community detection algorithms a comparative analysis uncovering the community structure exhibited by real networks is a crucial step toward an understanding of complex systems that goes beyond the local organization of their constituents many algorithms have been proposed so far but none of them has been subjected to strict tests to evaluate their performance most of the sporadic tests performed so far involved small networks with known community structure and or artificial graphs with a simplified structure which is very uncommon in real systems here we test several methods against a recently introduced class of benchmark graphs with heterogeneous distributions of degree and community size the methods are also tested against the benchmark by girvan and newman proc natl acad sci u s a 99 7821 2002 and on random graphs as a result of our analysis three recent algorithms introduced by rosvall and bergstrom proc natl acad sci u s a 104 7327 2007 proc natl acad sci u s a 105 1118 2008 blondel et al j stat mech theory exp 2008 p10008 and ronhovde and nussinov phys rev e 80 016109 2009 have an excellent performance with the additional advantage of low computational complexity which enables one to analyze large systems

benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities many complex networks display a mesoscopic structure with groups of nodes sharing many links with the other nodes in their group and comparatively few with nodes of different groups this feature is known as community structure and encodes precious information about the organization and the function of the nodes many algorithms have been proposed but it is not yet clear how they should be tested recently we have proposed a general class of undirected and unweighted benchmark graphs with heterogeneous distributions of node degree and community size an increasing attention has been recently devoted to develop algorithms able to consider the direction and the weight of the links which require suitable benchmark graphs for testing in this paper we extend the basic ideas behind our previous benchmark to generate directed and weighted networks with built in community structure we also consider the possibility that nodes belong to more communities a feature occurring in real systems such as social networks as a practical application we show how modularity optimization performs on our benchmark

feedback control of affine nonlinear singular control systems this paper discusses feedback control problems for affine nonlinear singular systems namely the problems of regularization regular singular systems have for a particular initial state and input a unique solution non interaction and exact linearization first an algorithm providing necessary and sufficient conditions for the regularizability of the affine nonlinear singular systems is introduced this algorithm resembles the well known constrained dynamics algorithm for affine nonlinear systems for regularizable affine nonlinear singular systems necessary and sufficient conditions for the solvability of the non interacting control problem are derived they are based on another algorithm producing a sequence of integers the generalization of the well known notion of relative degree for usual affine nonlinear systems finally the problem of feedback exact linearization of the dynamic part of singular systems is briefly addressed an example is provided to illustrate the main results

closed walks for community detection abstract in this paper we propose a novel measure that integrates both the concept of closed walks and clustering coefficients to replace the edge betweenness in the well known divisive hierarchical clustering algorithm the girvan and newman method gn the edges with the lowest value are removed iteratively until the network is degenerated into isolated nodes the experimental results on computer generated networks and real world networks showed that our method makes a better tradeoff of accuracy and runtime based on the analysis of the results we observe that the nontrivial closed walks of order three and four can be considered as the basic elements in constructing community structures meanwhile we discover that those nontrivial closed walks outperform trivial closed walks in the task of analyzing the structure of networks the double peak structure problem is mentioned in the last part of the article we find that our proposed method is a novel way to solve the double peak structure problem our work can provide us with a new perspective for understanding community structure in complex networks

dominating communities for hierarchical control of complex networks abstract well selected nodes driven by external signals in complex networks are of great importance for a dynamic system s structural controllability which can also be achieved by selecting nodes in the minimum dominating set mds of the networks as driver nodes however hierarchical structures such as communities are widely observed in complex networks which motivates us to develop the hierarchical control of complex networks by dominating communities and the control over whole networks is transformed into that within communities i e a non driver node is effectively controlled by its driver node if they belong to the same community for the hierarchical control we propose the structure driven minimum dominating set sd mds which assumes that a driver node can control a non driver node if the link between them belongs to a cyclic structure of the networks we further investigate the impact of community dynamics on our framework the results show that it is easier to control the networks with stronger communities and more heterogeneous community sizes and the sd mds achieves more effective control for non driver nodes than the mds this work also indicates that the number of driver nodes for the sd mds is associated with the degree distribution of the network

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 output tracking of nonlinear differential algebraic control systems abstract the problem of asymptotic output tracking is considered for control systems described by a class of nonlinear differential algebraic equations assumptions are introduced and an algorithm is developed based on the algorithm a nonlinear feedback control law is then constructed which ensures under appropriate conditions that the closed loop system has a unique bounded differentiable solution and the tracking error in the closed loop system approaches zero when time goes to infinity

a method of relational fuzzy clustering based on producing feature vectors using fastmap the first stage of organizing objects is to partition them into groups or clusters the clustering is generally done on individual object data representing the entities such as feature vectors or on object relational data incorporated in a proximity matrix this paper describes another method for finding a fuzzy membership matrix that provides cluster membership values for all the objects based strictly on the proximity matrix this is generally referred to as relational data clustering the fuzzy membership matrix is found by first finding a set of vectors that approximately have the same inter vector euclidian distances as the proximities that are provided these vectors can be of very low dimension such as 5 or less fuzzy c means fcm is then applied to these vectors to obtain a fuzzy membership matrix in addition two dimensional vectors are also created to provide a visual representation of the proximity matrix this allows comparison of the result of automatic clustering to visual clustering the method proposed here is compared to other relational clustering methods including nerfcm rouben s method and windhams a p method various clustering quality indices are also calculated for doing the comparison using various proximity matrices as input simulations show the method to be very effective and no more computationally expensive than other relational data clustering methods the membership matrices that are produced by the proposed method are less crisp than those produced by nerfcm and more representative of the proximity matrix that is used as input to the clustering process

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

alternative approach to community detection in networks the problem of community detection is relevant in many disciplines of science and modularity optimization is the widely accepted method for this purpose it has recently been shown that this approach presents a resolution limit by which it is not possible to detect communities with sizes smaller than a threshold which depends on the network size moreover it might happen that the communities resulting from such an approach do not satisfy the usual qualitative definition of commune i e nodes in a commune are more connected among themselves than to nodes outside the commune in this paper we present a different method for community detection in complex networks we define merit factors based on the weak and strong community definitions formulated by radicchi proc natl acad sci u s a 101 2658 2004 and we show that these local definitions avoid the resolution limit problem found in the modularity optimization approach

community detection by fuzzy clustering abstract how to measure the similarity between nodes is of great importance for fuzzy clustering when we use the approach to uncover communities in complex networks in this paper we first measure the similarity between nodes in a network based on edge centralities and model the network as a fuzzy relation then two fuzzy transitive rules rule i and rule ii are applied on the relation respectively by which the similarity information can be transferred from one node to another in the network until the relation reaches a stable state by choosing different thresholds our method finally can partition the network into several non overlapping subgroups we compare our method with some state of the art methods on the lfr benchmark and real world networks we find that our method based on rule i can correctly identify communities when the similarity between nodes of same groups is greater than that of different groups while it is just opposite to rule ii our method achieves better results than the state of the art methods when the pre planted communities of the random networks are vaguer

adequate is better based on the interaction of individuals particle swarm optimization pso is a well recognized algorithm to find optima in search space in its canonical version the trajectory of each particle is usually influenced by the best performer among its neighborhood which thus ignores some useful information from other neighbors to capture information of all the neighbors the fully informed pso is proposed which however may bring redundant information into the search process motivated by both scenarios here we present a particle swarm optimization with limited information which provides each particle adequate information yet avoids the waste of information by means of systematic analysis for the widely used standard test functions it is unveiled that our new algorithm outperforms both canonical pso and fully informed pso especially for multimodal test functions we further investigate the underlying mechanism from a microscopic point of view revealing that moderate velocity moderate diversity and best motion consensus facilitate a good balance between exploration and exploitation which results in the good performance

solvability of general differential algebraic equations in the last few years there has been considerable research on differential algebraic equations daes f t x x 0 where f x is identically singular most of this effort has focused on computing a solution that is assumed to exist that is the dae is assumed solvable more recently there have been existence results developed using differential geometry for complex higher index systems these characterizations can be hard to verify in practice in this paper the computational verification of solvability is investigated this first requires developing an alternative set of sufficient conditions for solvability which are more amenable to computation verification of these conditions using readily available numerical and symbolic software is then discussed an example from robotics where classical graph theoretical approaches give an incorrect answer is worked to illustrate the usefulness of the sufficient condition and the computational approach

combinatorial approach to modularity communities are clusters of nodes with a higher than average density of internal connections their detection is of great relevance to better understand the structure and hierarchies present in a network modularity has become a standard tool in the area of community detection providing at the same time a way to evaluate partitions and by maximizing it a method to find communities in this work we study the modularity from a combinatorial point of view our analysis as the modularity definition relies on the use of the configurational model a technique that given a graph produces a series of randomized copies keeping the degree sequence invariant we develop an approach that enumerates the null model partitions and can be used to calculate the probability distribution function of the modularity our theory allows for a deep inquiry of several interesting features characterizing modularity such as its resolution limit and the statistics of the partitions that maximize it additionally the study of the probability of extremes of the modularity in the random graph partitions opens the way for a definition of the statistical significance of network partitions

methods to find community based on edge centrality abstract divisive algorithms are of great importance for community detection in complex networks one algorithm proposed by girvan and newman gn based on an edge centrality named betweenness is a typical representative of this field here we studied three edge centralities based on network topology walks and paths respectively to quantify the relevance of each edge in a network and proposed a divisive algorithm based on the rationale of gn algorithm for finding communities that removes edges iteratively according to the edge centrality values in a certain order in addition we gave a comparison analysis of these measures with the edge betweenness and information centrality we found the principal difference among these measures in the partition procedure is that the edge centrality based on walks first removes the edge connected with a leaf vertex but the others first delete the edge as a bridge between communities it indicates that the edge centrality based on walks is harder to uncover communities than other edge centralities we also tested these measures for community detection the results showed that the edge information centrality outperforms other measures the edge centrality based on walks obtains the worst results and the edge betweenness gains better performance than the edge centrality based on network topology we also discussed our method s efficiency and found that the edge centrality based on walks has a high time complexity and is not suitable for large networks

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

kernel induced fuzzy clustering of image pixels with an improved differential evolution algorithm a modified differential evolution de algorithm is presented for clustering the pixels of an image in the gray scale intensity space the algorithm requires no prior information about the number of naturally occurring clusters in the image it uses a kernel induced similarity measure instead of the conventional sum of squares distance use of the kernel function makes it possible to partition data that is linearly non separable and non hyper spherical in the original input space into homogeneous groups in a transformed high dimensional feature space a novel search variable representation scheme is adopted for selecting the optimal number of clusters from several possible choices extensive performance comparison over a test suite of 10 gray scale images and objective comparison with manually segmented ground truth indicates that the proposed algorithm has an edge over a few state of the art algorithms for automatic multi class image segmentation

controllability and modularity of complex networks two primary properties of complex networks controllability and modularity not only are closely related to each other but also play an important role in understanding the networks characteristics in this paper we discuss an elastic model to enhance the control of undirected networks and study the controllability of random networks with built in gradually varied modularity as well as real world networks to elaborate the correlation between the networks controllability and modularity the results show that it is easier to control the networks with stronger modularity than that of weaker modularity and the networks with larger size communities probably need more driver nodes to control than that of smaller size communities when we fix both the number of nodes and the number of links of the networks in addition the robustness analysis indicates that the model enhances the resistance of networks against link failure this work shows that the controllability of complex networks is highly associated with the networks degree distribution as well as the networks modularity which gives a new insight into the understanding of controllability and modularity of complex networks

