Asymptotic normality of quadratic forms of martingale differences

We establish the asymptotic normality of a quadratic form QnQn in martingale difference random variables ηtηt when the weight matrix A of the quadratic form has an asymptotically vanishing diagonal. Such a result has numerous potential applications in time series analysis. While for i.i.d. random variables ηtηt, asymptotic normality holds under condition ||A||sp=o(||A||)||A||sp=o(||A||), where ||A||sp||A||sp and ||A|| are the spectral and Euclidean norms of the matrix A, respectively, finding corresponding sufficient conditions in the case of martingale differences ηtηt has been an important open problem. We provide such sufficient conditions in this paper

On the recurrence and robust properties of Lorenz'63 model

Lie-Poisson structure of the Lorenz'63 system gives a physical insight on its dynamical and statistical behavior considering the evolution of the associated Casimir functions. We study the invariant density and other recurrence features of a Markov expanding Lorenz-like map of the interval arising in the analysis of the predictability of the extreme values reached by particular physical observables evolving in time under the Lorenz'63 dynamics with the classical set of parameters. Moreover, we prove the statistical stability of such an invariant measure. This will allow us to further characterize the SRB measure of the system.Comment: 44 pages, 7 figures, revised version accepted for pubblicatio

Exactly solvable model of superstring in Ramond-Ramond plane wave background

We describe in detail the solution of type IIB superstring theory in the maximally supersymmetric plane-wave background with constant null Ramond-Ramond 5-form field strength. The corresponding light-cone Green-Schwarz action found in hep-th/0112044 is quadratic in both bosonic and fermionic coordinates. We find the spectrum of the light-cone Hamiltonian and the string representation of the supersymmetry algebra. The superstring Hamiltonian has a ``harmonic-oscillator'' form in both the string-oscillator and the zero-mode parts and thus has discrete spectrum in all 8 transverse directions. We analyze the structure of the zero-mode sector of the theory, establishing the precise correspondence between the lowest-lying ``massless'' string states and the type IIB supergravity fluctuation modes in the plane-wave background. The zero-mode spectrum has certain similarity to the supergravity spectrum in AdS_5 x S^5 of which the plane-wave background is a special limit. We also compare the plane-wave string spectrum with expected form of the light-cone gauge spectrum of superstring in AdS_5 x S^5.Comment: 33 pages, latex. v4: minor sign corrections in (1.5) and (3.62), to appear in PR

Genome-wide association study for type 2 diabetes in Indians identifies a new susceptibility locus at 2q21

Meta-AnalysisThis is the final version of the article. Available from the American Diabetes Association via the DOI in this record.Indians undergoing socioeconomic and lifestyle transitions will be maximally affected by epidemic of type 2 diabetes (T2D). We conducted a two-stage genome-wide association study of T2D in 12,535 Indians, a less explored but high-risk group. We identified a new type 2 diabetes-associated locus at 2q21, with the lead signal being rs6723108 (odds ratio 1.31; P = 3.32 × 10⁻⁹). Imputation analysis refined the signal to rs998451 (odds ratio 1.56; P = 6.3 × 10⁻¹²) within TMEM163 that encodes a probable vesicular transporter in nerve terminals. TMEM163 variants also showed association with decreased fasting plasma insulin and homeostatic model assessment of insulin resistance, indicating a plausible effect through impaired insulin secretion. The 2q21 region also harbors RAB3GAP1 and ACMSD; those are involved in neurologic disorders. Forty-nine of 56 previously reported signals showed consistency in direction with similar effect sizes in Indians and previous studies, and 25 of them were also associated (P < 0.05). Known loci and the newly identified 2q21 locus altogether explained 7.65% variance in the risk of T2D in Indians. Our study suggests that common susceptibility variants for T2D are largely the same across populations, but also reveals a population-specific locus and provides further insights into genetic architecture and etiology of T2D.The major funding for this work comes from Council for Scientific and Industrial Research, Government of India, in the form of the grant “Diabetes mellitus—New drug discovery R&D, molecular mechanisms, and genetic and epidemiological factors” (NWP0032-19). R.T. received a postdoctoral fellowship from the Fogarty International Center and the Eunice Kennedy Shriver National Institute of Child Health and Human Development at the National Institutes of Health (D43-HD-065249)

