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

Level-set based adaptive-active contour segmentation technique with long short-term memory for diabetic retinopathy classification

Diabetic Retinopathy (DR) is a major type of eye defect that is caused by abnormalities in the blood vessels within the retinal tissue. Early detection by automatic approach using modern methodologies helps prevent consequences like vision loss. So, this research has developed an effective segmentation approach known as Level-set Based Adaptive-active Contour Segmentation (LBACS) to segment the images by improving the boundary conditions and detecting the edges using Level Set Method with Improved Boundary Indicator Function (LSMIBIF) and Adaptive-Active Counter Model (AACM). For evaluating the DR system, the information is collected from the publically available datasets named as Indian Diabetic Retinopathy Image Dataset (IDRiD) and Diabetic Retinopathy Database 1 (DIARETDB 1). Then the collected images are pre-processed using a Gaussian filter, edge detection sharpening, Contrast enhancement, and Luminosity enhancement to eliminate the noises/interferences, and data imbalance that exists in the available dataset. After that, the noise-free data are processed for segmentation by using the Level set-based active contour segmentation technique. Then, the segmented images are given to the feature extraction stage where Gray Level Co-occurrence Matrix (GLCM), Local ternary, and binary patterns are employed to extract the features from the segmented image. Finally, extracted features are given as input to the classification stage where Long Short-Term Memory (LSTM) is utilized to categorize various classes of DR. The result analysis evidently shows that the proposed LBACS-LSTM achieved better results in overall metrics. The accuracy of the proposed LBACS-LSTM for IDRiD and DIARETDB 1 datasets is 99.43% and 97.39%, respectively which is comparably higher than the existing approaches such as Three-dimensional semantic model, Delimiting Segmentation Approach Using Knowledge Learning (DSA-KL), K-Nearest Neighbor (KNN), Computer aided method and Chronological Tunicate Swarm Algorithm with Stacked Auto Encoder (CTSA-SAE)

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)

End of life care of hospitalized patients with Parkinson disease: a retrospective analysis and brief review

BackgroundTowards the end of life (EOL), persons with parkinsonism (PwP) have complex needs and can present with unique palliative care (PC) challenges. There are no widely accepted guidelines to aid neurologists, hospitalists, or PC clinicians in managing the symptoms of PwP at EOL. We examined a population of PwP at EOL, aiming to describe trends of in-hospital management and utilization of PC services.MethodsAll PwP admitted to two hospitals during 2018 (N = 727) were examined retrospectively, assessing those who died in hospital or were discharged with hospice (EOL group, N = 35) and comparing them to the main cohort. Their demographics, clinical data, engagement of multidisciplinary and palliative services, code status changes, invasive care, frequency of admissions, and medication administration were assessed.ResultsAmong the EOL group, 8 expired in hospital, and 27 were discharged to hospice. Forty-six percent of EOL patients received a PC consultation during their admission. The median interval from admission to death was 37 days. Seventy-seven percent had a full code status on admission. Compared to hospice patients, those who expired in hospital had higher rates of invasive procedures and intensive care unit transfers (41% vs. 75%, in both variables), and lower rates of PC involvement (52% vs. 25%). The transition of code status change for the EOL group from Full code to Do Not Resuscitate (DNR) occurred at a median 4–5 days from admission. For patients that passed in the hospital, the median days from transition of code status to death was 0(IQR 0–1). Levodopa dose deviations were frequent in both EOL and non-EOL group, but contraindicated medications were infrequently administered (11% in EOL group vs. 9% in non-EOL group).ConclusionOur data suggest a low utilization of PC services and delayed discussions of goals of care. More work is needed to raise awareness of inpatient teams managing PwP regarding the unique but common challenges facing PwP with advanced disease. A brief narrative review summarizing the suggested management of symptoms common to hospitalized PwP near EOL is provided

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