Homoclinic chaos in the dynamics of a general Bianchi IX model

The dynamics of a general Bianchi IX model with three scale factors is examined. The matter content of the model is assumed to be comoving dust plus a positive cosmological constant. The model presents a critical point of saddle-center-center type in the finite region of phase space. This critical point engenders in the phase space dynamics the topology of stable and unstable four dimensional tubes $R \times S^3$, where $R$ is a saddle direction and $S^3$ is the manifold of unstable periodic orbits in the center-center sector. A general characteristic of the dynamical flow is an oscillatory mode about orbits of an invariant plane of the dynamics which contains the critical point and a Friedmann-Robertson-Walker (FRW) singularity. We show that a pair of tubes (one stable, one unstable) emerging from the neighborhood of the critical point towards the FRW singularity have homoclinic transversal crossings. The homoclinic intersection manifold has topology $R \times S^2$ and is constituted of homoclinic orbits which are bi-asymptotic to the $S^3$ center-center manifold. This is an invariant signature of chaos in the model, and produces chaotic sets in phase space. The model also presents an asymptotic DeSitter attractor at infinity and initial conditions sets are shown to have fractal basin boundaries connected to the escape into the DeSitter configuration (escape into inflation), characterizing the critical point as a chaotic scatterer.Comment: 11 pages, 6 ps figures. Accepted for publication in Phys. Rev.

Sex differences in schizophrenia, bipolar disorder and PTSD: Are gonadal hormones the link?

In this review, we describe the sex differences in prevalence, onset, symptom profiles and disease outcome that are evident in schizophrenia, bipolar disorder and post-traumatic stress disorder. Women with schizophrenia tend to exhibit less disease impairment than men; by contrast, women with post-traumatic stress disorder are more affected than men. The most likely candidates to explain these sex differences are gonadal hormones. This review details the clinical evidence that estradiol and progesterone are dysregulated in these psychiatric disorders. Notably, existing data on estradiol, and to a lesser extent, progesterone, suggest that low levels of these hormones may increase the risk of disease development and worsen symptom severity. We argue that future studies require a more inclusive, considered analysis of gonadal steroid hormones and the intricacies of the interactions between them, with methodological rigour applied, to enhance our understanding of the roles of steroid hormones in psychiatric disorders

Melatonin the "light of night" in human biology and adolescent idiopathic scoliosis

Melatonin "the light of night" is secreted from the pineal gland principally at night. The hormone is involved in sleep regulation, as well as in a number of other cyclical bodily activities and circadian rhythm in humans. Melatonin is exclusively involved in signalling the 'time of day' and 'time of year' (hence considered to help both clock and calendar functions) to all tissues and is thus considered to be the body's chronological pacemaker or 'Zeitgeber'. The last decades melatonin has been used as a therapeutic chemical in a large spectrum of diseases, mainly in sleep disturbances and tumours and may play a role in the biologic regulation of mood, affective disorders, cardiovascular system, reproduction and aging. There are few papers regarding melatonin and its role in adolescent idiopathic scoliosis (AIS). Melatonin may play a role in the pathogenesis of scoliosis (neuroendocrine hypothesis) but at present, the data available cannot clearly support this hypothesis. Uncertainties and doubts still surround the role of melatonin in human physiology and pathophysiology and future research is needed