From Spinor Geometry to Complex General Relativity

An attempt is made of giving a self-contained (although incomplete) introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, two-component spinor calculus, conformal gravity, alpha-planes in Minkowski space-time, alpha-surfaces and twistor geometry, anti-self-dual space-times and Penrose transform, spin-3/2 potentials, heaven spaces and heavenly equations.Comment: With kind permission from Springer Science and Business Media to use material in the first 5 sections taken from the 1995 Kluwer book "Complex General Relativity" by G. Esposito. In the revised version, 11 References have been adde

Non-Boolean almost perfect nonlinear functions on non-Abelian groups

The purpose of this paper is to present the extended definitions and characterizations of the classical notions of APN and maximum nonlinear Boolean functions to deal with the case of mappings from a finite group K to another one N with the possibility that one or both groups are non-Abelian.Comment: 17 page

Competitive dynamics of lexical innovations in multi-layer networks

We study the introduction of lexical innovations into a community of language users. Lexical innovations, i.e., new terms added to people's vocabulary, play an important role in the process of language evolution. Nowadays, information is spread through a variety of networks, including, among others, online and offline social networks and the World Wide Web. The entire system, comprising networks of different nature, can be represented as a multi-layer network. In this context, lexical innovations diffusion occurs in a peculiar fashion. In particular, a lexical innovation can undergo three different processes: its original meaning is accepted; its meaning can be changed or misunderstood (e.g., when not properly explained), hence more than one meaning can emerge in the population; lastly, in the case of a loan word, it can be translated into the population language (i.e., defining a new lexical innovation or using a synonym) or into a dialect spoken by part of the population. Therefore, lexical innovations cannot be considered simply as information. We develop a model for analyzing this scenario using a multi-layer network comprising a social network and a media network. The latter represents the set of all information systems of a society, e.g., television, the World Wide Web and radio. Furthermore, we identify temporal directed edges between the nodes of these two networks. In particular, at each time step, nodes of the media network can be connected to randomly chosen nodes of the social network and vice versa. In so doing, information spreads through the whole system and people can share a lexical innovation with their neighbors or, in the event they work as reporters, by using media nodes. Lastly, we use the concept of "linguistic sign" to model lexical innovations, showing its fundamental role in the study of these dynamics. Many numerical simulations have been performed.Comment: 23 pages, 19 figures, 1 tabl

Eigenvector localization as a tool to study small communities in online social networks

We present and discuss a mathematical procedure for identification of small "communities" or segments within large bipartite networks. The procedure is based on spectral analysis of the matrix encoding network structure. The principal tool here is localization of eigenvectors of the matrix, by means of which the relevant network segments become visible. We exemplified our approach by analyzing the data related to product reviewing on Amazon.com. We found several segments, a kind of hybrid communities of densely interlinked reviewers and products, which we were able to meaningfully interpret in terms of the type and thematic categorization of reviewed items. The method provides a complementary approach to other ways of community detection, typically aiming at identification of large network modules

Examination of Eco-Behavioral Assessments Designed for Understanding Complex Behaviors and Environments.

Second-generation intervention research requires methods for overcoming challenges to understanding complex learning ecologies and interactions of students. Eco-behavioral assessments (EBAs) are one solution to past intervention research challenges. EBAs record the effects of ecological variables in students’ behavior and daily interactions. The utility of EBAs in second-generation research has increased substantially. Numerous EBAs now exist for use with all ages of learners and provide a valid, reliable, and cost effective method for intervention research. This paper examines 18 EBAs as well as software systems designed to support and enhance the use of EBAs. The examination serves as a comprehensive resource to better understand how EBAs can be used in answering complex questions about students’ learning and for advancing second-generation research

The chiral and flavour projection of Dirac-Kahler fermions in the geometric discretization

It is shown that an exact chiral symmetry can be described for Dirac-Kahler fermions using the two complexes of the geometric discretization. This principle is extended to describe exact flavour projection and it is shown that this necessitates the introduction of a new operator and two new structures of complex. To describe simultaneous chiral and flavour projection, eight complexes are needed in all and it is shown that projection leaves a single flavour of chiral field on each.Comment: v2: 17 pages, Latex. 5 images eps. Added references, reformatted and clarification of some point

Neutral Massive Spin 1/2 Particles Emission in a Rindler Spacetime

The Unruh effect for the rate of emission and absorption of neutral massive Majorana spinor particles -- the most plausible consituents of Dark Matter -- in a Rindler spacetime is thoroughly investigated. The corresponding Bogolyubov coefficients are explicitly calculated and the consistency with Fermi-Dirac statistics and the Pauli principle is actually verified.Comment: v2: clarifications added to Introduction and Conclusions, added appendices; v3 removed review part, published versio