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

Magnetic Properties of Ni-Fe Nanowire Arrays: Effect of Template Material and Deposition Conditions

The objective of this work is to study the magnetic properties of arrays of Ni-Fe nanowires electrodeposited in different template materials such as porous silicon, polycarbonate and alumina. Magnetic properties were studied as a function of template material, applied magnetic field (parallel and perpendicular) during deposition, wire length, as well as magnetic field orientation during measurement. The results show that application of magnetic field during deposition strongly influences the c-axis preferred orientation growth of Ni-Fe nanowires. The samples with magnetic field perpendicular to template plane during deposition exhibits strong perpendicular anisotropy with greatly enhanced coercivity and squareness ratio, particularly in Ni-Fe nanowires deposited in polycarbonate templates. In case of polycarbonate template, as magnetic field during deposition increases, both coercivity and squareness ratio also increase. The wire length dependence was also measured for polycarbonate templates. As wire length increases, coercivity and squareness ratio decrease, but saturation field increases. Such magnetic behavior (dependence on template material, magnetic field, wire length) can be qualitatively explained by preferential growth phenomena, dipolar interactioComment: 26 pages, 7 figures, 5 Tables Submitted to Physical Review

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

Primary tubercular caecal perforation: a rare clinical entity

<p>Abstract</p> <p>Background</p> <p>Intestinal tuberculosis is a common problem in endemic areas, causing considerable morbidity and mortality. An isolated primary caecal perforation of tubercular origin is exceptionally uncommon.</p> <p>Case presentation</p> <p>We report the case of a 39 year old male who presented with features of perforation peritonitis, which on laparotomy revealed a caecal perforation with a dusky appendix. A standard right hemicolectomy with ileostomy and peritoneal toileting was done. Histopathology revealed multiple transmural caseating granulomas with Langerhans-type giant cells and acid-fast bacilli, consistent with tuberculosis, present only in the caecum.</p> <p>Conclusions</p> <p>We report this extremely rare presentation of primary caecal tuberculosis to sensitize the medical fraternity to its rare occurrence, which will be of paramount importance owing to the increasing incidence of tuberculosis all over the world, especially among the developing countries.</p

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)