The Ising-Sherrington-Kirpatrick model in a magnetic field at high temperature

We study a spin system on a large box with both Ising interaction and Sherrington-Kirpatrick couplings, in the presence of an external field. Our results are: (i) existence of the pressure in the limit of an infinite box. When both Ising and Sherrington-Kirpatrick temperatures are high enough, we prove that: (ii) the value of the pressure is given by a suitable replica symmetric solution, and (iii) the fluctuations of the pressure are of order of the inverse of the square of the volume with a normal distribution in the limit. In this regime, the pressure can be expressed in terms of random field Ising models

Non-equilibrium states of a photon cavity pumped by an atomic beam

We consider a beam of two-level randomly excited atoms that pass one-by-one through a one-mode cavity. We show that in the case of an ideal cavity, i.e. no leaking of photons from the cavity, the pumping by the beam leads to an unlimited increase in the photon number in the cavity. We derive an expression for the mean photon number for all times. Taking into account leaking of the cavity, we prove that the mean photon number in the cavity stabilizes in time. The limiting state of the cavity in this case exists and it is independent of the initial state. We calculate the characteristic functional of this non-quasi-free non-equilibrium state. We also calculate the energy flux in both the ideal and open cavity and the entropy production for the ideal cavity.Comment: Corrected energy production calculations and made some changes to ease the readin

Mapping alterations to the endogenous elemental distribution within the lateral ventricles and choroid plexus in brain disorders using X-ray fluorescence imaging

The choroid plexus and cerebral ventricles are critical structures for the production of cerebral spinal fluid (CSF) and play an important role in regulating ion and metal transport in the brain, however many aspects of its roles in normal physiology and disease states, such as psychiatric illness, remain unknown. The choroid plexus is difficult to examine in vivo, and in situ ex vivo, and as such has typically been examined indirectly with radiolabeled tracers or ex vivo stains, making measurements of the endogenous K+, Cl-, and Ca+ distributions unreliable. In the present study, we directly examined the distribution of endogenous ions and biologically relevant transition metals in the choroid plexus and regions surrounding the ventricles (ventricle wall, cortex, corpus callosum, striatum) using X-ray fluorescence imaging (XFI). We find that the choroid plexus was rich in Cl- and Fe while K+ levels increase further from the ventricle as Cl- levels decrease, consistent with the known role of ion transporters in the choroid plexus CSF production. A polyI:C offspring displayed enlarged ventricles, elevated Cl- surrounding the ventricles, and intraventricular calcifications. These observations fit with clinical findings in patients with schizophrenia and suggest maternal treatment with polyI:C may lead to dysfunctional ion regulation in offspring. This study demonstrates the power of XFI for examining the endogenous elemental distributions of the ventricular system in healthy brain tissue as well as disease models

Schizophrenia: do all roads lead to dopamine or is this where they start? Evidence from two epidemiologically informed developmental rodent models

The idea that there is some sort of abnormality in dopamine (DA) signalling is one of the more enduring hypotheses in schizophrenia research. Opinion leaders have published recent perspectives on the aetiology of this disorder with provocative titles such as ‘Risk factors for schizophrenia—all roads lead to dopamine' or ‘The dopamine hypothesis of schizophrenia—the final common pathway'. Perhaps, the other most enduring idea about schizophrenia is that it is a neurodevelopmental disorder. Those of us that model schizophrenia developmental risk-factor epidemiology in animals in an attempt to understand how this may translate to abnormal brain function have consistently shown that as adults these animals display behavioural, cognitive and pharmacological abnormalities consistent with aberrant DA signalling. The burning question remains how can in utero exposure to specific (environmental) insults induce persistent abnormalities in DA signalling in the adult? In this review, we summarize convergent evidence from two well-described developmental animal models, namely maternal immune activation and developmental vitamin D deficiency that begin to address this question. The adult offspring resulting from these two models consistently reveal locomotor abnormalities in response to DA-releasing or -blocking drugs. Additionally, as adults these animals have DA-related attentional and/or sensorimotor gating deficits. These findings are consistent with many other developmental animal models. However, the authors of this perspective have recently refocused their attention on very early aspects of DA ontogeny and describe reductions in genes that induce or specify dopaminergic phenotype in the embryonic brain and early changes in DA turnover suggesting that the origins of these behavioural abnormalities in adults may be traced to early alterations in DA ontogeny. Whether the convergent findings from these two models can be extended to other developmental animal models for this disease is at present unknown as such early brain alterations are rarely examined. Although it is premature to conclude that such mechanisms could be operating in other developmental animal models for schizophrenia, our convergent data have led us to propose that rather than all roads leading to DA, perhaps, this may be where they start

A Trotter-Kato product formul for a class of non-autonomous evolution equations

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