Generalized Bell Inequality Experiments and Computation

We consider general settings of Bell inequality experiments with many parties, where each party chooses from a finite number of measurement settings each with a finite number of outcomes. We investigate the constraints that Bell inequalities place upon the correlations possible in a local hidden variable theories using a geometrical picture of correlations. We show that local hidden variable theories can be characterized in terms of limited computational expressiveness, which allows us to characterize families of Bell inequalities. The limited computational expressiveness for many settings (each with many outcomes) generalizes previous results about the many-party situation each with a choice of two possible measurements (each with two outcomes). Using this computational picture we present generalizations of the Popescu-Rohrlich non-local box for many parties and non-binary inputs and outputs at each site. Finally, we comment on the effect of pre-processing on measurement data in our generalized setting and show that it becomes problematic outside of the binary setting, in that it allows local hidden variable theories to simulate maximally non-local correlations such as those of these generalised Popescu-Rohrlich non-local boxes.Comment: 16 pages, 2 figures, supplemental material available upon request. Typos corrected and references adde

Free-living Physical Activity and Executive Function : A Multi-Study Analysis of Age Groups and Times of Day

Acknowledgments The authors wish to thank all participants (and parents) for taking part in the studies. Additionally, we want to thank Merle Reuter and Ulrike Schwarz for their help in data collection and preparation of the AttentionGO project. We also thank the student assistants for their support in data collection in all studies. Further, we thank Patrick E. Shrout for his expert advice and valuable feedback on the first draft of the manuscript.Peer reviewedPublisher PD

Few smooth d-polytopes with n lattice points

We prove that, for fixed n there exist only finitely many embeddings of Q-factorial toric varieties X into P^n that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d and n, there are only finitely many smooth d-polytopes with n lattice points. We also enumerate all smooth 3-polytopes with at most 12 lattice points. In fact, it is sufficient to bound the singularities and the number of lattice points on edges to prove finiteness.Comment: 20+2 pages; major revision: new author, new structure, new result

An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

Flanker performance in female college students with ADHD: a diffusion model analysis

Attention-deficit hyperactivity disorder (ADHD) is characterized by poor adaptation to environmental demands, which leads to various everyday life problems. The present study had four aims: (1) to compare performance in a flanker task in female college students with and without ADHD (N = 39) in a classical analyses of reaction time and error rate and studying the underlying processes using a diffusion model, (2) to compare the amount of focused attention, (3) to explore the adaptation of focused attention, and (4) to relate adaptation to psychological functioning. The study followed a 2-between (group: ADHD vs. control) × 2-within (flanker conflict: incongruent vs. congruent) × 2-within (conflict frequency: 20 vs. 80 %) design. Compared to a control group, the ADHD group displayed prolonged response times accompanied by fewer errors in a flanker task. Results from the diffusion model analyses revealed that the members of the ADHD group showed deficits in non-decisional processes (i.e., higher non-decision time) and leaned more toward accuracy than participants without ADHD (i.e., setting higher boundaries). The ADHD group showed a more focused attention and less adaptation to the task conditions which is related to psychological functioning. Deficient non-decisional processes and poor adaptation are in line with theories of ADHD and presumably typical for the ADHD population, although this has not been shown using a diffusion model. However, we assume that the cautious strategy of trading speed of for accuracy is specific to the subgroup of female college students with ADHD and might be interpreted as a compensation mechanism