Global, regional, and national comparative risk assessment of 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks, 1990-2015: a systematic analysis for the Global Burden of Disease Study 2015

SummaryBackground The Global Burden of Diseases, Injuries, and Risk Factors Study 2015 provides an up-to-date synthesis of the evidence for risk factor exposure and the attributable burden of disease. By providing national and subnational assessments spanning the past 25 years, this study can inform debates on the importance of addressing risks in context. Methods We used the comparative risk assessment framework developed for previous iterations of the Global Burden of Disease Study to estimate attributable deaths, disability-adjusted life-years (DALYs), and trends in exposure by age group, sex, year, and geography for 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks from 1990 to 2015. This study included 388 risk-outcome pairs that met World Cancer Research Fund-defined criteria for convincing or probable evidence. We extracted relative risk and exposure estimates from randomised controlled trials, cohorts, pooled cohorts, household surveys, census data, satellite data, and other sources. We used statistical models to pool data, adjust for bias, and incorporate covariates. We developed a metric that allows comparisons of exposure across risk factors—the summary exposure value. Using the counterfactual scenario of theoretical minimum risk level, we estimated the portion of deaths and DALYs that could be attributed to a given risk. We decomposed trends in attributable burden into contributions from population growth, population age structure, risk exposure, and risk-deleted cause-specific DALY rates. We characterised risk exposure in relation to a Socio-demographic Index (SDI). Findings Between 1990 and 2015, global exposure to unsafe sanitation, household air pollution, childhood underweight, childhood stunting, and smoking each decreased by more than 25%. Global exposure for several occupational risks, high body-mass index (BMI), and drug use increased by more than 25% over the same period. All risks jointly evaluated in 2015 accounted for 57·8% (95% CI 56·6–58·8) of global deaths and 41·2% (39·8–42·8) of DALYs. In 2015, the ten largest contributors to global DALYs among Level 3 risks were high systolic blood pressure (211·8 million [192·7 million to 231·1 million] global DALYs), smoking (148·6 million [134·2 million to 163·1 million]), high fasting plasma glucose (143·1 million [125·1 million to 163·5 million]), high BMI (120·1 million [83·8 million to 158·4 million]), childhood undernutrition (113·3 million [103·9 million to 123·4 million]), ambient particulate matter (103·1 million [90·8 million to 115·1 million]), high total cholesterol (88·7 million [74·6 million to 105·7 million]), household air pollution (85·6 million [66·7 million to 106·1 million]), alcohol use (85·0 million [77·2 million to 93·0 million]), and diets high in sodium (83·0 million [49·3 million to 127·5 million]). From 1990 to 2015, attributable DALYs declined for micronutrient deficiencies, childhood undernutrition, unsafe sanitation and water, and household air pollution; reductions in risk-deleted DALY rates rather than reductions in exposure drove these declines. Rising exposure contributed to notable increases in attributable DALYs from high BMI, high fasting plasma glucose, occupational carcinogens, and drug use. Environmental risks and childhood undernutrition declined steadily with SDI; low physical activity, high BMI, and high fasting plasma glucose increased with SDI. In 119 countries, metabolic risks, such as high BMI and fasting plasma glucose, contributed the most attributable DALYs in 2015. Regionally, smoking still ranked among the leading five risk factors for attributable DALYs in 109 countries; childhood underweight and unsafe sex remained primary drivers of early death and disability in much of sub-Saharan Africa. Interpretation Declines in some key environmental risks have contributed to declines in critical infectious diseases. Some risks appear to be invariant to SDI. Increasing risks, including high BMI, high fasting plasma glucose, drug use, and some occupational exposures, contribute to rising burden from some conditions, but also provide opportunities for intervention. Some highly preventable risks, such as smoking, remain major causes of attributable DALYs, even as exposure is declining. Public policy makers need to pay attention to the risks that are increasingly major contributors to global burden. Funding Bill & Melinda Gates Foundation

