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

rough games modeled via l fuzzy ambiguous representations of semilattices abstract monotonic predicates and l fuzzy ambiguous representations of continuous semilattices with bottom elements are applied to describe rough normal form games and rough extensive form two player zero sum games with imperfect information payoff predicates are introduced to find best guaranteed gains of the players these predicates are calculated recursively via backward payoff predicate transformers which are also studied it is shown how payoff predicates determine almost optimal strategies an approximate minimax theorem is also stated

community detection in complex networks using density based clustering algorithm and manifold learning abstract like clustering analysis community detection aims at assigning nodes in a network into different communities fdp is a recently proposed density based clustering algorithm which does not need the number of clusters as prior input and the result is insensitive to its parameter however fdp cannot be directly applied to community detection due to its inability to recognize the community centers in the network to solve the problem a new community detection method named isofdp is proposed in this paper first we use isomap technique to map the network data into a low dimensional manifold which can reveal diverse pair wised similarity then fdp is applied to detect the communities in the network an improved partition density function is proposed to select the proper number of communities automatically we test our method on both synthetic and real world networks and the results demonstrate the effectiveness of our algorithm over the state of the art methods

discrete approximations of probability distributions practical limits on the size of most probabilistic models require that probability distributions be approximated by a few representative values and associated probabilities this paper demonstrates that methods commonly used to determine discrete approximations of probability distributions systematically underestimate the moments of the original distribution a new procedure based on gaussian quadrature is developed in this paper it can be used to decrease the error in the approximation to any desired level

rough approximation operators on two universes of discourse and their fuzzy extensions based on a crisp binary relation between two universes of discourse one crisp covering and three crisp binary relations on the single universe of discourse are induced in this paper based on these induced notions four pairs of rough approximation operators are formulated so that the approximating sets and the approximated sets are on the same universe of discourse furthermore basic properties of the new approximation operators are investigated and the relationships among the operators are also examined subsequently conditions under which some or all of these approximation operators are equivalent are obtained on the other hand the generalizations of these rough approximation operators are also made in a fuzzy approximation space via a fuzzy implicator i and a triangular norm t consequently four pairs of fuzzy rough approximation operators are constructed basic properties and comparison of the fuzzy rough approximation operators are discussed if i is an r implicator with respect to a t norm t then it is shown that three pairs of the fuzzy rough approximation operators are identical iff the induced fuzzy covering is a fuzzy t partition

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

multiresolution community detection for megascale networks by information based replica correlations we use a potts model community detection algorithm to accurately and quantitatively evaluate the hierarchical or multiresolution structure of a graph our multiresolution algorithm calculates correlations among multiple copies replicas of the same graph over a range of resolutions significant multiresolution structures are identified by strongly correlated replicas the average normalized mutual information the variation in information and other measures in principle give a quantitative estimate of the best resolutions and indicate the relative strength of the structures in the graph because the method is based on information comparisons it can in principle be used with any community detection model that can examine multiple resolutions our approach may be extended to other optimization problems as a local measure our potts model avoids the resolution limit that affects other popular models with this model our community detection algorithm has an accuracy that ranks among the best of currently available methods using it we can examine graphs over 40 ifmmode times else texttimes fi 10 6 nodes and more than 1 ifmmode times else texttimes fi 10 9 edges we further report that the multiresolution variant of our algorithm can solve systems of at least 200 text 000 nodes and 10 ifmmode times else texttimes fi 10 6 edges on a single processor with exceptionally high accuracy for typical cases we find a superlinear scaling o l 1 3 for community detection and o l 1 3 text text log text n for the multiresolution algorithm where l is the number of edges and n is the number of nodes in the system

three point approximations for continuous random variables this paper compares a number of approximations used to estimate means and variances of continuous random variables and or to serve as substitutes for the probability distributions of such variables with particular emphasis on three point approximations numerical results from estimating means and variances of a set of beta distributions indicate surprisingly large differences in accuracy among approximations in current use with some of the most popular ones such as the pert and triangular density function approximations faring poorly a simple new three point approximation which is a straightforward extension of earlier work by pearson and tukey outperforms the others significantly in these tests and also performs well in related multivariate tests involving the dirichlet family of distributions it offers an attractive alternative to currently used approximations in a variety of applications

