Unsharp Values, Domains and Topoi

The so-called topos approach provides a radical reformulation of quantum theory. Structurally, quantum theory in the topos formulation is very similar to classical physics. There is a state object, analogous to the state space of a classical system, and a quantity-value object, generalising the real numbers. Physical quantities are maps from the state object to the quantity-value object -- hence the `values' of physical quantities are not just real numbers in this formalism. Rather, they are families of real intervals, interpreted as `unsharp values'. We will motivate and explain these aspects of the topos approach and show that the structure of the quantity-value object can be analysed using tools from domain theory, a branch of order theory that originated in theoretical computer science. Moreover, the base category of the topos associated with a quantum system turns out to be a domain if the underlying von Neumann algebra is a matrix algebra. For general algebras, the base category still is a highly structured poset. This gives a connection between the topos approach, noncommutative operator algebras and domain theory. In an outlook, we present some early ideas on how domains may become useful in the search for new models of (quantum) space and space-time.Comment: 32 pages, no figures; to appear in Proceedings of Quantum Field Theory and Gravity, Regensburg (2010

Partial and Total Ideals of Von Neumann Algebras

A notion of partial ideal for an operator algebra is a weakening the notion of ideal where the defining algebraic conditions are enforced only in the commutative subalgebras. We show that, in a von Neumann algebra, the ultraweakly closed two-sided ideals, which we call total ideals, correspond to the unitarily invariant partial ideals. The result also admits an equivalent formulation in terms of central projections. We place this result in the context of an investigation into notions of spectrum of noncommutative $C^*$-algebras.Comment: 14 page

Partilha de informações como prevenção do Terrorismo: O estado das autoridades portuguesas

Projeto de Graduação apresentado à Universidade Fernando Pessoa como parte dos requisitos para a obtenção do grau de Licenciado em CriminologiaO fenómeno do terrorismo é um fenómeno bastante atual e cuja problemática apresenta efeitos colaterais de nível internacional, o que leva a que a melhor forma de o prevenir e combater tenha como base uma solução também ela internacional: a partilha de informações. Este trabalho consta da apresentação de um projeto de investigação que tem como objetivo recolher informações sobre os conhecimentos e a preparação das autoridades portuguesas em relação à problemática do terrorismo e à partilha de informações nesse âmbito. Outro objetivo este projeto pretende, com a informação recolhida, encontrar os pontos fracos na preparação das autoridades portuguesas e tornar possível a conceção de estratégias para o solucionamento destes problemas no futuro.The phenomenon of terrorism is a contemporary one, which presents collateral effects at an international level, making the best way to prevent/fight this problem international as well: intelligence sharing. This work presents an investigation project which has the objective of gathering intelligence about the knowledge and preparation of the Portuguese authorities towards the problematic of terrorism and information sharing about it. Another objective, this project wants, using the gathered information, to find the weak spots in the preparation of the Portuguese authorities and to make possible, in the future, the creation of strategies for the solution of those same weak spots

Experimentation with MANETs of Smartphones

Mobile AdHoc NETworks (MANETs) have been identified as a key emerging technology for scenarios in which IEEE 802.11 or cellular communications are either infeasible, inefficient, or cost-ineffective. Smartphones are the most adequate network nodes in many of these scenarios, but it is not straightforward to build a network with them. We extensively survey existing possibilities to build applications on top of ad-hoc smartphone networks for experimentation purposes, and introduce a taxonomy to classify them. We present AdHocDroid, an Android package that creates an IP-level MANET of (rooted) Android smartphones, and make it publicly available to the community. AdHocDroid supports standard TCP/IP applications, providing real smartphone IEEE 802.11 MANET and the capability to easily change the routing protocol. We tested our framework on several smartphones and a laptop. We validate the MANET running off-the-shelf applications, and reporting on experimental performance evaluation, including network metrics and battery discharge rate.Comment: 6 pages, 7 figures, 1 tabl

O acesso (unilateral e sem recurso a mecanismos de cooperação judiciária internacional) a dados armazenados em sistemas informáticos localizados no estrangeiro

The paper seeks to discuss, from a case (the United States v. Gorshkov-Ivanov case), whether (and, if so, to what extent) an access to data stored in computer systems located abroad may occur, more specifically unilaterally and outside the framework of resorting to international judicial cooperation mechanisms. Contrary to what is suggested by some Portuguese authors, in the paper it is sustained that the provision of Article 15(5) of the Portuguese Cybercrime Law cannot, in view of the Portuguese Constitution, be considered a sufficient enabling provision for this purpose and that the evidence obtained through this type of access may be considered invalid due to lack of a sufficient enabling provision and also in the context of the Portuguese constitutional system of prohibitions of proof.O artigo procura discutir, a partir de um caso (o caso United States v. Gorshkov-Ivanov), se (e, em caso afirmativo, em que medida) pode ocorrer o acesso a dados armazenados em sistemas informáticos localizados no estrangeiro, mais concretamente de forma unilateral e fora do quadro do recurso aos mecanismos de cooperação judiciária internacional. Ao invés do que sugerem alguns autores portugueses, no artigo defende-se que a disposição do artigo 15.º , n.º 5 da Lei do Cibercrime portuguesa não poderá, em face da Constituição Portuguesa, ser considerada uma norma habilitante suficiente para esse efeito e que a prova obtida mediante esse tipo de acesso poderá vir a ser considerada inválida por falta de uma habilitação normativa suficiente e também no contexto do sistema constitucional português de proibições de prova

