The CONEstrip algorithm

Uncertainty models such as sets of desirable gambles and (conditional) lower previsions can be represented as convex cones. Checking the consistency of and drawing inferences from such models requires solving feasibility and optimization problems. We consider finitely generated such models. For closed cones, we can use linear programming; for conditional lower prevision-based cones, there is an efficient algorithm using an iteration of linear programs. We present an efficient algorithm for general cones that also uses an iteration of linear programs

On the Relationship between Convex Bodies Related to Correlation Experiments with Dichotomic Observables

In this paper we explore further the connections between convex bodies related to quantum correlation experiments with dichotomic variables and related bodies studied in combinatorial optimization, especially cut polyhedra. Such a relationship was established in Avis, Imai, Ito and Sasaki (2005 J. Phys. A: Math. Gen. 38 10971-87) with respect to Bell inequalities. We show that several well known bodies related to cut polyhedra are equivalent to bodies such as those defined by Tsirelson (1993 Hadronic J. S. 8 329-45) to represent hidden deterministic behaviors, quantum behaviors, and no-signalling behaviors. Among other things, our results allow a unique representation of these bodies, give a necessary condition for vertices of the no-signalling polytope, and give a method for bounding the quantum violation of Bell inequalities by means of a body that contains the set of quantum behaviors. Optimization over this latter body may be performed efficiently by semidefinite programming. In the second part of the paper we apply these results to the study of classical correlation functions. We provide a complete list of tight inequalities for the two party case with (m,n) dichotomic observables when m=4,n=4 and when min{m,n}<=3, and give a new general family of correlation inequalities.Comment: 17 pages, 2 figure

A survey of maincrop potatoes I Estimates of yield 1948–50

The survey shows that objective estimates of the yield of maincrop potatoes can be obtained from small samples carefully selected and dug by hand. Samples taken from about 1000 fields gave estimates of the mean yield of all counties sampled with a standard error due to sampling of less than ± 0·2 ton/acre. The precision of the estimate could have been improved by a better distribution of samples among counties.The results point to underestimation on the part of the official estimates, in each of the 3 years, especially in the case of high yields in particular counties, and in particular years. The discrepancy between the official and the survey yields is of the order of 1¾ tons/acre, after all necessary corrections have been applied to the survey yields.The experience gained in the survey indicates that the method of sampling adopted provides an accurate and reliable method of estimating the yields of potatoes which could supplement, and, possibly, ultimately replace the present official estimates if more accurate estimates are required. A national scheme, properly designed, which would include all the potato-growing areas in due proportion should not be unduly expensive to operate. Estimates so obtained would not only be generally more accurate than those obtained by the present official method, but, perhaps more important, would indicate far more closely the fluctuation in yield from year to year

Bounds on the Complexity of Halfspace Intersections when the Bounded Faces have Small Dimension

We study the combinatorial complexity of D-dimensional polyhedra defined as the intersection of n halfspaces, with the property that the highest dimension of any bounded face is much smaller than D. We show that, if d is the maximum dimension of a bounded face, then the number of vertices of the polyhedron is O(n^d) and the total number of bounded faces of the polyhedron is O(n^d^2). For inputs in general position the number of bounded faces is O(n^d). For any fixed d, we show how to compute the set of all vertices, how to determine the maximum dimension of a bounded face of the polyhedron, and how to compute the set of bounded faces in polynomial time, by solving a polynomial number of linear programs

Comfort radicalism and NEETs: a conservative praxis

Young people who are not in education, employment or training (NEET) are construed by policy makers as a pressing problem about which something should be done. Such young people's lack of employment is thought to pose difficulties for wider society in relation to social cohesion and inclusion and it is feared that they will become a 'lost generation'. This paper(1) draws upon English research, seeking to historicise the debate whilst acknowledging that these issues have a much wider purchase. The notion of NEETs rests alongside longstanding concerns of the English state and middle classes, addressing unruly male working class youth as well as the moral turpitude of working class girls. Waged labour and domesticity are seen as a means to integrate such groups into society thereby generating social cohesion. The paper places the debate within it socio-economic context and draws on theorisations of cognitive capitalism, Italian workerism, as well as emerging theories of antiwork to analyse these. It concludes by arguing that ‘radical’ approaches to NEETs that point towards inequities embedded in the social structure and call for social democratic solutions veer towards a form of comfort radicalism. Such approaches leave in place the dominance of capitalist relations as well as productivist orientations that celebrate waged labour

Scalar field quantization on the 2+1 dimensional black hole background

The quantization of a massless conformally coupled scalar field on the 2+1 dimensional Anti de Sitter black hole background is presented. The Green's function is calculated, using the fact that the black hole is Anti de Sitter space with points identified, and taking into account the fact that the black hole spacetime is not globally hyperbolic. It is shown that the Green's function calculated in this way is the Hartle-Hawking Green's function. The Green's function is used to compute $\langle T^\mu_\nu \rangle$, which is regular on the black hole horizon, and diverges at the singularity. A particle detector response function outside the horizon is also calculated and shown to be a fermi type distribution. The back-reaction from $\langle T_{\mu\nu} \rangle$ is calculated exactly and is shown to give rise to a curvature singularity at $r=0$ and to shift the horizon outwards. For $M=0$ a horizon develops, shielding the singularity. Some speculations about the endpoint of evaporation are discussed.Comment: CTP 2243, 24 pages, RevTex. (The backreaction section is extended, and some confusing notation has been changed

Non-singular four-dimensional black holes and the Jackiw-Teitelboim theory

A four-dimensional dilaton-gravity action whose spherical reduction to two dimensions leads to the Jackiw-Teitelboim theory is presented. A nonsingular black hole solution of the theory is obtained and its physical interpretation is discussed. The classical and semiclassical properties of the solution and of its 2d counterpart are analysed. The 2d theory is also used to model the evaporation process of the near-extremal 4d black hole. We describe in detail the peculiarities of the black hole solutions, in particular the purely topological nature of the Hawking radiation, in the context of the Jackiw-Teitelboim theory.Comment: 24 pages, 6 figures available upon request, Plain Tex, INFN-CA-TH-94-2

Anti-de Sitter boundary in Poincare coordinates

We study the space-time boundary of a Poincare patch of Anti-de Sitter (AdS) space. We map the Poincare AdS boundary to the global coordinate chart and show why this boundary is not equivalent to the global AdS boundary. The Poincare AdS boundary is shown to contain points of the bulk of the entire AdS space. The Euclidean AdS space is also discussed. In this case one can define a semi-global chart that divides the AdS space in the same way as the corresponding Euclidean Poincare chart.Comment: In this revised version we add a discussion of the physical consequences of the choice of a coordinate system for AdS space. We changed figure 1 and added more references. Version to be published in Gen. Relat. Grav

The abolition of the General Teaching Council for England and the future of teacher discipline

With the abolition of the General Teaching Council for England in the 2011 Education Act, this article considers the future of teacher discipline in England. It provides a critique of the changes to the regulation of teacher misconduct and incompetence that draws on a Foucauldian framework, especially concerning the issue of public displays of discipline and the concomitant movement to more hidden forms. In addition, the external context of accountability that accompanies the reforms to teacher discipline are considered including the perfection of the panoptic metaphor presented by the changes to Ofsted practices such as the introduction of zero-notice inspections. The article concludes that the reforms will further move teachers from being occupational professionals to being organisational professionals marking them apart from comparable professions in medicine and law