with oscillatory coefficients are studied some new results are obtained

a dynamic evolutionary clustering perspective community detection in signed networks by reconstructing neighbor sets community detection in social networks has been intensively studied in recent years in this paper a novel similarity measurement is defined according to social balance theory for signed networks inter community positive links are found and deleted due to their low similarity the positive neighbor sets are reconstructed by this method then differential equations are proposed to imitate the constantly changing states of nodes each node will update its state based on the difference between its state and average state of its positive neighbors nodes in the same community will evolve together with time and nodes in the different communities will evolve far away communities are detected ultimately when states of nodes are stable experiments on real world and synthetic networks are implemented to verify detection performance the thorough comparisons demonstrate the presented method is more efficient than two acknowledged better algorithms

local resolution limit free potts model for community detection we report on an exceptionally accurate spin glass type potts model for community detection with a simple algorithm we find that our approach is at least as accurate as the best currently available algorithms and robust to the effects of noise it is also competitive with the best currently available algorithms in terms of speed and size of solvable systems we find that the computational demand often exhibits superlinear scaling o l 1 3 where l is the number of edges in the system and we have applied the algorithm to synthetic systems as large as 40 ifmmode times else texttimes fi 10 6 nodes and over 1 ifmmode times else texttimes fi 10 9 edges a previous stumbling block encountered by popular community detection methods is the so called resolution limit being a local measure of community structure our potts model is free from this resolution limit effect and it further remains a local measure on weighted and directed graphs we also address the mitigation of resolution limit effects for two other popular potts models

network of likes and dislikes conflict and membership abstract we all have friends and foes in the study of complex networks such a pairwise interaction is described by a directed link since the relation is not necessarily symmetric we study a real network constructed from a survey in which each individual chooses five members s he wants to work with and other five s he does not like to work together although everyone s outdegrees for such like and dislike links are fixed to five respectively it is found that indegree sequence for each type of links exhibits very different behaviors we also pursue to answer the question of proper divisions of the organization based on the concept of happiness defined for each directed relation for example two individuals connected by like dislike links in both directions are happy if they belong to the same different group s we then adopt the framework of the q state potts model with long ranged ferromagnetic and antiferromagnetic interactions and discuss the group structure in the organization that minimizes a suitably defined unhappiness

the persistence of nonoscillatory solutions of delay differential equations under impulsive perturbations abstract we obtain a sufficient condition for the persistence of nonoscillatory solutions of the delay differential equation under impulsive perturbations

limits of quasi fuchsian groups with small bending we study limits of quasi fuchsian groups for which the bending measures on the convex hull boundary tend to zero giving necessary and sufficient conditions for the limit group to exist and be fuchsian as an application we complete the proof of a conjecture made in 24 conjecture 6 5 that the closures of pleating varieties for quasi fuchsian groups meet fuchsian space exactly in kerckhoff s lines of minima of length functions doubling our examples gives rise to a large class of cone manifolds which degenerate to hyperbolic surfaces as the cone angles approach 2

weight conserving characterization of complex functional brain networks complex functional brain networks are large networks of brain regions and functional brain connections statistical characterizations of these networks aim to quantify global and local properties of brain activity with a small number of network measures important functional network measures include measures of modularity measures of the goodness with which a network is optimally partitioned into functional subgroups and measures of centrality measures of the functional influence of individual brain regions characterizations of functional networks are increasing in popularity but are associated with several important methodological problems these problems include the inability to characterize densely connected and weighted functional networks the neglect of degenerate topologically distinct high modularity partitions of these networks and the absence of a network null model for testing hypotheses of association between observed nontrivial network properties and simple weighted connectivity properties in this study we describe a set of methods to overcome these problems specifically we generalize measures of modularity and centrality to fully connected and weighted complex networks describe the detection of degenerate high modularity partitions of these networks and introduce a weighted connectivity null model of these networks we illustrate our methods by demonstrating degenerate high modularity partitions and strong correlations between two complementary measures of centrality in resting state functional magnetic resonance imaging mri networks from the 1000 functional connectomes project an open access repository of resting state functional mri datasets our methods may allow more sound and reliable characterizations and comparisons of functional brain networks across conditions and subjects

oscillation and stability of linear impulsive delay differential equations the main results of this paper are that the oscillation and the stability of a linear impulsive delay differential equation are equivalent respectively to the oscillation and the stability of a corresponding linear delay differential equation without impulses the results of this paper can be used to improve and derive some of the known results in the literature

the fenchel nielsen deformation the uniformization theorem provides that a riemann surface s of negative euler characteristic has a metric of constant curvature 1 a hyperbolic structure can be understood in terms of its deformations unfortunately the variation of the hyperbolic metric arising from a deformation is not determined by local data if z is a conformal coordinate for s and a ii h ii 00 1 a beltrami differential then dw dz p dj defines a new conformal coordinate and structure si the tensor p may vanish on the open set 0 c s and yet the hyperbolic metrics of s and si do not coincide on this phenomenon presents a s erious difficulty in the deformation theory of hyperbolic structures the fenchel nielsen twist deformation does not share this defect the deformation is defined by cutting the surface along a simple closed geodesic rotating one side of the cut relative to the other and attaching the sides in their new position a geodesic intersecting the cut is deformed to a broken geodesic the hyperbolic structure in the complement of the cut extends naturally to a hyperbolic structure on the new surface the deformation is concentrated at the cut the basic idea for the deformation appears in the work of fricke klein dehn and fenchel nielsen 71 8 in the fenchel nielsen manuscript the deformation was considered extensively coordinates for teichmiller space are defined in terms of the deformation the proper definition is given by a fuchsian group construction calculations are made in terms of unimodular matrices this approach is often cumbersome our basic objective is to give a description of the deformation in terms of quasiconformal mappings the bers embedding of teichmiiller space is central to the analytic theory of deformations using our characterization we calculate the first variation of the bers embedding for the fenchel nielsen deformation the result is a poincare series 6 which already appears in the work of petersson 16

