He has taught Electrical and Computer Engineering (ECE) and Applied Mathematics in their broadest sense at the university level for more than 51 years at the Smith College, the University of Massachusetts Lowell, the Indian Institute of Science (Bangalore, India), Polytechnic University, University of Pennsylvania, Villanova University, and Princeton University. In addition, he has taught Chemistry for one year in Loyola College, Madras, India. During this long stint of teaching multifarious subjects relating to the broad fields of Science and Engineering, he was guided largely by student interaction and feedback, resulting in the general philosophy of making any subject interesting enough to motivate the students to learn more. To this effect, histories of the development of the field along with the biographies of the persons responsible for its development were presented. Students were encouraged to ask questions in the class and every question was answered to their satisfaction. Research work was considered as a means to the result of dissemination of knowledge and not as an end in itself. Extra effort was made to give as many explanatory handouts as possible to supplement the textbook. Numerous homework problems that touched on the applicational aspects of the subject were given. All the homeworks were personally graded by him to gauge the extent of their understanding and exhaustive solutions were posted for these problems. His long standing and continued interest and effectiveness in teaching graduates and undergraduates for a period of over 5 decades garnered him the best teacher award at UMASS Lowell (2000), commendations from Smith College (2003), the Indian Institute of Science (1974) and Villanova University (1959). The same philosophy was pursued in advising research students that produced 8 Doctoral and 21 Masters theses.

This philosophy of dissemination of knowledge permeated in the publication of a definitive book, Probability and Random Processes by John Wiley in 2006 in their series Wiley Survival Guides in Engineering and Science. More than 300 examples and 400 diagrams were provided and every step was clearly stated. The second edition of this book will be published by John Wiley in August 2015 with added topics and an additional chapter by Kavitha Chandra. This book will have 350 examples and 450 carefully detailed diagrams. The same philosophy also resulted in the publication of the book by CRC Press in 1998 entitled Linear Systems Properties to be used by undergraduates and graduates as a study aid for subjects in science and engineering. The objective of this book was to present the basic methods of linear systems analysis and to provide demonstrations of their application. In the production of both these books, he undertook the drawing of all illustrations, creating tables, designing the covers, and other details.

He has taught undergraduate circuit theory and signals in the ECE Department, advanced circuits and statistics to part-time undergraduate students enrolled in Continuing Education's Engineering Technology program. In addition, he has taught Introductory Statistics for non-science majors in the Mathematics Department where the vast majority of the students enrolled were majors in the health related professions and criminal justice. A novel approach was adopted since the students' background in mathematics was limited. Emphasis was made on the physical understanding of the problems involved in randomized design of experiments, confidence limits in determining the efficacy of drugs and the chances of recovery from serious surgeries like open heart and brain. After presenting many practical examples, the basic mathematical aspects were then presented so that the students were motivated to understand. This course received one of the highest students' rating in the Mathematics Department.

During the 1999 academic year, he organized a university wide Calculus recitation program for freshmen that involved five other faculty members from the College of Engineering. This effort was initiated by the Dean of the College Engineering to address retention issues. This undertaking required the design of recitation lectures with carefully constructed recitation problems and student study aids. This project had a positive impact on all university students enrolled in Calculus-I, increasing the retention rate by about 30%.

At the graduate level, he has designed many advanced graduate courses and taught courses on Inertial Navigation and Guidance, Probability and Random Processes, Statistical Communication Theory, Stochastic Modeling in Telecommunications, Time Series Analysis and Forecasting, and Linear Systems. He was specifically requested by the Computer Science Department in 1997 whether he could develop the graduate course on Discrete Mathematics. This was a very big challenge because the student body was heterogeneous with engineers, scientists, economics and health sciences majors. The course was a major success where at one point the enrollment rose from about 15 to 60 students per semester.

During the early 80's, he undertook along with two other faculty members in the ECE Department the organization of the doctoral program at UMass Lowell. This program is now flourishing very well with over 60 doctorates being granted in the ECE Department.

Since the early 90's, he has played a research leadership role in the formation of the Center for Advanced Computation and Telecommunications (CACT) from the Laboratory of Advanced Computation started by Prof. Thompson in 1987. Students have conducted research on diverse range of topics including acoustics, fluid dynamics, chaos, signal and image processing, medical imaging and telecommunications and data networks. The majority of persons in this center are women engineers and scientists.

During 1968-1970 while he was with the Polytechnic Institute of Brooklyn, Bell laboratories entrusted him with the creation of a two year in-house Applied Mathematics program for their personnel. It was the first time that Bell Labs instituted during working hours, instruction for their members of technical staff. He designed the program on all aspects of applied mathematics and staffed it with the best available teachers. Based on the success of this program, Bell Labs introduced this program as a permanent feature.

During the years 1992-2002, he has directly influenced the careers of over fifty students in CACT. These students are now in research, development and management positions in industry and are directly involved in the use of system modeling skills they acquired during their tenure at CACT. Among some of his students outside of CACT, three hold chaired professorships at University of Texas, University of Connecticut and University of Oklahoma and, another is a director of Active Adpative Control Laboratory at MIT.

RESEARCH

He has published 48 journal and research monographs. The main focus of this body of work is on probability and its applications to queue distributions, medical imaging like emission tomography, time series analysis in modeling physical phenomena such as the drift rate of gyros, roughness of a runway, and navigation and guidance.

He has addressed the problem of estimating the steady state queue distributions for correlated traffic using linear and threshold autoregressive processes. Models for multiplexed variable bit rate (VBR) encoded streams were used to develop an approach for estimating buffer occupancy and the impact of correlated arrivals on delay distribution of buffer occupancy were investigated. Using methods based on probability theory and time series analysis, computational techniques were developed for estimating the steady state queue distributions.

He has also investigated the reconstruction of images in Transmission Computed Tomography (TCT) and Emission Computed Tomography (ECT) using statistical techniques. Bayesian maximum aposteriori techniques were implemented by applying the expectation maximization iterative algorithm using three types of priors like the Gibbs, the cross entropy distance and the hybrid. The potential functions used in the Gibbs prior were the sigmoid and the lncosh functions. The parameter settings were optimized for TCT and ECT. Computer simulations were performed on phantoms in 2D and 3D object spaces. The quantitative accuracy and resolution of the reconstructed images were considerably improved. The problem of incomplete projections was solved by first using a linear predictive extrapolation scheme and reconstruction achieved from the completed projections.

In tackling the problem related to airlane track separations, he with another colleague proposed a mixture of Gaussian density functions for more accurate separation of collision risks associated with airlane track separation standards. Each component of this mixture was attributable to physical causes such as pilot errors and effects of navigation equipment degradations and failures. This model was factored into the possibility of Automatic Dependent Surveillance (ADS) equipment to monitor airlane separations. With the separation of collision risks, it was shown that track separation standards could be considerably decreased with the same target level of safety if ADS was used.

After more than 10 years of research in the forefront of nonlinear filtering, he developed the fundamental concepts of nonlinear filtering and smoothing using Martingale theory. This was published as a book, Nonlinear Filtering and Smoothing-An Introduction to Martingales, Stochastic Integrals and Estimation in 1984 in the prestigious Mathematics series of the publisher John Wiley. It was the first book published by an engineer for engineers on the esoteric topic of martingales. This book was a serious effort to give engineering students and practitioners a clear physical understanding of the martingale approach to nonlinear filtering and smoothing. After defining white noise and white noise integrals, investigations into stochastic integrals and stochastic differential equations with the associated Ito calculus and its extensions, were undertaken. Since stochastic differential equations cannot be directly simulated on a computer, the correction terms needed to convert Ito stochastic differential equations to the Stratonovich form were explored. The optimal nonlinear filtering representation was derived in a different form from the classical results. The representation leads to a set of infinite stochastic differential equations involving conditional moments of increasingly higher order. In the linear Gaussian case, this results in a closed form solution since the third moment of a Gaussian is zero. Since closed form solutions in the general case are not possible, assumptions were made regarding the higher order moments to find a solution to a class of fault detection problems. In particular, changes in plant parameter and signal noise parameter were studied. This book has been republished by Dover Publications in 2005 with a new preface and a list of errata.

He has applied time series modeling and statistical analysis for establishing specifications for a new type of precision gyros used for navigation purposes. From the available data, time series modeling was used extensively to determine the drift characteristics of these gyros. They were then tested for interchangeability and repeatability using two-factor experiment and analysis of variance (ANOVA), and representative parameter values were established. In this process the equivalence of various statistical tests and their confidence limits were also investigated. Using the same time series modeling, he was able to characterize the roughness of runways.

RETIREMENT ACTIVITIES (LECTURING, WRITING, ETC.)

