Clifford Valued Differential Forms, and Some Issues in Gravitation, Electromagnetism and 'Unified' Theories

In this paper we show how to describe the general theory of a linear metric compatible connection with the theory of Clifford valued differential forms. This is done by realizing that for each spacetime point the Lie algebra of Clifford bivectors is isomorphic to the Lie algebra of Sl(2,C). In that way the pullback of the linear connection under a local trivialization of the bundle (i.e., a choice of gauge) is represented by a Clifford valued 1-form. That observation makes it possible to realize immediately that Einstein's gravitational theory can be formulated in a way which is similar to a Sl(2,C) gauge theory. Such a theory is compared with other interesting mathematical formulations of Einstein's theory. and particularly with a supposedly "unified" field theory of gravitation and electromagnetism proposed by M. Sachs. We show that his identification of Maxwell equations within his formalism is not a valid one. Also, taking profit of the mathematical methods introduced in the paper we investigate a very polemical issue in Einstein gravitational theory, namely the problem of the 'energy-momentum' conservation. We show that many statements appearing in the literature are confusing or even wrong.Comment: Misprints and errors in some equations of the printed version have been correcte

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