stabilization bound of singularly perturbed systems subject to actuator saturation this paper considers the stabilization bound problem for singularly perturbed systems spss subject to actuator saturation a state feedback stabilization controller design method is proposed and a basin of attraction depending on the singular perturbation parameter is constructed which facilitates the formulation of the convex optimization problem for maximizing the basin of attraction of spss finally examples are given to show the advantages and effectiveness of the obtained results

a complex networks approach for data clustering abstract this work proposes a method for data clustering based on complex networks theory a data set is represented as a network by considering different metrics to establish the connection between each pair of objects the clusters are obtained by taking into account five community detection algorithms the network based clustering approach is applied in two real world databases and two sets of artificially generated data the obtained results suggest that the exponential of the minkowski distance is the most suitable metric to quantify the similarities between pairs of objects in addition the community identification method based on the greedy optimization provides the best cluster solution we compare the network based clustering approach with some traditional clustering algorithms and verify that it provides the lowest classification error rate

robustness of dynamic output feedback control for singular perturbation systems abstract the problem of the robustness of dynamic output feedback control for singular perturbation systems is investigated the solution to this problem is reduced to the simultaneous design of static output feedback controllers for the fast subsystem and the so called auxiliary system of the slow subsystem some conditions are proposed to ensure the robustness of the actual closed loop system the exact upper bound of the parasitic parameter for the controlled system is also determined finally an actual model which failed in dynamic output feedback control in 4 is reexamined successfully here

a framework for detecting communities of unbalanced sizes in networks abstract community detection in large networks has been a focus of recent research in many of fields including biology physics social sciences and computer science most community detection methods partition the entire network into communities groups of nodes that have many connections within communities and few connections between them and do not identify different roles that nodes can have in communities we propose a community detection model that integrates more different measures that can fast identify communities of different sizes and densities we use node degree centrality strong similarity with one node from community maximal similarity of node to community compactness of communities and separation between communities each measure has its own strength and weakness thus combining different measures can benefit from the strengths of each one and eliminate encountered problems of using an individual measure we present a fast local expansion algorithm for uncovering communities of different sizes and densities and reveals rich information on input networks experimental results show that the proposed algorithm is better or as effective as the other community detection algorithms for both real world and synthetic networks while it requires less time

performance of modularity maximization in practical contexts although widely used in practice the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts here we present a broad characterization of its performance in such situations first we revisit and clarify the resolution limit phenomenon for modularity maximization second we show that the modularity function q exhibits extreme degeneracies it typically admits an exponential number of distinct high scoring solutions and typically lacks a clear global maximum third we derive the limiting behavior of the maximum modularity q max for one model of infinitely modular networks showing that it depends strongly both on the size of the network and on the number of modules it contains finally using three real world metabolic networks as examples we show that the degenerate solutions can fundamentally disagree on many but not all partition properties such as the composition of the largest modules and the distribution of module sizes these results imply that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts they also explain why many heuristics are often successful at finding high scoring partitions in practice and why different heuristics can disagree on the modular structure of the same network we conclude by discussing avenues for mitigating some of these behaviors such as combining information from many degenerate solutions or using generative models

community extraction for social networks analysis of networks and in particular discovering communities within networks has been a focus of recent work in several fields and has diverse applications most community detection methods focus on partitioning the entire network into communities with the expectation of many ties within communities and few ties between however many networks contain nodes that do not fit in with any of the communities and forcing every node into a community can distort results here we propose a new framework that extracts one community at a time allowing for arbitrary structure in the remainder of the network which can include weakly connected nodes the main idea is that the strength of a community should depend on ties between its members and ties to the outside world but not on ties between nonmembers the proposed extraction criterion has a natural probabilistic interpretation in a wide class of models and performs well on simulated and real networks for the case of the block model we establish asymptotic consistency of estimated node labels and propose a hypothesis test for determining the number of communities

