Giant number fluctuations in microbial ecologies

Statistical fluctuations in population sizes of microbes may be quite large depending on the nature of their underlying stochastic dynamics. For example, the variance of the population size of a microbe undergoing a pure birth process with unlimited resources is proportional to the square of its mean. We refer to such large fluctuations, with the variance growing as square of the mean, as Giant Number Fluctuations (GNF). Luria and Delbruck showed that spontaneous mutation processes in microbial populations exhibit GNF. We explore whether GNF can arise in other microbial ecologies. We study certain simple ecological models evolving via stochastic processes: (i) bi-directional mutation, (ii) lysis-lysogeny of bacteria by bacteriophage, and (iii) horizontal gene transfer (HGT). For the case of bi-directional mutation process, we show analytically exactly that the GNF relationship holds at large times. For the ecological model of bacteria undergoing lysis or lysogeny under viral infection, we show that if the viral population can be experimentally manipulated to stay quasi-stationary, the process of lysogeny maps essentially to one-way mutation process and hence the GNF property of the lysogens follows. Finally, we show that even the process of HGT may map to the mutation process at large times, and thereby exhibits GNF.Comment: 18 pages, 5 figure

Optimal Index Codes via a Duality between Index Coding and Network Coding

In Index Coding, the goal is to use a broadcast channel as efficiently as possible to communicate information from a source to multiple receivers which can possess some of the information symbols at the source as side-information. In this work, we present a duality relationship between index coding (IC) and multiple-unicast network coding (NC). It is known that the IC problem can be represented using a side-information graph $G$ (with number of vertices $n$ equal to the number of source symbols). The size of the maximum acyclic induced subgraph, denoted by $MAIS$ is a lower bound on the \textit{broadcast rate}. For IC problems with $MAIS=n-1$ and $MAIS=n-2$, prior work has shown that binary (over ${\mathbb F}_2$) linear index codes achieve the $MAIS$ lower bound for the broadcast rate and thus are optimal. In this work, we use the the duality relationship between NC and IC to show that for a class of IC problems with $MAIS=n-3$, binary linear index codes achieve the $MAIS$ lower bound on the broadcast rate. In contrast, it is known that there exists IC problems with $MAIS=n-3$ and optimal broadcast rate strictly greater than $MAIS$

Index Coding: Rank-Invariant Extensions

An index coding (IC) problem consisting of a server and multiple receivers with different side-information and demand sets can be equivalently represented using a fitting matrix. A scalar linear index code to a given IC problem is a matrix representing the transmitted linear combinations of the message symbols. The length of an index code is then the number of transmissions (or equivalently, the number of rows in the index code). An IC problem ${\cal I}_{ext}$ is called an extension of another IC problem ${\cal I}$ if the fitting matrix of ${\cal I}$ is a submatrix of the fitting matrix of ${\cal I}_{ext}$. We first present a straightforward $m$\textit{-order} extension ${\cal I}_{ext}$ of an IC problem ${\cal I}$ for which an index code is obtained by concatenating $m$ copies of an index code of ${\cal I}$. The length of the codes is the same for both ${\cal I}$ and ${\cal I}_{ext}$, and if the index code for ${\cal I}$ has optimal length then so does the extended code for ${\cal I}_{ext}$. More generally, an extended IC problem of ${\cal I}$ having the same optimal length as ${\cal I}$ is said to be a \textit{rank-invariant} extension of ${\cal I}$. We then focus on $2$-order rank-invariant extensions of ${\cal I}$, and present constructions of such extensions based on involutory permutation matrices

Conversations on greatest common divisor

Today I am going to share with you an interesting conversation between me and my cousin Apoorvi, who is a curious student of class 9. This conversation began after she saw me teaching Greatest Common Divisor to Priyanka. Priyanka lives in my neighborhood and she is a student of class four. Sometimes she visits my home for help in mathematics. One day after helping Priyanka with her homework, I started talking to Apoorvi

COMPARATIVE ASSESSMENT OF ANTIOXIDANT POTENTIAL OF CASSIA AURICULATA (LINN.) FLOWER, LEAF AND SEED METHANOLIC EXTRACTS

Objective: The present study aimed to investigate the antioxidant potential of the methanolic extract of flowers, leaves and seeds of Cassia auriculata (Linn.) along with the quantification of total phenolics and flavonoids content.Methods: The antioxidant activity of flowers, leaves and seeds of Cassia auriculata (Linn.) was assessed with the help of various in vitro antioxidant assay systems as 2,2-Diphenyl-1-picrylhydrazyl (DPPH) scavenging assay, reducing power assay and Nitric oxide scavenging assay. For the determination of phenolic content the Folin Ciocalteu method and for flavonoids Aluminium Chloride spectrophotometric method was adopted.Results: The flowers, leaves and seeds methanolic extracts of Cassia auriculata (Linn.) were screened for different phyto chemicals present and the major antioxidants polyphenols and flavonoids were quantified. All the extracts showed significant antioxidant activity in all assays with the same trend as in total phenolics and flavonoids content. Flowers show most antioxidant activity in all assay systems due to higher phenolics and flavonoids content. That indicated the direct correlation among antioxidant potential, total phenolics and flavonoids content.Conclusion: The result implies that the Cassia auriculata (Linn.) plant parts especially flowers can be serving as natural sources of antioxidants and could be used in the treatment of diseases that have free-radical origin and as a substitute for synthetic drugs. Â

Mitigation of Power Quality Problems Using Custom Power Devices: A Review

Electrical power quality (EPQ) in distribution systems is a critical issue for commercial, industrial and residential applications. The new concept of advanced power electronic based Custom Power Devices (CPDs) mainly distributed static synchronous compensator (D-STATCOM), dynamic voltage restorer (DVR) and unified power quality conditioner (UPQC) have been developed due to lacking the performance of traditional compensating devices to minimize power quality disturbances. This paper presents a comprehensive review on D-STATCOM, DVR and UPQC to solve the electrical power quality problems of the distribution networks. This is intended to present a broad overview of the various possible DSTATCOM, DVR and UPQC configurations for single-phase (two wire) and three-phase (three-wire and four-wire) networks and control strategies for the compensation of various power quality disturbances. Apart from this, comprehensive explanation, comparison, and discussion on D-STATCOM, DVR, and UPQC are presented. This paper is aimed to explore a broad prospective on the status of D-STATCOMs, DVRs, and UPQCs to researchers, engineers and the community dealing with the power quality enhancement. A classified list of some latest research publications on the topic is also appended for a quick reference

Performance Evaluation of Three Different Inverter Configurations of DVR for Mitigation of Voltage Events

The voltage events namely voltage sags and voltage swells represent the most common, frequent and important power quality events in today’s power system. Dynamic voltage restorer (DVR) is one of the key components used to mitigate the supply voltage quality disturbances in terms of voltage sags and swells in the distribution system. It consists of an energy storage unit, a voltage source inverter, a filter, a coupling transformer and the control system. This paper presents three different inverter configurations of dynamic voltage restorer (DVR) for mitigation of voltage events such as voltage sags and swells with sudden addition or removal of the nonlinear load. These three configurations are voltage source inverter based DVR (VSI-DVR), current source inverter based DVR (CSI-DVR) and impedance or Z-source inverter based DVR (ZSI-DVR). The d-q control technique is used to control the operation of the DVR. The response of ZSI-DVR for mitigation of voltage sags and swells are investigated and compared with VSI-DVR and CSI-DVR using MATLAB/SIMULINK environment

Removal of ocular artifacts from EEG signals using adaptive threshold PCA and Wavelet transforms

It becomes more difficult to identify and analyze the Electroencephalogram (EEG) signals when it is corrupted by eye movements and eye blinks. This paper gives the different methods how to remove the artifacts in EEG signals. In this paper we proposed wavelet based threshold method and Principal Component Analysis (PCA) based adaptive threshold method to remove the ocular artifacts. Compared to the wavelet threshold method PCA based adaptive threshold method will gives the better PSNR value and it will decreases the elapsed time