an efficient community detection algorithm using greedy surprise maximization community detection is an important and crucial problem in complex network analysis although classical modularity function optimization approaches are widely used for identifying communities the modularity function q suffers from its resolution limit recently the surprise function s was experimentally proved to be better than the q function however up until now there has been no algorithm available to perform searches to directly determine the maximal surprise values in this paper considering the superiority of the s function over the q function we propose an efficient community detection algorithm called agso algorithm based on greedy surprise optimization and its improved version fagso fast agso which are based on greedy surprise optimization and do not suffer from the resolution limit in addition f agso does not need the number of communities k to be specified in advance tests on experimental networks show that f agso is able to detect optimal partitions in both simple and even more complex networks moreover algorithms based on surprise maximization perform better than those algorithms based on modularity maximization including blondel guillaume lambiotte lefebvre bgll clauset newman moore cnm and the other state of the art algorithms such as infomap order statistics local optimization method oslom and label propagation algorithm lpa

stochastic dominance on unidimensional grids special stochastic dominance relations for probability distributions on a finite grid of evenly spaced points are considered the relations depend solely on iterated partial sums of grid point probabilities and are very computer efficient their corresponding classes of utility functions for expected utility comparisons consist of functions defined on the grid that mimic in the large the traditional continuous functions whose derivatives alternate in sign the first degree and second degree relations are identical to their traditional counterparts defined from iterated integrals of cumulative distribution functions the higher degree relations differ from the traditional relations in interesting and sometimes subtle ways the paper explores aspects of the partial sums relations including effects of grid refinements and extensions and describes their relationships to the traditional relations

ambiguous representations as fuzzy relations between sets crisp and l fuzzy ambiguous representations of closed subsets of one space by closed subsets of another space are introduced it is shown that for each pair of compact hausdorff spaces the set of crisp or l fuzzy ambiguous representations is a lattice and a compact hausdorff lawson upper semilattice the categories of ambiguous and l ambiguous representations are defined and investigated

sequential algorithm for fast clique percolation in complex network research clique percolation introduced by palla der enyi and vicsek nature london 435 814 2005 is a deterministic community detection method which allows for overlapping communities and is purely based on local topological properties of a network here we present a sequential clique percolation algorithm scp to do fast community detection in weighted and unweighted networks for cliques of a chosen size this method is based on sequentially inserting the constituent links to the network and simultaneously keeping track of the emerging community structure unlike existing algorithms the scp method allows for detecting k clique communities at multiple weight thresholds in a single run and can simultaneously produce a dendrogram representation of hierarchical community structure in sparse weighted networks the scp algorithm can also be used for implementing the weighted clique percolation method recently introduced by farkas et al new j phys 9 180 2007 the computational time of the scp algorithm scales linearly with the number of k cliques in the network as an example the method is applied to a product association network revealing its nested community structure

fuzzy sets and sheaves part ii this essay shows that large parts of fuzzy set theory are actually subfields of sheaf theory resp of the theory of complete w valued sets hence fuzzy set theory is closer to the mainstream in mathematics than many people would expect part ii of this series of two papers explains the sheaf theoretic basis of zadeh s operations on fuzzy sets with the exception of the complementation further the quotient problem w r t similarity relations and the quotient problem of fuzzy groups w r t fuzzy congruence relations are solved finally stratified fuzzy topologies are identified with internal topologies on constant sheaves

