on the accuracy of bonferroni significance levels for detecting outliers in linear models at present the first order bonferroni upper bound is the only practically useful tool for determining approximate critical values or p values for the maximum absolute studentized residual as a criterion for detecting a single outlier in a linear model available methods for assessing the accuracy of this bound require numerical integration and are difficult to apply routinely we present a relatively simple alternative method that can be applied to any linear model and is suitable for routine use the application to analyses of 2 m factorial experiments and regression models is illustrated with several examples

noncolliding brownian motion with drift and time dependent stieltjes wigert determinantal point process using the determinantal formula of biane bougerol and o connell we give multitime joint probability densities to the noncolliding brownian motion with drift where the number of particles is finite we study a special case such that the initial positions of particles are equidistant with a period a and the values of drift coefficients are well ordered with a scale we show that at each time t 0 the single time probability density of particle system is exactly transformed to the biorthogonal stieltjes wigert matrix model in the chern simons theory introduced by dolivet and tierz here one parameter extensions extensions of the stieltjes wigert polynomials which are themselves q extensions of the hermite polynomials play an essential role the two parameters a and of the process combined with time t are mapped to the parameters q and of the biorthogonal polynomials by the transformation of normalization factor of our probability density the partition function of the chern simons matrix model is readily obtained we study the determinantal structure of the matrix model and prove that at each time t 0 the present noncolliding brownian motion with drift is a determinantal point process in the sense that any correlation function is given by a determinant governed by a single integral kernel called the correlation kernel using the obtained correlation kernel we study time evolution of the noncolliding brownian motion with drift

detecting outlying cells in two way contingency table via backwards stepping when fitting a model to a contingency table a significant lack of fit can sometimes be caused by a few outlier cells with the model fitting the remaining cells well these cells can be identified by using deleted residuals the residual from the expected count with the cell deleted and tested using the drop in likelihood ratio goodness of fit statistic from the model with the cell included to the model with the cell deleted with the cells being tested from least extreme to most extreme backwards stepping this article shows that using a bonferroni bound for the outlier test at each step results in a conservative test with good power to detect multiple outliers backwards stepping and the use of deleted residuals results in the limiting of both masking and swamping effects the procedure generalizes easily to complicated probability models

range limited centrality measures in complex networks here we present a range limited approach to centrality measures in both nonweighted and weighted directed complex networks we introduce an efficient method that generates for every node and every edge its betweenness centrality based on shortest paths of lengths not longer than ensuremath ell 1 l in the case of nonweighted networks and for weighted networks the corresponding quantities based on minimum weight paths with path weights not larger than w ensuremath ell ensuremath ell ensuremath delta ensuremath ell 1 2 l r ensuremath delta these measures provide a systematic description on the positioning importance of a node edge with respect to its network neighborhoods one step out two steps out etc up to and including the whole network they are more informative than traditional centrality measures as network transport typically happens on all length scales from transport to nearest neighbors to the farthest reaches of the network we show that range limited centralities obey universal scaling laws for large nonweighted networks as the computation of traditional centrality measures is costly this scaling behavior can be exploited to efficiently estimate centralities of nodes and edges for all ranges including the traditional ones the scaling behavior can also be exploited to show that the ranking top list of nodes edges based on their range limited centralities quickly freezes as a function of the range and hence the diameter range top list can be efficiently predicted we also show how to estimate the typical largest node to node distance for a network of n nodes exploiting the afore mentioned scaling behavior these observations were made on model networks and on a large social network inferred from cell phone trace logs ensuremath sim 5 5 ifmmode times else texttimes fi 10 6 nodes and ensuremath sim 2 7 ifmmode times else texttimes fi 10 7 edges finally we apply these concepts to efficiently detect the vulnerability backbone of a network defined as the smallest percolating cluster of the highest betweenness nodes and edges and illustrate the importance of weight based centrality measures in weighted networks in detecting such backbones

a large k asymptotics of witten s invariant of seifert manifolds we calculate a largek asymptotic expansion of the exact surgery formula for witten ssu 2 invariant of some seifert manifolds the contributions of all flat connections are identified an agreement with the 1 loop formula is checked a contribution of the irreducible connections appears to contain only a finite number of terms in the asymptotic series a 2 loop correction to the contribution of the trivial connection is found to be proportional to casson s invariant

superstrings and topological strings at large n we embed the large n chern simons topological string duality in ordinary superstrings this corresponds to a large n duality between generalized gauge systems with n 1 supersymmetry in four dimensions and superstrings propagating on noncompact calabi yau manifolds with certain fluxes turned on we also show that in a particular limit of the n 1 gauge theory system certain superpotential terms in the n 1 system including deformations if spacetime is noncommutative are captured to all orders in 1 n by the amplitudes of noncritical bosonic strings propagating on a circle with self dual radius we also consider d brane anti d brane system wrapped over vanishing cycles of compact calabi yau manifolds and argue that at large n they induce a shift in the background to a topologically distinct calabi yau which we identify as the ground state system of the brane anti brane system

