A quantum group version of quantum gauge theories in two dimensions

For the special case of the quantum group $SL_q (2,{\bf C})\ (q= \exp \pi i/r,\ r\ge 3)$ we present an alternative approach to quantum gauge theories in two dimensions. We exhibit the similarities to Witten's combinatorial approach which is based on ideas of Migdal. The main ingredient is the Turaev-Viro combinatorial construction of topological invariants of closed, compact 3-manifolds and its extension to arbitrary compact 3-manifolds as given by the authors in collaboration with W. Mueller.Comment: 6 pages (plain TeX

Thermodynamics of weight loss diets

BACKGROUND: It is commonly held that "a calorie is a calorie", i.e. that diets of equal caloric content will result in identical weight change independent of macronutrient composition, and appeal is frequently made to the laws of thermodynamics. We have previously shown that thermodynamics does not support such a view and that diets of different macronutrient content may be expected to induce different changes in body mass. Low carbohydrate diets in particular have claimed a "metabolic advantage" meaning more weight loss than in isocaloric diets of higher carbohydrate content. In this review, for pedagogic clarity, we reframe the theoretical discussion to directly link thermodynamic inefficiency to weight change. The problem in outline: Is metabolic advantage theoretically possible? If so, what biochemical mechanisms might plausibly explain it? Finally, what experimental evidence exists to determine whether it does or does not occur? RESULTS: Reduced thermodynamic efficiency will result in increased weight loss. The laws of thermodynamics are silent on the existence of variable thermodynamic efficiency in metabolic processes. Therefore such variability is permitted and can be related to differences in weight lost. The existence of variable efficiency and metabolic advantage is therefore an empiric question rather than a theoretical one, confirmed by many experimental isocaloric studies, pending a properly performed meta-analysis. Mechanisms are as yet unknown, but plausible mechanisms at the metabolic level are proposed. CONCLUSIONS: Variable thermodynamic efficiency due to dietary manipulation is permitted by physical laws, is supported by much experimental data, and may be reasonably explained by plausible mechanisms

Quantum analogues of Hardy's nonlocality paradox

Hardy's nonlocality is a "nonlocality proof without inequalities": it exemplifies that quantum correlations can be qualitatively stronger than classical correlations. This paper introduces variants of Hardy's nonlocality in the CHSH scenario which are realized by the PR-box, but not by quantum correlations. Hence this new kind of Hardy-type nonlocality is a proof without inequalities showing that superquantum correlations can be qualitatively stronger than quantum correlations.Comment: minor fixe

The Bell Theorem as a Special Case of a Theorem of Bass

The theorem of Bell states that certain results of quantum mechanics violate inequalities that are valid for objective local random variables. We show that the inequalities of Bell are special cases of theorems found ten years earlier by Bass and stated in full generality by Vorob'ev. This fact implies precise necessary and sufficient mathematical conditions for the validity of the Bell inequalities. We show that these precise conditions differ significantly from the definition of objective local variable spaces and as an application that the Bell inequalities may be violated even for objective local random variables.Comment: 15 pages, 2 figure

Assessing Human Error Against a Benchmark of Perfection

An increasing number of domains are providing us with detailed trace data on human decisions in settings where we can evaluate the quality of these decisions via an algorithm. Motivated by this development, an emerging line of work has begun to consider whether we can characterize and predict the kinds of decisions where people are likely to make errors. To investigate what a general framework for human error prediction might look like, we focus on a model system with a rich history in the behavioral sciences: the decisions made by chess players as they select moves in a game. We carry out our analysis at a large scale, employing datasets with several million recorded games, and using chess tablebases to acquire a form of ground truth for a subset of chess positions that have been completely solved by computers but remain challenging even for the best players in the world. We organize our analysis around three categories of features that we argue are present in most settings where the analysis of human error is applicable: the skill of the decision-maker, the time available to make the decision, and the inherent difficulty of the decision. We identify rich structure in all three of these categories of features, and find strong evidence that in our domain, features describing the inherent difficulty of an instance are significantly more powerful than features based on skill or time.Comment: KDD 2016; 10 page

Telescopic actions

A group action H on X is called "telescopic" if for any finitely presented group G, there exists a subgroup H' in H such that G is isomorphic to the fundamental group of X/H'. We construct examples of telescopic actions on some CAT[-1] spaces, in particular on 3 and 4-dimensional hyperbolic spaces. As applications we give new proofs of the following statements: (1) Aitchison's theorem: Every finitely presented group G can appear as the fundamental group of M/J, where M is a compact 3-manifold and J is an involution which has only isolated fixed points; (2) Taubes' theorem: Every finitely presented group G can appear as the fundamental group of a compact complex 3-manifold.Comment: +higher dimension