structure properties of collaboration network with tunable clustering abstract a collaboration network model with improved triad formation itf step is proposed and denominated as one mode collaboration network with tunable clustering we systematically study its structural features and find this network model can much more accurately reflect cooperative relationship in real society we acquire expression of nodes degree distribution p k that possesses a power law form with exponent whose range is 1 3 expression of clustering coefficient c k for nodes with degree k is also obtained and composes of a power law section and a constant section we verify clustering coefficient of individual nodes increases monotonically with the increase of parameter p that is the probability of itf step occurring when specific forms of p k and c k are given the model s average clustering coefficient c can be derived approximately finally we analytically testify average path length l n increases with network size n in accordance with logarithmic form when n is fixed average path length of entire network decreases with the increase of p all theoretically predicted results are consistent with simulative experimental results

eigenvalues of tridiagonal pseudo toeplitz matrices abstract in this article we determine the eigenvalues of sequences of tridiagonal matrices that contain a toeplitz matrix in the upper left block

the weighted independent domination problem integer linear programming models and metaheuristic approaches abstract this work deals with the so called weighted independent domination problem which is an np hard combinatorial optimization problem in graphs in contrast to previous work this paper considers the problem from a non theoretical perspective the first contribution consists in the development of three integer linear programming models second two greedy heuristics are proposed finally the last contribution is a population based iterated greedy metaheuristic which is applied in two different ways 1 the metaheuristic is applied directly to each problem instance and 2 the metaheuristic is applied at each iteration of a higher level framework known as construct merge solve and adapt to sub instances of the tackled problem instances the results of the considered algorithmic approaches show that integer linear programming approaches can only compete with the developed metaheuristics in the context of graphs with up to 100 nodes when larger graphs are concerned the application of the populated based iterated greedy algorithm within the higher level framework works generally best the experimental evaluation considers graphs of different types sizes densities and ways of generating the node and edge weights

feedback stabilization of control systems described by a class of nonlinear differential algebraic equations a theoretical framework for the stabilization of con trol systems defined by a class of nonlinear differential alge braic equations is established assumptions are stated which guarantee that the nonlinear differential algebraic equations can be described by a nonlinear control system defined on a smooth manifold a procedure for obtaining a local state realization is developed conditions for local stabilization of a single equilibrium solution including one set of conditions which can easily be checked using standard computations are indicated

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

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

weighting links based on edge centrality for community detection abstract link weights have the equally important position as links in complex networks and they are closely associated with each other for the emergence of communities how to assign link weights to make a clear distinction between internal links of communities and external links connecting communities is of vital importance for community detection edge centralities provide a powerful approach for distinguishing internal links from external ones here we first use edge centralities such as betweenness information centrality and edge clustering coefficient to weight links of networks respectively to transform unweighted networks into weighted ones and then a weighted function that both considers links and link weights is adopted on the weighted networks for community detection we evaluate the performance of our approach on random networks as well as real world networks better results are achieved on weighted networks with stronger weights of internal links of communities and the results on unweighted networks outperform that of weighted networks with weaker weights of internal links of communities the availability of our findings is also well supported by the study of granovetter that the weak links maintain the global integrity of the network while the strong links maintain the communities especially in the karate club network all the nodes are correctly classified when we weight links by edge betweenness the results also give us a more comprehensive understanding on the correlation between links and link weights for community detection

spectra of certain large tridiagonal matrices abstract we characterize the eigenvalues and eigenvectors of a class of complex valued tridiagonal n by n matrices subject to arbitrary boundary conditions i e with arbitrary elements on the first and last rows of the matrix for large n we show there are up to 4 eigenvalues the so called special eigenvalues whose behavior depends sensitively on the boundary conditions the other eigenvalues the so called regular eigenvalues vary very little as function of the boundary conditions for large n we determine the regular eigenvalues up to o n 2 and the special eigenvalues up to o n for some 0 1 the components of the eigenvectors are determined up to o n 1 the matrices we study have important applications throughout the sciences among the most common ones are arrays of linear dynamical systems with nearest neighbor coupling and discretizations of second order linear partial differential equations in both cases we give examples where specific choices of boundary conditions substantially influence leading eigenvalues and therefore the global dynamics of the system

