CoachNet: The further development of a coordinated network for sport coaching in Europe

Leeds Metropolitan University (LMU), in partnership with the European Coaching Council (ECC), was successful in a bid to the European Commission under the Preparatory Action in the Field of Sport (EAC/18/2011). The project was designed to develop an innovative approach that would contribute to the strengthening of the organisation of sport in Europe as part of the ‘good governance, strand of the EU Preparatory Action in the Field of Sport. The primary objective was to examine ways in which the organisation of coaching could be enhanced in Europe, with a particular focus on the greater involvement of coaches in decisionmaking. In exploring ways to maximise the ‘voice of the coach’, the partnership between LMU and ECC was central to the project. ECC is the continental division of the International Council for Coaching Excellence (ICCE). Through its network, ECC was in a position to identify current organisational arrangements for coaching across Europe. LMU is a well established research and practice oriented university in the UK and played a lead role in coordinating the project and guiding the research methodology through its Sport Coaching and Physical Education (SCOPE) Research and Enterprise Centre. Varying arrangements for the development and management of coaching were observed through a study of European countries. Within this varied landscape, the representation of coaches was sporadic, ranging from no representative mechanism to a number of good practice examples that made provision for the tiered engagement of coaches depending on their role; sport and coaching status category. These examples included confederated models across sports; blended models across coaching status categories and single and multi-sport models for the engagement and representation of coaches. The study concluded that there is a need for a more considered approach to the involvement of coaches in decision-making, with a number of recommendations developed for consideration by member states and the European divisions of the International Federations. These recommendations proposed that the structure of ECC as the European arm of ICCE be reviewed, with the intention to more strongly engage organisations that have been established to represent the voice of coaches and leading to a re-structuring of the organisation. In this context, ICCE and ECC should play an even stronger advocacy, representative and action role in establishing coaching as a blended profession, which includes volunteer, part-time paid and full-time paid coaches. More coherent structures for the engagement of coaches in each sport and country are also recommended. This should occur as part of a wider commitment that the principle of listening to and hearing the voice of the coach should become more strongly embedded within the way in which sporting and related organisations operate. The EU is well placed to lead on this type of approach, ensuring the coaches are more fully engaged in social dialogue and in the process to further enhance the role of sport and coaching in Europe. Further research is also recommended on the nature, needs and demographics of the coaching workforce. All of these approaches need to be tempered with the realisation that coaches are individual decision-makers, operating in a wide variety of contexts and many of whom do not show a propensity for involvement in formal ‘representative’ structures. The need for alternative methods to connect with and engage coaches was, therefore, identified. These include a more segmented approach to engaging with coaches, depending on their coaching role and status, as well as the utilisation of more informal modes of web-based communication to connect directly with coaches in their daily lives. In all existing and future scenarios, the key role of federations at the national and international level in seeking, activating and allocating financial and other resources to connect with and support their coaches was highlighted. The findings have been notified to ICCE for formal consideration, leading to changes in the ways in which the voice of the coach is more clearly represented within the work of the organisation. ICCE should continue to work closely with the EU Sport Unit to ensure that the recommendations of this report are implemented and evaluated on an on-going basis

Generalized entropy arising from a distribution of q-indices

It is by now well known that the Boltzmann-Gibbs (BG) entropy $S_{BG}=-k\sum_{i=1}^W p_i \ln p_i$ can be usefully generalized into the entropy $S_q=k (1-\sum_{i=1}^Wp_i^{q}) / (q-1)$ ($q\in \mathcal{R}; S_1=S_{BG}$). Microscopic dynamics determines, given classes of initial conditions, the occupation of the accessible phase space (or of a symmetry-determined nonzero-measure part of it), which in turn appears to determine the entropic form to be used. This occupation might be a uniform one (the usual {\it equal probability hypothesis} of BG statistical mechanics), which corresponds to $q=1$; it might be a free-scale occupancy, which appears to correspond to $q \ne 1$. Since occupancies of phase space more complex than these are surely possible in both natural and artificial systems, the task of further generalizing the entropy appears as a desirable one, and has in fact been already undertaken in the literature. To illustrate the approach, we introduce here a quite general entropy based on a distribution of $q$-indices thus generalizing $S_q$. We establish some general mathematical properties for the new entropic functional and explore some examples. We also exhibit a procedure for finding, given any entropic functional, the $q$-indices distribution that produces it. Finally, on the road to establishing a quite general statistical mechanics, we briefly address possible generalized constraints under which the present entropy could be extremized, in order to produce canonical-ensemble-like stationary-state distributions for Hamiltonian systems.Comment: 14 pages including 3 figure

A nonextensive thermodynamical equilibrium approach in e+e−→hadronse^+ e^- \to hadrons

We show that the inclusion of long distance effect, expected in strong interactions, through a nonextensive thermodynamical approach is able to explain the experimental distribution of the transverse momentum of the hadrons with respect to the jet axis ($p_{t}$) $e^+ e^- \to hadron$ reaction. The observed deviation from the exponential behavior, predicted by the Boltzmann-Gibbs thermodynamical treatment, is automatically recovered by the nonextensive Tsallis statistics used here. We fitted the observed $p_{t}$ spectrum in the range of 14 GeV to 161 GeV and obtained, besides a good fit, the theoretical important fact that the temperature becomes independent of the primary energy.Comment: 9 pages, 2 eps figure

On a generalization of the binomial distribution and its Poisson-like limit

We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We discuss under which conditions this distribution can have a probabilistic interpretation.Comment: 17 pages, 6 figure

Option Pricing Formulas based on a non-Gaussian Stock Price Model

Options are financial instruments that depend on the underlying stock. We explain their non-Gaussian fluctuations using the nonextensive thermodynamics parameter $q$. A generalized form of the Black-Scholes (B-S) partial differential equation, and some closed-form solutions are obtained. The standard B-S equation ($q=1$) which is used by economists to calculate option prices requires multiple values of the stock volatility (known as the volatility smile). Using $q=1.5$ which well models the empirical distribution of returns, we get a good description of option prices using a single volatility.Comment: final version (published

Correlation functions in the factorization approach of nonextensive quantum statistics

We study the long range behavior of a gas whose partition function depends on a parameter q and it has been claimed to be a good approximation to the partition function proposed in the formulation of nonextensive statistical mechanics. We compare our results, at large temperatures and at the critical point, with the case of Boltzmann-Gibbs thermodynamics for the case of a Bose-Einstein gas. In particular, we find that for all temperatures the long range correlations in a Bose gas decrease when the value of q departs from the standard value q=1.Comment: revtex file, 10 pages, two eps style figures, packaged as a single tar.gz fil

Generalized Heisenberg Algebras and Fibonacci Series

We have constructed a Heisenberg-type algebra generated by the Hamiltonian, the step operators and an auxiliar operator. This algebra describes quantum systems having eigenvalues of the Hamiltonian depending on the eigenvalues of the two previous levels. This happens, for example, for systems having the energy spectrum given by Fibonacci sequence. Moreover, the algebraic structure depends on two functions f(x) and g(x). When these two functions are linear we classify, analysing the stability of the fixed points of the functions, the possible representations for this algebra.Comment: 24 pages, 2 figures, subfigure.st

On a generalised model for time-dependent variance with long-term memory

The ARCH process (R. F. Engle, 1982) constitutes a paradigmatic generator of stochastic time series with time-dependent variance like it appears on a wide broad of systems besides economics in which ARCH was born. Although the ARCH process captures the so-called "volatility clustering" and the asymptotic power-law probability density distribution of the random variable, it is not capable to reproduce further statistical properties of many of these time series such as: the strong persistence of the instantaneous variance characterised by large values of the Hurst exponent (H > 0.8), and asymptotic power-law decay of the absolute values self-correlation function. By means of considering an effective return obtained from a correlation of past returns that has a q-exponential form we are able to fix the limitations of the original model. Moreover, this improvement can be obtained through the correct choice of a sole additional parameter, $q_{m}$. The assessment of its validity and usefulness is made by mimicking daily fluctuations of SP500 financial index.Comment: 6 pages, 4 figure

Nonequilibrium Probabilistic Dynamics of the Logistic Map at the Edge of Chaos

We consider nonequilibrium probabilistic dynamics in logistic-like maps $x_{t+1}=1-a|x_t|^z$, $(z>1)$ at their chaos threshold: We first introduce many initial conditions within one among $W>>1$ intervals partitioning the phase space and focus on the unique value $q_{sen}<1$ for which the entropic form $S_q \equiv \frac{1-\sum_{i=1}^{W} p_i^q}{q-1}$ {\it linearly} increases with time. We then verify that $S_{q_{sen}}(t) - S_{q_{sen}}(\infty)$ vanishes like $t^{-1/[q_{rel}(W)-1]}$ [$q_{rel}(W)>1$]. We finally exhibit a new finite-size scaling, $q_{rel}(\infty) - q_{rel}(W) \propto W^{-|q_{sen}|}$. This establishes quantitatively, for the first time, a long pursued relation between sensitivity to the initial conditions and relaxation, concepts which play central roles in nonextensive statistical mechanics.Comment: Final version with new Title and small modifications. REVTeX, 8 pages and 4 eps figure