Geometric Reasoning with polymake

The mathematical software system polymake provides a wide range of functions for convex polytopes, simplicial complexes, and other objects. A large part of this paper is dedicated to a tutorial which exemplifies the usage. Later sections include a survey of research results obtained with the help of polymake so far and a short description of the technical background

Products of Foldable Triangulations

Regular triangulations of products of lattice polytopes are constructed with the additional property that the dual graphs of the triangulations are bipartite. The (weighted) size difference of this bipartition is a lower bound for the number of real roots of certain sparse polynomial systems by recent results of Soprunova and Sottile [Adv. Math. 204(1):116-151, 2006]. Special attention is paid to the cube case.Comment: new title; several paragraphs reformulated; 23 page

Zooming into daily life : Within-person associations between physical activity and affect in young adults

Funding The first author was funded by the LEAD Graduate School & Research Network [GSC1028], a project of the Excellence Initiative of the German federal and state governments. Acknowledgements We thank Laura Grube, Leona Hellwig, Parvin Nemati, and Sarah Schmid for their study assistance and all the individuals who participated and made this research feasible.Peer reviewedPostprin

simpcomp -- A GAP toolbox for simplicial complexes

simpcomp is an extension (a so called package) to GAP, the well known system for computational discrete algebra. The package enables the user to compute numerous properties of (abstract) simplicial complexes, provides functions to construct new complexes from existing ones and an extensive library of triangulations of manifolds.Comment: 4 page

ADHS: Mehr als nur eine Frage der Konzentration? : Mangelnde Selbstregulation bei Kindern mit Aufmerksamkeitsdefizit und Hyperaktivität

Sie sind nicht weniger intelligent als ihre gleichaltrigen Mitschüler, und doch sind ihre schulischen Leistungen meist schlechter: Kinder, die unter einer Störung mit Aufmerksamkeitsdefi zit und Hyperaktivität (ADHS) leiden, haben es schwer im Schulsystem. Wie können sie lernen, ihre Gefühle, Gedanken und Handlungen bewusst zu beeinfl ussen und sich nicht ständig ablenken zu lassen? Frankfurter Studien zeigen zum Beispiel, dass konkrete "Wenn-Dann-Pläne" ihre Konzentrationsfähigkeit deutlich verbessern können

Duration Discrimination Predicts Delay of Gratification In Children with and without ADHD

AbstractThe ability to delay gratification, to wait for a larger but delayed reward in the presence of a smaller but constantly available reward, has been shown to be predictive for various aspects of everyday life. For instance, preschool children who were better able to delay gratification achieved better school grades, a higher education, a better ability to cope with stress, as well as a reduced risk for being overweight or consume drugs up to 30 years later (Mischel et al., 2011). However, despite the importance of delay of gratification cognitive factors underlying individual differences are only poorly understood. Wittmann and Paulus (2008) suggested that individuals who overestimate the duration of time intervals experience waiting times as more costly and are, therefore, less likely to delay gratification. Furthermore, a recent study revealed an association between less accurate internal clock speed and a behavioral choice delay task (Corvi, Juergensen, Weaver, & Demaree, 2012). Further evidence for an association between temporal processing and delay of gratification can be derived from studies using clinical samples. For instance, children with attention-deficit/hyperactivity disorder (ADHD) consistently prefer smaller, immediate rewards over larger, delayed rewards and show impaired temporal processing (Sonuga-Barke, Bitsakou, & Thompson, 2010). However, no study has directly tested an association between a measure of temporal processing and a classical delay of gratification task in children with and without ADHD so far.As part of a larger study, 64 children (29 with ADHD) aged between 8 to 12 years performed a version of an auditory duration discrimination task and a delay of gratification task. In the duration discrimination task, the children were presented with two unfilled intervals indicated by two brief tones each. The baseline interval lasted for 400ms, while the comparison interval was always longer and adjusted up or down in 10ms steps securing an accuracy of 80%. In the delay of gratification task, the children were instructed that they could either opt for one chocolate bar immediately or that they could wait to receive two chocolate bars. Unbeknownst to the children, the waiting time lasted 25minutes but children were told that they could decide for the immediate chocolate bar at any time by ringing a bell.Children with ADHD did not differ in their performance from children without ADHD in the duration discrimination task or the delay of gratification task. However, in the whole sample of children with and without ADHD, children who waited for the additional chocolate bar showed a better duration discrimination than children who failed to wait for the additional chocolate bar [t(62) = -2.52, p = .01].We demonstrated an association between temporal processing ability and the ability to delay gratification. These results need to be replicated in further studies with larger sample sizes. Moreover, different tasks measuring temporal processing and delay of gratification should be used to further clarify the relationship of temporal processing, delay of gratification, and ADHD

Within-Person Link between Depressed Affect and Moderate-to-Vigorous Physical Activity in Adolescence : An Intensive Longitudinal Approach

ACKNOWLEDGEMENTS We thank Danijela Bacic, Hannah J€ockel, Lea K€ohler, Katrin Molsen, Marie Landenberger, and Annika Plambeck for their assistance with participant recruitment and data collection, Dale Esliger and Lauren Sherar for processing the accelerometry data, and Matthew Riccio for his helpful comments on the manuscript.Peer reviewedPostprin

ADHD symptoms in adolescents\u27 everyday life. Fluctuations and symptom structure within and between individuals

This study investigated whether self-reported ADHD symptoms fluctuate substantially within adolescents from day to day, and examined the underlying symptom factor structure on a within- and between-person level. Method: Adolescents (N = 166) rated their ADHD symptoms over the phone on eight consecutive evenings (total ratings: n = 1,264). Results: ADHD symptoms showed substantial fluctuations within adolescents from day to day, as indicated by within-person standard deviations and intraclass correlation coefficients. Both a two-level factor model with three correlated factors (inattention, hyperactivity, impulsivity) and a two-level bifactor model with a general ADHD symptom factor and a specific inattention factor provided acceptable to good accounts of the structure underlying daily ADHD symptom ratings on the between- and the within-person level. Conclusion: The study demonstrates that adolescents\u27 ADHD symptoms fluctuate from day to day and highlights the need for intensive diagnostic processes with repeated symptom assessments and interventions that address symptom fluctuations. (DIPF/Orig.

Isotropical Linear Spaces and Valuated Delta-Matroids

The spinor variety is cut out by the quadratic Wick relations among the principal Pfaffians of an n x n skew-symmetric matrix. Its points correspond to n-dimensional isotropic subspaces of a 2n-dimensional vector space. In this paper we tropicalize this picture, and we develop a combinatorial theory of tropical Wick vectors and tropical linear spaces that are tropically isotropic. We characterize tropical Wick vectors in terms of subdivisions of Delta-matroid polytopes, and we examine to what extent the Wick relations form a tropical basis. Our theory generalizes several results for tropical linear spaces and valuated matroids to the class of Coxeter matroids of type D