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

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

modeling uncertainty in multi criteria decision analysis abstract his paper provides a review of multiple criteria decision analysis mcda for cases where attribute evaluations are uncertain the main aim is to identify different tools which can be used to represent uncertain evaluations and to broadly survey the available decision models that can be used to support uncertain decision making the review includes models using probabilities or probability like quantities explicit risk measures such as quantiles and variances fuzzy numbers and scenarios the practical assessment of uncertain outcomes and preferences associated with these outcomes is also discussed

assessing non additive utility for multicriteria decision aid abstract in the framework of multi attribute utility theory maut several methods have been proposed to build a decision maker s dm utility function representing his her preferences among such methods the uta method infers an additive utility function from a set of exemplary decisions using linear programming however the uta method does not guarantee to find a utility function which is coherent with the available information this drawback is due to the underlying utility model of uta viz the additive one which does not allow to include additional information such as an interaction among criteria in this paper we present a methodology for building a non additive utility function in the framework of the so called fuzzy integrals which permits to model preference structures with interaction between criteria like in the uta method we aim at searching a utility function representing the dm s preferences but unlike uta the functional form is a specific fuzzy integral choquet integral as a result we obtain weights which can be interpreted as the importance of coalitions of criteria exploiting the potential interaction between criteria as already proposed by other authors however within the same framework we obtain also the marginal utility functions relative to each one of the considered criteria that are evaluated on a common scale as a consequence of the implemented methodology finally we illustrate our approach with an example

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

operationalizing approximate multiattribute utility functions for use in practice abstract decision analysis provides defensible methods for rank ordering alternatives based on the calculation of expected utility this technique can be quite time consuming and conceptually difficult for the decision maker as many input parameters are needed to be assessed the recognition of such difficulties prompted researchers to call for simplifying approximations which retain the integrity of the original problem but relieve the assessment burden on the decision maker winkler 1982 this call has been answered with the recent development by kirkwood of taylor series approximations to expected utility which have never been applied in practice this paper further addresses the need to simplify decision analysis through the development of a simulation based technique which allows the kirkwood approximations to be used in practice the technique generates confidence intervals for the true but unknown certain equivalents which are used to rank order alternatives

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

fuzzy sets and sheaves part ii sheaf theoretic foundations of fuzzy set theory with applications to algebra and topology this essay shows that large parts of fuzzy set theory are actually subfields of sheaf theory resp of the theory of complete valued sets hence fuzzy set theory is closer to the mainstream in mathematics than many people would expect part ii of this series of two papers explains the sheaf theoretic basis of zadeh s operations on fuzzy sets with the exception of the complementation further the quotient problem w r t similarity relations and the quotient problem of fuzzy groups w r t fuzzy congruence relations are solved finally stratified fuzzy topologies are identified with internal topologies on constant sheaves

rough sets and intelligent data analysis rough set based data analysis starts from a data table called an information system the information system contains data about objects of interest characterized in terms of some attributes often we distinguish in the information system condition and decision attributes such information system is called a decision table the decision table describes decisions in terms of conditions that must be satisfied in order to carry out the decision specified in the decision table with every decision table a set of decision rules called a decision algorithm can be associated it is shown that every decision algorithm reveals some well known probabilistic properties in particular it satisfies the total probability theorem and the bayes theorem these properties give a new method of drawing conclusions from data without referring to prior and posterior probabilities inherently associated with bayesian reasoning

rough sets decision algorithms and bayes theorem abstract rough set based data analysis starts from a data table called an information system the information system contains data about objects of interest characterized in terms of some attributes often we distinguish in the information system condition and decision attributes such information system is called a decision table the decision table describes decisions in terms of conditions that must be satisfied in order to carry out the decision specified in the decision table with every decision table a set of decision rules called a decision algorithm can be associated it is shown that every decision algorithm reveals some well known probabilistic properties in particular it satisfies the total probability theorem and bayes theorem these properties give a new method of drawing conclusions from data without referring to prior and posterior probabilities inherently associated with bayesian reasoning

generalized modularity matrices various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph clustering problems in this paper we put in evidence certain common traits of various modularity matrices and shed light on their spectral properties that are at the basis of various theoretical results and practical spectral type algorithms for community detection