Common Variants of Inflammatory Cytokine Genes Are Associated with Risk of Nephropathy in Type 2 Diabetes among Asian Indians

BACKGROUND: Inflammatory cytokine genes have been proposed as good candidate genes for conferring susceptibility to diabetic nephropathy. In the present study, we examined the combined effect of multiple alleles of pro inflammatory cytokine genes for determining the risk of nephropathy in type 2 diabetic patients. METHODOLOGY/PRINCIPAL FINDINGS: Eight single nucleotide polymorphisms (SNPs) of pro-inflammatory cytokine genes (CCL2, TGFB1, IL8, CCR5, and MMP9) were genotyped in two independently ascertained type 2 diabetic cohorts with (DN) and without nephropathy (DM); consisting of patients from North India (n = 495) and South India (n = 188). Genotyping was carried out using PCR, allele specific oligonucleotide-PCR (ASO-PCR), PCR-RFLP and TaqMan allelic discrimination assays and the gene-gene interaction among genetic variants were determined by multi dimensional reduction (MDR) software. Serum high sensitive CRP (hs-CRP) levels were measured by ELISA. The hs-CRP levels were significantly higher in DN as compared to the DM group (p<0.05). The CCL2, IL8, CCR5 and MMP9 polymorphisms were found to be associated with the risk of diabetic nephropathy. Frequency of CCL2 II, IL8 -251AA, CCR5 59029AA and MMP9 279Gln/Gln genotypes were significantly higher in DN than in DM group (p<0.05) and associated with an increased risk of nephropathy in both North and South Indian cohorts. CCR5 DD and IL8 -251AA genotypes were more prevalent in North Indian DN group only. The co-occurrence of risk associated genotypes (II, -2518GG (CCL2), DD (CCR5) and 279Gln/Gln (MMP9) conferred a tenfold increased risk of nephropathy among type 2 diabetics (p<0.0002). CONCLUSION: The present study highlights that common variants of inflammatory cytokine genes exert a modest effect on risk of DN and a combination of risk alleles confer a substantial increased risk of nephropathy in type 2 diabetes among Asian Indians

Fluoxetine Exerts Age-Dependent Effects on Behavior and Amygdala Neuroplasticity in the Rat

The selective serotonin reuptake inhibitor (SSRI) Prozac® (fluoxetine) is the only registered antidepressant to treat depression in children and adolescents. Yet, while the safety of SSRIs has been well established in adults, serotonin exerts neurotrophic actions in the developing brain and thereby may have harmful effects in adolescents. Here we treated adolescent and adult rats chronically with fluoxetine (12 mg/kg) at postnatal day (PND) 25 to 46 and from PND 67 to 88, respectively, and tested the animals 7–14 days after the last injection when (nor)fluoxetine in blood plasma had been washed out, as determined by HPLC. Plasma (nor)fluoxetine levels were also measured 5 hrs after the last fluoxetine injection, and matched clinical levels. Adolescent rats displayed increased behavioral despair in the forced swim test, which was not seen in adult fluoxetine treated rats. In addition, beneficial effects of fluoxetine on wakefulness as measured by electroencephalography in adults was not seen in adolescent rats, and age-dependent effects on the acoustic startle response and prepulse inhibition were observed. On the other hand, adolescent rats showed resilience to the anorexic effects of fluoxetine. Exploratory behavior in the open field test was not affected by fluoxetine treatment, but anxiety levels in the elevated plus maze test were increased in both adolescent and adult fluoxetine treated rats. Finally, in the amygdala, but not the dorsal raphe nucleus and medial prefrontal cortex, the number of PSA-NCAM (marker for synaptic remodeling) immunoreactive neurons was increased in adolescent rats, and decreased in adult rats, as a consequence of chronic fluoxetine treatment. No fluoxetine-induced changes in 5-HT1A receptor immunoreactivity were observed. In conclusion, we show that fluoxetine exerts both harmful and beneficial age-dependent effects on depressive behavior, body weight and wakefulness, which may relate, in part, to differential fluoxetine-induced neuroplasticity in the amygdala