text mining by tsallis entropy abstract long range correlations between the elements of natural languages enable them to convey very complex information complex structure of human language as a manifestation of natural languages motivates us to apply nonextensive statistical mechanics in text mining tsallis entropy appropriately ranks the terms relevance to document subject taking advantage of their spatial correlation length we apply this statistical concept as a new powerful word ranking metric in order to extract keywords of a single document we carry out an experimental evaluation which shows capability of the presented method in keyword extraction we find that tsallis entropy has reliable word ranking performance at the same level of the best previous ranking methods

nombre de points de hauteur bornee sur les surfaces de del pezzo de degre 5 we state manin s conjecture in the particular case of the split del pezzo s surfaces of degree 5 over q we show that for an open set u v nu q b card p u q h p b c b log b 4 b the constant c is the one conjectured by e peyre sommaire

deterministic walks in random networks an application to thesaurus graphs abstract in a landscape composed of n randomly distributed sites in euclidean space a walker tourist goes to the nearest one that has not been visited in the last steps this procedure leads to trajectories composed of a transient part and a final cyclic attractor of period p the tourist walk presents a simple scaling with respect to and can be performed in a wide range of networks that can be viewed as ordinal neighborhood graphs as an example we show that graphs defined by thesaurus dictionaries share some of the statistical properties of low dimensional d 2 euclidean graphs and are easily distinguished from random link networks which correspond to the d limit this approach furnishes complementary information to the usual clustering coefficient and mean minimum separation length

a directed network of greek and roman mythology abstract we construct a directed network using a dictionary of greek and roman mythology in which the nodes represent the entries listed in the dictionary and we make directional links from an entry to other entries that appear in its explanatory part we find that this network is clearly not a random network but a directed scale free network in which the distributions of out degree and in degree follow a power law with exponents out 3 0 and in 2 5 respectively also we measure several quantities which describe the topological properties of the network and compare it to that of other real networks

on the distribution of points of bounded height on equivariant compactifications of vector groups we prove asymptotic formulas for the number of rational points of bounded height on smooth equivariant compactifications of the affine space

a complex network based approach for boundary shape analysis this paper introduces a novel methodology to shape boundary characterization where a shape is modeled into a small world complex network it uses degree and joint degree measurements in a dynamic evolution network to compose a set of shape descriptors the proposed shape characterization method has an efficient power of shape characterization it is robust noise tolerant scale invariant and rotation invariant a leaf plant classification experiment is presented on three image databases in order to evaluate the method and compare it with other descriptors in the literature fourier descriptors curvature zernike moments and multiscale fractal dimension

a monoparametric family of metrics for statistical mechanics abstract in a recent paper we have studied a generalization of the jensen shannon divergence jsd physica a 329 2003 81 this generalization was made in the context of tsallis statistical mechanics the present work is devoted to an investigation of the metric character of the jsd generalization

lagrangean relaxation of the hull reformulation of linear generalized disjunctive programs and its use in disjunctive branch and bound abstract in this work we present a lagrangean relaxation of the hull reformulation of discrete continuous optimization problems formulated as linear generalized disjunctive programs gdp the proposed lagrangean relaxation has three important properties the first property is that it can be applied to any linear gdp the second property is that the solution to its continuous relaxation always yields 0 1 values for the binary variables of the hull reformulation finally it is simpler to solve than the continuous relaxation of the hull reformulation the proposed lagrangean relaxation can be used in different gdp solution methods in this work we explore its use as primal heuristic to find feasible solutions in a disjunctive branch and bound algorithm the modified disjunctive branch and bound is tested with several instances with up to 300 variables the results show that the proposed disjunctive branch and bound performs faster than other versions of the algorithm that do not include this primal heuristic

the complex networks approach for authorship attribution of books authorship analysis by means of textual features is an important task in linguistic studies we employ complex networks theory to tackle this disputed problem in this work we focus on some measurable quantities of word co occurrence network of each book for authorship characterization based on the network features attribution probability is defined for authorship identification furthermore two scaling exponents q parameter and exponent are combined to classify personal writing style with acceptable high resolution power the q parameter generally known as the nonextensivity measure is calculated for degree distribution and the exponent comes from a power law relationship between number of links and number of nodes in the co occurrence network constructed for different books written by each author the applicability of the presented method is evaluated in an experiment with thirty six books of five persian litterateurs our results show high accuracy rate in authorship attribution