mean variance approximations to expected logarithmic utility in this paper we investigate how closely functions of means and variances can approximate von neumann morgenstern expected utility modeled as a logarithmic utility of wealth function using historical security return data we computed portfolios maximizing expected logarithmic utility and compared them to those maximizing appropriate mean variance formulations in all cases the approximations were very good and in many cases the optimal portfolios were virtually identical we conclude that the mean variance model can serve as a useful surrogate to at least one popular alternative investment strategy

adaptive multi resolution modularity for detecting communities in networks abstract community structure is a common topological property of complex networks which attracted much attention from various fields optimizing quality functions for community structures is a kind of popular strategy for community detection such as modularity optimization here we introduce a general definition of modularity by which several classical multi resolution modularity can be derived and then propose a kind of adaptive multi resolution modularity that can combine the advantages of different modularity by applying the modularity to various synthetic and real world networks we study the behaviors of the methods showing the validity and advantages of the multi resolution modularity in community detection the adaptive modularity as a kind of multi resolution method can naturally solve the first type limit of modularity and detect communities at different scales it can quicken the disconnecting of communities and delay the breakup of communities in heterogeneous networks and thus it is expected to generate the stable community structures in networks more effectively and have stronger tolerance against the second type limit of modularity

detecting complex network modularity by dynamical clustering based on cluster desynchronization properties of phase oscillators we introduce an efficient method for the detection and identification of modules in complex networks the performance of the algorithm is tested on computer generated and real world networks whose modular structure is already known or has been studied by means of other methods the algorithm attains a high level of precision especially when the modular units are very mixed and hardly detectable by the other methods with a computational effort o kn on a generic graph with n nodes and k links

risk return skewness and preference this paper considers choice between individual projects and shows that when the choice set includes arbitrary distributions then any assumed relationship between expected utility theory and general moment preferences for individual decision makers is theoretically unsound in particular a risk averse investor with any common utility function may when choosing between two positive return opportunities prefer the project simultaneously having a lower mean higher variance and lower positive skewness moreover the decision maker can prefer opportunities with higher variance even when the opportunities are continuous unimodal and arbitrarily visually and statistically close to the normal distribution in shape our conclusions hold for any decision maker with a utility function whose derivatives alternate in sign being strictly positive or negative i e we exclude the uninteresting cases of quadratic and cubic utilities the method of analysis is based upon the theory of tchebychev systems of functions which deals with the expected value of utility functions of stochastic variables with known moments although we focus on the first three moments the results as presented here apply to all higher moments as well it is also shown that there can be extremely large deviations between the certainty equivalents of distributions having the same moments so this result is also pertinent to practical decision analysts as well the paper demonstrates that the properties of utility functions have implications which are much more subtle than previously recognized for evaluating distributions in terms of their moments

generalized t norm structures abstract this is a continuation of the work in drossos and navara eufit 96 aachen germany 1996 in this paper we investigate the possibility of defining a quantitative structure non idempotent on the top of a usual qualitative structure these generalized monoidal structures are very much related to the notion of t norms and t conorms defined on the closed interval 0 1 we would then like to define an appropriate generalization of the notion of t norm as a generalized monoidal structure which will reflect a minimum of properties of t norms defined on 0 1 considered as absolutely basic

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

estimating the impact of uncertainty on a deterministic multiattribute evaluation a method is presented to estimate the impact of uncertainty on the results of a multiattribute evaluation prior to conducting a complete probabilistic multiattribute utility analysis the method assumes that a deterministic analysis has been completed using a weighted additive multiattribute value evaluation function and that either an additive or multiplicative utility function is appropriate for the multiattribute utility analysis an approximation procedure is developed to estimate whether uncertainty about attribute levels could change the deterministic evaluation results an illustrative application investigates the accuracy of the procedure and its use to simplify analysis of the effects of uncertainty

a class of utility functions containing all the common utility functions this paper presents a class of utility functions class a that contains all of the utility functions commonly used for mathematical modeling the class consisting of those utility functions whose derivatives alternate in sign a simple representation via mixtures of exponential utilities is provided for this class which is both mathematically convenient and conducive to functional operations a connection with laplace transforms and the resultant implications for preference relations aggregation and utility assessment are discussed

local modularity measure for network clusterizations many complex networks have an underlying modular structure i e structural subunits communities or clusters characterized by highly interconnected nodes the modularity q has been introduced as a measure to assess the quality of clusterizations q has a global view while in many real world networks clusters are linked mainly locally among each other local cluster connectivity here we introduce a measure of localized modularity lq which reflects local cluster structure optimization of q and lq on the clusterization of two biological networks shows that the localized modularity identifies more cohesive clusters yielding a complementary view of higher granularity

effects of imprecise weighting in hierarchical preference programming abstract preference programming is a general term for multi criteria decision analytical approaches allowing incomplete preference information in the pairs method interval judgments are assigned to weight ratios between attributes to model imprecision in multi attribute value trees this paper studies the effects of a hierarchical model structure on the overall imprecision as the form of the hierarchy also affects the form of imprecision that can be assigned to the model the aim is to find out good procedural practices for reducing overall imprecision descending inherently from the model structure the study provides simulation results about the ability of various weighting schemes to identify dominated alternatives which are discussed with respect to other issues related to the weighting process according to the results a hierarchical model is structurally somewhat more unable to identify dominances than a corresponding nonhierarchical model but its cognitive advantages often cancel out this the results also suggest paying reasonable attention to the precision of the lower level judgments and to identifying possible correlations between the criteria

community detection in complex networks by dynamical simplex evolution we benchmark the dynamical simplex evolution dse method with several of the currently available algorithms to detect communities in complex networks by comparing correctly identified nodes for different levels of fuzziness of random networks composed of well defined communities the potential benefits of the dse method to detect hierarchical substructures in complex networks are discussed

detecting network communities by propagating labels under constraints we investigate the recently proposed label propagation algorithm lpa for identifying network communities we reformulate the lpa as an equivalent optimization problem giving an objective function whose maxima correspond to community solutions by considering properties of the objective function we identify conceptual and practical drawbacks of the label propagation approach most importantly the disparity between increasing the value of the objective function and improving the quality of communities found to address the drawbacks we modify the objective function in the optimization problem producing a variety of algorithms that propagate labels subject to constraints of particular interest is a variant that maximizes the modularity measure of community quality performance properties and implementation details of the proposed algorithms are discussed bipartite as well as unipartite networks are considered

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

mean variance approximations to expected utility abstract it is often asserted that the application of mean variance analysis assumes normal gaussian return distributions or quadratic utility functions this common mistake confuses sufficient versus necessary conditions for the applicability of modern portfolio theory if one believes as does the author that choice should be guided by the expected utility maxim then the necessary and sufficient condition for the practical use of mean variance analysis is that a careful choice from a mean variance efficient frontier will approximately maximize expected utility for a wide variety of concave risk averse utility functions this paper reviews a half century of research on mean variance approximations to expected utility the many studies in this field have been generally supportive of mean variance analysis subject to certain initially unanticipated caveats

comparison of weighting judgments in multiattribute utility measurement this paper compares four weighting methods in multiattribute utility measurement the ratio method the swing weighting method the tradeoff method and the pricing out method 200 subjects used these methods to weight attributes for evaluating nuclear waste repository sites in the united states the weighting methods were compared with respect to their internal consistency convergent validity and external validity internal consistency was measured by the degree to which ordinal and cardinal or ratio responses agreed within the same weighting method convergent validity was measured by the degree of agreement between the weights elicited with different methods external validity was determined by the degree to which weights elicited in this experiment agreed with weights that were elicited with managers of the department of energy in terms of internal consistency the tradeoff method fared worst in terms of convergent validity the pricing out method turned out to be an outlier in terms of external validity the pricing out method showed the best results while the ratio and swing methods are quite consistent and show a fair amount of convergent validity their external validity problems cast doubt on their usefulness the main recommendation for applications is to improve the internal consistency of the tradeoff method by careful interactive elicitation and to use it in conjunction with the pricing out method to enhance its external validity

limits of modularity maximization in community detection modularity maximization is the most popular technique for the detection of community structure in graphs the resolution limit of the method is supposedly solvable with the introduction of modified versions of the measure with tunable resolution parameters we show that multiresolution modularity suffers from two opposite coexisting problems the tendency to merge small subgraphs which dominates when the resolution is low the tendency to split large subgraphs which dominates when the resolution is high in benchmark networks with heterogeneous distributions of cluster sizes the simultaneous elimination of both biases is not possible and multiresolution modularity is not capable to recover the planted community structure not even when it is pronounced and easily detectable by other methods for any value of the resolution parameter this holds for other multiresolution techniques and it is likely to be a general problem of methods based on global optimization

the magnitude of errors in proximal multiattribute decision analysis with probabilistically dependent attributes this paper investigates the accuracy of an approximation procedure for evaluating alternatives under uncertainty with multiple evaluation attributes this approximation uses only the first two moments of the probability distributions for the alternatives and hence it can substantially reduce the amount of information which must be collected in order to evaluate alternatives when evaluation attributes are probabilistically dependent the accuracy of the approximation is investigated by comparing results from using it with exact calculations for a variety of situations representative of those found in decision analysis practice this investigation shows that the approximation is accurate for situations representative of many decision analysis applications however caution is needed in applying the approximation in some situations where it may give inaccurate results characteristics of cases where the approximation is less accurate are presented

community detection as an inference problem we express community detection as an inference problem of determining the most likely arrangement of communities we then apply belief propagation and mean field theory to this problem and show that this leads to fast accurate algorithms for community detection

identifying overlapping communities in networks using evolutionary method abstract community structure is a typical property of real world networks and has been recognized as a key to understand the dynamics of the networked systems in most of the networks overwhelming nodes apparently live in a community while there often exists a few nodes straddling several communities hence an ideal algorithm for community detection is that which can identify the overlapping communities in these networks we present an evolutionary method for detecting overlapping community structure in the network to represent an overlapping division of a network we develop an encoding scheme composed of two segments the first one represents a disjoint partition and the second one represents an extension of the partition that allows of multiple memberships we give two measures for the informativeness of a node and present a coevolutionary scheme between two segments over the population for solving the overlapping partition of the network experimental results show this method can give a better solution to a network it is also revealed that a best overlapping partition of the network might not be rooted from a best disjoint partition

constructing financial network based on pmfg and threshold method abstract based on planar maximally filtered graph p m f g and threshold method we introduced a correlation based network named p m f g based threshold network p t n we studied the community structure of p t n and applied i s o m a p algorithm to represent p t n in low dimensional euclidean space the results show that the community corresponds well to the cluster in the euclidean space further we studied the dynamics of the community structure and constructed the normalized mutual information n m i matrix based on the real data in the market we found that the volatility of the market can lead to dramatic changes in the community structure and the structure is more stable during the financial crisis

the three semantics of fuzzy sets abstract three main semantics for membership functions seem to exist in the literature similarity preference and uncertainty each semantics underlies a particular class of applications similarity notions are exploited in clustering analysis and fuzzy controllers uncertainty is captured by fuzzy sets in the framework of possibility theory the membership function of a fuzzy set is also sometimes a kind of utility function that represents flexible constraints in decision problems this paper advocates the claim that progress in operational semantics of membership functions presupposes that these distinct semantics be acknowledged and related to more basic measurement issues in terms of distance cost and frequency on which scientific traditions exist

spectral properties of networks with community structure in this paper we discuss the eigenspectra of networks with community structure it is shown that in many cases the spectrum of eigenvalues of the adjacency matrix of a network with community structure gives a clear indication of the number of communities in the network in particular for a network with n nodes and n c communities there will typically be n c eigenvalues that are significantly larger than the magnitudes of all the other n n c eigenvalues we discuss this property as well as its use and limitations for determining n c

