anti modularity and anti community detecting in complex networks abstract many networks of interest in sciences and social research can be divided naturally into anti communities the problem of detecting and characterizing such anti community structure has attracted recent attention in this paper we first define the anti modularity as a quantitative measure of anti community partitioning on a network we also theoretically and empirically show the reliability of anti modularity as a measurement of the quality of an anti community partitioning a label propagation algorithm lpad for anti community detection is proposed experimental results on synthetic and real world networks show that our algorithm lpad can obtain higher quality anti community partitioning than other methods

asymptotic stabilization of a nonlinear axially moving string by adaptive boundary control in this paper a robust adaptive boundary control for an axially moving string that shows nonlinear behavior resulting from spatially varying tension is investigated a hydraulic actuator equipped with a damper is used as the control actuator at the right boundary of the string the lyapunov redesign method is employed to derive a robust control algorithm employing adaptation laws that estimate three unknown system parameters mass per unit length of string lumped mass of hydraulic actuator and damping coefficient of damper and an unknown boundary disturbance the uniform asymptotic stability when the three parameters are all unknown the exponential stability when they are known and the uniform ultimate boundedness with a bounded boundary disturbance of the closed loop system are investigated the convergence of the parameter estimates to the true values is shown numerical simulations are performed to demonstrate the effectiveness of the proposed robust adaptive boundary control

families and clustering in a natural numbers network we develop a network in which the natural numbers are the vertices the decomposition of natural numbers by prime numbers is used to establish the connections we perform data collapse and show that the degree distribution of these networks scales linearly with the number of vertices we explore the families of vertices in connection with prime numbers decomposition we compare the average distance of the network and the clustering coefficient with the distance and clustering coefficient of the corresponding random graph in case we set connections among vertices each time the numbers share a common prime number the network has properties similar to a random graph if the criterion for establishing links becomes more selective only prime numbers greater than p l are used to establish links where the network has high clustering coefficient

technical communique exponential stabilization of an axially moving string by linear boundary feedback the system modeled by an axially moving string and a mass damper spring mds controller applied at the right hand side rhs boundary of the string is considered the feature of the controller is not restricted at all and is determined by the system implicitly the mathematical model of this system is composed of an ordinary differential equation ode describing the mds and a partial differential equation pde describing the string the c 0 semigroup theory provides an elegant state space representation for the analysis of the coupled system the exponential stability is verified through the total mechanical energy dissipation and the semigroup theory the lower bound of the feedback gain is obtained

a unified approach to the optimal synthesis of fixed point state space digital filters this paper proposes two expressions of the output error variance due to coefficient quantization of fixed point state space digital filters in the time domain one is the deterministic approach which gives precisely the output error variance of state space digital filters the other is the statistical approach where the errors of coefficient quantization are assumed to be independent random variables the statistical approach gives a simple and easy way to analyze the output error variance due to coefficient quantization of state space digital filters the statistical coefficient sensitivity introduced by the statistical approach is shown to be equivalent to the round off noise power gain thus state space digital filters which are optimal with respect to both coefficient sensitivity and roundoff noise can be synthesized by the method of minimization of the roundoff noise such optimal state space digital filters which could be of any order are proved to be free of autonomous overflow limit cycles a numerical example is given to illustrate the effectiveness of the analysis of the output error variance due to coefficient quantization and the synthesis method proposed here

a dynamic control law for the wave equation abstract we consider a system described by the one dimensional linear wave equation in a bounded domain with appropriate boundary conditions to stabilize the system we propose a dynamic boundary controller applied at the free end of the system the transfer function of the proposed controller is restricted to be a positive real function which could be strictly proper we then show that if the transfer function of the controller is strictly proper then the resulting closed loop system is asymptotically stable and if proper but not strictly proper then the resulting closed loop system is exponentially stable

a systematic approach to synthesis of limit cycle free digital filters a systematic approach to synthesis of limit cycle free digital filters under constant input conditions is proposed structures of limit cycle free digital filters under constant input conditions are easily led from structures of limit cycle free digital filters under zero input conditions there exist various realizations which can suppress limit cycles for constant input signals

robust boundary control of an axially moving string by using a pr transfer function in this note a scheme for the vibration suppression of a translating string using a positive real pr transfer function is investigated the transverse vibration of the string is controlled by hydraulic touch rolls located at the right end of the string the mathematical model of the system which consists of a hyperbolic partial differential equation pde describing the dynamics of the moving string and an ordinary differential equation ode for the actuator dynamics is derived by using hamilton s principle for translating continua the transfer function of the proposed boundary controller is a nonproper but pr function the asymptotic stability of the closed loop system in the presence of output disturbance is proved

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

spectral measures of bipartivity in complex networks we introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network spectral graph theory is used to quantify how close to bipartite a network is and the extent to which individual nodes and edges contribute to the global network bipartivity it is shown that the bipartivity characterizes the network structure and can be related to the efficiency of semantic or communication networks trophic interactions in food webs construction principles in metabolic networks or communities in social networks

on network bipartivity systems with two types of agents with a preference for heterophilous interaction produces networks that are more or less close to bipartite we propose two measures quantifying the notion of bipartivity the two measures one well known and natural but computationally intractable one computationally less complex but also less intuitive are examined on model networks that continuously interpolates between bipartite graphs and graphs with many odd circuits we find that the bipartivity measures increase as we tune the control parameters of the test networks to intuitively increase the bipartivity and thus conclude that the measures are quite relevant we also measure and discuss the values of our bipartivity measures for empirical social networks constructed from professional collaborations internet communities and field surveys here we find as expected that networks arising from romantic online interaction have high and professional collaboration networks have low bipartivity values in some other cases probably due to low average degree of the network the bipartivity measures cannot distinguish between romantic and friendship oriented interaction

modeling discrete combinatorial systems as alphabetic bipartite networks theory and applications genes and human languages are discrete combinatorial systems dcss in which the basic building blocks are finite sets of elementary units nucleotides or codons in a dna sequence and letters or words in a language different combinations of these finite units give rise to potentially infinite numbers of genes or sentences this type of dcss can be represented as an alphabetic bipartite network abn where there are two kinds of nodes one type represents the elementary units while the other type represents their combinations here we extend and generalize recent analytical findings for abns derived in peruani et al europhys lett 79 28001 2007 and empirically investigate two real world systems in terms of abns the codon gene and the phoneme language network the one mode projections onto the elementary basic units are also studied theoretically as well as in real world abns we propose the use of abns as a means for inferring the mechanisms underlying the growth of real world dcss

on the absence of limit cycles in a class of state space digital filters which contains minimum noise realizations this paper presents a theorem for the absence of limit cycles in a class of state space digital filters such a class contains minimum noise realizations of any order as a special case that is it is proved that the transition matrix a of minimum noise realizations of any order satisfies i a t a geq 0 and thus the realizations are free of limit cycles

revealing network communities with a nonlinear programming method the detection of network communities has attracted significant research attention lately to discover such structures a mathematical measure known as modularity is often used for optimization unfortunately the optimization is np hard and approximated solutions have to be sought for large networks in this paper we propose a nonlinear programming method for optimization that is based on the augmented lagrangian technique we further identify the inherent connection between the proposed method and positive semi definite programming and its low rank reduction which helps to justify the performance of the method compared with previously published approaches the proposed method is empirically efficient and effective at detecting underlying network communities

identification of overlapping and non overlapping community structure by fuzzy clustering in complex networks this paper proposes a novel method based on fuzzy clustering to detect community structure in complex networks in contrast to previous studies our method does not focus on a graph model but rather on a fuzzy relation model which uses the operations of fuzzy relation to replace a traversal search of the graph for identifying community structure in our method we first use a fuzzy relation to describe the relation between vertices as well as the similarity in network topology to determine the membership grade of the relation then we transform this fuzzy relation into a fuzzy equivalence relation finally we map the non overlapping communities as equivalence classes that satisfy a certain equivalence relation because most real world networks are made of overlapping communities e g in social networks people may belong to multiple communities we can consider the equivalence classes above as the skeletons of overlapping communities and extend our method by adding vertices to the skeletons to identify overlapping communities we evaluated our method on artificial networks with built in communities and real world networks with known and unknown communities the experimental results show that our method works well for detecting these communities and gives a new understanding of network division and community formation

adaptive vibration isolation for axially moving strings theory and experiment high speed transport of continuous materials such as belts webs filaments or bands can cause unwanted vibration vibration control for these systems often focuses on restricting the response resulting from external disturbances e g support roller eccentricity or aerodynamic excitation to areas not requiring high precision positioning this paper introduces vibration controllers for an axially moving string system consisting of a controlled span coupled to a disturbed span via an actuator the system model includes a partial differential equation for the two spans and an ordinary differential equation for the actuator exact model knowledge and adaptive isolation controllers based on lyapunov theory regulate the controlled span from bounded disturbances in the adjacent uncontrolled span assuming distributed damping in the uncontrolled span the exact model knowledge and adaptive controllers exponentially and asymptotically drive the controlled span displacement to zero respectively while ensuring bounded uncontrolled span displacement and control force experiments demonstrate the effectiveness of the proposed controller in isolating the controlled span from disturbances and damping the controlled span displacement

complex networks and economics abstract as the first step toward a study of complex networks in economics we consider business networks categorized into bipartite networks through empirical study we show the possibility that business networks will fall into the scale free category to have an idea about the clustering coefficient and the averaged path length for bipartite networks we perform a one mode reduction we calculate the quantities for networks constructed by banks and companies before after a merger among banks and quantitatively show that the merger among banks increases the cliquishness of companies and decreases the typical separation between two companies

