Convergence to stable laws for multidimensional stochastic recursions: the case of regular matrices

Given a sequence $(M_{n},Q_{n})_{n\ge 1}$ of i.i.d.\ random variables with generic copy $(M,Q) \in GL(d, \R) \times \R^d$, we consider the random difference equation (RDE) $$R_{n}=M_{n}R_{n-1}+Q_{n},$$ $n\ge 1$, and assume the existence of $\kappa >0$ such that \lim_{n \to \infty}(\E{\norm{M_1 ... M_n}^\kappa})^{\frac{1}{n}} = 1 . We prove, under suitable assumptions, that the sequence $S_n = R_1 + ... + R_n$, appropriately normalized, converges in law to a multidimensional stable distribution with index $\kappa$. As a by-product, we show that the unique stationary solution $R$ of the RDE is regularly varying with index $\kappa$, and give a precise description of its tail measure. This extends the prior work http://arxiv.org/abs/1009.1728v3 .Comment: 15 page

Human Umbilical Cord Blood Cells Restore Brain Damage Induced Changes in Rat Somatosensory Cortex

Intraperitoneal transplantation of human umbilical cord blood (hUCB) cells has been shown to reduce sensorimotor deficits after hypoxic ischemic brain injury in neonatal rats. However, the neuronal correlate of the functional recovery and how such a treatment enforces plastic remodelling at the level of neural processing remains elusive. Here we show by in-vivo recordings that hUCB cells have the capability of ameliorating the injury-related impairment of neural processing in primary somatosensory cortex. Intact cortical processing depends on a delicate balance of inhibitory and excitatory transmission, which is disturbed after injury. We found that the dimensions of cortical maps and receptive fields, which are significantly altered after injury, were largely restored. Additionally, the lesion induced hyperexcitability was no longer observed in hUCB treated animals as indicated by a paired-pulse behaviour resembling that observed in control animals. The beneficial effects on cortical processing were reflected in an almost complete recovery of sensorimotor behaviour. Our results demonstrate that hUCB cells reinstall the way central neurons process information by normalizing inhibitory and excitatory processes. We propose that the intermediate level of cortical processing will become relevant as a new stage to investigate efficacy and mechanisms of cell therapy in the treatment of brain injury

Prevalence and indirect costs of headache in a Brazilian Company

Employees from a Brazilian oil company research centre (n = 993) were interviewed on the occurrence of headache during a 30 days period. Headache prevalence was 49.8%, with a mean frequency of 4.3 +/- 7.0 attacks per month, lasting 12.2 +/- 21.4 hours each. According to the International Headache Society diagnostic criteria, migraine (5.5%), episodic tension-type headache (26.4%), chronic tension-type headache (1.7%) and headaches not fulfilling the criteria for such disorders (16.2%) were observed. Women suffered comparatively more headache and specifically migraine than men. The pain interfered with work productivity in 10% of the subjects, corresponding to 538.75 hours off. According to an indirect costs estimation for each headache, the company may loose up to US$125.98 per employee annually. Since among headaches migraine has the highest indirect cost, migraine prevention and treatment is particularly important at the working environment. Migraine frequency may be prevented to a large extent, resulting on positive effects in both the quality of life and productivity. The cost-benefit ratio clearly favours therapeutic and preventive programs against chronic headaches