On the efficiency of data representation on the modeling and characterization of complex networks

Specific choices about how to represent complex networks can have a substantial impact on the execution time required for the respective construction and analysis of those structures. In this work we report a comparison of the effects of representing complex networks statically by adjacency matrices or dynamically by adjacency lists. Three theoretical models of complex networks are considered: two types of Erdos-Renyi as well as the Barabasi-Albert model. We investigated the effect of the different representations with respect to the construction and measurement of several topological properties (i.e. degree, clustering coefficient, shortest path length, and betweenness centrality). We found that different forms of representation generally have a substantial effect on the execution time, with the sparse representation frequently resulting in remarkably superior performance. (C) 2011 Elsevier B.V. All rights reserved.

Identifying the borders of mathematical knowledge

Based on a divide and conquer approach, knowledge about nature has been organized into a set of interrelated facts, allowing a natural representation in terms of graphs: each `chunk` of knowledge corresponds to a node, while relationships between such chunks are expressed as edges. This organization becomes particularly clear in the case of mathematical theorems, with their intense cross-implications and relationships. We have derived a web of mathematical theorems from Wikipedia and, thanks to the powerful concept of entropy, identified its more central and frontier elements. Our results also suggest that the central nodes are the oldest theorems, while the frontier nodes are those recently added to the network. The network communities have also been identified, allowing further insights about the organization of this network, such as its highly modular structure.

Limit theorems for sequences of random trees

We consider a random tree and introduce a metric in the space of trees to define the ""mean tree"" as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we have laws of large numbers and central limit theorems for sequence of independent identically distributed random trees. As application we propose tests to check if two samples of random trees have the same law.

Matrix Representation of the Stationary Measure for the Multispecies TASEP

In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product formulation and the queueing theory picture of Ferrari and Martin. In particular, in the standard representation, the matrices act on the space of queue lengths. For N > 2 the matrices in fact become tensor products of elements of quadratic algebras. This enables us to give a purely algebraic proof of the stationary measure which we present for N=3.

Rigidity theorems for complete spacelike hypersurfaces with constant scalar curvature in De Sitter space

In this paper we give a partially affirmative answer to the following question posed by Haizhong Li: is a complete spacelike hypersurface in De Sitter space S(1)(n+1)(c), n >= 3, with constant normalized scalar curvature R satisfying n-2/nc <= R <= c totally umbilical? (C) 2008 Elsevier B.V. All rights reserved.

A family of Schroeder-Bernstein type theorems for Banach spaces

Motivated by a characterization of the complemented subspaces in Banach spaces X isomorphic to their squares X-2, we introduce the concept of P-complemented subspaces in Banach spaces. In this way, the well-known Pelczynski`s decomposition method can be seen as a Schroeder-Bernstein type theorem. Then, we give a complete description of the Schroeder-Bernstein type theorems for this new notion of complementability. By contrast, some very elementary questions on P-complementability are refinements of the Square-Cube Problem closely connected with some Banach spaces introduced by W.T. Gowers and B. Maurey in 1997. (C) 2007 Elsevier Inc. All rights reserved.

Some Schroeder-Bernstein type theorems for Banach spaces

We first introduce the notion of (p, q, r)-complemented subspaces in Banach spaces, where p, q, r is an element of N. Then, given a couple of triples {(p, q, r), (s, t, u)} in N and putting Lambda = (q + r - p)(t + u - s) - ru, we prove partially the following conjecture: For every pair of Banach spaces X and Y such that X is (p, q, r)-complemented in Y and Y is (s, t, u)-complemented in X, we have that X is isomorphic Y if and only if one of the following conditions holds: (a) Lambda not equal 0, Lambda divides p - q and s - t, p = 1 or q = 1 or s = 1 or t = 1. (b) p = q = s = t = 1 and gcd(r, u) = 1. The case {(2, 1, 1), (2, 1,1)} is the well-known Pelczynski`s decomposition method. Our result leads naturally to some generalizations of the Schroeder-B em stein problem for Banach spaces solved by W.T. Gowers in 1996. (C) 2007 Elsevier Inc. All rights reserved.

Representation type of Jordan algebras

The problem of classification of Jordan bit-nodules over (non-semisimple) finite dimensional Jordan algebras with respect to their representation type is considered. The notions of diagram of a Jordan algebra and of Jordan tensor algebra of a bimodule are introduced and a mapping Qui is constructed which associates to the diagram of a Jordan algebra J the quiver of its universal associative enveloping algebra S(J). The main results are concerned with Jordan algebras of semi-matrix type, that is, algebras whose semi-simple component is a direct sum of Jordan matrix algebras. In this case, criterion of finiteness and tameness for one-sided representations are obtained, in terms of diagram and mapping Qui, for Jordan tensor algebras and for algebras with radical square equals to 0. (c) 2010 Elsevier Inc. All rights reserved.

Landskommunens beslutsfattande kvinnor : Om kvinnors representation i kommunalfullmäktige ochförekomst i fullmäktigeprotokoll i Kalmar länslandskommuner 1939-1951

Syftet med denna uppsats är att undersöka den kvinnliga representationen i Kalmar läns landskommuners kommunalfullmäktige från 1938 till kommunsammanslagningen 1951. Detta innefattar att söka en översikt över i vilken grad kvinnor är representerade i länets kommunalfullmäktigeförsamlingaroch att undersöka hur dessa kvinnliga ledamöter syns i protokollsmaterial i ett par kommuners fullmäktigeprotokoll. Södra Möckelby och Vickleby kommuner med relativt hög andel kvinnliga ledamöter har valts som exempel.Undersökningen av valstatistiken visar en ökning i både antal kvinnor och antal kommunalfullmäktige med kvinnlig representation under perioden. Länet ligger under riksgenomsnittet, men ökningen är ungefär densamma i relativa termer. Närläsningen av protokoll visar att kvinnor främst omnämns vid frånvaro, vid val till olika uppdrag eller vid uppföljning av dessa val. I den kommun som har en längre tradition av relativt hög kvinnlig representation märks kvinnor i fler sammanhang som förutsätter att man tar ett större utrymme på mötena. Dessa tillfällen sammanfaller med en speciell kvinnas aktiva period i fullmäktige och försvinner när den kvinnliga representationen minskar till en ensam kvinna.

La confrontation de la laideur avec la beauté dans lesromans Mercure et Attentat. Une étude sur lareprésentation de la dualité thématique laideur-beautéchez Amélie Nothomb. : "Where there is Quasimodo, there is also Esmeralda." The confrontationbetween ugliness and beauty in the novels Mercure and Attentat. Astudy on the representation of the duality beauty-ugliness in the worksof Amélie Nothomb.

This paper studies one of the recurrent topics of writing found in Amélie Nothomb’snovels: beauty and ugliness. The novels Mercure and Attentat are analyzed in detail,with respect to figures of speech used to describe the extreme physical appearance ofthe protagonists and the role of the duality beauty-ugliness in the advancement of theplot.

Representation and interpretation : textbooks, teachers, and historical culture

This article presents a study of how contemporary Swedish lower secondary school textbooks present the emergence of the Cold War and how 10 active lower secondary school history teachers interpreted a quotation that was ambiguous in relation to the general narrative in the studied Swedish textbooks, seeking to analyse textbooks both from the perspectives of content and reception. Applying a theoretical framework of uses of history, the study finds that the narratives presented in the studied textbooks are what could be called traditional in the sense that they do not acknowledge perspective and representation in history. While the interviewed teachers generally acknowledged that textbook narratives are representations of history and contingent on perspective, few teachers extended this to include how their own views affect their interpretations, suggesting an intermediary appreciation of the contextual contingency of historical narratives.

Representations of culture in EIL : Cultural representation in Swedish EFL textbooks

The English language has become an international language and is globally used as a lingua franca. Therefore, there has been a shift in English-language education toward teaching English as an interna-tional language (EIL). Teaching from the EIL paradigm means that English is seen as an international language used in communication by people from different linguistic and cultural backgrounds. As the approach to English-language education changes from the traditional native-speaker, target country context, so does the role of culture within English-language teaching. The aim of this thesis is to in-vestigate and analyse cultural representations in two Swedish EFL textbooks used in upper-secondary school to see how they correspond with the EIL paradigm. This is done by focusing on the geograph-ical origin of the cultural content as well as looking at what kinds of culture are represented in the textbooks. A content analysis of the textbooks is conducted, using Kachru’s Concentric Circles of English as the model for the analysis of the geographical origin. Horibe’s model of the three different kinds of culture in EIL is the model used for coding the second part of the analysis. The results of the analysis show that culture of target countries and "Culture as social custom" dominate the cultural content of the textbook. Thus, although there are some indications that the EIL paradigm has influ-enced the textbooks, the traditional approach to culture in language teaching still prevails in the ana-lysed textbooks. Because of the relatively small sample included in the thesis, further studies need to be conducted in order to make conclusions regarding the Swedish context as a whole.

All maximal-pairs in step-leap representation of melodic sequence

This paper proposes an efficient pattern extraction algorithm that can be applied on melodic sequences that are represented as strings of abstract intervallic symbols; the melodic representation introduces special “binary don’t care” symbols for intervals that may belong to two partially overlapping intervallic categories. As a special case the well established “step–leap” representation is examined. In the step–leap representation, each melodic diatonic interval is classified as a step (±s), a leap (±l) or a unison (u). Binary don’t care symbols are used to represent the possible overlapping between the various abstract categories e.g. *=s, *=l and #=-s, #=-l. We propose an O(n+d(n-d)+z)-time algorithm for computing all maximal-pairs in a given sequence x=x[1..n], where x contains d occurrences of binary don’t cares and z is the number of reported maximal-pairs.