Abhishek Bhattacharya

This book introduces in a systematic manner a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. The theory has important and varied applications in medical diagnostics, image analysis, and machine vision. An early chapter of examples establishes the effectiveness of the new methods and demonstrates how they outperform their parametric counterparts. Inference is developed for both intrinsic and extrinsic Fréchet means of probability distributions on manifolds, then applied to shape spaces defined as orbits of landmarks under a Lie group of transformations - in particular, similarity, reflection similarity, affine and projective transformations. In addition, nonparametric Bayesian theory is adapted and extended to manifolds for the purposes of density estimation, regression and classification. Ideal for statisticians who analyze manifold data and wish to develop their own methodology, this book is also of interest to probabilists, mathematicians, computer scientists, and morphometricians with mathematical training.

In a distributed computing system (DCS), we need to allocate a number of tasks to different processors for execution. The problem of task assignment in heterogeneous computing systems has been studied for many years with many variations and to accomplish various objectives, such as throughput maximization, reliability maximization, and cost minimization. There are also exists a set of system constraints related to memory and communication link capacity. Most of the existing approaches for task allocation deal with a single objective only. In this project we construct the task allocation problem as a multi-objective optimization problem to consider system constraints. The goal programming technique is used with pre-emptive priority structure to find the optimal allocation that not only optimize system reliability but also optimize memory as well as path load. The genetic algorithm is used to find the optimal allocations. Genetic algorithm is used to find the optimal allocations.

This book introduces in a systematic manner a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. The theory has important and varied applications in medical diagnostics, image analysis, and machine vision. An early chapter of examples establishes the effectiveness of the new methods and demonstrates how they outperform their parametric counterparts. Inference is developed for both intrinsic and extrinsic Fréchet means of probability distributions on manifolds, then applied to shape spaces defined as orbits of landmarks under a Lie group of transformations - in particular, similarity, reflection similarity, affine and projective transformations. In addition, nonparametric Bayesian theory is adapted and extended to manifolds for the purposes of density estimation, regression and classification. Ideal for statisticians who analyze manifold data and wish to develop their own methodology, this book is also of interest to probabilists, mathematicians, computer scientists, and morphometricians with mathematical training.