Microscopic origin of non-Gaussian distributions of financial returns

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumption, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process. In this approximation, we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero-drift modified log-returns. We verify that the Dow-Jones Industrial Average index indeed follows this scaling. We then focus on two popular stochastic volatility models, the Heston and Hull-White models. In particular, we show that in the Hull-White model the resulting probability distribution of log-returns in this approximation corresponds to the Tsallis (t-Student) distribution. The Tsallis parameters are given in terms of the microscopic stochastic volatility model. Finally, we show that the log-returns for 30 years Dow Jones index data is well fitted by a Tsallis distribution, obtaining the relevant parameters. (c) 2007 Elsevier B.V. All rights reserved.

Right adolescent idiopathic thoracic curve (Lenke 1 A and B): does cost of instrumentation and implant density improve radiographic and cosmetic parameters?

In adolescent idiopathic scoliosis (AIS) there has been a shift towards increasing the number of implants and pedicle screws, which has not been proven to improve cosmetic correction. To evaluate if increasing cost of instrumentation correlates with cosmetic correction using clinical photographs. 58 Lenke 1A and B cases from a multicenter AIS database with at least 3 months follow-up of clinical photographs were used for analysis. Cosmetic parameters on PA and forward bending photographs included angular measurements of trunk shift, shoulder balance, rib hump, and ratio measurements of waist line asymmetry. Pre-op and follow-up X-rays were measured for coronal and sagittal deformity parameters. Cost density was calculated by dividing the total cost of instrumentation by the number of vertebrae being fused. Linear regression and spearman`s correlation were used to correlate cost density to X-ray and photo outcomes. Three independent observers verified radiographic and cosmetic parameters for inter/interobserver variability analysis. Average pre-op Cobb angle and instrumented correction were 54A degrees (SD 12.5) and 59% (SD 25) respectively. The average number of vertebrae fused was 10 (SD 1.9). The total cost of spinal instrumentation ranged from $6,769 to $21,274 (Mean $12,662, SD $3,858). There was a weak positive and statistically significant correlation between Cobb angle correction and cost density (r = 0.33, p = 0.01), and no correlation between Cobb angle correction of the uninstrumented lumbar spine and cost density (r = 0.15, p = 0.26). There was no significant correlation between all sagittal X-ray measurements or any of the photo parameters and cost density. There was good to excellent inter/intraobserver variability of all photographic parameters based on the intraclass correlation coefficient (ICC 0.74-0.98). Our method used to measure cosmesis had good to excellent inter/intraobserver variability, and may be an effective tool to objectively assess cosmesis from photographs. Since increasing cost density only improves mildly the Cobb angle correction of the main thoracic curve and not the correction of the uninstrumented spine or any of the cosmetic parameters, one should consider the cost of increasing implant density in Lenke 1A and B curves. In the area of rationalization of health care expenses, this study demonstrates that increasing the number of implants does not improve any relevant cosmetic or radiographic outcomes.

Creatine Supplementation Prevents the Accumulation of Fat in the Livers of Rats Fed a High-Fat Diet

The aim of the present study was to examine the effects of creatine supplementation on liver fat accumulation induced by a high-fat diet in rats. Rats were fed 1 of 3 different diets for 3 wk: a control liquid diet (C), a high-fat liquid diet (HF), or a high-fat liquid diet supplemented with creatine (HFC). The C and HF diets contained, respectively, 35 and 71% of energy derived from fat. Creatine supplementation involved the addition of 1% (wt:v) of creatine monohydrate to the liquid diet. The HF diet increased total liver fat concentration, liver TG, and liver TBARS and decreased the hepatic S-adenosylmethionine (SAM) concentration. Creatine supplementation normalized all of these perturbations. Creatine supplementation significantly decreased the renal activity of L-arginine:glycine amidinotransferase and plasma guanidinoacetate and prevented the decrease in hepatic SAM concentration in rats fed the HF diet. However, there was no change in either the phosphatidylcholine:phosphatidylethanolamine (PE) ratio or PE N-methyltransferase activity. The HF diet decreased mRNA for PPAR as well as 2 of its targets, carnitine palmitoyltransferase and long-chain acylCoA dehydrogenase. Creatine supplementation normalized these mRNA levels. In conclusion, creatine supplementation prevented the fatty liver induced by feeding rats a HF diet, probably by normalization of the expression of key genes of beta-oxidation. J. Nutr. 141: 1799-1804, 2011.