Finite morphic pp-groups

According to Li, Nicholson and Zan, a group $G$ is said to be morphic if, for every pair $N_{1}, N_{2}$ of normal subgroups, each of the conditions $G/N_{1} \cong N_{2}$ and $G/N_{2} \cong N_{1}$ implies the other. Finite, homocyclic $p$-groups are morphic, and so is the nonabelian group of order $p^{3}$ and exponent $p$, for $p$ an odd prime. It follows from results of An, Ding and Zhan on self dual groups that these are the only examples of finite, morphic $p$-groups. In this paper we obtain the same result under a weaker hypotesis.Comment: 7 pages. Critical reference added, and manuscript revised accordingl

Elements of prime order in the upper central series of a group of prime-power order

We investigate the occurrence of elements of order $p$ in the upper central series of a finite $p$-group.Comment: 6 page

CRITICAL (Phi^{4}_{3,\epsilon})

The Euclidean (\phi^{4})_{3,\epsilon model in $R^3$ corresponds to a perturbation by a $\phi^4$ interaction of a Gaussian measure on scalar fields with a covariance depending on a real parameter $\epsilon$ in the range $0\le \epsilon \le 1$. For $\epsilon =1$ one recovers the covariance of a massless scalar field in $R^3$. For $\epsilon =0$ $\phi^{4}$ is a marginal interaction. For $0\le \epsilon < 1$ the covariance continues to be Osterwalder-Schrader and pointwise positive. After introducing cutoffs we prove that for $\epsilon > 0$, sufficiently small, there exists a non-gaussian fixed point (with one unstable direction) of the Renormalization Group iterations. These iterations converge to the fixed point on its stable (critical) manifold which is constructed.Comment: 49 pages, plain tex, macros include

Pro-p groups with few normal subgroups

Motivated by the study of pro-p groups With finite coclass, we consider the class of pro-p groups with few normal subgroups. This is not a well defined class and we offer several different definitions and study the connections between them. Furthermore, we propose a definition of periodicity for pro-p groups, thus, providing a general framework for some periodic patterns that have already been observed in the existing literature. We then focus oil examples and show that strikingly all the interesting examples not only have few normal Subgroups, but in addition have periodicity in the lattice of normal subgroups. (C) 2008 Elsevier Inc. All rights reserved

Immune regulation of neurodevelopment at the mother–foetus interface: the case of autism

Autism spectrum disorder (ASD) is a neurodevelopmental disorder defined by deficits in social communication and stereotypical behaviours. ASD’s aetiology remains mostly unclear, because of a complex interaction between genetic and environmental factors. Recently, a strong consensus has developed around ASD’s immune-mediated pathophysiology, which is the subject of this review. For many years, neuroimmunological studies tried to understand ASD as a prototypical antibody- or cell-mediated disease. Other findings indicated the importance of autoimmune mechanisms such as familial and individual autoimmunity, adaptive immune abnormalities and the influence of infections during gestation. However, recent studies have challenged the idea that autism may be a classical autoimmune disease. Modern neurodevelopmental immunology shows the double-edged nature of many immune effectors, which can be either beneficial or detrimental depending on tissue homeostasis, stressors, neurodevelopmental stage, inherited and de novo gene mutations and other variables. Nowadays, mother–child interactions in the prenatal environment appear to be crucial for the occurrence of ASD. Studies of animal maternal–foetal immune interaction are being fruitfully carried out using different combinations of type and timing of infection, of maternal immune response and foetal vulnerability and of resilience factors to hostile events. The derailed neuroimmune crosstalk through the placenta initiates and maintains a chronic foetal neuroglial activation, eventually causing the alteration of neurogenesis, migration, synapse formation and pruning. The importance of pregnancy can also allow early immune interventions, which can significantly reduce the increasing risk of ASD and its heavy social burden

Tunneling and Metastability of continuous time Markov chains

We propose a new definition of metastability of Markov processes on countable state spaces. We obtain sufficient conditions for a sequence of processes to be metastable. In the reversible case these conditions are expressed in terms of the capacity and of the stationary measure of the metastable states

Foreign Policy and the Ideology of Post-ideology: The Case of Matteo Renzi’s Partito Democratico

The post-communist Italian Left has experienced a long phase of ideational misalignment between ideas placed at different levels, as a qualified discursive institutionalist approach demonstrates. Background public philosophies have often clashed with post-communist political ideology, while foreign policy programmes have often contradicted specific policies. Under the leadership of Matteo Renzi, however, the PD is now experiencing a moment of remarkable ideational consistency. Rather than being founded on entirely new premises, this new consensus folds old elements into new ones and shows all the defining traits of post-ideology. Yet, by espousing post-ideology, Renzi is making an ultimately ideological move whose limitations may soon start to show

A Method to Study Relaxation of Metastable Phases: Macroscopic Mean-Field Dynamics

We propose two different macroscopic dynamics to describe the decay of metastable phases in many-particle systems with local interactions. These dynamics depend on the macroscopic order parameter $m$ through the restricted free energy $F(m)$ and are designed to give the correct equilibrium distribution for $m$. The connection between macroscopic dynamics and the underlying microscopic dynamic are considered in the context of a projection- operator formalism. Application to the square-lattice nearest-neighbor Ising ferromagnet gives good agreement with droplet theory and Monte Carlo simulations of the underlying microscopic dynamic. This includes quantitative agreement for the exponential dependence of the lifetime on the inverse of the applied field $H$, and the observation of distinct field regions in which the derivative of the lifetime with respect to $1/H$ depends differently on $H$. In addition, at very low temperatures we observe oscillatory behavior of this derivative with respect to $H$, due to the discreteness of the lattice and in agreement with rigorous results. Similarities and differences between this work and earlier works on finite Ising models in the fixed-magnetization ensemble are discussed.Comment: 44 pages RevTeX3, 11 uuencoded Postscript figs. in separate file