He retired in 2002 from UMass Lowell and was commended for his services by Governor Jane Swift, acting Governor of Massachusetts, 2001-2003.

After retirement he was offered a visiting professorship during Spring 2003 in Smith College, Northampton, MA. He developed and taught a course on Signals and Systems in their newly created Engineering Program. He taught the course with the same philosophy of approach discussed earlier. This course was very well appreciated as seen by the commendations he received from the students at the end of the semester.

As Professor Emeritus in UMass Lowell, he undertook writing textbooks along with technical and general papers. His research book on Nonlinear Filtering and Smoothing originally published by Wiley in 1984 was republished by Dover Publications in 2005 with a new preface and corrections. It has been well received in Financial Engineering discipline.

After more than four decades of teaching probability he wrote a definitive book on Probability and Random Processes, which was published in 2006 by John Wiley in the Wiley Survival Guide in Engineering and Science. This book has garnered good reviews internationally.

In 2009 he was invited to contribute a chapter on Classification of Stochastic Processes in the International Encyclopedia of Statistical Science. This monumental reference book of about 2000 pages with over 600 authors including Nobel Laureates from over 100 countries was published by Springer in 2010. The editors of this book were nominated for Nobel Peace Prize for 2011. He was also one of the keynote speakers by video link for the promotion of this book held in Banja Luka, Bosnia in April, 2011.

In 2012, he ws imvited by Wiley to publish a second edition of the book on Probability and Random Processes. More topics on Newton_Pepys problem, Spearman and Kendall correlation functions, Recursive Least Squares (RLS) and Least Mean Square (LMS) estimation techniques, Birth and Death processes and Renewal theory were added. An additional chapter on Tele-Traffic control written by Kavitha Chandra was also added. This second edition has been published in July 2015.

Indian music was developed and practiced nearly three thousand years ago. It consisted of musical styles and schools evolved by blending Vedic chants and folk music. The South Indian Classical music practiced in Tamil Nadu, Andhra Pradesh, Kerala and Karnataka is called Carnatic Music. It starts from the diatonic scale of seven note, octave-repeating scale comprising of the swaras Sa, Ri, Ga, Ma, Pa, Da, Ni along with five semi tones. It was systematized in the fifteenth century and mathematically formalized in the seventeenth century by Venkatamakhin (1666) in his landmark work 'Chaturdandi Prakasika' and continues to be refined. This essay discusses the Mathematical aspects of Melakartha Ragas, which contain all the seven notes and the octave in its scale.

The next paper is a short essay on the origin, tenets and practice of Hinduism, which is considered as the world's oldest way of life. It is not a religion in the accepted sense, but it is a righteous way of life called Sanatana Dharma followed by the people of India for the past 5000 years. The very basic ideas and tenets of Hinduism are explored.

On January 15, 2009, A US airways flight with code sign Cactus 1549 took off from LaGuardia airport bound for Charlotte, North Carolina. A passing flock of geese hit the ascending plane two minutes after take-off at 2,700 feet and all power was lost. The pilot had no recourse except to land the plane on the Hudson river in Manhattan. The paper The Remarkable Flight of Cactus 1549 discusses the events that followed, and how the plane was forced to land on the Hudson river in Manhattan. All the passengers were rescued and among them only two had very minor injuries. There were three other forced landings during the years 1956 - 2009 where there were no loss of lives. Comparisons are made to these three water landings.

The origin of the ballad of Sundara Kandam is unkown. It was given by word of mouth by his grandmother Sundari Ammal alias Lakshmi Ammal familiarly called as Etchi Patti. It describes in very colloquial Tamil a particular episode in Ramayana, where Hanuman sets forth to find Sita after Ravana had abducted her. The whole ballad is in the words of Hanuman as he describes the obstacles he encountered on his way to Lanka, how he found Sita in the Ashoka forest there, and what transpired after that.

Being versed in Sanskrit, investigations on the birth of one of the greatest philosophers of India, Sankaracharya, in a remote village of Kaladi in Kerala State in India is undertaken. After concluding these investigations into his birth, the paper Bhaja Govindam translates the famous work Bhaja Govindam of Sankara from Sanskrit into English.

CONCLUDING REMARKS

It is apropos that this write-up should conclude with the following quote from A Psalm of Life by the famous American poet, Henry Wadsworth Longfellow (1807-1882), the only American poet who has been honored with a memorial bust in the Poet's corner in Wesminster Abbey in London, England.