Theory of differential inequalities with appliciations to singular perturbiation problems and method of lines

During recent years, the theory of differential inequalities has been extensively used to discuss singular perturbation problems and method of lines to partial differential equations. The present thesis deals with some differential inequality theorems and their applications to singularly perturbed initial value problems, boundary value problems for ordinary differential equations in Banach space and initial boundary value problems for parabolic differential equations. The method of lines to parabolic and elliptic differential equations are also dealt The thesis is organised into nine chapters

Quadratic Predictor based Differential Encoding and Decoding of Speech Signals

Modeling nonlinear systems using Volterra series is a century old method but practical realizations were hampered by inadequate hardware to handle the increased computational complexity stemming from its use. But interest is renewed recently, in designing and implementing filters which can model much of the polynomial nonlinearities inherent in practical systems. The key advantage in resorting to Volterra power series for this purpose is that nonlinear filters so designed can be made to work in parallel with the existing LTI systems, yielding improved performance. This paper describes the inclusion of a quadratic predictor (with nonlinearity order 2) with a linear predictor in an analog source coding system. Analog coding schemes generally ignore the source generation mechanisms but focuses on high fidelity reconstruction at the receiver. The widely used method of differential pnlse code modulation (DPCM) for speech transmission uses a linear predictor to estimate the next possible value of the input speech signal. But this linear system do not account for the inherent nonlinearities in speech signals arising out of multiple reflections in the vocal tract. So a quadratic predictor is designed and implemented in parallel with the linear predictor to yield improved mean square error performance. The augmented speech coder is tested on speech signals transmitted over an additive white gaussian noise (AWGN) channel.

Differential induction, isolation, physicochemical and molecular characterization of temperate phages of environmental Vibrio cholerae as evidence of phage mediated Horizontal Gene Transfer

The resurgence of the enteric pathogen Vibrio cholerae, the causative organism of epidemic cholera, remains a major health problem in many developing countries like India. The southern Indian state of Kerala is endemic to cholera. The outbreaks of cholera follow a seasonal pattern in regions of endemicity. Marine aquaculture settings and mangrove environments of Kerala serve as reservoirs for V. cholerae. The non-O1/non-O139 environmental isolates of V. cholerae with incomplete ‘virulence casette’ are to be dealt with caution as they constitute a major reservoir of diverse virulence genes in the marine environment and play a crucial role in pathogenicity and horizontal gene transfer. The genes coding cholera toxin are borne on, and can be infectiously transmitted by CTXΦ, a filamentous lysogenic vibriophages. Temperate phages can provide crucial virulence and fitness factors affecting cell metabolism, bacterial adhesion, colonization, immunity, antibiotic resistance and serum resistance. The present study was an attempt to screen the marine environments like aquafarms and mangroves of coastal areas of Alappuzha and Cochin, Kerala for the presence of lysogenic V. cholerae, to study their pathogenicity and also gene transfer potential. Phenotypic and molecular methods were used for identification of isolates as V. cholerae. The thirty one isolates which were Gram negative, oxidase positive, fermentative, with or without gas production on MOF media and which showed yellow coloured colonies on TCBS (Thiosulfate Citrate Bile salt Sucrose) agar were segregated as vibrios. Twenty two environmental V. cholerae strains of both O1 and non- O1/non-O139 serogroups on induction with mitomycin C showed the presence of lysogenic phages. They produced characteristic turbid plaques in double agar overlay assay using the indicator strain V. cholerae El Tor MAK 757. PCR based molecular typing with primers targeting specific conserved sequences in the bacterial genome, demonstrated genetic diversity among these lysogen containing non-O1 V. cholerae . Polymerase chain reaction was also employed as a rapid screening method to verify the presence of 9 virulence genes namely, ctxA, ctxB, ace, hlyA, toxR, zot,tcpA, ninT and nanH, using gene specific primers. The presence of tcpA gene in ALPVC3 was alarming, as it indicates the possibility of an epidemic by accepting the cholera. Differential induction studies used ΦALPVC3, ΦALPVC11, ΦALPVC12 and ΦEKM14, underlining the possibility of prophage induction in natural ecosystems, due to abiotic factors like antibiotics, pollutants, temperature and UV. The efficiency of induction of prophages varied considerably in response to the different induction agents. The growth curve of lysogenic V. cholerae used in the study drastically varied in the presence of strong prophage inducers like antibiotics and UV. Bacterial cell lysis was directly proportional to increase in phage number due to induction. Morphological characterization of vibriophages by Transmission Electron Microscopy revealed hexagonal heads for all the four phages. Vibriophage ΦALPVC3 exhibited isometric and contractile tails characteristic of family Myoviridae, while phages ΦALPVC11 and ΦALPVC12 demonstrated the typical hexagonal head and non-contractile tail of family Siphoviridae. ΦEKM14, the podophage was distinguished by short non-contractile tail and icosahedral head. This work demonstrated that environmental parameters can influence the viability and cell adsorption rates of V. cholerae phages. Adsorption studies showed 100% adsorption of ΦALPVC3 ΦALPVC11, ΦALPVC12 and ΦEKM14 after 25, 30, 40 and 35 minutes respectively. Exposure to high temperatures ranging from 50ºC to 100ºC drastically reduced phage viability. The optimum concentration of NaCl required for survival of vibriophages except ΦEKM14 was 0.5 M and that for ΦEKM14 was 1M NaCl. Survival of phage particles was maximum at pH 7-8. V. cholerae is assumed to have existed long before their human host and so the pathogenic clones may have evolved from aquatic forms which later colonized the human intestine by progressive acquisition of genes. This is supported by the fact that the vast majority of V. cholerae strains are still part of the natural aquatic environment. CTXΦ has played a critical role in the evolution of the pathogenicity of V. cholerae as it can transmit the ctxAB gene. The unusual transformation of V. cholerae strains associated with epidemics and the emergence of V. cholera O139 demonstrates the evolutionary success of the organism in attaining greater fitness. Genetic changes in pathogenic V. cholerae constitute a natural process for developing immunity within an endemically infected population. The alternative hosts and lysogenic environmental V. cholerae strains may potentially act as cofactors in promoting cholera phage ‘‘blooms’’ within aquatic environments, thereby influencing transmission of phage sensitive, pathogenic V. cholerae strains by aquatic vehicles. Differential induction of the phages is a clear indication of the impact of environmental pollution and global changes on phage induction. The development of molecular biology techniques offered an accessible gateway for investigating the molecular events leading to genetic diversity in the marine environment. Using nucleic acids as targets, the methods of fingerprinting like ERIC PCR and BOX PCR, revealed that the marine environment harbours potentially pathogenic group of bacteria with genetic diversity. The distribution of virulence associated genes in the environmental isolates of V. cholerae provides tangible material for further investigation. Nucleotide and protein sequence analysis alongwith protein structure prediction aids in better understanding of the variation inalleles of same gene in different ecological niche and its impact on the protein structure for attaining greater fitness of pathogens. The evidences of the co-evolution of virulence genes in toxigenic V. cholerae O1 from different lineages of environmental non-O1 strains is alarming. Transduction studies would indicate that the phenomenon of acquisition of these virulence genes by lateral gene transfer, although rare, is not quite uncommon amongst non-O1/non-O139 V. cholerae and it has a key role in diversification. All these considerations justify the need for an integrated approach towards the development of an effective surveillance system to monitor evolution of V. cholerae strains with epidemic potential. Results presented in this study, if considered together with the mechanism proposed as above, would strongly suggest that the bacteriophage also intervenes as a variable in shaping the cholera bacterium, which cannot be ignored and hinting at imminent future epidemics.