Dynamical systems of type (m,n) and their C*-algebras

Given positive integers n and m, we consider dynamical systems in which n copies of a topological space is homeomorphic to m copies of that same space. The universal such system is shown to arise naturally from the study of a C*-algebra we denote by Om;n, which in turn is obtained as a quotient of the well known Leavitt C*-algebra Lm;n, a process meant to transform the generating set of partial isometries of Lm;n into a tame set. Describing Om;n as the crossed-product of the universal (m; n) -dynamical system by a partial action of the free group Fm+n, we show that Om;n is not exact when n and m are both greater than or equal to 2, but the corresponding reduced crossed-product, denoted Or m;n, is shown to be exact and non-nuclear. Still under the assumption that m; n &= 2, we prove that the partial action of Fm+n is topologically free and that Or m;n satisfies property (SP) (small projections). We also show that Or m;n admits no finite dimensional representations. The techniques developed to treat this system include several new results pertaining to the theory of Fell bundles over discrete groups.

The generator problem for Z-stable C*-algebras

The generator problem was posed by Kadison in 1967, and it remains open until today. We provide a solution for the class of C*-algebras absorbing the Jiang-Su algebra Z tensorially. More precisely, we show that every unital, separable, Z-stable C*-algebra A is singly generated, which means that there exists an element x є A that is not contained in any proper sub-C*- algebra of A. To give applications of our result, we observe that Z can be embedded into the reduced group C*-algebra of a discrete group that contains a non-cyclic, free subgroup. It follows that certain tensor products with reduced group C*-algebras are singly generated. In particular, C*r (F ∞) ⨂ C*r (F ∞) is singly generated.

Analogs of Cuntz algebras on Lp-spaces

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Contribution to Asterisk Open Source Project

With this final master thesis we are going to contribute to the Asterisk open source project. Asterisk is an open source project that started with the main objective of develop an IP telephony platform, completely based on Software (so not hardware dependent) and under an open license like GPL. This project was started on 1999 by the software engineer Mark Spencer at Digium. The main motivation of that open source project was that the telecommunications sector is lack of open solutions, and most of the available solutions are based on proprietary standards, which are close and not compatible between them. Behind the Asterisk project there is a company, Digum, which is the project leading since the project was originated in its laboratories. This company has some of its employees fully dedicated to contribute to the Asterisk project, and also provide the whole infrastructure required by the open source project. But the business of Digium isn't based on licensing of products due to the open source nature of Asterisk, but it's based on offering services around Asteriskand designing and selling some hardware components to be used with Asterisk. The Asterisk project has grown up a lot since its birth, offering in its latest versions advanced functionalities for managing calls and compatibility with some hardware that previously was exclusive of proprietary solutions. Due to that, Asterisk is becoming a serious alternative to all these proprietaries solutions because it has reached a level of maturity that makes it very stable. In addition, as it is open source, it can be fully customized to a givenrequirement, which could be impossible with the proprietaries solutions. Due to the bigness that is reaching the project, every day there are more companies which develop value added software for telephony platforms, that are seriously evaluating the option of make their software fully compatible withAsterisk platforms. All these factors make Asterisk being a consolidated project but in constant evolution, trying to offer all those functionalities offered by proprietaries solutions. This final master thesis will be divided mainly in two blocks totally complementaries. In the first block we will analyze Asterisk as an open source project and Asterisk as a telephony platform (PBX). As a result of this analysis we will generate a document, written in English because it is Asterisk project's official language, which could be used by future contributors as an starting point on joining Asterisk. On the second block we will proceed with a development contribution to the Asterisk project. We will have several options in the form that we do the contribution, such as solving bugs, developing new functionalities or start an Asterisk satellite project. The type of contribution will depend on the needs of the project on that moment.

Aplicación de gestión de ficheros de configuración de Asterisk : Conexión de Asterisk con Google App corportativo

El objetivo de este trabajo es desarrollar una aplicación web que sirva de gestión de los aparatos conectados a la centralita Asterisk y generar los ficheros de configuración, tanto para los terminales como para el correcto funcionamiento de la centralita. Además, se instalará un servidor que conecte centralita y Google Apps para que los usuarios puedan usar el videochat de Gmail como softphone, permitiéndoles enviar y recibir llamadas a través de la centralita de la universidad en cualquier parte del mundo.

Operator algebras: an informal overview

This article is an informal introduction to some classical results of the theory of operator algebras. It aims to illustrate the richness and diversity of possible applications of this topic.