oscillation of impulsive neutral delay differential equations abstract in this paper effective sufficient conditions for the oscillation of all solutions of impulsive neutral delay differential equations of the form x t p t x t q t x t sgn x t 0 t t 0 x t k b k x t k k 1 2 are established our results reveal the fact that the oscillatory properties of all solutions of eqs and may be caused by the impulsive perturbations though the corresponding neutral delay differential equation without impulses i e eq admits a nonoscillatory solution it is also seen that the oscillatory behavior of all solutions of eq can be inherited by eqs and under certain impulsive perturbations some examples are also given to illustrate the applicability of the results obtained

community detectability and structural balance dynamics in signed networks we investigate signed networks with community structure with respect to their spectra and their evolution under a dynamical model of structural balance a prominent theory of signed social networks the spectrum of the adjacency matrix generated by a stochastic block model with two equal size communities shows detectability transitions in which the community structure becomes manifest when its signal eigenvalue appears outside the main spectral band the spectrum also exhibits sociality transitions involving the homogeneous structure representing the average tie value we derive expressions for the eigenvalues associated with the community and homogeneous structure as well as the transition boundaries all in good agreement with numerical results using the stochastically generated networks as initial conditions for a simple model of structural balance dynamics yields three outcome regimes two hostile factions that correspond with the initial communities two hostile factions uncorrelated with those communities and a single harmonious faction of all nodes the detectability transition predicts the boundary between the assortative and mixed two faction states and the sociality transition predicts that between the mixed and harmonious states our results may yield insight into the dynamics of cooperation and conflict among actors with distinct social identities

spectral theory for dynamics on graphs containing attractive and repulsive interactions many applied problems can be posed as a dynamical system defined on a network with attractive and repulsive interactions examples include synchronization of nonlinear oscillator networks the behavior of groups or cliques in social networks and the study of optimal convergence for consensus algorithm it is important to determine the index of a matrix i e the number of positive and negative eigenvalues and the dimension of the kernel in this paper we consider the common examples where the matrix takes the form of a signed graph laplacian we show that the there are topological constraints on the index of the laplacian matrix related to the dimension of a certain homology group when the homology group is trivial the index of the operator is determined only by the topology of the network and is independent of the strengths of the interactions in general these constraints give bounds on the number of positive and negative eigenvalues with the dimension of the homology group counting the number

oscillation of nonlinear delay impulsive differential equations and inequalities the oscillatory and asymptotic behavior of first order nonlinear delay impulsive differential equations and inequalities is studied some new sharp sufficient conditions for oscillation and nonoscillation of solutions of the equations and inequalities are obtained many known results are improved in particular the conditions are necessary and sufficient if the equations and inequalities are autonomous

modular structure of functional networks in olfactory memory graph theory enables the study of systems by describing those systems as a set of nodes and edges graph theory has been widely applied to characterize the overall structure of data sets in the social technological and biological sciences including neuroscience modular structure decomposition enables the definition of sub networks whose components are gathered in the same module and work together closely while working weakly with components from other modules this processing is of interest for studying memory a cognitive process that is widely distributed we propose a new method to identify modular structure in task related functional magnetic resonance imaging fmri networks the modular structure was obtained directly from correlation coefficients and thus retained information about both signs and weights the method was applied to functional data acquired during a yes no odor recognition memory task performed by young and elderly adults four response categories were explored correct hit and incorrect false alarm fa recognition and correct and incorrect rejection we extracted time series data for 36 areas as a function of response categories and age groups and calculated condition based weighted correlation matrices overall condition based modular partitions were more homogeneous in young than elderly subjects using partition similarity based statistics and a posteriori statistical analyses we demonstrated that several areas including the hippocampus caudate nucleus and anterior cingulate gyrus belonged to the same module more frequently during hit than during all other conditions modularity values were negatively correlated with memory scores in the hit condition and positively correlated with bias scores liberal conservative attitude in the hit and fa conditions we further demonstrated that the proportion of positive and negative links between areas of different modules i e the proportion of correlated and anti correlated areas accounted for most of the observed differences in signed modularity taken together our results provided some evidence that the neural networks involved in odor recognition memory are organized into modules and that these modular partitions are linked to behavioral performance and individual strategies

the maximum balanced subgraph of a signed graph applications and solution approaches the maximum balanced subgraph problem mbsp is the problem of finding a subgraph of a signed graph that is balanced and maximizes the cardinality of its vertex set this paper is the first one to discuss applications of the mbsp arising in three different research areas the detection of embedded structures portfolio analysis in risk management and community structure the efficient solution of the mbsp is also in the focus of this paper we discuss pre processing routines and heuristic solution approaches to the problem a grasp metaheuristic is developed and improved versions of a greedy heuristic are discussed extensive computational experiments are carried out on a set of instances from the applications previously mentioned as well as on a set of random instances

stability of sets of functional differential equations with impulse effect abstract in this paper we investigate stability of sets for a class of impulsive functional differential equations by using piecewise continuous lyapunov functions with razumickhin techniques some sufficient conditions for stability of sets are established and some known stability theorems also are generalized

asymptotic behavior of solutions of impulsive delay differential equations abstract effective sufficient conditions for the asymptotic stability of the trivial solution of impulsive delay differential equation formula are obtained by investigating respectively the asymptotic behavior of the nonoscillatory solutions and oscillatory solutions of the equation