Short lists for shortest descriptions in short time

Is it possible to find a shortest description for a binary string? The well-known answer is "no, Kolmogorov complexity is not computable." Faced with this barrier, one might instead seek a short list of candidates which includes a laconic description. Remarkably such approximations exist. This paper presents an efficient algorithm which generates a polynomial-size list containing an optimal description for a given input string. Along the way, we employ expander graphs and randomness dispersers to obtain an Explicit Online Matching Theorem for bipartite graphs and a refinement of Muchnik's Conditional Complexity Theorem. Our main result extends recent work by Bauwens, Mahklin, Vereschchagin, and Zimand

How powerful are integer-valued martingales?

In the theory of algorithmic randomness, one of the central notions is that of computable randomness. An infinite binary sequence X is computably random if no recursive martingale (strategy) can win an infinite amount of money by betting on the values of the bits of X. In the classical model, the martingales considered are real-valued, that is, the bets made by the martingale can be arbitrary real numbers. In this paper, we investigate a more restricted model, where only integer-valued martingales are considered, and we study the class of random sequences induced by this model.Comment: Long version of the CiE 2010 paper

On approximate decidability of minimal programs

An index $e$ in a numbering of partial-recursive functions is called minimal if every lesser index computes a different function from $e$. Since the 1960's it has been known that, in any reasonable programming language, no effective procedure determines whether or not a given index is minimal. We investigate whether the task of determining minimal indices can be solved in an approximate sense. Our first question, regarding the set of minimal indices, is whether there exists an algorithm which can correctly label 1 out of $k$ indices as either minimal or non-minimal. Our second question, regarding the function which computes minimal indices, is whether one can compute a short list of candidate indices which includes a minimal index for a given program. We give some negative results and leave the possibility of positive results as open questions

Einflüsse der gesellschaftlichen Verpflichtungen und des Chronotyps auf das Trainingsverhalten im Breitensport

Hintergrund: Die Arbeit hat vor dem Hintergrund diverser Untersuchungen zum zirkadianen Rhythmus bei Athleten/-innen und Breitensportler/-innen in der Trainings- und Sozialwis-senschaft zum Ziel, die Verteilung von Chronotypen und deren Trainingszeitpunkten im Breitensport zu messen und die Einflussstärke von den gesellschaftlichen Strukturen, welche unseren Alltag bestimmen (wie beispielsweise der Familie oder der Arbeit), im Sinne eines optimalen Trainings darauf zu prüfen. Methode: Für die Beantwortung der Fragestellung wurden 591 Personen mittels Fragebogen zu ihrem demographischen Profil, dem Schlaf- und Wachrhythmus und ihrem Trainingsver-halten mit 50 Items befragt. Die Auswertung erfolgte durch eine binär logistische Regressi-onsanalyse in SPSS. Resultate: Die Teilnehmer und Teilnehmerinnen der Untersuchung betreiben wöchentli-chen, sehr vielseitigen und in verschiedenen Organisationsformen vorkommenden Sport. Die Trainings finden regelmässig und mit einer Tendenz gegen Abend statt, was aufgrund des Arbeitspensums, des Alters und des Mannschaftssports nicht allen Teilnehmern gemäss ihrem Leistungsoptimum entspricht und schliesslich indirekt mit dem Chronotyp zusam-menhängt. Diskussion: Obwohl das Bewusstsein für ein Training nach den für den Chronotyp günstigen Bedingungen nicht vorhanden ist, können die Personen immerhin und aufgrund der gesell-schaftlichen Strukturen regelmässig trainieren. Zudem scheint der Morgentyp öfters Indivi-dualsport zu treiben und hat eine leicht erhöhte Flexibilität bei der Auswahl der Trainings-zeit. Background: Based on the research of Athlete's performances on circadian rhythm, this pa-per seeks to determine amateur sportspeople's chronotype, analyze their preferred time of training and weigh these factors against the potential effects of daily patterns including work and family structure on optimal time of day training. Methods: Applying solely quantitative means of data collection, 591 participants have been asked to provide information on their demographic profile, their sleep and wake cycle and their training-specific comportment. Evaluation was conducted employing a binary logistic regression model in SPSS (Version 23.0.0.0). Results: On a weekly basis, participants engage regularly in a wide range of physical activ-ities. Time of training is skewed towards eveningness and highly influenced by the work-load, age and whether physical activity takes place in a group or team setting. As a result, chronotype could be indirectly associated with time of training and not everyone being able to train according to their individual peak performance. Discussion: Despite being unaware of one's inner circadian rhythm and his or her attached peak performances, participants in this paper were able to mainly set their training at the same time of day. In addition, individual sports seem to be linked to a predominance of morning types uttering greater flexibility to the probability of optimal training

Translating the Cantor set by a random

We determine the constructive dimension of points in random translates of the Cantor set. The Cantor set "cancels randomness" in the sense that some of its members, when added to Martin-Lof random reals, identify a point with lower constructive dimension than the random itself. In particular, we find the Hausdorff dimension of the set of points in a Cantor set translate with a given constructive dimension

Estimating the costs and benefits of providing free public transit passes to students in Los Angeles County: lessons learned in applying a health lens to decision-making.

In spite of increased focus by public health to engage and work with non-health sector partners to improve the health of the general as well as special populations, only a paucity of studies have described and disseminated emerging lessons and promising practices that can be used to undertake this work. This article describes the process used to conduct a Health Impact Assessment of a proposal to provide free public transportation passes to students in Los Angeles County. This illustrative case example describes opportunities and challenges encountered in working with an array of cross-sector partners and highlights four important lessons learned: (1) the benefits and challenges associated with broad conceptualization of public issues; (2) the need for more comprehensive, longitudinal data systems and dynamic simulation models to inform decision-making; (3) the importance of having a comprehensive policy assessment strategy that considers health impacts as well as costs and feasibility; and (4) the need for additional efforts to delineate the interconnectivity between health and other agency priorities. As public health advances cross-sector work in the community, further development of these priorities will help advance meaningful collaboration among all partners

A structured management approach to implementation of health promotion interventions in Head Start.

Improving the health and health literacy of low-income families is a national public health priority in the United States. The federal Head Start program provides a national infrastructure for implementation of health promotion interventions for young children and their families. The Health Care Institute (HCI) at the Anderson School of Management at the University of California, Los Angeles, developed a structured approach to health promotion training for Head Start grantees using business management principles. This article describes the HCI approach and provides examples of implemented programs and selected outcomes, including knowledge and behavior changes among Head Start staff and families. This prevention-focused training platform has reached 60,000 Head Start families in the United States since its inception in 2001. HCI has demonstrated consistent outcomes in diverse settings and cultures, suggesting both scalability and sustainability