Tecnologia VOIP com Asterisk (UM@STERISK)

Este trabalho trata do software livre Asterisk (Elastix), uma central telefónica privada IP ou (PBX IP) que suporta inúmeros protocolos e codecs da tecnologia de voz sobre IP, Abordando a sua instalação, configuração e compatibilidade com hardware de telefonia. O crescimento das redes IP, as técnicas avançadas de digitalização de voz e os mecanismos que permitem a qualidade dos serviços, permitiram a consolidação da telefonia IP. A telefonia IP está em todo-poderoso crescimento, pois além de reduzir os custos das ligações telefónicas, ela permite a ligação entre as redes de dados e de voz, criando uma infra-estrutura única, facilitando a instalação, a manutenção e o gerenciamento. Este trabalho tem como objetivo fazer um estudo da Tecnologia VoIP (Voz sob IP), propor uma estrutura e implementar um ambiente de teste, uma central telefónica VoIP com o uso do Asterisk. A central telefónica VoIP baseada no software livre Asterisk possibilita a interligação de localidades geograficamente distantes uma das outras através das redes IP, sem a necessidade de pagar os altos valores cobrados pelos fabricantes de centrais telefónicas, de hardware proprietário, pela manutenção, fornecimento de equipamentos e licenças, mas permite que se obtenha os mesmos resultados, como por exemplo, que todos os Funcionários e ou colaboradores de uma empresa realizem chamadas telefónicas entre si sem precisar pagar altas taxas cobradas pelas operadoras de telefonia pública. Através da pesquisa bibliográfica sobre a tecnologia VoIP e do estudo do software livre Asterisk, será proposta a implantação da tecnologia através da implementação de um central VoIP. A verificação dessa implantação será realizada através de testes práticos em um ambiente que será desenvolvido.

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defind by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincare-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

On the depth of blowup algebras of ideals with analytic deviation one

Let I be an ideal in a local Cohen-Macaulay ring (A, m). Assume I to be generically a complete intersection of positive height. We compute the depth of the Rees algebra and the form ring of I when the analytic deviation of I equals one and its reduction number is also at most one. The formu- las we obtain coincide with the already known formulas for almost complete intersection ideals.

Newton-Hooke algebras, nonrelativistic branes, and generalized pp-wave metrics

The Newton-Hooke algebras in d dimensions are constructed as contractions of dS(AdS) algebras. Nonrelativistic brane actions are WZ terms of these Newton-Hooke algebras. The NH algebras appear also as subalgebras of multitemporal relativistic conformal algebras, SO(d+1,p+2). We construct generalizations of pp-wave metrics from these algebras.

Implantación de un sistema VoIP basado en software libre con Asterisk

Este proyecto busca analizar, diseñar e implementar una nueva solución de telefonía para el Centro Social de Oficiales de la Policía Nacional contemplando la posibilidad de optar por una migración hacia un sistema VoIP bajo software libre con Asterisk. En consecuencia, se deben evaluar las tecnologías actuales buscando proveer nuevas funcionalidades en el servicio telefónico generando bajos costos en su implementación, funcionamiento y mantenimiento.

Generating finite integral relation algebras

Relation algebras and categories of relations in particular have proven to be extremely useful as a fundamental tool in mathematics and computer science. Since relation algebras are Boolean algebras with some well-behaved operations, every such algebra provides an atom structure, i.e., a relational structure on its set of atoms. In the case of complete and atomic structure (e.g. finite algebras), the original algebra can be recovered from its atom structure by using the complex algebra construction. This gives a representation of relation algebras as the complex algebra of a certain relational structure. This property is of particular interest because storing the atom structure requires less space than the entire algebra. In this thesis I want to introduce and implement three structures representing atom structures of integral heterogeneous relation algebras, i.e., categorical versions of relation algebras. The first structure will simply embed a homogeneous atom structure of a relation algebra into the heterogeneous context. The second structure is obtained by splitting all symmetric idempotent relations. This new algebra is in almost all cases an heterogeneous structure having more objects than the original one. Finally, I will define two different union operations to combine two algebras into a single one.

Generating Relation Algebras for Qualitative Spatial Reasoning

Basic relationships between certain regions of space are formulated in natural language in everyday situations. For example, a customer specifies the outline of his future home to the architect by indicating which rooms should be close to each other. Qualitative spatial reasoning as an area of artificial intelligence tries to develop a theory of space based on similar notions. In formal ontology and in ontological computer science, mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts. We shall introduce abstract relation algebras and present their structural properties as well as their connection to algebras of binary relations. This will be followed by details of the expressiveness of algebras of relations for region based models. Mereotopology has been the main basis for most region based theories of space. Since its earliest inception many theories have been proposed for mereotopology in artificial intelligence among which Region Connection Calculus is most prominent. The expressiveness of the region connection calculus in relational logic is far greater than its original eight base relations might suggest. In the thesis we formulate ways to automatically generate representable relation algebras using spatial data based on region connection calculus. The generation of new algebras is a two pronged approach involving splitting of existing relations to form new algebras and refinement of such newly generated algebras. We present an implementation of a system for automating aforementioned steps and provide an effective and convenient interface to define new spatial relations and generate representable relational algebras.