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

analysis of weighted networks the connections in many networks are not merely binary entities either present or not but have associated weights that record their strengths relative to one another recent studies of networks have by and large steered clear of such weighted networks which are often perceived as being harder to analyze than their unweighted counterparts here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph allowing us to apply standard techniques for unweighted graphs to weighted ones as well we give a number of examples of the method including an algorithm for detecting community structure in weighted networks and a simple proof of the maximum flow minimum cut theorem

detecting communities in clustered networks based on group action on set abstract in this paper we propose a well targeted algorithm gas algorithm for detecting communities in high clustered networks by presenting group action technology on community division during the processing of this algorithm the underlying community structure of a clustered network emerges simultaneously as the corresponding partition of orbits by the permutation groups acting on the node set are achieved as the derivation of the orbit partition an algebraic structure r cycle can be considered as the origin of the community to be a priori estimation for the community structure of the algorithm the community separability is introduced to indicate whether a network has distinct community structure by executing the algorithm on several typical networks and the lfr benchmark it shows that this gas algorithm can detect communities accurately and effectively in high clustered networks furthermore we compare the gas algorithm and the clique percolation algorithm on the lfr benchmark it is shown that the gas algorithm is more accurate at detecting non overlapping communities in clustered networks it is suggested that algebraic techniques can uncover fresh light on detecting communities in complex networks

overview of metrics and their correlation patterns for multiple metric topology analysis on heterogeneous graph ensembles this study is an overview of network topology metrics and a computational approach to analyzing graph topology via multiple metric analysis on graph ensembles the paper cautions against studying single metrics or combining disparate graph ensembles from different domains to extract global patterns this is because there often exists considerable diversity among graphs that share any given topology metric patterns vary depending on the underlying graph construction model and many real data sets are not actual statistical ensembles as real data examples we present five airline ensembles comprising temporal snapshots of networks of similar topology wikipedia language networks are shown as an example of a nontemporal ensemble general patterns in metric correlations as well as exceptions are discussed by representing the data sets via hierarchically clustered correlation heat maps most topology metrics are not independent and their correlation patterns vary across ensembles in general density related metrics and graph distance based metrics cluster and the two groups are orthogonal to each other metrics based on degree degree correlations have the highest variance across ensembles and cluster the different data sets on par with principal component analysis namely the degree correlation the s metric their elasticities and the rich club moments appear to be most useful in distinguishing topologies

block lyapunov sum with applications to integral controllability and maximal stability of singularly perturbed systems a new block structured lyapunov sum for partitioned matrices is defined and basic properties are established it has similar properties to a lyapunov matrix but preserves the block structure and has similar properties to the block kronecker sum but with about half the dimension it is used to solve a maximal stability problem of integral controllability and is also used to solve for the maximal stability range of singularly perturbed systems in both cases closed formulae are obtained with lower dimensions than existing formulae

mixing patterns in networks we study assortative mixing in networks the tendency for vertices in networks to be connected to other vertices that are like or unlike them in some way we consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age as a special example of the latter we consider mixing according to vertex degree i e according to the number of connections vertices have to other vertices do gregarious people tend to associate with other gregarious people we propose a number of measures of assortative mixing appropriate to the various mixing types and apply them to a variety of real world networks showing that assortative mixing is a pervasive phenomenon found in many networks we also propose several models of assortatively mixed networks both analytic ones based on generating function methods and numerical ones based on monte carlo graph generation techniques we use these models to probe the properties of networks as their level of assortativity is varied in the particular case of mixing by degree we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices

new stability performance results for singularly perturbed systems the guardian map theory of generalized stability of parametrized linear time invariant systems is used to prove new results on stability performance of linear time invariant singularly perturbed systems with an exogenous parameter i e systems that contain in addition to a singular parameter another uncertain parameter the results give necessary and sufficient conditions for generalized stability for all sufficiently small values of and all values of in a given interval 1 2 in addition explicit expressions for the largest upper bound on for guaranteed stability and performance are given and the cases leading to finite or infinite are clearly delineated thus the results represent a significant addition to the classical klimushev krasovskii theorem while at the same time providing closed form expressions for the maximum parameter range for stability and performance

