Thermodynamics and conformal properties of XXZ chains with alternating spins

The quantum periodic XXZ chain with alternating spins is studied. The properties of the related R-matrix and Hamiltonians are discussed. A compact expression for the ground state energy is obtained. The corresponding conformal anomaly is found via the finite-size computations and also by means of the Bethe ansatz method. In the presence of an external magnetic field, the magnetic susceptibility is derived. The results are also generalized to the case of a chain containing several different spins.Comment: 28 pages, LaTeX2

Migraine aura: retracting particle-like waves in weakly susceptible cortex

Cortical spreading depression (SD) has been suggested to underlie migraine aura. Despite a precise match in speed, the spatio-temporal patterns of SD and aura symptoms on the cortical surface ordinarily differ in aspects of size and shape. We show that this mismatch is reconciled by utilizing that both pattern types bifurcate from an instability point of generic reaction-diffusion models. To classify these spatio-temporal pattern we suggest a susceptibility scale having the value [sigma]=1 at the instability point. We predict that human cortex is only weakly susceptible to SD ([sigma]<1), and support this prediction by directly matching visual aura symptoms with anatomical landmarks using fMRI retinotopic mapping. We discuss the increased dynamical repertoire of cortical tissue close to [sigma]=1, in particular, the resulting implications on migraine pharmacology that is hitherto tested in the regime ([sigma]>>1), and potentially silent aura occurring below a second bifurcation point at [sigma]=0 on the susceptible scale

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

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f(R) theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcom