Harish Parthasarathy

This book examines quantum neural networks through renormalization techniques, supersymmetric field theory, and noisy harmonic oscillator systems. The book's analysis covers adaptive beamforming applications, brain modeling, gravitational control mechanisms, and mixed-state dynamics in superstring theory, and also includes: Comprehensive analysis of quantum neural networks through renormalization techniques and supersymmetric field theory applications in computational modeling Investigation of quantum field dynamics with noise integration, filtering mechanisms, and scattering processes in curved spacetime environments Study of adaptive beamforming methodologies combined with quantum neural networks for brain modeling and evolving field system applications Examination of mixed-state dynamics in superstring theory frameworks with emphasis on quantum noisy fields and supersymmetric effects Analysis of extended Kalman filter integration with quantum neural networks for transmission line control and field estimation optimization The work explores extended Kalman filter methodologies for transmission line control, field estimation, and symmetry-broken dynamics in signal processing systems for advanced computational modeling applications. This title has been co-published with Manakin Press. T&F does not sell or distribute the print editions in Bangladesh, Bhutan, India, Nepal, Pakistan, and Sri lanka.

This book presents a comprehensive treatment of quantum theory using theoretical variables as its foundation. The work progresses from fundamental quantum mechanical principles to sophisticated applications in quantum field theory and gravity. It provides rigorous mathematical frameworks while establishing connections between theoretical physics and practical engineering applications and includes: Presents an advanced treatment of quantum theory across two interconnected parts Examines Bell experiments, quantum probability, information theory, and connections to relativity Extends these foundations to explore quantum field theory, gravity, and noise theory Bridges the gap between theoretical physics and engineering applications Covers topics from Yang-Mills fields, quantum gravity to neural networks and biomedical applications of quantum electrodynamics Addresses quantum measurement of gravitons, Hawking radiation, classical and quantum neural networks with practical examples Provides mathematical frameworks for understanding quantum phenomena in applied contexts Particularly suitable for graduate students and researchers in physics, mathematics, and engineering disciplines seeking to understand quantum phenomena across theoretical and applied domains. This title has been co-published with Manakin Press. Taylor & Francis does not sell or distribute the print edition in India, Pakistan, Nepal, Bhutan, Sri Lanka and Bangladesh.

This book covers quantum mechanics and its applications across multiple fields, starting with parameter estimation and probability density functions, and examines quantum systems, statistical image processing, and mathematical frameworks. The book connects theoretical physics with applications in robotics, neural networks, and computer vision. Quantum mechanics with stochastic calculus and filtering theory Radon transform applications in image reconstruction Quantum field theories and chiral anomalies Algebraic geometry and group theory applications Supersymmetry, cohomology, and quantum effective action Suitable for graduate students and researchers in physics, mathematics, and computer science, this book provides theoretical foundations and practical applications for understanding quantum systems and computational implementations. This title has been co-published with Manakin Press. Taylor & Francis does not sell or distribute the print edition in India, Pakistan, Nepal, Bhutan, Sri Lanka and Bangladesh.

This book is on the nonlinear random medium analysis that includes subtopics of terahertz imaging, inverse scattering, plasmonics, quantum optics/communication laser modes, and terahertz photonic antennas.

This book introduces the vast subject of supersymmetry along with many specific examples of engineering applications, for example:The design of quantum unitary gates using supersymmetric actionsBosonic and Fermionic noise in quantum systems using the Hudson-Parthasarathy quantum stochastic calculusSuperstring theory applied to the quantum mechanics of neurons and supersymmetric quantum filtering theory which can, for example, be used to filter out the noise in a cavity resonator electromagnetic field produced by the presence electrons and positrons in a bath surrounding itSimplified versions of super-Yang-Mills theory with gauge and gaugino fields, both transforming under the adjoint representation of the gauge group and elementary super-gravity models have also been introducedAll through the book, emphasis is laid upon exploiting the supersymmetry existing in the nature of Boson-Fermion exchange in designing engineering systems like quantum computers and analyzing the performance of systems in the presence of supersymmetric quantum noise.

This book developed from a course given by the author to undergraduate and postgraduate students. It takes up Matrix Theory, Antenna Theory, and Probability Theory in detail.The first chapter on matrix theory discusses in reasonable depth the theory of Lie Algebras leading upto Cartan’s Classification Theory. It also discusses some basic elements of Functional Analysis and Operator Theory in infinite dimensional Banach and Hilbert spaces. The second chapter discusses Basic Probability Theory and the topics discussed find applications to Stochastic Filtering Theory for differential equations driven by white Gaussian noise. The third chapter is on Antenna Theory with a focus on Modern Quantum Antenna Theory.The book will be a valuable resource to students and early career researchers in the field of Mathametical Physics.

This book deals with a variety of problems in Physics and Engineering where the large deviation principle of probability finds application. Large deviations is a branch of probability theory dealing with approximate computation of the probabilities of rare events. It contains applications of the LDP to pattern recognition problems like analysis of the performance of the EM algorithm for optimal parameter estimation in the presence of weak noise, analysis and control of non-Abelian gauge fields in the presence of noise, and quantum gravity wherein we are concerned with perturbation to the quadratic component of the Einstein-Hilbert Hamiltonian caused by higher order nonlinear terms in the position fields and their effect on the Gibbs statistics and consequently quantum probabilities of events computed using the quantum Gibbs state. The reader will also find in this book applications of LDP to quantum filtering theory as developed by Belavkin based on the celebrated Hudson-Parthasarathy quantum stochastic calculus.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan and Bhutan).

This book is based on three undergraduate and postgraduate courses taught by the author on Matrix theory, Probability theory and Antenna theory over the past several years.It discusses Matrix theory, Probability theory and Antenna theory with solved problems. It will be useful to undergraduate and postgraduate students of Electronics and Communications Engineering.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan and Bhutan).

This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems, electromagnetics, statistical signal processing, quantum information theory, quantum neural network theory, quantum filtering theory, quantum electrodynamics, quantum general relativity, string theory, problems in biology and classical and quantum fluid dynamics. The selection of the problems has been based on courses taught by the author to undergraduates and postgraduates in Electronics and Communications Engineering.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).

This book deals with certain important problems in Classical and Quantum Information Theory Quantum Information Theory, A Selection of Matrix Inequalities Stochastic Filtering Theory Applied to Electromagnetic Fields and Strings Wigner-distributions in Quantum Mechanics Quantization of Classical Field Theories Statistical Signal Processing Quantum Field Theory, Quantum Statistics, Gravity, Stochastic Fields and Information Problems in Information TheoryIt will be very helpful for students of Undergraduate and Postgraduate Courses in Electronics, Communication and Signal Processing.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).

The chapters in this book deal with:Basic formulation of waveguide cavity resonator equations especially when the cross sections of the guides and resonators have arbitrary shapes. The focus is on expressing the total field energy within such a cavity resonator as a quadratic form in the complex coefficients that determine the modal expansions of the electromagnetic fieldThe reviews of basic statistical signal processing covering linear models, fast algorithms for estimating the parameters in such linear models, applications of group representation theory to image processing problems especially the representations of the permutation groups and induced representation theory applied to image processing problems involving the three dimensional Euclidean motion groupThe Hartree-Fock equations for approximately solving the two electron atomic problem taking spin-orbit magnetic field interactions into account has been discussed. In the limit as the lattice tends to a continuum, the convergence of the stochastic differential equations governing interacting particles on the lattice to a hydrodynamic scaling limitIt will be useful to undergraduate and postgraduate students with courses on transmission lines and waveguides, and statistical signal processing.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).

This book is on the nonlinear random medium analysis that includes subtopics of terahertz imaging, inverse scattering, plasmonics, quantum optics/communication laser modes, and terahertz photonic antennas. Here in this book, a mathematical framework is developed to analyze the impact of dimensions and chemical potential on nano-antenna channels.

This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems, electromagnetics, statistical signal processing, quantum information theory, quantum neural network theory, quantum filtering theory, quantum electrodynamics, quantum general relativity, string theory, problems in biology and classical and quantum fluid dynamics. The selection of the problems has been based on courses taught by the author to undergraduates and postgraduates in Electronics and Communications Engineering.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).

