The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems

We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low spatial dimension at finite size, a physical scenario where tensor network methods, both Density Matrix Renormalization Group and beyond, have long proven to be winning strategies. Here we explore in detail the numerical frameworks and methods employed to deal with low-dimension physical setups, from a computational physics perspective. We focus on symmetries and closed-system simulations in arbitrary boundary conditions, while discussing the numerical data structures and linear algebra manipulation routines involved, which form the core libraries of any tensor network code. At a higher level, we put the spotlight on loop-free network geometries, discussing their advantages, and presenting in detail algorithms to simulate low-energy equilibrium states. Accompanied by discussions of data structures, numerical techniques and performance, this anthology serves as a programmer's companion, as well as a self-contained introduction and review of the basic and selected advanced concepts in tensor networks, including examples of their applications.Comment: 115 pages, 56 figure

Group theory in cryptography

This paper is a guide for the pure mathematician who would like to know more about cryptography based on group theory. The paper gives a brief overview of the subject, and provides pointers to good textbooks, key research papers and recent survey papers in the area.Comment: 25 pages References updated, and a few extra references added. Minor typographical changes. To appear in Proceedings of Groups St Andrews 2009 in Bath, U

TAPAs: A Tool for the Analysis of Process Algebras

Process algebras are formalisms for modelling concurrent systems that permit mathematical reasoning with respect to a set of desired properties. TAPAs is a tool that can be used to support the use of process algebras to specify and analyze concurrent systems. It does not aim at guaranteeing high performances, but has been developed as a support to teaching. Systems are described as process algebras terms that are then mapped to labelled transition systems (LTSs). Properties are verified either by checking equivalence of concrete and abstract systems descriptions, or by model checking temporal formulae over the obtained LTS. A key feature of TAPAs, that makes it particularly suitable for teaching, is that it maintains a consistent double representation of each system both as a term and as a graph. Another useful didactical feature is the exhibition of counterexamples in case equivalences are not verified or the proposed formulae are not satisfied

Geometrical aspects and connections of the energy-temperature fluctuation relation

Recently, we have derived a generalization of the known canonical fluctuation relation $k_{B}C=\beta^{2}$ between heat capacity $C$ and energy fluctuations, which can account for the existence of macrostates with negative heat capacities $C<0$. In this work, we presented a panoramic overview of direct implications and connections of this fluctuation theorem with other developments of statistical mechanics, such as the extension of canonical Monte Carlo methods, the geometric formulations of fluctuation theory and the relevance of a geometric extension of the Gibbs canonical ensemble that has been recently proposed in the literature.Comment: Version accepted for publication in J. Phys. A: Math and The

Stylization and representation in subtitles: can less be more?

This article considers film dialogues and interlingual subtitles from the point of view of linguistic and cultural representation, and revisits from that perspective the question of loss, as a platform for considering alternative views on the topic and broader theoretical issues. The cross-cultural pragmatics perspective and focus on viewers’ reactions that dealing with representation entails cast the question of loss in a different light and opens up avenues for alternative modes of analysis. They make room for subtitles to be construed as producing their own systems of multimodal textual representation and modes of interpretation, and for their text to be recognised as having a greater expressive and representational potential than face values might suggest. This is the argument, informed by Fowler's Theory of Mode (1991, 2000), that is taken up in the paper, and harnessed to the review of examples or observations from recent studies on subtitles, and complementary evidence from dubbing. The capacity of subtitles to produce insights into the cultures and languages represented is of particular interest, and has wider implications for the culturally instrumental functions of subtitles and translation strategies

Understanding safety-critical interactions with a home medical device through Distributed Cognition

As healthcare shifts from the hospital to the home, it is becoming increasingly important to understand how patients interact with home medical devices, to inform the safe and patient-friendly design of these devices. Distributed Cognition (DCog) has been a useful theoretical framework for understanding situated interactions in the healthcare domain. However, it has not previously been applied to study interactions with home medical devices. In this study, DCog was applied to understand renal patients’ interactions with Home Hemodialysis Technology (HHT), as an example of a home medical device. Data was gathered through ethnographic observations and interviews with 19 renal patients and interviews with seven professionals. Data was analyzed through the principles summarized in the Distributed Cognition for Teamwork methodology. In this paper we focus on the analysis of system activities, information flows, social structures, physical layouts, and artefacts. By explicitly considering different ways in which cognitive processes are distributed, the DCog approach helped to understand patients’ interaction strategies, and pointed to design opportunities that could improve patients’ experiences of using HHT. The findings highlight the need to design HHT taking into consideration likely scenarios of use in the home and of the broader home context. A setting such as home hemodialysis has the characteristics of a complex and safety-critical socio-technical system, and a DCog approach effectively helps to understand how safety is achieved or compromised in such a system