Axially Symmetric Post-Newtonian Stellar Systems

We introduce a method to obtain self-consistent, axially symmetric, thin disklike stellar models in the first post-Newtonian (1PN) approximation. The models obtained are fully analytical and corresponds to the post-Newtonian generalizations of classical ones. By introducing in the field equations provided by the 1PN approximation a known distribution function (DF) corresponding to a Newtonian model, two fundamental equations determining the 1PN corrections are obtained, which are solved using the Hunter method. The rotation curves of the 1PN-corrected models differs from the classical ones and, for the generalized Kalnajs discs, the 1PN corrections are clearly appreciable with values of the mass and radius of a typical galaxy. On the other hand, the relativistic mass correction can be ignored for all models.Comment: 13 pages, 4 figures, to be published at Rev.Integr.Temas Ma

Text authorship identified using the dynamics of word co-occurrence networks

The identification of authorship in disputed documents still requires human expertise, which is now unfeasible for many tasks owing to the large volumes of text and authors in practical applications. In this study, we introduce a methodology based on the dynamics of word co-occurrence networks representing written texts to classify a corpus of 80 texts by 8 authors. The texts were divided into sections with equal number of linguistic tokens, from which time series were created for 12 topological metrics. The series were proven to be stationary (p-value>0.05), which permits to use distribution moments as learning attributes. With an optimized supervised learning procedure using a Radial Basis Function Network, 68 out of 80 texts were correctly classified, i.e. a remarkable 85% author matching success rate. Therefore, fluctuations in purely dynamic network metrics were found to characterize authorship, thus opening the way for the description of texts in terms of small evolving networks. Moreover, the approach introduced allows for comparison of texts with diverse characteristics in a simple, fast fashion

Network features for authorship attribution

O reconhecimento de autoria é uma área de pesquisa efervescente, com muitas aplicações, incluindo detecção de plágio, análise de textos históricos, reconhecimento de mensagens terroristas ou falsificação de documentos. Modelos teóricos de redes complexas já são usados para o reconhecimento de autoria, mas alguns aspectos importantes têm sido ignorados. Neste trabalho, exploramos a dinâmica de redes de co-ocorrência e a relação com as palavras que representam os nós e descobrimos que ambas são claras assinaturas de autoria. Com otimização dos descritores da topologia das redes e de algoritmos de aprendizado de máquina, foi possível obter taxas de acerto maiores que 85%, sendo atingida uma taxa de 98.75% em um caso específico, para coleções de 80 livros, cada uma compilada de 8 autores de língua inglesa com 10 livros por autor. Esta tese demonstra que existem ainda aspectos inexplorados das redes de co-ocorrência de textos, o que deve permitir avanços ainda maiores no futuro próximo.Authorship attribution is an active research area with many applications, including detection of plagiarism, analysis of historical texts, terrorist message identification or document falsification. Theoretical models of complex networks are already used for authorship attribution, but some issues have been ignored. In this thesis, we explore the dynamics of co-occurrence networks and the role of words, and found that they are both clear signatures of authorship. Using optimized descriptors for the network topology and machine learning algorithms, it has been possible to achieve accuracy rates above 85%, with a rate of 98.75% being reached in a particular case, for collections of 80 books produced by 8 English-speaking writers with 10 books per author. It is also shown that there are still many unexplored aspects of co-occurrence networks of texts, which seems promising for near future developments

Avalanches and complex networks in Kinouchi-Copelli model

A capacidade de um sistema sensorial detectar estímulos eficientemente é tradicionalmente dimensionada pela faixa dinâmica, que é simplesmente uma medida da extensão do intervalo de intensidades de estímulo para as quais a rede é suficientemente sensível. Muitas vezes, sistemas biológicos exibem largas faixas dinâmicas, que abrangem diversas ordens de magnitude. A compreensão desse fenômeno não é trivial, haja vista que todos os neurônios apresentam janelas de sensibilidade muito estreitas. Tentativas de explicação baseadas em argumentos de recrutamento sequencial dos neurônios sensoriais, com efeitos essencialmente aditivos, simplesmente não são realísticas, haja vista que seria preciso que os limiares de ativação das unidades também apresentassem um escalonamento por várias ordens de magnitude, para cobrir a faixa dinâmica empiricamente observada em nível macroscópico. Notavelmente, o modelo Kinouchi-Copelli (KC), que carrega o nome de seus idealizadores, mostrou que aquele comportamento pode ser um efeito coletivo (não aditivo) do conjunto de neurônios sensoriais. O modelo KC é uma rede de unidades excitáveis com dinâmicas estocásticas e acoplados segundo uma topologia de grafo aleatório. Kinouchi e Copelli mostraram que a taxa espontânea de disparo dos neurônios (ou atividade média) sinaliza uma transição de fase fora do equilíbrio do tipo ordem-desordem, e que exatamente no ponto crítico desta transição (em termos de um parâmetro ligado às características estruturais da rede) a sensibilidade a estímulos externos é máxima, ou seja, a faixa dinâmica exibe uma otimização crítica. Neste trabalho, investigamos como o ponto crítico depende da topologia, utilizando os modelos mais comuns das chamadas redes complexas. Além disso, estudamos computacionalmente os padrões de atividade (avalanches neuronais) exibidos pelo modelo, com especial atenção às mudanças qualitativas de comportamento devido às mudanças de topologia. Comentaremos também a relação desses resultados com experimentos recentes de monitoramento de dinâmicas neurais.The capacity of a sensory system in efficiently detecting stimuli is usually given by the dynamic range, a simple measure of the range of stimulus intensity over which the network is sensible enough. Many times biological systems exhibit large dynamic ranges, covering many orders of magnitude. There is no easy explanation for that, since individual neurons present very short dynamic ranges isolatedly. Arguments based on sequential recruitment are doomed to failure since the corresponding arrangement of the limiar thresholds of the units over many orders of magnitude is unrealistic. Notably the so-called Kinouchi-Copelli (KC) model strongly suggested that large dynamic range should be a collective effect of the sensory neurons. The KC model is a network of stochastic excitable elements coupled as a random graph. KC showed the spontaneous activity of the network signals an order-disorder nonequilibrium phase transition and that the dynamic range exhibits an optimum precisely at the critical point (in terms of a control parameter related to structural properties of the network). In this work, we investigate how the critical point depends on the topology, considering the alternatives among the standard complex networks. We also study the burts of activity (neuronal avalanches) exhibited by the model, focusing on the qualitative changes due to alternative topologies. Finally we comment on possible connections among our results and recent observations of neural dynamics

Validation and visualization of complex network measurements.

<p>(a) Validation of the classification without dimensionality reduction (red), and with feature extraction using PCA (green) and Isomap (blue). (b) Reduction to two-dimensional attribute space using Isomap. Each point represents a book and each color represents an author.</p

Time series for Moby Dick by Herman Melville.

<p>The horizontal axis denotes the index of realizations, and the vertical axis brings the base 10 logarithm of the metrics identified in the inset.</p

Example of co-occurrence network.

<p>The network was obtained for the text “<i>It was the best of times; it was the worst of times; it was the age of wisdom; it was the age of foolishness</i>”, which is an extract from the book “A Tale of Two Cities”, by Charles Dickens. Note that, after the removal of stopwords (such as “it” and “was”) and lemmatization process (“times” is mapped to “time”), the remaining words are linked if they are adjacent.</p

Success scores and combinations of attributes using the variance threshold and score-based feature selection.

<p>In (a), (b) the maximum values with minimum number of attributes are marked with circles. In (c), (d) for each network metric (represented by a label in the horizontal axis) the four first moments are presented in increasing order from left to right. A black cell indicates that the attribute is present in the combination. For the variance threshold feature selection, there is a unique combination for every threshold denoted by the vertical axis in (c). For instance, thresholds for the four maximum scores in (a) are marked in (c) by the four dashed horizontal lines. For the score-based feature selection there can be multiple combinations of attributes with the same number of attributes and the same score. Only the combinations with maximum scores and marked with circles in (b) are presented in (d); for KNN algorithm there were two combinations with maximum score.</p

Autocorrelation and histograms for Moby Dick.

<p>(a) Autocorrelation for the series of clustering coefficient of Moby Dick by Herman Melville. Dashed lines mark the 5% threshold which is surpassed only by chance. (b) Histograms for time series of degree <i>K</i> (connectivity) from all books on the collection grouped by author. The distributions have characteristic moments for each author.</p