Pictures of complete positivity in arbitrary dimension

Two fundamental contributions to categorical quantum mechanics are presented. First, we generalize the CP-construction, that turns any dagger compact category into one with completely positive maps, to arbitrary dimension. Second, we axiomatize when a given category is the result of this construction.Comment: Final versio

Differences in intention to use educational RSS feeds between Lebanese and British students: A multi‑group analysis based on the technology acceptance model

Really Simple Syndication (RSS) offers a means for university students to receive timely updates from virtual learning environments. However, despite its utility, only 21% of home students surveyed at a university in Lebanon claim to have ever used the technology. To investigate whether national culture could be an influence on intention to use RSS, the survey was extended to British students in the UK. Using the Technology Adoption Model (TAM) as a research framework, 437 students responded to a questionnaire containing four constructs: behavioral intention to use; attitude towards benefit; perceived usefulness; and perceived ease of use. Principle components analysis and structural equation modelling were used to explore the psychometric qualities and utility of TAM in both contexts. The results show that adoption was significantly higher, but also modest, in the British context at 36%. Configural and metric invariance were fully supported, while scalar and factorial invariance were partially supported. Further analysis shows significant differences between perceived usefulness and perceived ease of use across the two contexts studied. Therefore, it is recommended that faculty demonstrate to students how educational RSS feeds can be used effectively to increase awareness and emphasize usefulness in both contexts

Formalization of Universal Algebra in Agda

In this work we present a novel formalization of universal algebra in Agda. We show that heterogeneous signatures can be elegantly modelled in type-theory using sets indexed by arities to represent operations. We prove elementary results of heterogeneous algebras, including the proof that the term algebra is initial and the proofs of the three isomorphism theorems. We further formalize equational theory and prove soundness and completeness. At the end, we define (derived) signature morphisms, from which we get the contravariant functor between algebras; moreover, we also proved that, under some restrictions, the translation of a theory induces a contra-variant functor between models.Fil: Gunther, Emmanuel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Gadea, Alejandro Emilio. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Pagano, Miguel Maria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin

A universe of processes and some of its guises

Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can then be converted into mathematical structure. With very little structural effort (i.e. in very abstract terms) and in a very short time span the categorical quantum mechanics (CQM) research program has reproduced a surprisingly large fragment of quantum theory. It also provides new insights both in quantum foundations and in quantum information, and has even resulted in automated reasoning software called `quantomatic' which exploits the deductive power of CQM. In this paper we complement the available material by not requiring prior knowledge of category theory, and by pointing at connections to previous and current developments in the foundations of physics. This research program is also in close synergy with developments elsewhere, for example in representation theory, quantum algebra, knot theory, topological quantum field theory and several other areas.Comment: Invited chapter in: "Deep Beauty: Understanding the Quantum World through Mathematical Innovation", H. Halvorson, ed., Cambridge University Press, forthcoming. (as usual, many pictures

An Algebra of Hierarchical Graphs

We define an algebraic theory of hierarchical graphs, whose axioms characterise graph isomorphism: two terms are equated exactly when they represent the same graph. Our algebra can be understood as a high-level language for describing graphs with a node-sharing, embedding structure, and it is then well suited for defining graphical representations of software models where nesting and linking are key aspects

Toward designing a quantum key distribution network simulation model

As research in quantum key distribution network technologies grows larger and more complex, the need for highly accurate and scalable simulation technologies becomes important to assess the practical feasibility and foresee difficulties in the practical implementation of theoretical achievements. In this paper, we described the design of simplified simulation environment of the quantum key distribution network with multiple links and nodes. In such simulation environment, we analyzed several routing protocols in terms of the number of sent routing packets, goodput and Packet Delivery Ratio of data traffic flow using NS-3 simulator

Optimal Iris Fuzzy Sketches

Fuzzy sketches, introduced as a link between biometry and cryptography, are a way of handling biometric data matching as an error correction issue. We focus here on iris biometrics and look for the best error-correcting code in that respect. We show that two-dimensional iterative min-sum decoding leads to results near the theoretical limits. In particular, we experiment our techniques on the Iris Challenge Evaluation (ICE) database and validate our findings.Comment: 9 pages. Submitted to the IEEE Conference on Biometrics: Theory, Applications and Systems, 2007 Washington D