Optimal Linear Shrinkage Estimator for Large Dimensional Precision Matrix

In this work we construct an optimal shrinkage estimator for the precision matrix in high dimensions. We consider the general asymptotics when the number of variables $p\rightarrow\infty$ and the sample size $n\rightarrow\infty$ so that $p/n\rightarrow c\in (0, +\infty)$. The precision matrix is estimated directly, without inverting the corresponding estimator for the covariance matrix. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal shrinkage intensities and estimate them consistently. The resulting distribution-free estimator has almost surely the minimum Frobenius loss. Additionally, we prove that the Frobenius norms of the inverse and of the pseudo-inverse sample covariance matrices tend almost surely to deterministic quantities and estimate them consistently. At the end, a simulation is provided where the suggested estimator is compared with the estimators for the precision matrix proposed in the literature. The optimal shrinkage estimator shows significant improvement and robustness even for non-normally distributed data.Comment: 26 pages, 5 figures. This version includes the case c>1 with the generalized inverse of the sample covariance matrix. The abstract was updated accordingl

SInC: An accurate and fast error-model based simulator for SNPs, Indels and CNVs coupled with a read generator for short-read sequence data

We report SInC (SNV, Indel and CNV) simulator and read generator, an open-source tool capable of simulating biological variants taking into account a platform-specific error model. SInC is capable of simulating and generating single- and paired-end reads with user-defined insert size with high efficiency compared to the other existing tools. SInC, due to its multi-threaded capability during read generation, has a low time footprint. SInC is currently optimised to work in limited infrastructure setup and can efficiently exploit the commonly used quad-core desktop architecture to simulate short sequence reads with deep coverage for large genomes. Sinc can be downloaded from https://sourceforge.net/projects/sincsimulator/

TO STUDY THE EFFICACY OF KANCHNAR GUGGULU AND DASHMOOL MATRA BASTI IN THE MANAGEMENT OF VATASHTHEELA W.S.R TO BENIGN PROSTATIC HYPERPLASIA

Benign prostatic hyperplasia is a common senile disease. It is a non-cancerous [benign] enlargement of the prostate gland, also called as fibromyoadenoma. It is involuntary hyperplasia due to disturbance of the ratio and quantity of circulating androgens and estrogens. As the age advances the serum testosterone levels slowly but significantly decreases, but levels of oestrogenic steroids are not decreased equally. According to this theory the prostate enlarges because of increased oestrogenic effects. It is likely that the secretion of intermediate peptide growth factors plays a part in the development of BPH. Vatashtheela as described in Ayurveda, closely resembles benign prostatic hyperplasia of modern medicine in its signs and symptoms. In the Vatashtheela, Mutravaha Srotodushti and vitiation of Vata and Kapha Doshas are involved. So Vata Kapha pacifying drugs along with Matra Basti considered to be helpful in reducing the size of prostate and enhancing the tonicity of urinary bladder. This study was conducted to find out the potency of Ayurvedic regimen of Kanchnar Gugglu orally and Dashmool Tail Matra Basti for the treatment of Vatashtheela as the Kanchnar Gugglu is having Granthihar property and Dashmool Tail pacifies Vata and having Tridoshghana, Deepana, Anulomana, Shothghana and Shoolghana properties. The drug Kanchnar Gugglu was given to 30 patients of group -1, with the dose of 500mg TDS before meals for 30 days. And Dashmool Tail Matra Basti was given to 30 patients of group – 2, with the dose of 50ml once a day for 15 days

Ayurveda View on Raktamokshan and its Mode of Action as per Modern Science

Ayurveda is old science which deals with many surgical and parasurgical procedures for the management of different pathological conditions. Amongst the many unique modalities Raktamokshan (bloodletting) is one of the important modality which provides health benefits in many diseases. Acharya Sushruta described importance of this procedure in conditions involving vitiation of Rakta and Dosha. Vitiation of Rakta is responsible for many health issues including skin problems and Raktamokshan helps greatly in this regard. Leech therapy, venesection and cupping therapy are subtype of Raktamokshan which helps in blood purification. The bloodletting therapies gaining attention of modern science due to their technical advancement. Raktamokshana mainly involves various techniques of blood liberation. Raktamokshan helps to treat conditions like eczema, swellings, inflammations and poisoning, etc