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

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

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

The Edge of Quantum Chaos

We identify a border between regular and chaotic quantum dynamics. The border is characterized by a power law decrease in the overlap between a state evolved under chaotic dynamics and the same state evolved under a slightly perturbed dynamics. For example, the overlap decay for the quantum kicked top is well fitted with $[1+(q-1) (t/\tau)^2]^{1/(1-q)}$ (with the nonextensive entropic index $q$ and $\tau$ depending on perturbation strength) in the region preceding the emergence of quantum interference effects. This region corresponds to the edge of chaos for the classical map from which the quantum chaotic dynamics is derived.Comment: 4 pages, 4 figures, revised version in press PR

Construction of coherent states for physical algebraic systems

We construct a general state which is an eigenvector of the annihilation operator of the Generalized Heisenberg Algebra. We show for several systems, which are characterized by different energy spectra, that this general state satisfies the minimal set of conditions required to obtain Klauder's minimal coherent states.Comment: 15 pages, 3 figure

Logarithmic diffusion and porous media equations: a unified description

In this work we present the logarithmic diffusion equation as a limit case when the index that characterizes a nonlinear Fokker-Planck equation, in its diffusive term, goes to zero. A linear drift and a source term are considered in this equation. Its solution has a lorentzian form, consequently this equation characterizes a super diffusion like a L\'evy kind. In addition is obtained an equation that unifies the porous media and the logarithmic diffusion equations, including a generalized diffusion equation in fractal dimension. This unification is performed in the nonextensive thermostatistics context and increases the possibilities about the description of anomalous diffusive processes.Comment: 5 pages. To appear in Phys. Rev.