Speeding up Glauber Dynamics for Random Generation of Independent Sets

The maximum independent set (MIS) problem is a well-studied combinatorial optimization problem that naturally arises in many applications, such as wireless communication, information theory and statistical mechanics. MIS problem is NP-hard, thus many results in the literature focus on fast generation of maximal independent sets of high cardinality. One possibility is to combine Gibbs sampling with coupling from the past arguments to detect convergence to the stationary regime. This results in a sampling procedure with time complexity that depends on the mixing time of the Glauber dynamics Markov chain. We propose an adaptive method for random event generation in the Glauber dynamics that considers only the events that are effective in the coupling from the past scheme, accelerating the convergence time of the Gibbs sampling algorithm

An Applied Approach to Attacking Effectiveness in Professional Football

With ever growing financial invest in elite (association) football (soccer), it becomes increasingly more important to operate at the highest possible standard. A stable football organisation allows for more long-term success and greater investments. With this, objective and thorough analyses of the work done and future requirements become irreplaceable. This in turn opens the door for the instalment or development of analysis departments and analyst positions within elite football teams. These analysts, usually coming from a scientific background, rely on accurate and reliable data. The quality of the analyses, or analysts for that matter, then depends on the work done and choices made. The current research programme was designed to guide practitioners to effectively analyse and apply the data currently collected in elite football. Because match analysis in football has come a long way since first mentioned in a scientific journal in 1968. From basic notational metrics collected live during matches, through comprehensively studying video footage and having computers take over the collection of match parameters altogether. Currently, no matter whether positional time-motion data, metrics describing all on-the-ball match events or computerised combinations of the two are taken into consideration, the possibilities are seemingly endless. That means, analysts should be aware of the context of the data in order to appropriately interpret the results. Generally speaking, the focus and goals of the analyses should be clear and that is where this research programme started off. In many elite sports, like football, being successful depends on winning. Whether this is a short-term requirement or is treated as a long-term process with potential setbacks anticipated, is a decision made by clubs and directors. On the field, where the coach is responsible and analysts often support decision making, success often depends on scoring goals. Regardless of the fact one wants to score more or concede less than the opponent, at least one goal is required to win. That is why the current research programme acknowledged a goal to be the most decisive event in elite football. With that notion in mind, multiple studies were designed to answer the question of how teams can become more effective in scoring goals. The first study was designed to determine the differences between shots that led to a goal and shots that did not. This was done by studying attempts made from statistically identical locations on the pitch, however with changing situational circumstances (context). It was found that the magnitude of effect of opponent positioning changed for different shooting locations and offensive players. The results showed that the selected contextual factors were not able to explain all variance in shooting outcome, however that they should be kept in mind whilst analysing match events. Generally, since opponent presence and pressure were found to influence some shots, the notion that time (e.g. space) is of importance during an attacking sequence came to light. How and when this space between opposing players came to be, was studied in the second investigation of the current programme. Since (theoretically) balance exists between both teams of eleven players, a perturbation of this balance needs to occur prior to a goal scoring opportunity. Expert observers qualitatively analysed a series of match events between elite teams from ball recovery to the moment of the shot. Specific playing styles or actions were not identified to disturb a team's balance; however, agreement was found for a timepoint approximately five seconds prior to the shot to be most detrimental. Furthermore, experts showed stronger agreements when a sequence led to a goal, although they were unaware of the outcome. This importance of a strong perturbation, highlighted, again, the significance of sufficient space for an attacker to release a threatening shot. Finally, also since the balance was disturbed some time before the shot, there seems to be more at hand during a successful attack than a simply well-executed shot. After validating a low-cost tracking system in the third study, so this could be used in a sub-elite environment with a team willing to share full time-motion and tactical data, the final, fourth, study was designed. Here, physical parameters prior to shooting attempts were compared for different outcomes. It was found that an increased physical output, describing both the covered distance and intensity of movements, and fewer defenders behind the ball related to greater attacking success. Similarly, when defenders had to cover more distance prior to a shot, the chances of conceding a goal increased too. Together with a noteworthy relationship between lower match output and both attacking as well as defensive success, the importance of creating space or covering opponents were highlighted once more. Conclusively, by taking football's most decisive event, a goal, into account, the understanding of how to play more effectively has considerably grown. At the same time, the current research programme showed how analysts could effectively apply commonly collected match data into day-to-day practice. By identifying and acknowledging the context during crucial events, more information towards improved decision making and player profiling may be gathered. Future scientific studies may take this applied approach as a guideline for worthwhile large-scale solutions. With machines capable of learning along the way and taking comprehensive datasets into account, the potential for match analysts is substantial. With science supporting practitioners to answer the questions asked by coached and directors, financial investments in both fields may follow and allow for a bright future

The Iray Light Transport Simulation and Rendering System

While ray tracing has become increasingly common and path tracing is well understood by now, a major challenge lies in crafting an easy-to-use and efficient system implementing these technologies. Following a purely physically-based paradigm while still allowing for artistic workflows, the Iray light transport simulation and rendering system allows for rendering complex scenes by the push of a button and thus makes accurate light transport simulation widely available. In this document we discuss the challenges and implementation choices that follow from our primary design decisions, demonstrating that such a rendering system can be made a practical, scalable, and efficient real-world application that has been adopted by various companies across many fields and is in use by many industry professionals today

A Nation Deceived: How Schools Hold Back America's Brightest Students, Volume II

Provides a comprehensive review of research on the academic acceleration of gifted students

What Do Parents Really Want? Parent Perspectives on Gifted Education

In this research study, the correlation between the strategies that previous research had indicated as effective for gifted education and the programming sought by parents of gifted children was examined. Survey results and interviews with parents revealed several strategies that parents wanted to be implemented in gifted education as well as powerful practices that would enhance gifted education if implemented by school leaders. The problem of underachievement among gifted students is also discussed as well as strategies to reverse it

Relationships between unilateral horizontal and vertical drop jumps and 20 metre sprint performance

Objectives: The purpose of this study was to compare the relationships between horizontal (HDJ) and vertical drop jumps (VDJ) to sprint performance. Design: Exploratory Study. Setting: Laboratory. Participants: Nineteen male collegiate participants (22.5 ± 3.2 years, 181.1 ± 6.7 cm, 80.3 ± 9.6 kg). Main outcome measures: All participants performed VDJ and HDJ from a 20 cm height onto an AMTI force platform sampling at 1200 Hz before performing three 20 m sprints.Sprint times (5, 10, 15, 20, 5-10, 10-15, 15-20 m) were measured using a LAVEG speed gun. Results: All jump and sprint measures showed excellent within session reliability (ICC: 0.954 to 0.99). Pearson's and Spearman's correlations revealed significant (p < 0.01) moderate to high correlations between jump measures and sprint times (R: -0.665 to -0.769). Stepwise multiple regression revealed jump distance normalised by body height (HDJ) was the best predictor for 10, 20, 5-10, 10-15 and 15-20 m sprint times (R2 = 41% to 48%). Conclusions: HDJ performance measures provide stronger relationships to sprint performance than VDJ's. Thus,HDJ's should be considered in test batteries to monitor training and rehabilitation for athletes in sprint related sports

Perfect sampling of Jackson Queueing Networks

We consider open Jackson networks with losses with mixed finite and infinite queues and analyze the efficiency of sampling from their exact stationary distribution. We show that perfect sampling is possible, although the underlying Markov chain may have an infinite state space. The main idea is to use a Jackson network with infinite buffers (that has a product form stationary distribution) to bound the number of initial conditions to be considered in the coupling from the past scheme. We also provide bounds on the sampling time of this new perfect sampling algorithm for acyclic or hyperstable networks. These bounds show that the new algorithm is considerably more efficient than existing perfect samplers even in the case where all queues are finite. We illustrate this efficiency through numerical experiments. We also extend our approach to non-monotone networks such as queueing networks with negative customers.On considère les réseaux de Jackson avec perte comportant des files finies et infinies, et l'on s'intéresse à l'efficacité des techniques d'échantillonnage de leur distribution stationnaire exacte. Nous démontrons que la simulation parfaite est possible même si la chaîne de Markov sous-jacente a un espace d'états potentiellement infini. L'idée principale est d'utiliser un réseau de Jackson aux files infinies (qui admet une distribution de forme-produit) pour borner les conditions initiales à considérer dans l'algorithme de simulation parfaite. Nous donnons également des bornes sur le temps d'échantillonnage de ce nouvel algorithme dans le cas des réseaux acycliques, ainsi que pour des réseaux hyperstables. Ces bornes prouvent que le nouvel algorithme est considérablement plus efficace que les échantillonneurs parfaits acuels, même dans le cas où toutes les files sont finies. Nous illustrons cette efficacité par des expériences numériques. Enfin, nous généralisons notre approche au cas des réseaux non-monotones comme les réseaux aux clients négatifs