on the topology of the world exchange arrangements web abstract exchange arrangements among different countries over the world are foundations of the world economy which generally stand behind the daily economic evolution as the first study of the world exchange arrangements web weaw we built a bipartite network with countries as one type of nodes and currencies as the other and found it to have a prominent scale free feature with a power law degree distribution in a further empirical study of the currency section of the weaw we calculated the clustering coefficients average nearest neighbors degree and average shortest distance as an essential economic network the weaw is found to be a correlated disassortative network with a hierarchical structure possessing a more prominent scale free feature than the world trade web wtw

two dimensional digital filters without overflow oscillations and instability due to finite word length new criteria for the absence of finite word length effects such as overflow oscillations and instability in two dimensional digital filters are presented the criteria are formulated using the state space representations and are based on results concerning the 2d lyapunov equation several examples illustrate the theoretical results

robust adaptive boundary control of an axially moving string under a spatiotemporally varying tension in this paper a vibration suppression scheme for an axially moving string under a spatiotemporally varying tension and an unknown boundary disturbance is investigated the lower bound of the tension variation is assumed to be sufficiently larger than the derivatives of the tension the axially moving string system is divided into two spans i e a controlled span and an uncontrolled span by a hydraulic touch roll actuator which is located in the middle section of the string the transverse vibration of the controlled span part of the string is controlled by the hydraulic touch roll actuator and the position of the actuator is considered as the right boundary of the controlled span part the mathematical model of the system which consists of a hyperbolic partial differential equation describing the dynamics of the moving string and an ordinary differential equation describing the actuator dynamics is derived by using the hamilton s principle the lyapunov method is employed to design a robust boundary control law and adaptation laws for ensuring the vibration reduction of the controlled span part the asymptotic stability of the closed loop system under the robust adaptive boundary control scheme is proved through the use of semigroup theory simulation results verify the effectiveness of the robust adaptive boundary controller proposed

absolute stability of the kirchhoff string with sector boundary control this paper addresses the stability problem of the nonlinear kirchhoff string with nonlinear boundary control the nonlinear boundary control is the negative feedback of the transverse velocity of the string at one end which satisfies a sector constraint employing the integral type multiplier method we establish explicit absolute exponential stability of the kirchhoff string system

stabilization for the kirchhoff type equation from an axially moving heterogeneous string modeling with boundary feedback control abstract the first objective of this paper is to make the mathematical model for vibration suppression of an axially moving heterogeneous string in order to describe the geometrical nonlinearity due to finite transverse deformation the exact expression of the strain is used the mathematical modeling is derived first by using hamilton s principle and variational lemma and the derived nonlinear pde system is the kirchhoff type equation with boundary feedback control next we show the existence and uniqueness of strong solutions of the pde system via techniques of functional analysis mainly a theorem of compactness for the analysis of the approximation of the faedo galerkin method and estimate a decay rate for the energy the theoretical results are assured by numerical results of the solution s shape and asymptotic behavior for the system

active boundary control of elastic cables theory and experiment cables are lightweight structural elements used in a variety of engineering applications in this paper an active boundary control system is introduced that damps undesirable vibrations in a cable using hamilton s principle the governing non linear partial differential equations for an elastic cable are derived including the natural boundary conditions associated with boundary force control based on lyapunov theory passive and active vibration controllers are developed a galerkin approach generates the linearized closed loop modal dynamics equations for out of plane vibration simulations and experiments demonstrate the improved damping provided by the active boundary controller

power law classification scheme of time series correlations on the example of g20 group abstract a power law classification scheme plcs of time series correlations is proposed it is shown that plcs provides the ability to classify nonlinear correlations and measure their stability plcs has been applied to gross domestic product gdp per capita of g20 members and their correlations analysed it has been shown that the method does not only recognise linear correlations properly but also allows to point out converging time series as well as to distinguish nonlinear correlations plcs is capable of crash recognition as it is shown in the argentina example finally the strength of correlations and the stability of correlation matrices have been used to construct a minimum spanning tree mst the results were compared with those based on the ultrametric distance ud comparing the structures of mst ud and plcs indicates that the latter one is more complicated but better fits the expected economic relations within the g20

detecting overlapping communities of weighted networks via a local algorithm abstract identification of communities is significant in understanding the structures and functions of networks since some nodes naturally belong to several communities the study of overlapping communities has attracted increasing attention recently and many algorithms have been designed to detect overlapping communities in this paper an overlapping communities detecting algorithm is proposed whose main strategies are finding an initial partial community from a node with maximal node strength and adding tight nodes to expand the partial community seven real world complex networks and one synthetic network are used to evaluate the algorithm experimental results demonstrate that the algorithm proposed is efficient for detecting overlapping communities in weighted networks