This book deals with certain important problems in Classical and Quantum Information Theory Quantum Information Theory, A Selection of Matrix Inequalities Stochastic Filtering Theory Applied to Electromagnetic Fields and Strings Wigner-distributions in Quantum Mechanics Quantization of Classical Field Theories Statistical Signal Processing Quantum Field Theory, Quantum Statistics, Gravity, Stochastic Fields and Information Problems in Information TheoryIt will be very helpful for students of Undergraduate and Postgraduate Courses in Electronics, Communication and Signal Processing.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).

This book is based on three undergraduate and postgraduate courses taught by the author on Matrix theory, Probability theory and Antenna theory over the past several years.It discusses Matrix theory, Probability theory and Antenna theory with solved problems. It will be useful to undergraduate and postgraduate students of Electronics and Communications Engineering.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan and Bhutan).

This book deals with a variety of problems in Physics and Engineering where the large deviation principle of probability finds application. Large deviations is a branch of probability theory dealing with approximate computation of the probabilities of rare events. It contains applications of the LDP to pattern recognition problems like analysis of the performance of the EM algorithm for optimal parameter estimation in the presence of weak noise, analysis and control of non-Abelian gauge fields in the presence of noise, and quantum gravity wherein we are concerned with perturbation to the quadratic component of the Einstein-Hilbert Hamiltonian caused by higher order nonlinear terms in the position fields and their effect on the Gibbs statistics and consequently quantum probabilities of events computed using the quantum Gibbs state. The reader will also find in this book applications of LDP to quantum filtering theory as developed by Belavkin based on the celebrated Hudson-Parthasarathy quantum stochastic calculus.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan and Bhutan).

The chapters in this book deal with:Basic formulation of waveguide cavity resonator equations especially when the cross sections of the guides and resonators have arbitrary shapes. The focus is on expressing the total field energy within such a cavity resonator as a quadratic form in the complex coefficients that determine the modal expansions of the electromagnetic fieldThe reviews of basic statistical signal processing covering linear models, fast algorithms for estimating the parameters in such linear models, applications of group representation theory to image processing problems especially the representations of the permutation groups and induced representation theory applied to image processing problems involving the three dimensional Euclidean motion groupThe Hartree-Fock equations for approximately solving the two electron atomic problem taking spin-orbit magnetic field interactions into account has been discussed. In the limit as the lattice tends to a continuum, the convergence of the stochastic differential equations governing interacting particles on the lattice to a hydrodynamic scaling limitIt will be useful to undergraduate and postgraduate students with courses on transmission lines and waveguides, and statistical signal processing.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).

This book surveys some of the important research work carried out by Indian scientists in the field of pure and applied probability, quantum probability, quantum scattering theory, group representation theory and general relativity. It reviews the axiomatic foundations of probability theory by A.N. Kolmogorov and how the Indian school of probabilists and statisticians used this theory effectively to study a host of applied probability and statistics problems like parameter estimation, convergence of a sequence of probability distributions, and martingale characterization of diffusions.It will be an important resource to students and researchers of Physics and Engineering, especially those working with Advanced Probability and Statistics.

This book covers a variety of problems, and offers solutions to some, in:Statistical state and parameter estimation in nonlinear stochastic dynamical system in both the classical and quantum scenariosPropagation of electromagnetic waves in a plasma as described by the Boltzmann Kinetic Transport EquationClassical and Quantum General RelativityIt will be of use to Engineering undergraduate students interested in analysing the motion of robots subject to random perturbation, and also to research scientists working in Quantum Filtering.

This book introduces the vast subject of supersymmetry along with many specific examples of engineering applications, for example:The design of quantum unitary gates using supersymmetric actionsBosonic and Fermionic noise in quantum systems using the Hudson-Parthasarathy quantum stochastic calculusSuperstring theory applied to the quantum mechanics of neurons and supersymmetric quantum filtering theory which can, for example, be used to filter out the noise in a cavity resonator electromagnetic field produced by the presence electrons and positrons in a bath surrounding itSimplified versions of super-Yang-Mills theory with gauge and gaugino fields, both transforming under the adjoint representation of the gauge group and elementary super-gravity models have also been introducedAll through the book, emphasis is laid upon exploiting the supersymmetry existing in the nature of Boson-Fermion exchange in designing engineering systems like quantum computers and analyzing the performance of systems in the presence of supersymmetric quantum noise.