Convergence of Gibbs Sampling: Coordinate Hit-And-Run Mixes Fast

The Gibbs Sampler is a general method for sampling high-dimensional distributions, dating back to 1971. In each step of the Gibbs Sampler, we pick a random coordinate and re-sample that coordinate from the distribution induced by fixing all the other coordinates. While it has become widely used over the past half-century, guarantees of efficient convergence have been elusive. We show that for a convex body K in ?? with diameter D, the mixing time of the Coordinate Hit-and-Run (CHAR) algorithm on K is polynomial in n and D. We also give a lower bound on the mixing rate of CHAR, showing that it is strictly worse than hit-and-run and the ball walk in the worst case

SEASONAL VARIATION IN THE CONTENT OF MANGIFERIN IN LEAVES OF MANGIFERA INDICA L.

Objective: Mangifera indica L., a member of the genus of evergreen trees, is cultivated extensively in India. The various parts of the tree find its use in the Ayurvedic system of medicine against diseases like diarrhoea, dysentery, dyspepsia, sprue and carbuncle. The major constituent of the stem bark and leaves of M. indica is mangiferin and the various activities associated with the stem bark or the leaves are reported to be due to this component. Mangiferin is currently of interest due to its activities like antidiabetic, hypolipidemic, gastroprotective, antibacterial, chemopreventive and many more. The objective of the current study was to evaluate the variation in the mangiferin content with time, in leaves of M. indica, throughout the year.Methods: Samples of M. indica leaves were collected every month for a period of one year and the content of mangiferin was assessed at these time points. Mangiferin was quantified using the HPLC method.Results: Seasonal variation was seen in the mangiferin content of the leaves. Highest content was seen during the month of April.Conclusions: Content of mangiferin changes with the different seasons and reaches its highest value during fruit ripening.Â

Reductive Biotransformation of Ethyl Acetoacetate: A Comparative Studies using Free and Immobilized Whole Yeast Cells

Bioreduction of ethyl acetoacetate with free and immobilized yeast whole cell was achieved by using water and sucrose combination. After detachment from immobilized beads under basic condition, the corresponding ethyl(S)-(+)-3-hydroxybutanoate was isolated with 98 to 100% yield. Immobilized beads of yeast whole cell were prepared at different temperature which affects the morphology and physiology of the beads for the diffusion of the enzyme, which shown the maximum conversion of the substrate to products as compared to the free yeast whole cell

An insight to ocular in situ gelling systems

Eye is delicate organ of body whose defence mechanism restricts entry of exogenous substances. Conventional drug delivery systems get washed off within a short period of time and results in poor ocular bioavailability. Development of in situ gel having protracted ocular residence time is one of the mile stone triumphs by pharmaceutical researcher for treatment of eye aliments. This polymeric system showed sol-to-gel phase transition by change in physiological parameters in pre-corneal area which includes pH, temperature or ionic interactions etc. Three types of in situ gels are well known based on mechanism involved in phase transition viz. temperature dependent, pH sensitive, ion activated systems. Gel formed after phase transitions have high viscosity along with bio-adhesive property, which increases resistance for instantaneous rinse off due to defence contrivance. Plus it prevents nasal-lachrymal drainage and avoids the systemic side effects. Recently, in situ gels have been vexed in amalgamation with another drug delivery system. It may include use of two or more stimuli systems together or added advantages of nano-technology. Combination of in situ gel with nano-particles is utmost remedy for ocular treatment with water insoluble drugs

OPTIMIZATION OF EXTRACTION PARAMETERS FOR TOTAL FLAVONOIDS FROM GARDENIA GUMMIFERA GUM RESIN BY RESPONSE SURFACE METHODOLOGY

Objective: To optimize the extraction parameters for determining the highest yield of Total Flavonoids from Gardenia gummifera gum resin.Methods: In the present study, response surface methodology (RSM) with three level Box Behenken design (BBD) was performed to optimize extraction parameters for total flavonoids. Solvent concentration(A), extraction time (B) and extraction temperature(C) were considered for single factor experiment.Results: The highest flavonoid concentration was obtained with acetone 45.00% v/v, time 101.46 min, temperature 41.57 °C. The average experimental TFC under optimal conditions was 161.14 mg/g which was in close agreement with the predicted value of 163.42 mg/g.Conclusion: RSM-BBD is successfully applied in optimizing extraction conditions for extraction of total flavonoids from G. gummifera gum resin

Reducing Isotropy and Volume to KLS: An O(n3ψ2)O(n^3\psi^2) Volume Algorithm

We show that the the volume of a convex body in ${\mathbb R}^{n}$ in the general membership oracle model can be computed with $\widetilde{O}(n^{3}\psi^{2}/\varepsilon^{2})$ oracle queries, where $\psi$ is the KLS constant ($\widetilde{O}$ suppresses polylogarithmic terms. $O^{*}$suppresses dependence on error parameters as well as polylogarithmic terms.). With the current bound of $\psi\lesssim n^{\frac{1}{4}}$, this gives an $\widetilde{O}(n^{3.5}/\varepsilon^{2})$ algorithm, the first general improvement on the Lov\'{a}sz-Vempala $\widetilde{O}(n^{4}/\varepsilon^{2})$ algorithm from 2003. The main new ingredient is\emph{ }an $\widetilde{O}(n^{3}\psi^{2})$ algorithm for isotropic transformation, following which we can apply the $\widetilde{O}(n^{3}/\varepsilon^{2})$ volume algorithm of Cousins and Vempala for well-rounded convex bodies. A positive resolution of the KLS conjecture would imply an $\widetilde{O}(n^{3}/\epsilon^{2})$ volume algorithm. We also give an efficient implementation of the new algorithm for convex polytopes defined by $m$ inequalities in ${\mathbb R}^{n}$: polytope volume can be estimated in time $\widetilde{O}(mn^{c}/\varepsilon^{2})$ where $c<3.7$ depends on the current matrix multiplication exponent and improves on the the previous best bound.Comment: 23 pages, 1 figur

NUTRITIONAL AND PHYTOCHEMICAL ASSESMENT OF WILD EDIBLE FRUIT OF AEGLE MARMELOS (LINN.) USED BY THE TRIBES OF BHIWAPUR TAHSIL NAGPUR DISTRICT, INDIA

Objectives: Wild edible plants play an important role in human life and are the vital constituent of the traditional diet. People of the Bhiwapur Tahsilare very close to the nature, wild fruits like Aegle marmelos (Bael), which is one of the natural resources in the Tahsil. They have a direct dependence onthe wild plants for their sustenance. Owing to the easy accessibility, the fruits are very commonly utilized by the tribal populations and travelers.Thepresent investigation aimed to assess the nutritional and phytochemical analysis of ripened fruits of a popularly known medicinal plant A. marmelose.Methods: The study includes the estimation of ash content, protein, carbohydrate (sugar), vitamins and mineral contents (Cu, Fe, Mn, Zn, Ca, Na, K)of Bael fruit. The water extract was screened for the qualitative phytochemical analysis.Results: The fresh fruits were found a rich source of protein (6.91±0.11 g/100 g), carbohydrate (22.55±0.15 g/100 g) fiber (7.26±0.23 g/100 g) andenergy (133.14 Kcal/100 g). The fruits were found to contain high calcium (86.69±0.01 mg/100 g) content and may be considered as a rich sourceto facilitate the rehabilitation of bone problems in the human being. The Na/K and Zn/Cu ratio were found to be 0.012 and 12.26 may attribute themedicinal properties in cardiovascular disorders. The water extract showed the presence of carbohydrates, proteins, sterols, alkaloids, glycosides,saponins, polyphenols, and flavonoids.Conclusion: The nutritional and phytochemical analysis reveals that the fruits are not only acting as supplementary foods, but is the tonic requirementsof the tribal's and deprived of poor Bhiwapur Tahsil.Keywords: Aegle marmelos, Bhiwapur, nutritional, Phytochemical, Tribal

DEVELOPMENT AND VALIDATION OF HPLC METHOD FOR ESTIMATION OF BRIMONIDINE TARTRATE AS BULK DRUG AND IN OPHTHALMIC FORMULATION

The optimized reverse phase high performance liquid chromatographic method was developed for estimation of Brimonidine Tartrate in bulk drug and pharmaceutical dosage form. Chromatography was performed on Kromasil C 18 ( 250 mm X 4.6 mm i.d. , 5 μm particle size) column with mobile phase citric acid monohydrate buffer:water:methanol (30:50:20 v/v/v) and  pH 3 was maintained by using triethylamine. The flow rate was 1.0 ml/min. Elute was detected at 246 nm and it effectively separated at Retention Time of 5.96 min. The LOD and LOQ was 1.47 and 4.47 μg/ml respectively. A linear response was observed over the concentration range 40-80 μg/ml for Brimonidine Tartrate. Thus the proposed HPLC method was found accurate, specific, precise, robust and reproducible

Towards Loop Quantization of Plane Gravitational Waves

The polarized Gowdy model in terms of Ashtekar-Barbero variables is further reduced by including the Killing equations for plane-fronted parallel gravitational waves with parallel rays. The resulting constraint algebra, including one constraint derived from the Killing equations in addition to the standard ones of General Relativity, are shown to form a set of first-class constraints. Using earlier work by Banerjee and Date the constraints are expressed in terms of classical quantities that have an operator equivalent in Loop Quantum Gravity, making space-times with pp-waves accessible to loop quantization techniques.Comment: 14 page