residue formulas for the large k asymptotics of witten s invariants of seifert manifolds the case of su 2 we derive the largek asymptotics of the surgery formula forsu 2 witten s invariants of general seifert manifolds the contributions of connected components of the moduli space of flat connections are identified the contributions of irreducible connections are presented in the residue form this allows us to express them in terms of intersection numbers on their moduli spaces

routing betweenness centrality betweenness centrality measure is often used in social and computer communication networks to estimate the potential monitoring and control capabilities a vertex may have on data flowing in the network in this article we define the routing betweenness centrality rbc measure that generalizes previously well known betweenness measures such as the shortest path betweenness flow betweenness and traffic load centrality by considering network flows created by arbitrary loop free routing strategies we present algorithms for computing rbc of all the individual vertices in the network and algorithms for computing the rbc of a given group of vertices where the rbc of a group of vertices represents their potential to collaboratively monitor and control data flows in the network two types of collaborations are considered i conjunctive the group is a sequences of vertices controlling traffic where all members of the sequence process the traffic in the order defined by the sequence and ii disjunctive the group is a set of vertices controlling traffic where at least one member of the set processes the traffic the algorithms presented in this paper also take into consideration different sampling rates of network monitors accommodate arbitrary communication patterns between the vertices traffic matrices and can be applied to groups consisting of vertices and or edges for the cases of routing strategies that depend on both the source and the target of the message we present algorithms with time complexity of o n2m where n is the number of vertices in the network and m is the number of edges in the routing tree or the routing directed acyclic graph dag for the cases of multi path routing strategies the time complexity can be reduced by an order of n if we assume that the routing decisions depend solely on the target of the messages finally we show that a preprocessing of o n2m time supports computations of rbc of sequences in o kn time and computations of rbc of sets in o n3n time where k in the number of vertices in the sequence or the set

chern simons theory matrix integrals and perturbative three manifold invariants the universal perturbative invariants of rational homology spheres can be extracted from the chern simons partition function by combining perturbative and nonperturbative results we spell out the general procedure to compute these invariants and we work out in detail the case of seifert spaces by extending some previous results of lawrence and rozansky the chern simons partition function with arbitrary simply laced group for these spaces is written in terms of matrix integrals the analysis of the perturbative expansion amounts to the evaluation of averages in a gaussian ensemble of random matrices as a result explicit expressions for the universal perturbative invariants of seifert homology spheres up to order five are presented

location of multiple outliers in two way tables using tetrads using residuals to isolate multiple outhers in a two way table may lead to very poor results a new diagnostic is proposed the median of the tetrads associated with a cell this procedure can efficiently identify multiple outliers in a single step the use of a half normal plot provides a good indicator of the actual number of outhers in the table

fast algorithm for successive computation of group betweenness centrality in this paper we propose a method for rapid computation of group betweenness centrality whose running time after preprocessing does not depend on network size the calculation of group betweenness centrality is computationally demanding and therefore it is not suitable for applications that compute the centrality of many groups in order to identify new properties our method is based on the concept of path betweenness centrality defined in this paper we demonstrate how the method can be used to find the most prominent group then we apply the method for epidemic control in communication networks we also show how the method can be used to evaluate distributions of group betweenness centrality and its correlation with group degree the method may assist in finding further properties of complex networks and may open a wide range of research opportunities

witten reshetikhin turaev invariants of seifert manifolds for seifert homology spheres we derive a holomorphic function of k whose value at integer k is the sl2 witten reshetikhin turaev invariant zk at q exp 2 i k this function is expressed as a sum of terms which can be naturally corresponded to the contributions of flat connections in the stationary phase expansion of the witten chern simons path integral the trivial connection contribution is found to have an asymptotic expansion in powers of k 1 which for k an odd prime power converges k adically to the exact total value of the invariant zk at that root of unity evaluations at rational k are also discussed using similar techniques an expression for the coloured jones polynomial of a torus knot is obtained providing a trivial connection contribution which is an analytic function of the colour this demonstrates that the stationary phase expansion of the chern simons witten theory is exact for seifert manifolds and for torus knots in s3 the possibility of generalising such results is also discussed

tunable path centrality quantifying the importance of paths in networks abstract centrality is a fundamental measure in network analysis specifically centrality of a path describes the importance of the path with respect to the remaining part of the network in this paper we propose a tunable path centrality tpc measure which quantifies the centrality of a path by integrating the path degree pd number of neighbors of the path and the path bridge pb number of bridges in the path with a control parameter considering the complexity of large scale and dynamical topologies of many real world networks both pd and pb are computed with only the local topological structure of a path we demonstrate the distribution of the three path centralities tpc pd and pb in computer generated networks and real world networks furthermore we apply the three path centralities to the network fragility problem and exploit the distribution of the optimal control parameter o p t through simulation and analysis finally the simulation results show that generally tpc is more efficient than pd and pb in the network fragility problem these path centralities are also applicable in many other network problems including spread control prediction and so on

efficient algorithms for updating betweenness centrality in fully dynamic graphs devise an algorithm for updating betweenness centrality in fully dynamic graphs recalculate centrality without computing all pairs shortest paths in the entire graph adapt a highest centrality edge finding algorithm based on the proposed algorithm adapt a community detection algorithm using the proposed algorithms experimental results show the proposed algorithm outperforms existing algorithms betweenness centrality of a vertex edge in a graph is a measure for the relative participation of the vertex edge in the shortest paths in the graph betweenness centrality is widely used in various areas such as biology transportation and social networks in this paper we study the update problem of betweenness centrality in fully dynamic graphs the proposed update algorithm substantially reduces the number of shortest paths which should be re computed when a graph is changed in addition we adapt a community detection algorithm using the proposed algorithm to show how much benefit can be obtained from the proposed algorithm in a practical application experimental results on real graphs show that the proposed algorithm efficiently update betweenness centrality and detect communities in a graph

isolating one cell interactions robust regression can be used to identify one cell interactions in multiway factorial designs one cell interactions appear as mean slippage outliers to a low order model and robust regression gives these cells low mean weight i use mean cell weight as a diagnostic criterion for one cell interactions and provide approximate critical values for mean cell weights several examples illustrate the method

some results on approximate 1 median selection in metric spaces a 1 median in a finite metric space is a point with the minimum average distance to all other points given a positive integer n and oracle access to a distance metric on 1 2 n we study the problem of finding a 1 median in particular we show the nonexistence of 1 deterministic o 1 approximation o n query algorithms 2 deterministic email protected 1 approximation o n 2 query algorithms for graph metrics 3 deterministic email protected 1 approximation o n 2 query algorithms and 4 monte carlo email protected 1 approximation o n query algorithms with an w 1 probability of success we also show a monte carlo email protected approximation o log 2 1 e e 3 query algorithm with a 1 o e probability of success where email protected 0 1

matrix models and stochastic growth in donaldson thomas theory we show that the partition functions which enumerate donaldson thomas invariants of local toric calabi yau threefolds without compact divisors can be expressed in terms of specializations of the schur measure we also discuss the relevance of the hall littlewood and jack measures in the context of bps state counting and study the partition functions at arbitrary points of the kahler moduli space this rewriting in terms of symmetric functions leads to a unitary one matrix model representation for donaldson thomas theory we describe explicitly how this result is related to the unitary matrix model description of chern simons gauge theory this representation is used to show that the generating functions for donaldson thomas invariants are related to tau functions of the integrable toda and toeplitz lattice hierarchies the matrix model also leads to an interpretation of donaldson thomas theory in terms of non intersecting paths in the lock step model of vicious walkers we further show that these generati

oscillatory matrix model in chern simons theory and jacobi theta determinantal point process the partition function of the chern simons theory on the three sphere with the unitary group u n provides a one matrix model the corresponding n particle system can be mapped to the determinantal point process whose correlation kernel is expressed by using the stieltjes wigert orthogonal polynomials the matrix model and the point process are regarded as q extensions of the random matrix model in the gaussian unitary ensemble and its eigenvalue point process respectively we prove the convergence of the n particle system to an infinite dimensional determinantal point process in n in which the correlation kernel is expressed by jacobi s theta functions we show that the matrix model obtained by this limit realizes the oscillatory matrix model in chern simons theory discussed by de haro and tierz

matrix integration and combinatorics of modular groups integration over gaussian matrix ensembles was used to obtain the virtual euler characteristics of mapping class groups we present some simplifications in the combinatorial part of the calculation

a contribution of the trivial connection to the jones polynomial and witten s invariant of 3d manifolds ii we extend the results of our previous paper 1 from knots to links by using a formula for the jones polynomial of a link derived recently by n reshetikhin we establish a relation between the parameters of this formula and the multivariable alexander polynomial this relation is illustrated by an example of a torus link we check that our expression for the alexander polynomial satisfies some of its basic properties finally we derive a link surgery formula for the loop corrections to the trivial connection contribution to witten s invariant of rational homology spheres

chern simons matrix models and stieltjes wigert polynomials employing the random matrix formulation of chern simons theory on seifert manifolds we show how the stieltjes wigert orthogonal polynomials are useful in exact computations in chern simons matrix models we construct a biorthogonal extension of the stieltjes wigert polynomials not available in the literature necessary to study chern simons matrix models when the geometry is a lens space we also study the relationship between stieltjes wigert and rogers szego polynomials and the corresponding equivalence with a unitary matrix model finally we give a detailed proof of a result that relates quantum dimensions with averages of schur polynomials in the stieltjes wigert ensemble

