From Matrices to Strings and Back

We discuss an explicit construction of a string dual for the Gaussian matrix model. Starting from the matrix model and employing Strebel differential techniques we deduce hints about the structure of the dual string. Next, following these hints a worldheet theory is constructed. The correlators in this string theory are assumed to localize on a finite set of points in the moduli space of Riemann surfaces. To each such point one associates a Feynman diagram contributing to the correlator in the dual matrix model, and thus recasts the worldsheet expression as a sum over Feynman diagrams.Comment: 27 pages, 3 figure

Information Flow in Secret Sharing Protocols

The entangled graph states have emerged as an elegant and powerful quantum resource, indeed almost all multiparty protocols can be written in terms of graph states including measurement based quantum computation (MBQC), error correction and secret sharing amongst others. In addition they are at the forefront in terms of implementations. As such they represent an excellent opportunity to move towards integrated protocols involving many of these elements. In this paper we look at expressing and extending graph state secret sharing and MBQC in a common framework and graphical language related to flow. We do so with two main contributions. First we express in entirely graphical terms which set of players can access which information in graph state secret sharing protocols. These succinct graphical descriptions of access allow us to take known results from graph theory to make statements on the generalisation of the previous schemes to present new secret sharing protocols. Second, we give a set of necessary conditions as to when a graph with flow, i.e. capable of performing a class of unitary operations, can be extended to include vertices which can be ignored, pointless measurements, and hence considered as unauthorised players in terms of secret sharing, or error qubits in terms of fault tolerance. This offers a way to extend existing MBQC patterns to secret sharing protocols. Our characterisation of pointless measurements is believed also to be a useful tool for further integrated measurement based schemes, for example in constructing fault tolerant MBQC schemes

Discursive design thinking: the role of explicit knowledge in creative architectural design reasoning

The main hypothesis investigated in this paper is based upon the suggestion that the discursive reasoning in architecture supported by an explicit knowledge of spatial configurations can enhance both design productivity and the intelligibility of design solutions. The study consists of an examination of an architect’s performance while solving intuitively a well-defined problem followed by an analysis of the spatial structure of their design solutions. One group of architects will attempt to solve the design problem logically, rationalizing their design decisions by implementing their explicit knowledge of spatial configurations. The other group will use an implicit form of such knowledge arising from their architectural education to reason about their design acts. An integrated model of protocol analysis combining linkography and macroscopic coding is used to analyze the design processes. The resulting design outcomes will be evaluated quantitatively in terms of their spatial configurations. The analysis appears to show that an explicit knowledge of the rules of spatial configurations, as possessed by the first group of architects can partially enhance their function-driven judgment producing permeable and well-structured spaces. These findings are particularly significant as they imply that an explicit rather than an implicit knowledge of the fundamental rules that make a layout possible can lead to a considerable improvement in both the design process and product. This suggests that by externalizing th

Elastic-plastic defect interaction in (a)symmetrical double edge notched tension specimens

Interaction of defects tends to intensify their crack driving force response compared to the situation where these defects act independently. The interaction between multiple defects is addressed in engineering critical assessment standards like BS7910 and ASME B&PV Section XI. Nonetheless, the accuracy of these rules is open to debate since all of them are based on re-characterization procedures which in essence introduce conservativeness. The authors have developed a fully parametric finite element (FE) model able to generate multiple notches in different topologies, in order to investigate their interaction effect. An experimental validation study is conducted to verify the FE model in terms of CTOD response and surface strain distribution. To that end, symmetrically and asymmetrically double edge notched tension specimens are tensile tested and their deformation monitored by means of 3D digital image correlation. In this study the CTOD is opted as a local criterion to evaluate the interaction between notches. These results are compared with an evaluation of strain patterns on a specimen’s surface, as a global interaction evaluation. Through this comparison a deeper understanding is gained to allow us to develop a novel approach to address flaw interaction. Moreover, the validation of the FE model allows future studies of interaction between other defect types (e.g., semi-elliptical, surface breaking) in plate-like geometries

Self-similarity of complex networks and hidden metric spaces

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization