Diffusion limits of the random walk Metropolis algorithm in high dimensions

Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular, they lead directly to precise estimates of the number of steps required to explore the target measure, in stationarity, as a function of the dimension of the state space. However, to date such results have mainly been proved for target measures with a product structure, severely limiting their applicability. The purpose of this paper is to study diffusion limits for a class of naturally occurring high-dimensional measures found from the approximation of measures on a Hilbert space which are absolutely continuous with respect to a Gaussian reference measure. The diffusion limit of a random walk Metropolis algorithm to an infinite-dimensional Hilbert space valued SDE (or SPDE) is proved, facilitating understanding of the computational complexity of the algorithm.Comment: Published in at http://dx.doi.org/10.1214/10-AAP754 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Geometric erogdicity of a bead-spring pair with stochastic Stokes forcing

We consider a simple model for the uctuating hydrodynamics of a exible polymer in dilute solution, demonstrating geometric ergodicity for a pair of particles that interact with each other through a nonlinear spring potential while being advected by a stochastic Stokes uid velocity field. This is a generalization of previous models which have used linear spring forces as well as white-in-time uid velocity fields. We follow previous work combining control theoretic arguments, Lyapunov functions, and hypo-elliptic diffusion theory to prove exponential convergence via a Harris chain argument. To this, we add the possibility of excluding certain "bad" sets in phase space in which the assumptions are violated but from which the systems leaves with a controllable probability. This allows for the treatment of singular drifts, such as those derived from the Lennard-Jones potential, which is an novel feature of this work

Coral reefs of India, their conservation and management

Coral reefs are natural gift to mankind, and are built in thousands of years by millions of tiny coral polyps. Reefs give food for mankind, material for scientific research, ample opportunities for recreation and past time. We need the reef, reefs need our attention; certainly we should keep them for future generation

Coral reef ecosystems

Coral reefs constitute the most dominant marine benthic ecosystem of tropical seas. The complexity of. the biotic and abiotic interactions, coupled with rich biodiversity of reef dwelling and reef building fauna and flora are comparable to those prevailing in tropical rain forests. Several important problems related to coral reefs all over the world, such as, biodiversity, biogeochemical cycles, nutrient flux, environmental degradation and ecological collapse, exploitation of reef resources- their conservation and management, have been addresse

An assessment of the effects of environment and human interference on the coral reefs of Palk Bay and Gulf of Mannar along the Indian Coast

The environmental and man-made changes that affects the coral growth and associated animals and fishery in Palk Bay and Gulf of Mannar along the Indian coast are discussed. Quarrying of corals for industrial use has turned out to be a serious threat to the reefs. Removal of corals in several places has caused settlement of sand and growth of sea-grass and algae at former sites of well developed reefs

Corals

Corals art objects of beauty and utility. They are found only in the sea, mainly in tropical and subtropics1 regions. Only very few, other than students of biology know that they are sedentary animals possessing a hard internal or external skeleton. They have attracted the attention of the biologists only recently and several problems related to them are still not explained to our fullest satisfaction. Earlier naturalists regarded them as marine plants, probably due to their sedentary habit and plant-like growth form, It was only in the latter half of the cigbteenth century Peyssonnel proved the animal nature of corals, But even middle nineteenth century students of natural history assigned them a place only between animals and plants and wore accordingly called 'zoophytes'

A review of the status of corals and coral reefs of India

Precise estimation of the biodiversity of corals from any area is subject to variation due to uncertainty of synonymy. Corals exhibit very high intraspecific skeletal variation depending on the physiographic and hydrographic condition. The present paper describes overview of coral resources in Indian seas, their biology and taxonomy, anthropogenic stress on coral reefs, conservation and research efforts being put by various organisation

On a large adult Zebra shark landed at Pamban

The article describes about the catch of adult zebra shark, Stegostoma faciatum a rare species in Indian waters

Some Observations On Dolphins In Mandapam Area With A Note On Their Food

The dolphins are common in the Gulf of Mannar near Mandapam. Five of them were caught by the fishermen in trawler or gill net in the neighbourhood of Krusadai Island in the Gulf of Mannar in the winter months of 1980 to 1982. They were studied for the species identity and their stomach contents. Data regarding the date, place of collection weight, sex and essential body measurements of all specimens were recorded

Report on the Stony Corals from the Maldive Archipelago

The Maldive Archipelago, situated at the southwest of India, consists of 22 atolls, extending over a length of nearly 470km in a north-south direction. The northern limit is Ihavandiffulu Atoll (7"'05'N, 72' 55'E), while Addu, one of the scientifically well known atolls, is located at the southern tip (0' 40'5, 73'1 O'E). The largest among the Maldivian atolls is located in the northern half of the chain and is known by twO names, a nonhern smaller part called Tiladummati, and the southern part Miladummadulu. At the middle pan of the Archipelago the atolls are arranged in two almost parallel rows, incorporating a great number of Faros with their small lagoon-like water bodies, termed Velu. The type locality of Atolls and Faros are the Maldives, the names originating from the Maldivian language. Nearly 2000 small islands enter into the geography of the Maldives, of which circa 200 are inhabited with a population of nearly 120000