Radio interferometric gain calibration as a complex optimization problem

Recent developments in optimization theory have extended some traditional algorithms for least-squares optimization of real-valued functions (Gauss-Newton, Levenberg-Marquardt, etc.) into the domain of complex functions of a complex variable. This employs a formalism called the Wirtinger derivative, and derives a full-complex Jacobian counterpart to the conventional real Jacobian. We apply these developments to the problem of radio interferometric gain calibration, and show how the general complex Jacobian formalism, when combined with conventional optimization approaches, yields a whole new family of calibration algorithms, including those for the polarized and direction-dependent gain regime. We further extend the Wirtinger calculus to an operator-based matrix calculus for describing the polarized calibration regime. Using approximate matrix inversion results in computationally efficient implementations; we show that some recently proposed calibration algorithms such as StefCal and peeling can be understood as special cases of this, and place them in the context of the general formalism. Finally, we present an implementation and some applied results of CohJones, another specialized direction-dependent calibration algorithm derived from the formalism.Comment: 18 pages; 6 figures; accepted by MNRA

Genetic similarity promotes evolution of cooperation under lethal intergroup competition

Altruism (helping others at a cost to oneself) may evolve via group selection if the cost of altruism to the individual is compensated for by growth differences among groups when (1) there is high genetic variation among members of different groups; (2) more altruistic groups grow faster and (3) between-group migration is low. Nevertheless, group selection may not fully explain the actual evolution of helping behaviour if between-group migration was sufficiently common to have reduced between-group genetic variance. Lethal intergroup competition, which amplifies such growth differences between groups, appears to have been frequent in humans'; ancestral environments and could bear importantly on the evolution of altruism. Here we show that between-group migration and resulting genetic similarity can promote the evolution of costly helping behavior in the context of lethal intergroup conflict, albeit by selection at the individual level and not by group selection. The standard group selection models do not capture such basic elements of lethal intergroup competition as the possibility of an individual's altruism being critical to the group's success when that possibility is inversely proportional to genetic variation among members of the competing groups

Weyl images of Kantor pairs

Kantor pairs arise naturally in the study of 5-graded Lie algebras. In this article, we begin the study of simple Kantor pairs of arbitrary dimension. We introduce Weyl images of Kantor pairs and use them to construct examples of Kantor pairs including a new class of central simple Kantor pairs.Comment: 43 pages. In the last section of this new version, the assumption that the ring of scalars is a field is dropped. This allows the construction of many forms of split Kantor pairs of type $E_6$ over rings. To facilitate this change, some small revisions are made in earlier sections. To be published in the Canadian Journal of Mathematic

Workings of the Melting Pot: Social Networks and the Evolution of Population Attributes

This paper links the two nascent economic literatures on social networks and cultural assimilation by investigating the evolution of population attributes in a simple model where agents are influenced by their acquaintances. The main conclusion of the analysis is that attributes converge to a melting-pot equilibrium, where everyone is identical, provided the social network exhibits a sufficient degree of interconnectedness. When the model is extended to allow an expanding acquaintance set, convergence is guaranteed provided a weaker interconnectedness condition is satisfied, and convergence is rapid. If the intensity of interactions with acquaintances becomes endogenous, convergence (when it occurs) is slowed when agents prefer to interact with people like themselves and hastened when interaction with dissimilar agents is preferred.melting pot, social networks, cultural assimilation, population attributes

Context-Equivalence of Algebras with Involutions.

Conferencia CientíficaMorita equivalence is the central concept of celebrated Morita theory. Two algebras are Morita equivalent if their categories of modules are equivalent. A Morita context is a useful technical concept that allows one to establish Morita equivalence. Based on this concept B. Muller introduced the notion of context-equivalence in 1972. Later S. A. Amitsur showed that although the context-equivalence is coarser than Morita equivalence, many algebraic properties are still invariant relative to this new equivalence. In this talk we will we will present a version of context-equivalence suitable for the category of algebras with involution. The main result is a criterion of context-equivalence of such algebras.Departamento de Álgebra, Geometría y Topología. Facultad de Ciencias, Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech