Mathematical models of games of chance: Epistemological taxonomy and potential in problem-gambling research

Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of the knowledge attached to mathematical models of games of chance and the act of modeling, arguing that such knowledge holds potential in the prevention and cognitive treatment of excessive gambling, and I propose further research in this direction

Perturbative calculation of quasi-potential in non-equilibrium diffusions: a mean-field example

In stochastic systems with weak noise, the logarithm of the stationary distribution becomes proportional to a large deviation rate function called the quasi-potential. The quasi-potential, and its characterization through a variational problem, lies at the core of the Freidlin-Wentzell large deviations theory%.~\cite{freidlin1984}.In many interacting particle systems, the particle density is described by fluctuating hydrodynamics governed by Macroscopic Fluctuation Theory%, ~\cite{bertini2014},which formally fits within Freidlin-Wentzell's framework with a weak noise proportional to $1/\sqrt{N}$, where $N$ is the number of particles. The quasi-potential then appears as a natural generalization of the equilibrium free energy to non-equilibrium particle systems. A key physical and practical issue is to actually compute quasi-potentials from their variational characterization for non-equilibrium systems for which detailed balance does not hold. We discuss how to perform such a computation perturbatively in an external parameter $\lambda$, starting from a known quasi-potential for $\lambda=0$. In a general setup, explicit iterative formulae for all terms of the power-series expansion of the quasi-potential are given for the first time. The key point is a proof of solvability conditions that assure the existence of the perturbation expansion to all orders. We apply the perturbative approach to diffusive particles interacting through a mean-field potential. For such systems, the variational characterization of the quasi-potential was proven by Dawson and Gartner%. ~\cite{dawson1987,dawson1987b}. Our perturbative analysis provides new explicit results about the quasi-potential and about fluctuations of one-particle observables in a simple example of mean field diffusions: the Shinomoto-Kuramoto model of coupled rotators%. ~\cite{shinomoto1986}. This is one of few systems for which non-equilibrium free energies can be computed and analyzed in an effective way, at least perturbatively

The Onset of Synchronization in Systems of Globally Coupled Chaotic and Periodic Oscillators

A general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled, heterogeneous, continuous-time dynamical systems. The formalism allows for the simultaneous presence of ensemble members exhibiting chaotic and periodic behavior, and, in a special case, yields the Kuramoto model for globally coupled periodic oscillators described by a phase. Numerical experiments using different types of ensembles of Lorenz equations with a distribution of parameters are presented.Comment: 26 pages and 26 figure

Linking Research and Policy: Assessing a Framework for Organic Agricultural Support in Ireland

This paper links social science research and agricultural policy through an analysis of support for organic agriculture and food. Globally, sales of organic food have experienced 20% annual increases for the past two decades, and represent the fastest growing segment of the grocery market. Although consumer interest has increased, farmers are not keeping up with demand. This is partly due to a lack of political support provided to farmers in their transition from conventional to organic production. Support policies vary by country and in some nations, such as the US, vary by state/province. There have been few attempts to document the types of support currently in place. This research draws on an existing Framework tool to investigate regionally specific and relevant policy support available to organic farmers in Ireland. This exploratory study develops a case study of Ireland within the framework of ten key categories of organic agricultural support: leadership, policy, research, technical support, financial support, marketing and promotion, education and information, consumer issues, inter-agency activities, and future developments. Data from the Irish Department of Agriculture, Fisheries and Food, the Irish Agriculture and Food Development Authority (Teagasc), and other governmental and semi-governmental agencies provide the basis for an assessment of support in each category. Assessments are based on the number of activities, availability of information to farmers, and attention from governmental personnel for each of the ten categories. This policy framework is a valuable tool for farmers, researchers, state agencies, and citizen groups seeking to document existing types of organic agricultural support and discover policy areas which deserve more attention

Violation of Finite-Size Scaling in Three Dimensions

We reexamine the range of validity of finite-size scaling in the $\phi^4$ lattice model and the $\phi^4$ field theory below four dimensions. We show that general renormalization-group arguments based on the renormalizability of the $\phi^4$ theory do not rule out the possibility of a violation of finite-size scaling due to a finite lattice constant and a finite cutoff. For a confined geometry of linear size $L$ with periodic boundary conditions we analyze the approach towards bulk critical behavior as $L \to \infty$ at fixed $\xi$ for $T > T_c$ where $\xi$ is the bulk correlation length. We show that for this analysis ordinary renormalized perturbation theory is sufficient. On the basis of one-loop results and of exact results in the spherical limit we find that finite-size scaling is violated for both the $\phi^4$ lattice model and the $\phi^4$ field theory in the region $L \gg \xi$. The non-scaling effects in the field theory and in the lattice model differ significantly from each other.Comment: LaTex, 51 page

On dynamical systems approaches and methods in f(R)f(R) cosmology

We discuss dynamical systems approaches and methods applied to flat Robertson-Walker models in $f(R)$-gravity. We argue that a complete description of the solution space of a model requires a global state space analysis that motivates globally covering state space adapted variables. This is shown explicitly by an illustrative example, $f(R) = R + \alpha R^2$, $\alpha > 0$, for which we introduce new regular dynamical systems on global compactly extended state spaces for the Jordan and Einstein frames. This example also allows us to illustrate several local and global dynamical systems techniques involving, e.g., blow ups of nilpotent fixed points, center manifold analysis, averaging, and use of monotone functions. As a result of applying dynamical systems methods to globally state space adapted dynamical systems formulations, we obtain pictures of the entire solution spaces in both the Jordan and the Einstein frames. This shows, e.g., that due to the domain of the conformal transformation between the Jordan and Einstein frames, not all the solutions in the Jordan frame are completely contained in the Einstein frame. We also make comparisons with previous dynamical systems approaches to $f(R)$ cosmology and discuss their advantages and disadvantages.Comment: 36 pages, 7 figures. v2: references added, matches published versio

Coherent and semiclassical states in magnetic field in the presence of the Aharonov-Bohm solenoid

A new approach to constructing coherent states (CS) and semiclassical states (SS) in magnetic-solenoid field is proposed. The main idea is based on the fact that the AB solenoid breaks the translational symmetry in the xy-plane, this has a topological effect such that there appear two types of trajectories which embrace and do not embrace the solenoid. Due to this fact, one has to construct two different kinds of CS/SS, which correspond to such trajectories in the semiclassical limit. Following this idea, we construct CS in two steps, first the instantaneous CS (ICS) and the time dependent CS/SS as an evolution of the ICS. The construction is realized for nonrelativistic and relativistic spinning particles both in (2+1)- and (3+1)- dimensions and gives a non-trivial example of SS/CS for systems with a nonquadratic Hamiltonian. It is stressed that CS depending on their parameters (quantum numbers) describe both pure quantum and semiclassical states. An analysis is represented that classifies parameters of the CS in such respect. Such a classification is used for the semiclassical decompositions of various physical quantities.Comment: 35 pages, 2 figures. Some typos in (77), (101), and (135) corrected with respect to the published version. Results unchange

Quantum Theory of Gravity I: Area Operators

A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces are introduced and shown to be self-adjoint on the underlying (kinematical) Hilbert space of states. It is shown that their spectra are {\it purely} discrete indicating that the underlying quantum geometry is far from what the continuum picture might suggest. Indeed, the fundamental excitations of quantum geometry are 1-dimensional, rather like polymers, and the 3-dimensional continuum geometry emerges only on coarse graining. The full Hilbert space admits an orthonormal decomposition into finite dimensional sub-spaces which can be interpreted as the spaces of states of spin systems. Using this property, the complete spectrum of the area operators is evaluated. The general framework constructed here will be used in a subsequent paper to discuss 3-dimensional geometric operators, e.g., the ones corresponding to volumes of regions.Comment: 33 pages, ReVTeX, Section 4 Revised: New results on the effect of topology of a surface on the eigenvalues and eigenfunctions of its area operator included. The proof of the bound on the level spacing of eigenvalues (for large areas) simplified and its ramification to the Bekenstein-Mukhanov analysis of black-hole evaporation made more explicit. To appear in CQ