an efficient algorithm for finding the d stability bound of discrete singularly perturbed systems with multiple time delays in this paper we present an original work on the d stabilization problem of discrete singularly perturbed systems with multiple time delays a new robust d stability criterion in terms of stability radius is first derived to guarantee that all poles of the discrete multiple time delay systems remain inside the specific disk d alpha r uncertainties then by using the technique of time scale separation we derive the corresponding slow and fast subsystems of a discrete multiple time delay singularly perturbed system the state feedback controls for the d stabilization of the slow and the fast subsystems are separately designed and a composite state feedback control for the original system is subsequently synthesized from these state feedback controls thereafter we derive a frequency domain epsilon dependent dstability criterion for the original discrete multiple time delay singularly perturbed system under the composite state feedback control if any one of the conditions of this criterion is fulfilled

finding local community structure in networks although the inference of global community structure in networks has recently become a topic of great interest in the physics community all such algorithms require that the graph be completely known here we define both a measure of local community structure and an algorithm that infers the hierarchy of communities that enclose a given vertex by exploring the graph one vertex at a time this algorithm runs in time o k2d for general graphs when d is the mean degree and k is the number of vertices to be explored for graphs where exploring a new vertex is time consuming the running time is linear o k we show that on computer generated graphs the average behavior of this technique approximates that of algorithms that require global knowledge as an application we use this algorithm to extract meaningful local clustering information in the large recommender network of an online retailer

a local multiresolution algorithm for detecting communities of unbalanced structures abstract in complex networks such as computer and information networks social networks or biological networks a community structure is a common and important property community detection in complex networks has attracted a lot of attention in recent years community detection is the problem of finding closely related groups within a network modularity optimisation is a widely accepted method for community detection it has been shown that the modularity optimisation has a resolution limit because it is unable to detect communities with sizes smaller than a certain number of vertices defined with network size in this paper we propose a metric for describing community structures that enables community detection better than other metrics we present a fast local expansion algorithm for community detection the proposed algorithm provides online multiresolution community detection from a source vertex experimental results show that the proposed algorithm is efficient in both real world and synthetic networks

on the importance of blood rheology for bulk flow in hemodynamic models of the carotid bifurcation abstract here we present a study on the impact of assumptions on image based hemodynamic simulations of healthy carotid bifurcations in particular we evaluate to which extent assumptions on blood rheology influence bulk flow features driven by the fact that few studies have provided adequate insights into the influence of assumptions to confidently model the 4d hemodynamics within the bifurcation the final goal is to complement integrate and extend with a quantitative characterization of the bulk flow the description currently adopted to classify altered hemodynamics which is based on wall shear stress wss hemodynamic simulations of two image based carotid bifurcation geometries were carried out assuming a reference newtonian viscosity two non newtonian rheology models and newtonian viscosities based on characteristic shear rates wss based and lagrangian based metrics for helical flow quantification and for vorticity dynamics quantification were calculated our findings suggest that the assumption of newtonian rheology 1 could be reasonable for bulk flow metrics differences from non newtonian behavior are lower than 10 2 influences at different levels the wss based indicators depending on the bifurcation model even if in our study it is lower than the major source of uncertainty as recognized by the literature i e uncertainty on geometry reconstruction

tolerating the community detection resolution limit with edge weighting communities of vertices within a giant network such as the world wide web are likely to be vastly smaller than the network itself however fortunato and barthelemy have proved that modularity maximization algorithms for community detection may fail to resolve communities with fewer than l 2 edges where l is the number of edges in the entire network this resolution limit leads modularity maximization algorithms to have notoriously poor accuracy on many real networks fortunato and barthelemy s argument can be extended to networks with weighted edges as well and we derive this corollary argument we conclude that weighted modularity algorithms may fail to resolve communities with less than we 2 total edge weight where w is the total edge weight in the network and e is the maximum weight of an intercommunity edge if e is small then small communities can be resolved given a weighted or unweighted network we describe how to derive new edge weights in order to achieve a low e we modify the clauset newman and moore cnm community detection algorithm to maximize weighted modularity and we show that the resulting algorithm has greatly improved accuracy in experiments with an emerging community standard benchmark we find that our simple cnm variant is competitive with the most accurate community detection methods yet proposed

