The constraints-based approach to motor learning : Implications for a non-linear pedagogy in sport and physical education

Recently, a constraints- led approach has been promoted as a framework for understanding how children and adults acquire movement skills for sport and exercise (see Davids, Button & Bennett, 2008; Araújo et al., 2004). The aim of a constraints- led approach is to identify the nature of interacting constraints that influence skill acquisition in learners. In this chapter the main theoretical ideas behind a constraints- led approach are outlined to assist practical applications by sports practitioners and physical educators in a non- linear pedagogy (see Chow et al., 2006, 2007). To achieve this goal, this chapter examines implications for some of the typical challenges facing sport pedagogists and physical educators in the design of learning programmes.

Asymptotic and numerical results for a model of solvent-dependent drug diffusion through polymeric spheres

A model for drug diffusion from a spherical polymeric drug delivery device is considered. The model contains two key features. The first is that solvent diffuses into the polymer, which then transitions from a glassy to a rubbery state. The interface between the two states of polymer is modelled as a moving boundary, whose speed is governed by a kinetic law; the same moving boundary problem arises in the one-phase limit of a Stefan problem with kinetic undercooling. The second feature is that drug diffuses only through the rubbery region, with a nonlinear diffusion coefficient that depends on the concentration of solvent. We analyse the model using both formal asymptotics and numerical computation, the latter by applying a front-fixing scheme with a finite volume method. Previous results are extended and comparisons are made with linear models that work well under certain parameter regimes. Finally, a model for a multi-layered drug delivery device is suggested, which allows for more flexible control of drug release.

Optimal-stopping control for airborne collision avoidance and return-to-course flight

This paper considers an aircraft collision avoidance design problem that also incorporates design of the aircraft’s return-to-course flight. This control design problem is formulated as a non-linear optimal-stopping control problem; a formulation that does not require a prior knowledge of time taken to perform the avoidance and return-to-course manoeuvre. A dynamic programming solution to the avoidance and return-to-course problem is presented, before a Markov chain numerical approximation technique is described. Simulation results are presented that illustrate the proposed collision avoidance and return-to-course flight approach.

The impact of temperature on mortality in Tianjin, China : a case-crossover design with a distributed lag non-linear model

Background There has been increasing interest in assessing the impacts of temperature on mortality. However, few studies have used a case–crossover design to examine non-linear and distributed lag effects of temperature on mortality. Additionally, little evidence is available on the temperature-mortality relationship in China, or what temperature measure is the best predictor of mortality. Objectives To use a distributed lag non-linear model (DLNM) as a part of case–crossover design. To examine the non-linear and distributed lag effects of temperature on mortality in Tianjin, China. To explore which temperature measure is the best predictor of mortality; Methods: The DLNM was applied to a case¬−crossover design to assess the non-linear and delayed effects of temperatures (maximum, mean and minimum) on deaths (non-accidental, cardiopulmonary, cardiovascular and respiratory). Results A U-shaped relationship was consistently found between temperature and mortality. Cold effects (significantly increased mortality associated with low temperatures) were delayed by 3 days, and persisted for 10 days. Hot effects (significantly increased mortality associated with high temperatures) were acute and lasted for three days, and were followed by mortality displacement for non-accidental, cardiopulmonary, and cardiovascular deaths. Mean temperature was a better predictor of mortality (based on model fit) than maximum or minimum temperature. Conclusions In Tianjin, extreme cold and hot temperatures increased the risk of mortality. Results suggest that the effects of cold last longer than the effects of heat. It is possible to combine the case−crossover design with DLNMs. This allows the case−crossover design to flexibly estimate the non-linear and delayed effects of temperature (or air pollution) whilst controlling for season.

Multi-objective optimisation of bijective s-boxes

In this paper we investigate the heuristic construction of bijective s-boxes that satisfy a wide range of cryptographic criteria including algebraic complexity, high nonlinearity, low autocorrelation and have none of the known weaknesses including linear structures, fixed points or linear redundancy. We demonstrate that the power mappings can be evolved (by iterated mutation operators alone) to generate bijective s-boxes with the best known tradeoffs among the considered criteria. The s-boxes found are suitable for use directly in modern encryption algorithms.