rational points on pencils of conics and quadrics with many degenerate fibres for any pencil of conics or higher dimensional quadrics over q with all degenerate bres dened over q we show that the brauer manin obstruction controls weak approximation the proof is based on the hasse principle and weak approximation for some special intersections of quadrics over q which is a consequence of recent advances in additive combinatorics

counting algebraic numbers with large height ii let denote the field of rational numbers open image in new window an algebraic closure of and h open image in new window the absolute multiplicative weil height for each positive integer d and real number mathcal h geqslant 1 it is well known that the number open image in new window of points in open image in new window having degree d over and satisfying h left alpha right leqslant mathcal h is finite this is the one dimensional case of northcott s theorem 8 see also 5 page 59 the systematic study of the counting function open image in new window and that of related functions in higher dimensions was begun by schmidt 10 it is relatively easy to prove the existence of a positive constant c c d such that open image in new window 1 and also the existence of positive constants c c d and mathcal h 0 mathcal h 0 left d right such that open image in new window 2

facets of the complementarity knapsack polytope we present a polyhedral study of the complementarity knapsack problem traditionally complementarity constraints are modeled by introducing auxiliary binary variables and additional constraints and the model is tightened by introducing strong inequalities valid for the resulting mip we use an alternative approach in which we keep in the model only the continuous variables and we tighten the model by introducing inequalities that define facets of the convex hull of the set of feasible solutions in the space of the continuous variables to obtain the facet defining inequalities we extend the concepts of cover and cover inequality commonly used in 0 1 programming for this problem and we show how to sequentially lift cover inequalities we obtain tight bounds for the lifting coefficients and we present two families of facet de ning inequalities that can be derived by lifting cover inequalities we show that unlike 0 1 knapsack polytopes in which different facet defining inequalities can be derived by fixing variables at 0 or 1 and then sequentially lifting cover inequalities valid for the projected polytope any sequentially lifted cover inequality for the complementarity knapsack polytope can be obtained by fixing variables at 0

percolation in directed scale free networks many complex networks in nature have directed links a property that affects the network s navigability and large scale topology here we study the percolation properties of such directed scale free networks with correlated in and out degree distributions we derive a phase diagram that indicates the existence of three regimes determined by the values of the degree exponents in the first regime we regain the known directed percolation mean field exponents in contrast the second and third regimes are characterized by anomalous exponents which we calculate analytically in the third regime the network is resilient to random dilution i e the percolation threshold is pc 1

generalized exponential function and discrete growth models abstract here we show that a particular one parameter generalization of the exponential function is suitable to unify most of the popular one species discrete population dynamic models into a simple formula a physical interpretation is given to this new introduced parameter in the context of the continuous richards model which remains valid for the discrete case from the discretization of the continuous richards model generalization of the gompertz and verhulst models one obtains a generalized logistic map and we briefly study its properties notice however that the physical interpretation for the introduced parameter persists valid for the discrete case next we generalize the scramble competition ricker discrete model and analytically calculate the fixed points as well as their stabilities in contrast to previous generalizations from the generalized ricker model one is able to retrieve either scramble or contest models

topological structure of dictionary graphs we investigate the topological structure of the subgraphs of dictionary graphs constructed from wordnet and moby thesaurus data in the process of learning a foreign language the learner knows only a subset of all words of the language corresponding to a subgraph of a dictionary graph when this subgraph grows with time its topological properties change we introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers that is one first learns words with a high pseudocore number followed by smaller pseudocores we also propose an alternative strategy for vocabulary growth involving decreasing core numbers as opposed to pseudocore numbers we find that as the core or pseudocore grows in size the clustering coefficient first decreases then reaches a minimum and starts increasing again the minimum occurs when the vocabulary reaches a size between 103 and 104 a simple model exhibiting similar behavior is proposed the model is based on a generalized geometric random graph possible implications for language learning are discussed

big rational surfaces we prove that the cox ring of a smooth rational surface with big anticanonical class is finitely generated we classify surfaces of this type that are blow ups of mathbb p 2 at distinct points lying on a possibly reducible cubic

