Diffusion and localization of relative strategy scores in the Minority Game

We study the equilibrium distribution of relative strategy scores of agents in the asymmetric phase ($\alpha\equiv P/N\gtrsim 1$) of the basic Minority Game using sign-payoff, with $N$ agents holding two strategies over $P$ histories. We formulate a statistical model that makes use of the gauge freedom with respect to the ordering of an agent's strategies to quantify the correlation between the attendance and the distribution of strategies. The relative score $x\in\mathbb{Z}$ of the two strategies of an agent is described in terms of a one dimensional random walk with asymmetric jump probabilities, leading either to a static and asymmetric exponential distribution centered at $x=0$ for fickle agents or to diffusion with a positive or negative drift for frozen agents. In terms of scaled coordinates $x/\sqrt{N}$ and $t/N$ the distributions are uniquely given by $\alpha$ and in quantitative agreement with direct simulations of the game. As the model avoids the reformulation in terms of a constrained minimization problem it can be used for arbitrary payoff functions with little calculational effort and provides a transparent and simple formulation of the dynamics of the basic Minority Game in the asymmetric phase

Parametrization of translational surfaces

The algebraic translational surface is a typical modeling surface in computer aided design and architecture industry. In this paper, we give a necessary and sufficient condition for that algebraic surface having a standard parametric representation and our proof is constructive. If the given algebraic surface is translational, then we can compute a standard parametric representation for the surface

Linking Induction and Transrepression of PPARβ/δ with Cellular Function

The copyrights of all papers published in this journal are retained by the respective authors as per the 'Creative Commons Attribution License' (http://creativecommons.org/licenses/by/3.0/).Peroxisome proliferator activated receptors (PPARs) are ligand-activated transcription factors and members of the nuclear hormone receptor superfamily. PPARβ/δ is ubiquitously expressed and has a central role in homeostasis, and has been suggested as a therapeutic target for a number of metabolic and cardiovascular disorders. This important nuclear receptor controls transcription under different modes of molecular activity which directly control the cellular function and fate of tissues. This complex activity of induction and transrepression of gene expression (with and without exogenous ligands) is poorly understood and yet understanding this molecular control through novel drug development would led to control over a key molecular switch in all cells. This review outlines the main molecular mechanisms of PPARβ/δ, and links the modes of activity to the signalling pathways in inflammation, proliferation and senescence, with the goal to understand how this will translate into novel drug design to control the PPARβ/δ molecular switch.Peer reviewe

An empirical calibration of nebular abundances based on the sulphur emission lines

We present an empirical calibration of nebular abundances based on the strong emission lines of [SII] and [SIII] in the red part of the spectrum through the definition of a sulphur abundance parameter S23. This calibration presents two important advantages against the commonly used one based on the optical oxygen lines: it remains single-valued up to abundances close to solar and is rather independent of the degree of ionization of the nebula.Comment: 10 pages, 8 figures. Accepted for publication in MNRA