certainty equivalents for three point discrete distribution approximations three point discrete distribution approximations are often used in decision and risk analyses to represent probability distributions for continuous random variables e g as probability nodes in decision or probability trees performance evaluations of such approximations have generally been based on their accuracies in estimating moments for the underlying distributions however moment based comparisons for recently proposed approximations have been limited moreover very little research has addressed the accuracies of any such approximations in representing expected utilities or certainty equivalents of the underlying distributions this is of potential concern since recent research shows three point discrete distribution approximations exist that match the first several moments of an underlying distribution exactly while counterintuitively approximating its certainty equivalents poorly this paper compares the best two approximations for estimating means and variances identified in an earlier study with promising approximations proposed more recently specifically it examines how accurately six simple general purpose three point approximations represent certainty equivalents for continuous random variables as the level of risk aversion is varied as well as how accurately they estimate means and variances the results show that several of these are quite accurate over a variety of test distributions when the level of risk aversion and the characteristics of the distributions are within reasonable bounds their robust performance is significant for decision analysis practice

replica inference approach to unsupervised multiscale image segmentation we apply a replica inference based potts model method to unsupervised image segmentation on multiple scales this approach was inspired by the statistical mechanics problem of community detection and its phase diagram specifically the problem is cast as identifying tightly bound clusters communities or solutes against a background or solvent within our multiresolution approach we compute information theory based correlations among multiple solutions replicas of the same graph over a range of resolutions significant multiresolution structures are identified by replica correlations manifest by information theory overlaps we further employ such information theory measures such as normalized mutual information and variation of information thermodynamic quantities such as the system entropy and energy and dynamic measures monitoring the convergence time to viable solutions as metrics for transitions between various solvable and unsolvable phases within the solvable phase transitions between contending solutions such as those corresponding to segmentations on different scales may also appear with the aid of these correlations as well as thermodynamic measures the phase diagram of the corresponding potts model is analyzed at both zero and finite temperatures optimal parameters corresponding to a sensible unsupervised segmentations appear within the easy phase of the potts model our algorithm is fast and shown to be at least as accurate as the best algorithms to date and to be especially suited to the detection of camouflaged images

partial information dominance and potential optimality in multiattribute utility theory when a multiattribute utility function is only partially specified by prior preference statements what can be said about the relative desirability of actual alternatives this question is addressed for the cases of additively separable cardinal utility with unknown scaling constants multiplicatively separable cardinal utility with unknown scaling constants and additively separable ordinal utility we review previous approaches and treat issues of consistency is the prior information consistent dominance does the prior preference information imply that one outcome is preferred to another and potential optimality are there utility functions of the given form consistent with prior preference information under which a particular outcome is preference optimal in the additive cases a key relationship between dominance and potential optimality may be derived the paper concludes by presenting an example application to a well known nuclear siting study

decision quality using ranked attribute weights three published approximation formulae for selecting the best multiattribute alternative based on rank ordered weights are evaluated all formulae are surprisingly efficacious in determining the best multiattribute alternative rank order centroid roc weights are more accurate than the other rank based formulae furthermore the roc formula generalizes to incorporate both other forms of partial information about attribute weights and partial rank order information as well because a roc based analysis is so straightforward and efficacious it provides an appropriate implementation tool

evidential weights of multiple preferences for competitiveness the alternative selections or feasible sets in multi attribute utility theory usually face problems of inaccuracy or inconsistency in weighting evidential weight and weight of evidence still have not resolved these problems in an efficient manner this research proposes evidential weights of multiple preferences by using evidence and inference based on the rough set theory an evidential probability is constructed to resolve this weight technically the evidential probability is required to satisfy the following conditions uniqueness independence and consistency to identify various evidence and noise and to provide quantities of certain evidence to resolve weights empirically the resolved weights are fused into competitiveness utility for verification a practical case successfully classifies dominating nations of world competitiveness yearbook another case analyzes the competitiveness trends of china during 1997 to 2012 predicting china will continue rising in near future

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