generalized hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series a nonlinear dynamics approach can be used in order to quantify complexity in written texts as a first step a one dimensional system is examined two written texts by one author lewis carroll are considered together with one translation into an artificial language i e esperanto are mapped into time series their corresponding shuffled versions are used for obtaining a baseline two different one dimensional time series are used here one based on word lengths lts the other on word frequencies fts it is shown that the generalized hurst exponent h q and the derived f curves of the original and translated texts show marked differences the original texts are far from giving a parabolic f function in contrast to the shuffled texts moreover the esperanto text has more extreme values this suggests cascade model like with multiscale time asymmetric features as finally written texts a discussion of the difference and complementarity of mapping into a lts or fts is presented the fts f curves are more opened than the lts ones

keyword extraction by nonextensivity measure the presence of a long range correlation in the spatial distribution of a relevant word type in spite of random occurrences of an irrelevant word type is an important feature of human written texts we classify the correlation between the occurrences of words by nonextensive statistical mechanics for the word ranking process in particular we look at the nonextensivity parameter as an alternative metric to measure the spatial correlation in the text from which the words may be ranked in terms of this measure finally we compare different methods for keyword extraction

correlation analysis of short text based on network model abstract correlation of words in the text is of great importance in text analysis like text retrieval keywords extraction and text clustering for short text because of the limited information of text content it is difficult to catch the correlation well among words in this paper we propose an algorithm based on the complex network to calculate the correlation of words in short texts a new variable edge degree is proposed and used in studying the network model of texts by using fluctuation analysis we give the condition that edge degree correlation between words exists beyond nearest neighbors further analysis shows that numerical results of the fluctuation function of edge degree act a power law distribution and that the scaling exponent diverges at a long distance under the finite size effect and varies in different texts the fluctuation function separates the words in a text into different clusters and this property is used to measure inner correlation of different words hub nodes act a significant influence on the long range edge degree correlation through changing the linear trend of the fluctuation function in a log log plot

a hierarchy of relaxations for nonlinear convex generalized disjunctive programming we propose a framework to generate alternative mixed integer nonlinear programming formulations for disjunctive convex programs that lead to stronger relaxations we extend the concept of basic steps defined for disjunctive linear programs to the nonlinear case a basic step is an operation that takes a disjunctive set to another with fewer number of conjuncts we show that the strength of the relaxations increases as the number of conjuncts decreases leading to a hierarchy of relaxations we prove that the tightest of these relaxations allows in theory the solution of the disjunctive convex program as a nonlinear programming problem we present a methodology to guide the generation of strong relaxations without incurring an exponential increase of the size of the reformulated mixed integer program finally we apply the theory developed to improve the computational efficiency of solution methods for nonlinear convex generalized disjunctive programs gdp this methodology is validated through a set of numerical examples

strong correlations between text quality and complex networks features abstract concepts of complex networks have been used to obtain metrics that were correlated to text quality established by scores assigned by human judges texts produced by high school students in portuguese were represented as scale free networks word adjacency model from which typical network features such as the in outdegree clustering coefficient and shortest path were obtained another metric was derived from the dynamics of the network growth based on the variation of the number of connected components the scores assigned by the human judges according to three text quality criteria coherence and cohesion adherence to standard writing conventions and theme adequacy development were correlated with the network measurements text quality for all three criteria was found to decrease with increasing average values of outdegrees clustering coefficient and deviation from the dynamics of network growth among the criteria employed cohesion and coherence showed the strongest correlation which probably indicates that the network measurements are able to capture how the text is developed in terms of the concepts represented by the nodes in the networks though based on a particular set of texts and specific language the results presented here point to potential applications in other instances of text analysis

rational points of bounded height on general conic bundle surfaces a conjecture of manin predicts the asymptotic distribution of rational points of bounded height on fano varieties in this paper we use conic bundles to obtain correct lower bounds for a wide class of surfaces over number fields for which the conjecture is still far from being proved for example we obtain the conjectured lower bound of manin s conjecture for any del pezzo surface whose picard rank is sufficiently large or for arbitrary del pezzo surfaces after possibly an extension of the ground field of small degree

continuous growth models in terms of generalized logarithm and exponential functions abstract consider the one parameter generalizations of the logarithmic and exponential functions which are obtained from the integration of non symmetrical hyperboles these generalizations coincide to the one obtained in the context of non extensive thermostatistics we show that these functions are suitable to describe and unify the great majority of continuous growth models which we briefly review physical interpretation to the generalization function parameter is given for the richards model which has an underlying microscopic model to justify it

