Median Sets and Median Number of a Graph

A profile is a finite sequence of vertices of a graph. The set of all vertices of the graph which minimises the sum of the distances to the vertices of the profile is the median of the profile. Any subset of the vertex set such that it is the median of some profile is called a median set. The number of median sets of a graph is defined to be the median number of the graph. In this paper, we identify the median sets of various classes of graphs such as Kp − e, Kp,q forP > 2, and wheel graph and so forth. The median numbers of these graphs and hypercubes are found out, and an upper bound for the median number of even cycles is established.We also express the median number of a product graph in terms of the median number of their factors.

Quantile based entropy function

Quantile functions are efficient and equivalent alternatives to distribution functions in modeling and analysis of statistical data (see Gilchrist, 2000; Nair and Sankaran, 2009). Motivated by this, in the present paper, we introduce a quantile based Shannon entropy function. We also introduce residual entropy function in the quantile setup and study its properties. Unlike the residual entropy function due to Ebrahimi (1996), the residual quantile entropy function determines the quantile density function uniquely through a simple relationship. The measure is used to define two nonparametric classes of distributions

Sequential interactions of Silver-silica nanocomposite (Ag-SiO2NC) with cell wall, metabolism and genetic stability of Psedomonas aeruginosa, a multiple antibiotic resistant bacterium

The study was carried out to understand the effect of silver-silica nanocomposite (Ag-SiO2NC) on the cell wall integrity, metabolism and genetic stability of Pseudomonas aeruginosa, a multiple drugresistant bacterium. Bacterial sensitivity towards antibiotics and Ag-SiO2NC was studied using standard disc diffusion and death rate assay, respectively. The effect of Ag-SiO2NC on cell wall integrity was monitored using SDS assay and fatty acid profile analysis while the effect on metabolism and genetic stability was assayed microscopically, using CTC viability staining and comet assay, respectively. P. aeruginosa was found to be resistant to β-lactamase, glycopeptidase, sulfonamide, quinolones, nitrofurantoin and macrolides classes of antibiotics. Complete mortality of the bacterium was achieved with 80 μgml-1 concentration of Ag-SiO2NC. The cell wall integrity reduced with increasing time and reached a plateau of 70 % in 110 min. Changes were also noticed in the proportion of fatty acids after the treatment. Inside the cytoplasm, a complete inhibition of electron transport system was achieved with 100 μgml-1 Ag-SiO2NC, followed by DNA breakage. The study thus demonstrates that Ag-SiO2NC invades the cytoplasm of the multiple drug-resistant P. aeruginosa by impinging upon the cell wall integrity and kills the cells by interfering with electron transport chain and the genetic stability

An Improved Design of Combinational Digital Circuits with Multiplexers using Genetic Algorithm

This paper presents a new approach to the design of combinational digital circuits with multiplexers using Evolutionary techniques. Genetic Algorithm (GA) is used as the optimization tool. Several circuits are synthesized with this method and compared with two design techniques such as standard implementation of logic functions using multiplexers and implementation using Shannon’s decomposition technique using GA. With the proposed method complexity of the circuit and the associated delay can be reduced significantly

Analysis of Stochastic Volatility Sequences Generated by Product Autoregressive Models

The classical methods of analysing time series by Box-Jenkins approach assume that the observed series uctuates around changing levels with constant variance. That is, the time series is assumed to be of homoscedastic nature. However, the nancial time series exhibits the presence of heteroscedasticity in the sense that, it possesses non-constant conditional variance given the past observations. So, the analysis of nancial time series, requires the modelling of such variances, which may depend on some time dependent factors or its own past values. This lead to introduction of several classes of models to study the behaviour of nancial time series. See Taylor (1986), Tsay (2005), Rachev et al. (2007). The class of models, used to describe the evolution of conditional variances is referred to as stochastic volatility modelsThe stochastic models available to analyse the conditional variances, are based on either normal or log-normal distributions. One of the objectives of the present study is to explore the possibility of employing some non-Gaussian distributions to model the volatility sequences and then study the behaviour of the resulting return series. This lead us to work on the related problem of statistical inference, which is the main contribution of the thesis