Spin texture on the Fermi surface of tensile strained HgTe

We present ab initio and k.p calculations of the spin texture on the Fermi surface of tensile strained HgTe, which is obtained by stretching the zincblende lattice along the (111) axis. Tensile strained HgTe is a semimetal with pointlike accidental degeneracies between a mirror symmetry protected twofold degenerate band and two nondegenerate bands near the Fermi level. The Fermi surface consists of two ellipsoids which contact at the point where the Fermi level crosses the twofold degenerate band along the (111) axis. However, the spin texture of occupied states indicates that neither ellipsoid carries a compensating Chern number. Consequently, the spin texture is locked in the plane perpendicular to the (111) axis, exhibits a nonzero winding number in that plane, and changes winding number from one end of the Fermi ellipsoids to the other. The change in the winding of the spin texture suggests the existence of singular points. An ordered alloy of HgTe with ZnTe has the same effect as stretching the zincblende lattice in the (111) direction. We present ab initio calculations of ordered Hg_xZn_1-xTe that confirm the existence of a spin texture locked in a 2D plane on the Fermi surface with different winding numbers on either end.Comment: 8 pages, 8 figure

Mathematical practice, crowdsourcing, and social machines

The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. Crowdsourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs too long and complicated for humans to comprehend. Mathematical practice is an emerging interdisciplinary field which draws on philosophy and social science to understand how mathematics is produced. Online mathematical activity provides a novel and rich source of data for empirical investigation of mathematical practice - for example the community question answering system {\it mathoverflow} contains around 40,000 mathematical conversations, and {\it polymath} collaborations provide transcripts of the process of discovering proofs. Our preliminary investigations have demonstrated the importance of "soft" aspects such as analogy and creativity, alongside deduction and proof, in the production of mathematics, and have given us new ways to think about the roles of people and machines in creating new mathematical knowledge. We discuss further investigation of these resources and what it might reveal. Crowdsourced mathematical activity is an example of a "social machine", a new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. We outline a future research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, with the potential to change the way people do mathematics, and to transform the reach, pace, and impact of mathematics research.Comment: To appear, Springer LNCS, Proceedings of Conferences on Intelligent Computer Mathematics, CICM 2013, July 2013 Bath, U

How to think about informal proofs

This document is the Accepted Manuscript version of the following article: Brendan Larvor, ‘How to think about informal proofs’, Synthese, Vol. 187(2): 715-730, first published online 9 September 2011. The final publication is available at Springer via doi:10.1007/s11229-011-0007-5It is argued in this study that (i) progress in the philosophy of mathematical practice requires a general positive account of informal proof; (ii) the best candidate is to think of informal proofs as arguments that depend on their matter as well as their logical form; (iii) articulating the dependency of informal inferences on their content requires a redefinition of logic as the general study of inferential actions; (iv) it is a decisive advantage of this conception of logic that it accommodates the many mathematical proofs that include actions on objects other than propositions; (v) this conception of logic permits the articulation of project-sized tasks for the philosophy of mathematical practice, thereby supplying a partial characterisation of normal research in the fieldPeer reviewedFinal Accepted Versio

Reasoning at the frontier of knowledge: introductory essay

The advancement of knowledge is the big goal in human understanding. To get it, we often have to push beyond the frontier of knowledge, where our understanding dissolves and where new, strange entities appear. These require bold explorations and the consequent discoveries are not idle mind games, but crucial tools for our future life. And to have a method for carrying out these explorations is essential. The papers in the volume focus on a set of issues that are at the center of the development of ways of reasoning at the frontier of knowledge and of constructing ‘methods’ of discovery

Per un archivio dei materiali da demolizione nei territori della ricostruzione / A repository of recovered materials from post-earthquake reconstruction areas

Following the series of 'severe' seismic events that began in 2009, Italian legislation classified demolition debris as urban waste, despite Directive 200898EC calling for the reuse/recycling of 70% of all waste from human activities by 2020. This choice will produce a technical, cultural, environmental and economic impoverishment in territories already under heavy strain. Considering the convergence between the paradigms of the Circular Economy and Smartness, the essay identifies possible technological innovations for creating repositories of recovered materials. Collective activities and spatialities tied to processes of selection, reuse and recycling can generate forms of social-organisational-collective resilience required to confront the losses and damages suffered by a community

Do quantity-frequency data underestimate drinking-related health risks?

Identifying health impairment related to ethanol consumption is one of the major objectives of public health research. The most frequently used method for assessing drinking behavior in public health surveys and related research has been estimation formulae, like the Quantity-Frequency (QF) method which derives an estimate of typical/average levels of daily consumption. In recent years, questions have arisen as to whether the QF method can accurately reflect actual drinking patterns. This study compares a QF method of assessing daily drinking behavior with a newer, more quantitative method (Time-Line, TL) of assessing daily drinking. The QF and TL methods yielded similar mean daily ethanol consumption levels; however, in contrast to the TL method, the QF method seriously masked subjects' actual drinking patterns by failing to identify certain types of ethanol consumption days, especially those thought to be associated with health risks. These findings, while provocative, were obtained with a small number of subjects (N = 40). Extrapolation to populations other than problem drinkers, while likely, awaits further empirical validation