Profiling in sport using momentum and perturbations

Examining a team’s performance from a physical point of view their momentum might indicate unexpected turning points in defeat or success. Physicists describe this value as to require some effort to be started, but also that it is relatively easy to keep it going once a sufficient level is reached (Reed and Hughes, 2006). Unlike football, rugby, handball and many more sports, a regular volleyball match is not limited by time but by points that need to be gathered. Every minute more than one point is won by either one team or the other. That means a series of successive points enlarges the gap between the teams making it more and more difficult to catch up with the leading one. This concept of gathering momentum, or the reverse in a performance, can give the coaches, athletes and sports scientists further insights into winning and losing performances. Momentum investigations also contain dependencies between performances or questions if future performances are reliant upon past streaks. Squash and volleyball share the characteristic of being played up to a certain amount of points. Squash was examined according to the momentum of players by Hughes et al. (2006). The initial aim was to expand normative profiles of elite squash players using momentum graphs of winners and errors to explore ‘turning points’ in a performance. Dynamic systems theory has enabled the definition of perturbations in sports exhibiting rhythms (Hughes et al., 2000; McGarry et al., 2002; Murray et al., 2008), and how players and teams cause these disruptions of rhythm can inform on the way they play, these techniques also contribute to profiling methods. Together with the analysis of one’s own performance it is essential to have an understanding of your oppositions’ tactical strengths and weaknesses. By modelling the oppositions’ performance it is possible to predict certain outcomes and patterns, and therefore intervene or change tactics before the critical incident occurs. The modelling of competitive sport is an informative analytic technique as it directs the attention of the modeller to the critical aspects of data that delineate successful performance (McGarry & Franks, 1996). Using tactical performance profiles to pull out and visualise these critical aspects of performance, players can build justified and sophisticated tactical plans. The area is discussed and reviewed, critically appraising the research completed in this element of Performance Analysis.

Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l ∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel–Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system’s data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504–1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system’s coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.

A note on the periodic orbits of a self excited rigid body

The aim of the present paper is to study the periodic orbits of a perturbed self excited rigid body with a fixed point. For studying these periodic orbits we shall use averaging theory of first order.

Stability in Linear Optimization Under Perturbations of the Left-Hand Side Coefficients

This paper studies stability properties of linear optimization problems with finitely many variables and an arbitrary number of constraints, when only left hand side coefficients can be perturbed. The coefficients of the constraints are assumed to be continuous functions with respect to an index which ranges on certain compact Hausdorff topological space, and these properties are preserved by the admissible perturbations. More in detail, the paper analyzes the continuity properties of the feasible set, the optimal set and the optimal value, as well as the preservation of desirable properties (boundedness, uniqueness) of the feasible and of the optimal sets, under sufficiently small perturbations.

Efficient split eld FDTD analysis of third-order nonlinear materials in two-dimensionally periodic media

In this work the split-field finite-difference time-domain method (SF-FDTD) has been extended for the analysis of two-dimensionally periodic structures with third-order nonlinear media. The accuracy of the method is verified by comparisons with the nonlinear Fourier Modal Method (FMM). Once the formalism has been validated, examples of one- and two-dimensional nonlinear gratings are analysed. Regarding the 2D case, the shifting in resonant waveguides is corroborated. Here, not only the scalar Kerr effect is considered, the tensorial nature of the third-order nonlinear susceptibility is also included. The consideration of nonlinear materials in this kind of devices permits to design tunable devices such as variable band filters. However, the third-order nonlinear susceptibility is usually small and high intensities are needed in order to trigger the nonlinear effect. Here, a one-dimensional CBG is analysed in both linear and nonlinear regime and the shifting of the resonance peaks in both TE and TM are achieved numerically. The application of a numerical method based on the finite- difference time-domain method permits to analyse this issue from the time domain, thus bistability curves are also computed by means of the numerical method. These curves show how the nonlinear effect modifies the properties of the structure as a function of variable input pump field. When taking the nonlinear behaviour into account, the estimation of the electric field components becomes more challenging. In this paper, we present a set of acceleration strategies based on parallel software and hardware solutions.