Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Branching processes and computational collapse of discretized unimodal mappings

In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systems induced by unimodal mappings of the unit interval. The problem reduces to studying set-valued negative semitrajectories of the discretized system. As the grid is refined, the asymptotic behavior of the cardinality structure of the semitrajectories follows probabilistic laws corresponding to a branching process. The transition probabilities of this process are explicitly calculated. These results are illustrated by the example of the discretized logistic mapping.

Quantum Parrondo's games

Parrondo's paradox arises when two losing games are combined to produce a winning one. A history-dependent quantum Parrondo game is studied where the rotation operators that represent the toss of a classical biased coin are replaced by general SU(2) operators to transform the game into the quantum domain. In the initial state, a superposition of qubits can be used to couple the games and produce interference leading to quite different payoffs to those in the classical case. (C) 2002 Elsevier Science B.V. All rights reserved.

Effect of periparturient diseases accompanied by excessive vulval discharge and weaning to mating interval on sow reproductive performance

Objective To evaluate the effect of periparturient disease accompanied by vulval discharge, and weaning-to-mating intervals, on sow fertility and litter size. Design Reproductive data were collected and analysed from 19 Hungarian swine herds over a 4 year period. Conception rates, farrowing rates and litter sizes of sows with periparturient disease accompanied by vulval discharge were used to evaluate the relationship between duration of vulval discharge and subsequent fertility and litter size. The possibility of interactions between weaning-to-mating intervals and duration of vulval discharges was investigated to determine if there was any effect on subsequent fertility and litter size. Results and conclusions Both parity 1 and parity 2 to 8 sows having had periparturient disease accompanied by vulval discharge in excess of 6 days duration had significantly (P < 0.001) lower subsequent fertility (conception, farrowing and adjusted farrowing rates) compared with sows of similar parity where the duration of vulval discharge was < 4 or 4 to 6 days. There was no difference in fertility rates between sows, in both parity categories, with vulval discharge for < 4 days compared with 4 to 6 days. A duration of vulval discharge in excess of 6 days in parity 1 sows significantly reduced litter size (total born and live-born) in subsequent farrowings, but not in parity 2 to 8 sows. There was no interaction between the duration of vulval discharge and post-weaning to mating intervals. However sows with weaning to mating intervals between 7 and 10 days had smaller (P < 0.001) subsequent litter sizes compared with 3 to 6 or 11 to 14 day intervals. It was concluded that the duration of vulval discharge in excess of 6 days was an indication of a severe persistent endometritis adversely affecting fertility of sows.

Interval training program optimization in highly trained endurance cyclists

Purpose: The purpose of this study was to examine the influence of three different high-intensity interval training (HIT) regimens on endurance performance in highly trained endurance athletes. Methods: Before, and after 2 and 4 wk of training, 38 cyclists and triathletes (mean +/- SD; age = 25 +/- 6 yr; mass = 75 +/- 7 kg; (V)over dot O-2peak = 64.5 +/- 5.2 mL.kg(-1).min(-1)) performed: 1) a progressive cycle test to measure peak oxygen consumption ((V)over dotO(2peak)) and peak aerobic power output (PPO), 2) a time to exhaustion test (T-max) at their (V)over dotO(2peak) power output (P-max), as well as 3) a 40-kin time-trial (TT40). Subjects were matched and assigned to one of four training groups (G(1), N = 8, 8 X 60% T-max P-max, 1:2 work:recovery ratio; G(2), N = 9, 8 X 60% T-max at P-max, recovery at 65% HRmax; G(3), N = 10, 12 X 30 s at 175% PPO, 4.5-min recovery; G(CON), N = 11). In addition to G(1) G(2), and G(3) performing HIT twice per week, all athletes maintained their regular low-intensity training throughout the experimental period. Results: All HIT groups improved TT40 performance (+4.4 to +5.8%) and PPO (+3.0 to +6.2%) significantly more than G(CON) (-0.9 to + 1.1 %; P < 0.05). Furthermore, G(1) (+5.4%) and G(2) (+8.1%) improved their (V)over dot O-2peak significantly more than G(CON) (+ 1.0%; P < 0.05). Conclusion: The present study has shown that when HIT incorporates P-max as the interval intensity and 60% of T-max as the interval duration, already highly trained cyclists can significantly improve their 40-km time trial performance. Moreover, the present data confirm prior research, in that repeated supramaximal HIT can significantly improve 40-km time trial performance.

Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods

There has been a resurgence of interest in the mean trace length estimator of Pahl for window sampling of traces. The estimator has been dealt with by Mauldon and Zhang and Einstein in recent publications. The estimator is a very useful one in that it is non-parametric. However, despite some discussion regarding the statistical distribution of the estimator, none of the recent works or the original work by Pahl provide a rigorous basis for the determination a confidence interval for the estimator or a confidence region for the estimator and the corresponding estimator of trace spatial intensity in the sampling window. This paper shows, by consideration of a simplified version of the problem but without loss of generality, that the estimator is in fact the maximum likelihood estimator (MLE) and that it can be considered essentially unbiased. As the MLE, it possesses the least variance of all estimators and confidence intervals or regions should therefore be available through application of classical ML theory. It is shown that valid confidence intervals can in fact be determined. The results of the work and the calculations of the confidence intervals are illustrated by example. (C) 2003 Elsevier Science Ltd. All rights reserved.

Induction in the timed interval calculus

The Timed Interval Calculus, a timed-trace formalism based on set theory, is introduced. It is extended with an induction law and a unit for concatenation, which facilitates the proof of properties over trace histories. The effectiveness of the extended Timed Interval Calculus is demonstrated via a benchmark case study, the mine pump. Specifically, a safety property relating to the operation of a mine shaft is proved, based on an implementation of the mine pump and assumptions about the environment of the mine. (C) 2002 Elsevier Science B.V. All rights reserved.

Augmented Reality for Games

In this text, we intend to explore augmented reality as a means to visualise interactive communication projects. With ARToolkit, Virtools and 3ds Max applications, we aim to show how to create a portable interactive platform that resorts to the environment and markers for constructing the game’s scenario. We plan to show that the realism of simulation, together with the merger of artificial objects with the real world, can generate interactive empathy between players and their avatars.

The uncanny valley, notes on the realism of “living” creatures in digital games and their relationships with the player

Neste artigo argumenta-se que as simulações numéricas fomentam e exploram relações complexas entre o jogador e o sistema cibernético da máquina que com este se relaciona através da jogabilidade, ou seja, da real aplicação às regras de jogo de tácticas e estratégias usadas pelo participante durante o seu trajecto na aplicação lúdica. Considera-se que o espaço mágico imposto pelo tabuleiro de jogo é mais do que um espaço de confusão entre real e artificial mas antes se apresenta como uma cortina ou interface entre o corpo próprio do participante e a simulação digital inerente ao sistema computacional.

Ball Recovery in the Handball Tournament of the 2008 Beijing Olympic Games: Sequential Analysis of Positional Play as Used by the Spanish Team’s Defence

In sport there is a great need to obtain as much information as possible about the factors which affect the dynamics of play. This study uses sequential analysis and temporal patterns (T-patterns)to examine the evolution of defence (against an equal number of attackers)as used by the Spanish handball team at the Beijing 2008 Olympic Games. The aim is to help handball coaches (during their training and gathering of professional experience)to understand the importance of the structure of defensive systems. This can be achieved through observational processes that reveal the evolution and adaptation of these defensive systems according to different variables: the match score, the response of the opposing team and progress through the tournament.

Agreement between data obtained from repeated interviews with a six-years interval

The objective of the study was to compare information collected through face-to-face interviews at first time and six years later in a city of Southeastern Brazil. In 1998, 32 mothers (N=32) of children aged 20 to 30 months answered a face-to-face interview with structured questions regarding their children's brushing habits. Six years later this same interview was repeated with the same mothers. Both interviews were compared for overall agreement, kappa and weighted kappa. Overall agreement between both interviews varied from 41 to 96%. Kappa values ranged from 0.00 to 0.65 (very bad to good) without any significant differences. The results showed lack of agreement when the same interview is conducted six years later, showing that the recall bias can be a methodological problem of interviews.