A comonadic view of simulation and quantum resources

We study simulation and quantum resources in the setting of the sheaf-theoretic approach to contextuality and non-locality. Resources are viewed behaviourally, as empirical models. In earlier work, a notion of morphism for these empirical models was proposed and studied. We generalize and simplify the earlier approach, by starting with a very simple notion of morphism, and then extending it to a more useful one by passing to a co-Kleisli category with respect to a comonad of measurement protocols. We show that these morphisms capture notions of simulation between empirical models obtained via `free' operations in a resource theory of contextuality, including the type of classical control used in measurement-based quantum computation schemes.Comment: To appear in Proceedings of LiCS 201

A complete characterisation of All-versus-Nothing arguments for stabiliser states

An important class of contextuality arguments in quantum foundations are the All-versus-Nothing (AvN) proofs, generalising a construction originally due to Mermin. We present a general formulation of All-versus-Nothing arguments, and a complete characterisation of all such arguments which arise from stabiliser states. We show that every AvN argument for an n-qubit stabiliser state can be reduced to an AvN proof for a three-qubit state which is local Clifford-equivalent to the tripartite GHZ state. This is achieved through a combinatorial characterisation of AvN arguments, the AvN triple Theorem, whose proof makes use of the theory of graph states. This result enables the development of a computational method to generate all the AvN arguments in $\mathbb{Z}_2$ on n-qubit stabiliser states. We also present new insights into the stabiliser formalism and its connections with logic.Comment: 18 pages, 6 figure

On monogamy of non-locality and macroscopic averages: examples and preliminary results

We explore a connection between monogamy of non-locality and a weak macroscopic locality condition: the locality of the average behaviour. These are revealed by our analysis as being two sides of the same coin. Moreover, we exhibit a structural reason for both in the case of Bell-type multipartite scenarios, shedding light on but also generalising the results in the literature [Ramanathan et al., Phys. Rev. Lett. 107, 060405 (2001); Pawlowski & Brukner, Phys. Rev. Lett. 102, 030403 (2009)]. More specifically, we show that, provided the number of particles in each site is large enough compared to the number of allowed measurement settings, and whatever the microscopic state of the system, the macroscopic average behaviour is local realistic, or equivalently, general multipartite monogamy relations hold. This result relies on a classical mathematical theorem by Vorob'ev [Theory Probab. Appl. 7(2), 147-163 (1962)] about extending compatible families of probability distributions defined on the faces of a simplicial complex -- in the language of the sheaf-theoretic framework of Abramsky & Brandenburger [New J. Phys. 13, 113036 (2011)], such families correspond to no-signalling empirical models, and the existence of an extension corresponds to locality or non-contextuality. Since Vorob'ev's theorem depends solely on the structure of the simplicial complex, which encodes the compatibility of the measurements, and not on the specific probability distributions (i.e. the empirical models), our result about monogamy relations and locality of macroscopic averages holds not just for quantum theory, but for any empirical model satisfying the no-signalling condition. In this extended abstract, we illustrate our approach by working out a couple of examples, which convey the intuition behind our analysis while keeping the discussion at an elementary level.Comment: In Proceedings QPL 2014, arXiv:1412.810

Offer price : a contribution to the explanation of the IPO underpricing puzzle

The IPO underpricing phenomenon has inspired a significant number of explanatory theories over the last decades. Fascinatingly, one of the variables that would allow an interesting revision of the past literature is, at the same, one of the least studied in this field: the offer price. Thus, this study explores the relation between the offer price and the level of underpricing, its dynamics throughout the IPO cycle and the implication of these findings to prior studies. Based in a univariate, bivariate and multivariate analysis, our conclusions are threefold: (i) there is a positive relation between the offer price and the first day return; (ii) this relation gets stronger in hot IPO markets; (iii) our findings shed certain doubts on the premises and conclusions of some asymmetry of information theories and corroborate the view that IPO underpricing can be seen as an illiquidity premium

Constrangimentos dos métodos de Fry e Rf/φ e transecção de dobras: um exemplo de deformação progressiva no Varisco Ibérico

A utilização dos métodos de Rf/φ e de Fry na quantificação da deformação em tectonitos não é linear, pois as estruturas podem ser o resultado da actuação de diferentes processos; à escala do grão,a acomodação destas estruturas implica mecanismos intra-, trans- ou intergranular. Como os métodos normalmente utilizados nos estudos de deformação finita referidos apresentam diferentes sensibilidadesaos diferentes mecanismos, o mesmo tectonito pode apresentar diferentes valores da intensidade de deformação, consoante o método de quantificação utilizado. Este trabalho mostra que, embora o método de Fry dê valores mais próximos da totalidade da deformação, os resultados obtidos por ambos os métodos apresentam tipos de elipsóide semelhantes. Sendo a região da Apúlia caracterizada pela transecção dos dobramentos variscos, os valores da quantificação obtida pelos diferentes métodos ajudam a perceber a génese da obliquidade entre o plano axial das dobras e a clivagem