fractal power law in literary english we present in this paper a numerical investigation of literary texts by various well known english writers covering the first half of the twentieth century based upon the results obtained through corpus analysis of the texts a fractal power law is obtained for the lexical wealth defined as the ratio between the number of different words and the total number of words of a given text by considering as a signature of each author the exponent and the amplitude of the power law and the standard deviation of the lexical wealth it is possible to discriminate works of different genres and writers and show that each writer has a very distinct signature either considered among other literary writers or compared with writers of non literary texts it is also shown that for a given author the signature is able to discriminate between short stories and novels

manin s conjecture for quartic del pezzo surfaces with a conic fibration an asymptotic formula is established for the number of q rational points of bounded height on a non singular quartic del pezzo surface with a conic bundle structure

tamagawa numbers of diagonal cubic surfaces numerical evidence a refined version of manin sconjecture aboutthe asymptotics of points of bounded height on fano varieties has been developped by batyrev and the authors we test numerically this refined conjecture for some diagonal cubic surfaces

detecting communities in large networks we develop an algorithm to detect community structure in complex networks the algorithm is based on spectral methods and takes into account weights and link orientation since the method detects efficiently clustered nodes in large networks even when these are not sharply partitioned it turns to be specially suitable for the analysis of social and information networks we test the algorithm on a large scale data set from a psychological experiment of word association in this case it proves to be successful both in clustering words and in uncovering mental association patterns

shakespeare and other english renaissance authors as characterized by information theory complexity quantifiers abstract we introduce novel information theory quantifiers in a computational linguistic study that involves a large corpus of english renaissance literature the 185 texts studied 136 plays and 49 poems in total with first editions that range from 1580 to 1640 form a representative set of its period our data set includes 30 texts unquestionably attributed to shakespeare in addition we also included a lover s complaint a poem which generally appears in shakespeare collected editions but whose authorship is currently in dispute our statistical complexity quantifiers combine the power of jensen shannon s divergence with the entropy variations as computed from a probability distribution function of the observed word use frequencies our results show among other things that for a given entropy poems display higher complexity than plays that shakespeare s work falls into two distinct clusters in entropy and that his work is remarkable for its homogeneity and for its closeness to overall means

a metric to search for relevant words abstract we propose a new metric to evaluate and rank the relevance of words in a text the method uses the density fluctuations of a word to compute an index that measures its degree of clustering highly significant words tend to form clusters while common words are essentially uniformly spread in a text if a word is not rare the metric is stable when we move any individual occurrence of this word in the text furthermore we prove that the metric always increases when words are moved to form larger clusters or when several independent documents are merged using the holy bible as an example we show that our approach reduces the significance of common words when compared to a recently proposed statistical metric

optimal design of truss structures by logic based branch and cut the truss design problem is to find the optimal placement and size of structural bars that can support a given load the problem is nonlinear and in the version addressed here the bars must take certain discrete sizes it is shown that a logic based method that dispenses with integer variables and branches directly on logical disjunctions can solve substantially larger problems than mixed integer programming even though the nonlinearities disappear in the mixed integer model a primary purpose of the paper is to investigate whether advantages of logic based branching that have been demonstrated elsewhere for linear problems extend to nonlinear programming

improved asymptotic analysis of the average number of steps performed by the self dual simplex algorithm in this paper we analyze the average number of steps performed by the self dual simplex algorithm for linear programming under the probabilistic model of spherical symmetry the model was proposed by smale consider a problem ofn variables withm constraints smale established that for every number of constraintsm there is a constantc m such that the number of pivot steps of the self dual algorithm m n is less thanc m lnn m m 1 we improve upon this estimate by showing that m n is bounded by a function ofm only the symmetry of the function inm andn implies that m n is in fact bounded by a function of the smaller ofm andn

quadratic families of elliptic curves and unirationality of degree 1 conic bundles we study families of elliptic curves whose coefficients are degree 2 polynomials in a variable t all such curves together form an algebraic surface which is birational to a conic bundle with 7 singular fibers we prove that such conic bundles are unirational as a consequence one obtains that for infinitely many values of t the resulting elliptic curve has rank at least 1

giant strongly connected component of directed networks we describe how to calculate the sizes of all giant connected components of a directed graph including the strongly connected one in particular the world wide web is a directed network the results are obtained for graphs with statistically uncorrelated vertices and an arbitrary joint in and out degree distribution p k i k o we show that if p k i k o does not factorize the relative size of the giant strongly connected component deviates from the product of the relative sizes of the giant in and out components the calculations of the relative sizes of all the giant components are demonstrated using the simplest examples we explain that the giant strongly connected component may be less resilient to random damage than the giant weakly connected one