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

tracking control designs for both holonomic and non holonomic constrained mechanical systems a unified viewpoint a tracking control design is proposed for both holonomic and non holonomic constrained mechanical systems from a unified viewpoint it will be shown that according to the number of control inputs if the state variables are available and the output variables are chosen properly then the exponentially global tracking of positions and constraint forces on the constraint manifold is achieved for holonomic control systems by a static state feedback controller from the same point of view for non holonomic control systems the globally exponential tracking of positions is achieved by just a dynamic state feedback controller finally by means of much discussion and many simulations two typical non holonomic examples edge and a vertical wheel are given to illustrate the essential features of the proposed design method

local disturbance decoupling of nonlinear singular systems the problem of local disturbance decoupling is considered for a class of non linear singular control systems assumptions are introduced and an algorithm is developed such that the control system can be expressed in a simple form a nonlinear feedback control law is then constructed which ensures the closed loop system has a unique solution without impulses and its output is unaffected by disturbances sufficient and necessary conditions for the existence of such a feedback are derived an example is provided to illustrate the results of the paper

semi global robust output regulation for a class of singular nonlinear systems via nonlinear internal model abstractmost of existing results on robust output regulation problem of singular nonlinear systems are limited to local solutions in this paper the semi global robust output regulation problem for a class of singular nonlinear systems is investigated by using a nonlinear internal model attaching a nonlinear internal model to the singular nonlinear system yields an augmented singular nonlinear system whose semi global robust stabilisation solution leads to the solution of the semi global robust output regulation problem of the original singular nonlinear system the solvability conditions of the semi global output regulation problem are established by addressing the solvability of the robust stabilisation problem of augmented singular nonlinear system finally a numerical simulation example is used to illustrate the design of the semi global regulator for the singular nonlinear systems

automated traffic and the finite size resonance we investigate in detail what one might call the canonical automated traffic problem a long string of n 1 cars numbered from 0 to n moves along a one lane road in formation at a constant velocity and with a unit distance between successive cars each car monitors the relative velocity and position of only its neighboring cars this information is then fed back to its own engine which decelerates brakes or accelerates according to the information it receives the question is what happens when due to an external influence a traffic light turning green the zero th car the leader accelerates

transients of platoons with asymmetric and different laplacians abstract we consider an asymmetric control of platoons of identical vehicles with nearest neighbor interaction recent results show that if the vehicle uses different asymmetries for position and velocity errors the platoon has a short transient and low overshoots in this paper we investigate the properties of vehicles with friction to achieve consensus an integral part is added to the controller making the vehicle a third order system we show that the parameters can be chosen so that the platoon behaves as a wave equation with different wave velocities simulations suggest that our system has a better performance than other nearest neighbor scenarios moreover an optimization based procedure is used to find the controller properties

optimizing controllability of complex networks by minimum structural perturbations to drive a large complex networked dynamical system toward some desired state using as few external signals as possible is a fundamental issue in the emerging field of controlling complex networks optimal control is referred to the situation where such a network can be fully controlled using only one driving signal we propose a general approach to optimizing the controllability of complex networks by judiciously perturbing the network structure the principle of our perturbation method is validated theoretically and demonstrated numerically for homogeneous and heterogeneous random networks and for different types of real networks as well the applicability of our method is discussed in terms of the relative costs of establishing links and imposing external controllers besides the practical usage of our approach its implementation elucidates interestingly the intricate relationship between certain structural properties of the network and its controllability

identification of overlapping community structure in complex networks using fuzzy c means clustering abstract identification of overlapping communities clusters in a complex network is a general problem in data mining of network data sets in this paper we devise a novel algorithm to identify overlapping communities in complex networks by the combination of a new modularity function based on generalizing ng s q function an approximation mapping of network nodes into euclidean space and fuzzy c means clustering experimental results indicate that the new algorithm is efficient at detecting both good clusterings and the appropriate number of clusters

control and stabilization of nonholonomic dynamic systems a class of inherently nonlinear control problems has been identified the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system models are presented for mechanical systems with nonholonomic constraints represented both by differential algebraic equations and by reduced state equations control issues for this class of systems are studied and a number of fundamental results are derived although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested

method to find community structures based on information centrality community structures are an important feature of many social biological and technological networks here we study a variation on the method for detecting such communities proposed by girvan and newman and based on the idea of using centrality measures to define the community boundaries m girvan and m e j newman proc natl acad sci u s a 99 7821 2002 we develop an algorithm of hierarchical clustering that consists in finding and removing iteratively the edge with the highest information centrality we test the algorithm on computer generated and real world networks whose community structure is already known or has been studied by means of other methods we show that our algorithm although it runs to completion in a time o n4 is very effective especially when the communities are very mixed and hardly detectable by the other methods

tracking in nonlinear differential algebraic control systems with applications to constrained robot systems we consider the design of a feedback control law for control systems described by a class of nonlinear differential algebraic equations so that certain desired outputs track given reference inputs the nonlinear differential algebraic control system being considered is not in state variable form assumptions are introduced and a procedure is developed such that an equivalent state realization of the control system described by nonlinear differential algebraic equations is expressed in a familiar normal form a nonlinear feedback control law is then proposed which ensures under appropriate assumptions that the tracking error in the closed loop differential algebraic system approaches zero exponentially applications to simultaneous contact force and position tracking in constrained robot systems with rigid joints constrained robot systems with joint flexibility and constrained robot systems with significant actuator dynamics are discussed

maximizing modularity intensity for community partition and evolution most previous studies of community partition have often focused on the network topology the topology and link weights are in fact closely associated with each other for community formation in complex networks this paper proposes a function modularity intensity a variation of modularity density d value for evaluating the cohesiveness of a community which considers links between vertices as well as link weights the results showed that maximizing the modularity intensity not only can resolve the resolution limits problem but also achieve better performance for community partition to further evaluate the function and clarify the weight topology correlation with communities we give a simple model to simulate the topology and link weights development for community evolution and use the modularity intensity to capture communities of networks in each step of this process in this model a network is treated as a fuzzy relation and two operations of the fuzzy relation are used to make the link weights stronger and weaker respectively with the growth of the network in each evolutionary step by simulation experiments we found that in the model the modularity intensity catches communities of networks that undergo a gradual transition from faintness to clearness our model also reproduces the finding of granovetter that strong links are confined mainly in tight communities and the links between communities are predominantly weak from the results above we believe that the modularity intensity gives a more comprehensive evaluation for communities and by studying the weight topology correlation this model provides a new view for community evolution

a multi temperature kinetic ising model and the eigenvalues of some perturbed jacobi matrices in this paper we analyze the eigenvalues of some perturbed jacobi matrices the results contain as particular cases the known spectra of several classes of tridiagonal matrices studied recently as a motivation we discuss a three and a four temperature kinetic ising model that can be analyzed using some perturbed jacobi matrices the analytical results can also be used for the associated reaction diffusion systems to solve for the particle density

stabilization of non linear differential algebraic equation systems in this paper the feedback stabilization problem is investigated for non linear differential algebraic equation systems the paper is composed of two algorithms namely a regularization algorithm and a stabilization algorithm it is shown that the feasibility of the regularization algorithm guarantees that there exists a feedback so that the closed loop system admits a unique impulse free solution the application of the stabilization algorithm produces a set of new coordinates in which the original system can be expressed as a standard form based on the standard form a stabilizing feedback is constructed which guarantees that the closed loop system admits a unique impulse free solution and is locally asymptotically stable at the origin