Optimistic linear programming gives logarithmic regret for irreducible MDPs

We present an algorithm called Optimistic Linear Programming (OLP) for learning to optimize average reward in an irreducible but otherwise unknown Markov decision process (MDP). OLP uses its experience so far to estimate the MDP. It chooses actions by optimistically maximizing estimated future rewards over a set of next-state transition probabilities that are close to the estimates, a computation that corresponds to solving linear programs. We show that the total expected reward obtained by OLP up to time T is within C(P) log T of the reward obtained by the optimal policy, where C(P) is an explicit, MDP-dependent constant. OLP is closely related to an algorithm proposed by Burnetas and Katehakis with four key differences: OLP is simpler, it does not require knowledge of the supports of transition probabilities, the proof of the regret bound is simpler, but our regret bound is a constant factor larger than the regret of their algorithm. OLP is also similar in flavor to an algorithm recently proposed by Auer and Ortner. But OLP is simpler and its regret bound has a better dependence on the size of the MDP.

High-probability regret bounds for bandit online linear optimization

We present a modification of the algorithm of Dani et al. [8] for the online linear optimization problem in the bandit setting, which with high probability has regret at most O ∗ ( √ T) against an adaptive adversary. This improves on the previous algorithm [8] whose regret is bounded in expectation against an oblivious adversary. We obtain the same dependence on the dimension (n 3/2) as that exhibited by Dani et al. The results of this paper rest firmly on those of [8] and the remarkable technique of Auer et al. [2] for obtaining high probability bounds via optimistic estimates. This paper answers an open question: it eliminates the gap between the high-probability bounds obtained in the full-information vs bandit settings.

Some novel techniques of parameter estimation for the dynamical models in biological systems

Inverse problems based on using experimental data to estimate unknown parameters of a system often arise in biological and chaotic systems. In this paper, we consider parameter estimation in systems biology involving linear and non-linear complex dynamical models, including the Michaelis–Menten enzyme kinetic system, a dynamical model of competence induction in Bacillus subtilis bacteria and a model of feedback bypass in B. subtilis bacteria. We propose some novel techniques for inverse problems. Firstly, we establish an approximation of a non-linear differential algebraic equation that corresponds to the given biological systems. Secondly, we use the Picard contraction mapping, collage methods and numerical integration techniques to convert the parameter estimation into a minimization problem of the parameters. We propose two optimization techniques: a grid approximation method and a modified hybrid Nelder–Mead simplex search and particle swarm optimization (MH-NMSS-PSO) for non-linear parameter estimation. The two techniques are used for parameter estimation in a model of competence induction in B. subtilis bacteria with noisy data. The MH-NMSS-PSO scheme is applied to a dynamical model of competence induction in B. subtilis bacteria based on experimental data and the model for feedback bypass. Numerical results demonstrate the effectiveness of our approach.

Linear models for endocytic transformations from live cell imaging

Endocytosis is the process by which cells internalise molecules including nutrient proteins from the extracellular media. In one form, macropinocytosis, the membrane at the cell surface ruffles and folds over to give rise to an internalised vesicle. Negatively charged phospholipids within the membrane called phosphoinositides then undergo a series of transformations that are critical for the correct trafficking of the vesicle within the cell, and which are often pirated by pathogens such as Salmonella. Advanced fluorescent video microscopy imaging now allows the detailed observation and quantification of these events in live cells over time. Here we use these observations as a basis for building differential equation models of the transformations. An initial investigation of these interactions was modelled with reaction rates proportional to the sum of the concentrations of the individual constituents. A first order linear system for the concentrations results. The structure of the system enables analytical expressions to be obtained and the problem becomes one of determining the reaction rates which generate the observed data plots. We present results with reaction rates which capture the general behaviour of the reactions so that we now have a complete mathematical model of phosphoinositide transformations that fits the experimental observations. Some excellent fits are obtained with modulated exponential functions; however, these are not solutions of the linear system. The question arises as to how the model may be modified to obtain a system whose solution provides a more accurate fit.