lobby index as a network centrality measure we study the lobby index l index for short as a local node centrality measure for complex networks the l index is compared with degree a local measure betweenness and eigenvector centralities two global measures in the case of a biological network yeast interaction protein protein network and a linguistic network moby thesaurus ii in both networks the l index has a poor correlation with betweenness but correlates with degree and eigenvector centralities although being local the l index carries more information about its neighbors than degree centrality also it requires much less time to compute when compared with eigenvector centrality results show that the l index produces better results than degree and eigenvector centrality for ranking purposes

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

rational points of bounded height on fano varieties a prime pe7z let v be an algebraic variety defined over f and li a metrized line bundle on v i e a system l consisting of a line bundle l and a family of banach v adic metrics on l f for all v s satisfying well known conditions cf 1 chap vi then we can define a height function hl x f i r by the formula h x is x 1 where s is a local section of l non vanishing

on manin s conjecture for a family of châtelet surfaces the manin conjecture is established for ch telet surfaces over q arising as minimal proper smooth models of the surface y 2 z 2 f x where f is a totally reducible polynomial of degree 3 without repeated roots these surfaces do not satisfy weak approximation

descent on fibrations over the projective line we formulate a general set up for the descent method of j l colliot thelene and j j sansuc applied to varieties fibred over the projective line over a number field this makes it possible to prove that the manin obstruction to the hasse principle and weak approximation is the only one provided there are only few degenerate fibres usually two three in some cases and that sufficiently many smooth fc fibres satisfy the hasse principle and weak approximation we introduce a new concept of what should be called a degenerate fibre the so called split fibres the property which depends only on the generic fibre and not on the choice of a particular model this yields a simpler and more general approach to the previous results of that kind 0 introduction motivated by hasse s theorem on quadratic forms one says that the hasse principle holds for a family of geometrically integral smooth and proper varieties over a number field k9 if for every member of this family the existence of rational points over all the completions of k implies the existence of a rational point the fact that the hasse principle holds for some family signif icantly simplifies the study of its arithmetic because the problem of determining whether or not there is a rational point is then reduced to a finite number of

technical note on generating cutting planes from combinatorial disjunctions this paper develops a technique for generating deep valid inequalities based on combinatorial disjunctions that state that at least p out of some q p constraints must be satisfied this technique provides a general framework which subsumes existing methods for generating cutting planes based on such disjunctions it has potential applications for example in multiple choice and generalized lattice point programming problems including mixed integer zero one programming problems and the extreme point mathematical programming problem

counting rational points on quartic del pezzo surfaces with a rational conic upper and lower bounds of the expected order of magnitude are obtained for the number of rational points of bounded height on any quartic del pezzo surface over mathbb q that contains a conic defined over mathbb q

an algorithm for disjunctive programs abstract a disjunctive program is a linear program complicated by disjunctions that is sets of constraints of which at least one must be true the commonest example is the fixed cost problem in which either production of an item is zero or a fixed cost is incurred the conventional solution technique is to re express each disjunction in terms of binary variables and solve the resulting mixed integer program this paper demonstrates that this re expression is unnecessary it is possible and usually advantageous to arbitrate on the logical relationships amongst constraints themselves the advantages include easier matrix generation smaller nodal problems and the availability of good arbitration criteria an example is given and computational results are summarized

thesaurus as a complex network abstract a thesaurus is one out of many possible representations of term or word connectivity the terms of a thesaurus are seen as the nodes and their relationship as the links of a directed graph the directionality of the links retains all the thesaurus information and allows the measurement of several quantities this has lead to a new term classification according to the characteristics of the nodes for example nodes with no links in no links out etc using an electronic available thesaurus we have obtained the incoming and outgoing link distributions while the incoming link distribution follows a stretched exponential function the lower bound for the outgoing link distribution has the same envelope of the scientific paper citation distribution proposed by tsallis and albuquerque eur phys j b 13 2000 777 however a better fit is obtained by simpler function which is the solution of ricatti s differential equation we conjecture that this differential equation is the continuous limit of a stochastic growth model of the thesaurus network we also propose a new manner to arrange a thesaurus using the inversion method