Limit theorems for von Mises statistics of a measure preserving transformation

For a measure preserving transformation $T$ of a probability space $(X,\mathcal F,\mu)$ we investigate almost sure and distributional convergence of random variables of the form $$x \to \frac{1}{C_n} \sum_{i_1<n,...,i_d<n} f(T^{i_1}x,...,T^{i_d}x),\, n=1,2,...,$$ where $f$ (called the \emph{kernel}) is a function from $X^d$ to $\R$ and $C_1, C_2,...$ are appropriate normalizing constants. We observe that the above random variables are well defined and belong to $L_r(\mu)$ provided that the kernel is chosen from the projective tensor product $$L_p(X_1,\mathcal F_1, \mu_1) \otimes_{\pi}...\otimes_{\pi} L_p(X_d,\mathcal F_d, \mu_d)\subset L_p(\mu^d)$$ with $p=d\,r,\, r\ \in [1, \infty).$ We establish a form of the individual ergodic theorem for such sequences. Next, we give a martingale approximation argument to derive a central limit theorem in the non-degenerate case (in the sense of the classical Hoeffding's decomposition). Furthermore, for $d=2$ and a wide class of canonical kernels $f$ we also show that the convergence holds in distribution towards a quadratic form $\sum_{m=1}^{\infty} \lambda_m\eta^2_m$ in independent standard Gaussian variables $\eta_1, \eta_2,...$. Our results on the distributional convergence use a $T$--\,invariant filtration as a prerequisite and are derived from uni- and multivariate martingale approximations

A chemosensory GPCR as a potential target to control the Root-Knot Nematode Meloidogyne incognita parasitism in plants.

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Community-wide assessment of GPCR structure modelling and ligand docking: GPCR Dock 2008

Recent breakthroughs in the determination of the crystal structures of G protein-coupled receptors (GPCRs) have provided new opportunities for structure-based drug design strategies targeting this protein family. With the aim of evaluating the current status of GPCR structure prediction and ligand docking, a community-wide, blind prediction assessment - GPCR Dock 2008 - was conducted in coordination with the publication of the crystal structure of the human adenosine A2Areceptor bound to the ligand ZM241385. Twenty-nine groups submitted 206 structural models before the release of the experimental structure, which were evaluated for the accuracy of the ligand binding mode and the overall receptor model compared with the crystal structure. This analysis highlights important aspects for success and future development, such as accurate modelling of structurally divergent regions and use of additional biochemical insight such as disulphide bridges in the extracellular loops

Leadership and style in the French Fifth Republic:Nicolas Sarkozy’s presidency in historical and cultural perspective

This article contributes to the body of the developing theoretical research in leadership and presidential studies by adding analysis of what I have termed ‘comportmental style’ as a factor in leader/follower relations. Within institutionalism and the wider structure/agency debate in political science, one of the challenges as regards the study of leadership is to identify factors that offer scope to or else militate against leaders’ performance. The comportmental style of Nicolas Sarkozy (President of the French Republic 2007–2012), deployed in the context of the – changing – institution of the presidency, was a major factor in his extreme unpopularity, and contributed to his defeat in 2012. What this tells us about the nature of the changing French presidency and the role of style will be discussed in the conclusion