A Stochastic Approximation Algorithm for Quantile Estimation

In this paper, we present two new stochastic approximation algorithms for the problem of quantile estimation. The algorithms uses the characterization of the quantile provided in terms of an optimization problem in 1]. The algorithms take the shape of a stochastic gradient descent which minimizes the optimization problem. Asymptotic convergence of the algorithms to the true quantile is proven using the ODE method. The theoretical results are also supplemented through empirical evidence. The algorithms are shown to provide significant improvement in terms of memory requirement and accuracy.

Empirical Analysis of Sampling Based Estimators for Evaluating RBMs

The Restricted Boltzmann Machines (RBM) can be used either as classifiers or as generative models. The quality of the generative RBM is measured through the average log-likelihood on test data. Due to the high computational complexity of evaluating the partition function, exact calculation of test log-likelihood is very difficult. In recent years some estimation methods are suggested for approximate computation of test log-likelihood. In this paper we present an empirical comparison of the main estimation methods, namely, the AIS algorithm for estimating the partition function, the CSL method for directly estimating the log-likelihood, and the RAISE algorithm that combines these two ideas.

Hydrogen Bonds Computing Server (HBCS): an online web server to compute hydrogen-bond interactions and their precision

Hydrogen bonds in biological macromolecules play significant structural and functional roles. They are the key contributors to most of the interactions without which no living system exists. In view of this, a web-based computing server, the Hydrogen Bonds Computing Server (HBCS), has been developed to compute hydrogen-bond interactions and their standard deviations for any given macromolecular structure. The computing server is connected to a locally maintained Protein Data Bank (PDB) archive. Thus, the user can calculate the above parameters for any deposited structure, and options have also been provided for the user to upload a structure in PDB format from the client machine. In addition, the server has been interfaced with the molecular viewers Jmol and JSmol to visualize the hydrogen-bond interactions. The proposed server is freely available and accessible via the World Wide Web at http://bioserver1.physics.iisc.ernet.in/hbcs/.

A simulation model of a floating half zone

A simulation model of a floating half zone was suggested by steady numerical simulation and experiment respectively, in the previous papers [Q.S. Chen, W.R. Hu, Int. J. Mass Heat Transfer 40 (1997) 757; J.H. Han, Y. Ar, R. Zhou, W.R. Hue, Int. J. Mass Heat Transfer 40 (1997) 2671]. In the present paper, the simulation model is studied by using the method of unsteady and three-dimensional numerical simulation, and the transient process from steady convection to oscillatory convection is especially analyzed. Comparison of onsets of oscillation for both simulation model and the usual model were obtained, and the results show that the critical Marangoni number of the simulation model is obviously smaller than that of the usual model for the same slender liquid bridge. This implies that the usual model of a floating half zone gives a lower estimation on the onset of oscillation for floating zone convection.