a comparison of heuristic best first algorithms for bicriterion shortest path problems abstract a variety of algorithms have been proposed to solve the bicriterion shortest path problem this article analyzes and compares the performance of three best first label setting algorithms that accept heuristic information to improve efficiency these are namoa moa and tung chew s algorithm tc a set of experiments explores the impact of heuristic information in search efficiency and the relative performance of the algorithms the analysis reveals that namoa is the best option for difficult problems its time performance can benefit considerably from heuristic information though not in all cases the performance of tc is similar but somewhat worse however the time performance of moa is found to degrade considerably with the use of heuristic information in most cases explanations are provided for these phenomena

chern simons perturbation theory ii we study the perturbation theory for three dimensional chern simons quantum field theory on a general compact three manifold without boundary we show that after a simple change of variables the action obtained by brs gauge fixing in the lorentz gauge has a superspace formulation the basic properties of the propagator and the feynman rules are written in a precise manner in the language of differential forms using the explicit description of the propagator singularities we prove that the theory is finite finally the anomalous metric dependence of the 2 loop partition function on the riemannian metric which was introduced to define the gauge fixing can be cancelled by a local counterterm as in the 1 loop case in fact the counterterm is equal to the chern simons action of the metric connection normalized precisely as one would expect based on the framing dependence of witten s exact solution invited talk at the xxth conference on differential geometric methods in physics new york june 1991

asymptotic expansions for q gamma q exponential and q bessel functions abstract new asymptotic expansions are given for the q gamma function the q exponential functions and for the hahn exton q bessel function for the theta functions four expansions are given and for the hahn exton q bessel difference equation a new solution is given which forms with the hahn exton q bessel function a numerically satisfactory pair of solutions

wall crossing as seen by matrix models the number of bps bound states of d branes on a calabi yau manifold depends on two sets of data the bps charges and the stability conditions for d0 and d2 branes bound to a single d6 brane wrapping a calabi yau 3 fold x both are naturally related to the kahler moduli space mathcal m x we construct unitary one matrix models which count such bps states for a class of toric calabi yau manifolds at infinite t hooft coupling the matrix model for the bps counting on x turns out to give the topological string partition function for another calabi yau manifold y whose kahler moduli space mathcal m y contains two copies of mathcal m x one related to the bps charges and another to the stability conditions the two sets of data are unified in mathcal m y the matrix models have a number of other interesting features they compute spectral curves and mirror maps relevant to the remodeling conjecture for finite t hooft coupling they give rise to yet more general geometry widetilde y containing y

scale free characteristics of random networks the topology of the world wide web the world wide web forms a large directed graph whose vertices are documents and edges are links pointing from one document to another here we demonstrate that despite its apparent random character the topology of this graph has a number of universal scale free characteristics we introduce a model that leads to a scale free network capturing in a minimal fashion the self organization processes governing the world wide web c 2000 elsevier science b v all rights reserved pacs 84 35 i 64 60 fr 87 23 ge

random point fields associated with certain fredholm determinants i fermion poisson and boson point processes we introduce certain classes of random point fields including fermion and boson point processes which are associated with fredholm determinants of certain integral operators and study some of their basic properties limit theorems correlation functions palm measures etc also we propose a conjecture on an analogue of the determinant and permanent

efficient algorithms for game theoretic betweenness centrality betweenness centrality measures the ability of different nodes to control the flow of information in a network in this article we extend the standard definition of betweenness centrality using semivalues a family of solution concepts from cooperative game theory that includes among others the shapley value and the banzhaf power index any semivalue based betweenness centrality measure such as for example the shapley value based betweenness centrality measure has the advantage of evaluating the importance of individual nodes by considering the roles they each play in different groups of nodes our key result is the development of a general polynomial time algorithm to compute the semivalue based betweenness centrality measure and an even faster algorithm to compute the shapley value based betweenness centrality measure both for weighted and unweighted networks interestingly for the unweighted case our algorithm for computing the shapley value based centrality has the same complexity as the best known algorithm for computing the standard betweenness centrality due to brandes 15 we empirically evaluate our measures in a simulated scenario where nodes fail simultaneously we show that compared to the standard measure the ranking obtained by our measures reflects more accurately the influence that different nodes have on the functionality of the network we propose a betweenness centrality based on the shapley value and semivalue we develop polynomial algorithms for our game theoretic metrics we evaluate our measures in scenarios where simultaneous node failures occur our measures obtain better results than standard betweenness centrality we provide an empirical evaluation of algorithms on real life and random graphs