weak signal transmission in complex networks and its application in detecting connectivity we present a network model of coupled oscillators to study how a weak signal is transmitted in complex networks through both theoretical analysis and numerical simulations we find that the response of other nodes to the weak signal decays exponentially with their topological distance to the signal source and the coupling strength between two neighboring nodes can be figured out by the responses this finding can be conveniently used to detect the topology of unknown network such as the degree distribution clustering coefficient and community structure etc by repeatedly choosing different nodes as the signal source through four typical networks i e the regular one dimensional small world random and scale free networks we show that the features of network can be approximately given by investigating many fewer nodes than the network size thus our approach to detect the topology of unknown network may be efficient in practical situations with large network size

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

characterization and computation for the bound e in linear time variantsingularly perturbed systems abstract this paper gives a complete solution to the bound problem in a linear time invariant singularly perturbed system a criterion is presented to determine the existence of the bound

stability bounds of singularly perturbed discrete systems the authors propose a systematic approach to determine the exact stability bound of singularly perturbed discrete time systems by combining three conditions of the critical stability criterion with a bialternate product for discrete time systems the stability problems of two types of singularly perturbed discrete time systems can be solved via the derived scheme several examples are given to illustrate the proposed results

a new characterization on stability bounds for singularity perturbed systems abstract in this short paper we characterize the upper bound e for the parasitic parameter e in a singularly perturbed systems which ensures stability of such a system if 0 at the same time a method is established to testify the system stability without the slow fast decomposition required in the existing literature it will be shown that this upper bound is just the minimum positive eigenvalue of a matrix pair which is explicitly constructed from the system matrix this reveals a direct relationship between the stability bound and the system matrix and may be useful in the study of robust control problems for such systems

finding community structure in very large networks the discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community but most methods proposed so far are unsuitable for very large networks because of their computational cost here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms its running time on a network with n vertices and m edges is o md phantom rule 0 2em 0ex mathrm log phantom rule 0 2em 0ex n where d is the depth of the dendrogram describing the community structure many real world networks are sparse and hierarchical with m ensuremath sim n and d ensuremath sim mathrm log phantom rule 0 2em 0ex n in which case our algorithm runs in essentially linear time o n phantom rule 0 2em 0ex mathrm log 2 phantom rule 0 2em 0ex n as an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on line retailer items in the network being linked if they are frequently purchased by the same buyer the network has more than 400 000 vertices and 2 ifmmode times else texttimes fi 10 6 edges we show that our algorithm can extract meaningful communities from this network revealing large scale patterns present in the purchasing habits of customers

complementary results on the stability bounds of singularly perturbed systems in this note we will provide a new systematic approach to characterize and compute the stability bound of a singularly perturbed linear system the approach is based on the feedback system representation of an additional matrix perturbation problem the idea is to change the stability bound problem to the stability problem of an underlying feedback system this approach allows multiple choices in formulating the underlying feedback system and thus has the potential of characterizing and computing the stability bound in a number of different ways by formulating two kinds of different feedback systems some existing and new results on the stability bounds are derived based on the feedback system approach the new results complement the existing frequency domain based stability criteria and make the frequency domain technique more applicable and useful to the stability bound problem an example is provided to show the new stability criterion is effective and useful in determining the stability bound

control synthesis of singularly perturbed fuzzy systems this paper considers the problem of designing stabilizing and hinfin controllers for nonlinear singularly perturbed systems described by takagi sugeno fuzzy models with the consideration of the bound of singular perturbation parameter e for the synthesis problem of simultaneously designing the bound of e and stabilizing or hinfin controllers linear matrix inequalities lmi based methods are presented for evaluating the upper bound of e subject to stability or a prescribed hinfin performance bound constraint for the resulting closed loop system sufficient conditions are developed respectively for the stabilizing and hinfin control synthesis without the consideration of improving the bound of e new design methods are also given in terms of solutions to a set of lmis examples are given to illustrate the efficiency of the proposed methods

robust stability of singularly perturbed discrete delay systems this paper presents new sufficient conditions for the robust stability of singularly perturbed discrete systems subjected to multiple delayed perturbations for a given spl epsi spl isin 0 spl epsi sub 0 where spl epsi sub 0

stabilization bound of discrete two time scale systems abstract in this paper the exact bound problem in various types of discrete two time scale tts system is considered a set of stability criteria based on the frequency domain representation is derived two interesting examples are used to demonstrate the proposed scheme

a new parameter estimate in singular perturbations abstract a new upper bound is obtained for the singular perturbation parameter of an asymptotically stable singularly perturbed system general time invariant systems with a single small parameter are considered the paper employs a riccati equation whose solution is known to facilitate the exact decoupling of fast and slow dynamics an application of the brouwer fixed point theorem to the riccati equation and of liapunov s direct method to the fast and slow subsystems results in the desired upper bound computation of the estimate requires only the solution of two liapunov matrix equations

on the stability bounds of singularly perturbed systems the stability bound problem of linear time invariant singularly perturbed systems is considered a set of new stability conditions based on the frequency domain representation is derived the stability criteria can be easily verified by computing certain singular values within finite frequency intervals illustrative examples show that the proposed criteria actually induce a less conservative epsilon bound than the existing criteria and for certain cases an infinite epsilon bound may be obtained

stability bounds of singularity perturbed systems a necessary and sufficient condition is developed for computing the upper bound in sub 0 of the parasitic parameter in in a singularly perturbed system which ensures stability of such a system if 0

adjusting from disjoint to overlapping community detection of complex networks abstract the investigation of community structures is one of the most important problems in the field of complex networks and has countless applications in different disciplines biology computer social sciences etc many community detection algorithms have been developed in various fields recently the vast majority of these algorithms only find disjoint communities however in many real world networks communities often overlap to some extent in this paper we propose an efficient method for adjusting these classical algorithms to match the requirement for discovering overlapping communities in complex networks which is based on a local definition of community strength the method can in principle be applied with any clustering algorithm tests on a set of computer generated and real world networks give excellent results in particular we show that the method can also allow one to availably analyze the problem of unstable nodes in community detection which is very helpful for understanding the structural properties of the networks correctly and comprehensively

differential equations as a tool for community identification we consider the task of identification of a cluster structure in random networks the results of two methods are presented i the newman algorithm m e j newman and m girvan phys rev e 69 026113 2004 and ii our method based on differential equations a series of computer experiments is performed to check if in applying these methods we are able to determine the structure of the network the trial networks consist initially of well defined clusters and are disturbed by introducing noise into their connectivity matrices further we show that an improvement of the previous version of our method is possible by an appropriate choice of the threshold parameter beta with this change the results obtained by the two methods above are similar and our method works better for all the computer experiments we have done

applications of singular perturbation techniques to control problems this paper discusses typical applications of singular perturbation techniques to control problems in the last fifteen years the first three sections are devoted to the standard model and its time scale stability and controllability properties the next two sections deal with linear quadratic optimal control and one with cheap near singular control then the composite control and trajectory optimization are considered in two sections and stochastic control in one section the last section returns to the problem of modeling this time in the context of large scale systems the bibliography contains more than 250 titles

robust stability of singularly perturbed systems the robust stability problem of linear time invariant singularly perturbed systems is discussed where the system matrix may have a parameter perturbation bounded by the h norm a sufficient condition for the upper bound of e is given such that the stability of the actual system or the full order model can be inferred from the analysis of the reduced order system or the slow model in separate time scales

block bialternate sum and associated stability formulae abstract a new block bialternate sum of a partitioned square matrix with itself is defined and some basic properties established it has similar properties to the bialternate sum but it preserves the block structure of the summand it is used in place of the block kronecker sum and the block lyapunov sum to solve maximal stability problems of stable systems under low gain integral control and of singularly perturbed systems it is also used to find the critical gains for a first order controller with a scalar plant from which all stabilizing first order controllers can be constructed in each stability problem the internal dimensions of the resulting closed formulae are lower than those currently available

