A geometric view of conjugate priors

In Bayesian machine learning, conjugate priors are popular, mostly due to mathematical convenience. In this paper, we show that there are deeper reasons for choosing a conjugate prior. Specifically, we formulate the conjugate prior in the form of Bregman divergence and show that it is the inherent geometry of conjugate priors that makes them appropriate and intuitive. This geometric interpretation allows one to view the hyperparameters of conjugate priors as the effective sample points, thus providing additional intuition. We use this geometric understanding of conjugate priors to derive the hyperparameters and expression of the prior used to couple the generative and discriminative components of a hybrid model for semi-supervised learning.     

Classifying Problems on Linear Congruences and Abelian Permutation Groups Using Logspace Counting Classes

In this paper we classify the complexity of several problems based on Abelian permutation groups and linear congruences using logspace counting classes. The problems we consider were defined by McKenzie & Cook (1987).     

Temperature dependent H2S and Cl2 sensing selectivity of Cr2O3 thin films

The conductometric gas sensing characteristics of Cr₂O₃ thin films - prepared by electron-beam deposition of Cr films on quartz substrate followed by oxygen annealing - have been investigated for a host of gases (CH₄, CO, NO₂, Cl₂, NH₃ and H₂S) as a function of operating temperature (between 30 and 300 °C) and gas concentration (1-30 ppm). We demonstrate that these films are highly selective to H₂S at an operating temperature of 100 °C, while at 220 °C the films become selective to Cl₂. This result has been explained on the basis of depletion of chemisorbed oxygen from the surface of films due to temperature and/or interaction with Cl₂/H₂S, which is supported experimentally by carrying out the work function measurements using Kelvin probe method. The temperature dependent selectivity of Cr₂O₃ thin films provides a flexibility to use same film for the sensing of Cl₂ as well as H₂S.     

On the impact of analyzing customer information and prioritizing in a service system

This paper examines prioritization in a service system and analyzes whether, in the presence of heterogeneous customers who have different needs and a costly sorting process, it pays to prioritize. In particular, in our model, sorting is costly because the task of gathering information to prioritize jobs consumes resources. We investigate a stylized model in which there are two classes of jobs — one whose waiting cost is high, called urgent, and the other whose waiting cost is low, called non-urgent. There are two types of employees, sorters, who collect information on a job and then decide whether it is urgent or non-urgent, and processors, who execute the job or provide the service. We begin by assuming that sorters categorize customers perfectly, and we relax this assumption later in the paper. We optimize two performance metrics, waiting costs (under a given budget) and total costs, and find the conditions under which prioritization is beneficial for these two metrics.     

Fuzzy parametric programming model for multi-objective integrated solid waste management under uncertainty

Solid waste management is increasingly becoming a challenging task for the municipal authorities due to increasing waste quantities, changing waste composition, decreasing land availability for waste disposal sites and increasing awareness about the environmental risk associated with the waste management facilities. The present study focuses on the optimum selection of the treatment and disposal facilities, their capacity planning and waste allocation under uncertainty associated with the long-term planning for solid waste management. The fuzzy parametric programming model is based on a multi-objective, multi-period system for integrated planning for solid waste management. The model dynamically locates the facilities and allocates the waste considering fuzzy waste quantity and capacity of waste management facility. The model addresses uncertainty in waste quantity as well as uncertainties in the operating capacities of waste management facilities simultaneously. It was observed that uncertainty in waste quantity is likely to affect the planning for waste treatment/disposal facilities more as compared with the uncertainty in the capacities of the waste management facilities. The relationship between increase in waste quantity and increase in the total cost/risk involved in waste management is found to be nonlinear. Therefore, it is possible that a marginal change in waste quantity could increase the total cost/risk substantially. The information obtained from the analysis of modeling results can be effectively used for understanding the effect of changing the priorities and objectives of planning decisions on facility selections and waste diversions.     

Apparatus for studies of high-temperature chemical reactions in single particle systems

We report a compact microgravity flight apparatus for characterization of high-temperature chemical reactions in single particle systems. The apparatus employs an infrared CO(2) laser to ignite 1-5 mm samples while video images, thermocouple measurements, laser on/off status, and XYZ accelerometer signals are synchronously recorded. Different operating modes permit preignition quenching, ignition, and combustion experiments to be performed. The apparatus was successfully utilized during microgravity experiments on board NASA research aircraft.     

VEDA: a web-based virtual environment for dynamic atomic force microscopy

We describe here the theory and applications of virtual environment dynamic atomic force microscopy (VEDA), a suite of state-of-the-art simulation tools deployed on nanoHUB (www.nanohub.org) for the accurate simulation of tip motion in dynamic atomic force microscopy (dAFM) over organic and inorganic samples. VEDA takes advantage of nanoHUB's cyberinfrastructure to run high-fidelity dAFM tip dynamics computations on local clusters and the teragrid. Consequently, these tools are freely accessible and the dAFM simulations are run using standard web-based browsers without requiring additional software. A wide range of issues in dAFM ranging from optimal probe choice, probe stability, and tip-sample interaction forces, power dissipation, to material property extraction and scanning dynamics over hetereogeneous samples can be addressed.     

Stochastic behaviour of a two-unit cold standby redundant electronic equipment under human failure

This paper presents a mathematical model to evaluate availability and M.T.T.F. of a two-unit cold standby system with three possible states of each unit; viz. good, partially failed and failed, incorporating the concept of human failure. The model has been developed for exponential failures and general repairs. Single service facility is available in each state during the operational stage of the electronic equipment. Laplace transforms of the various state probabilities have been obtained. Steady-state probabilities, steady-state availability and mean time to failure have been derived.