spectral tripartitioning of networks we formulate a spectral graph partitioning algorithm that uses the two leading eigenvectors of the matrix corresponding to a selected quality function to split a network into three communities in a single step in so doing we extend the recursive bipartitioning methods developed by newman m e j newman proc natl acad sci u s a 103 8577 2006 phys rev e 74 036104 2006 to allow one to consider the best available two way and three way divisions at each recursive step we illustrate the method using simple bucket brigade examples and then apply the algorithm to examine the community structures of the coauthorship graph of network scientists and of u s congressional networks inferred from roll call voting similarities

a community detection method based on local similarity and degree clustering information community detection is of great importance to understand the structures and functions of networks in this paper a novel algorithm is proposed based on local similarity and degree clustering information local similarity is employed to measure the similarity between nodes and their neighbors in order to form communities within which nodes are closely connected degree clustering information a hybrid criterion combining local neighborhood ratio with degree ratio make a large number of nodes with low degree to embrace a small amount of nodes with high degree furthermore each node in small scale communities has the duty to try to connect the nodes with high degree to expand communities and finally the optimal community structure can be obtained simulation results on real and artificial networks show that the proposed algorithm has the excellent performance in terms of accuracy

detect local communities in networks with an outside rate coefficient abstract in this paper we present a local method for detecting communities in networks we define an outside rate coefficient o u t in our method o u t has a very simple form and is easy to calculate the local community enclosing a starting node can be detected by agglomerating the node with the smallest o u t at each time step when there are two or more nodes having the same smallest outside rate coefficient o u t we agglomerate the node with the largest k i n this operation is remarkably beneficial to the accuracy of our method and simulations on benchmark networks and real networks demonstrate that our local method is efficient to detect communities in networks

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

robust stability of two time scale systems with nonlinear uncertainties this note is concerned with the robust stability problem of uncertain two time scale systems where the only information available for system uncertainties is their norm upper bounds the stability bound spl epsiv sup is derived via a state transformation and the constructive use of a lyapunov function finally examples are given to illustrate the applications of the proposed results

criterions for locally dense subgraphs abstract community detection is one of the most investigated problems in the field of complex networks although several methods were proposed there is still no precise definition of communities as a step toward a definition i highlight two necessary properties of communities separation and internal cohesion the latter being a new concept i propose a local method of community detection based on two dimensional local optimization which i tested on common benchmarks and on the word association database

sliding mode control for singularly perturbed systems this paper addresses the design of sliding mode controllers for singularly perturbed systems the full order system is separated into slow and fast subsystems and a sliding mode controller is designed for each subsystem a composite of these controls is then implemented on the full order system it is shown that if specific reaching conditions are satisfied for the reduced order models and an additional condition is met then the reaching conditions are also satisfied for the full order model furthermore sufficient conditions are derived which guarantee that the approximation error between the controlled reduced order response and the controlled full order model response is small a numerical example is given which successfully demonstrates the techniques developed in this paper

multiobjective control for t s fuzzy singularly perturbed systems this paper investigates the problem of multiobjective control for a class of takagi sugeno t s fuzzy singularly perturbed systems based on a linear matrix inequality lmi approach a state feedback controller that depends on the singular perturbation parameter epsiv is developed such that 1 the h infin performance of the resulting closed loop system is less than or equal to some prescribed value 2 the closed loop poles of each local system are within a prespecified lmi stability region and 3 for a given upper bound epsivmacr for the singular perturbation parameter epsiv both 1 and 2 are guaranteed for all epsiv isin 0 epsivmacr it is shown that the epsiv dependent controller is well defined for any epsiv isin 0 epsivmacr and can be reduced to an epsiv independent one if epsiv is sufficiently small finally a practical example is given to show the feasibility and effectiveness of the obtained method

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