Elements of The Theory of Computation

The only single-source——now completely updated and revised——to offer a unified treatment of the theory, methodology, and applications of the EM algorithm
omplete with updates that capture developments from the past decade, The EM Algorithm and Extensions, Second Edition successfully provides a basic understanding of the EM algorithm by describing its inception, implementation, and applicability in numerous statistical contexts. In conjunction with the fundamentals of the topic, the authors discuss convergence issues and computation of standard errors, and, in addition, unveil many parallels and connections between the EM algorithm and Markov chain Monte Carlo algorithms. Thorough discussions on the complexities and drawbacks that arise from the basic EM algorithm, such as slow convergence and lack of an in-built procedure to compute the covariance matrix of parameter estimates, are also presented.

Introduction I. General remarks . 1 II. Notations . . 5 III. Lie algebras: some basics . 8 Chapter 1 Operator calculus and Appell systems I. Boson calculus . 17 II. Holomorphic canonical calculus . . 18 III. Canonical Appell systems . . 23 Chapter 2 Representations of Lie groups I. Coordinates on Lie groups . . . 28 II. Dual representations. 29 III. Matrix elements. . . 37 IV. Induced representations and homogeneous spaces . . 40 General Appell systems Chapter 3 I. Convolution and stochastic processes . 44 II. Stochastic processes on Lie groups . . 46 III. Appell systems on Lie groups. . 49 Chapter 4 Canonical systems in several variables I. Homogeneous spaces and Cartan decompositions . . 54 II. Induced representation and coherent states . 62 III. Orthogonal polynomials in several variables . 68 Chapter 5 Algebras with discrete spectrum I. Calculus on groups: review of the theory .. 83 II. Finite-difference algebra . 85 III. q-HW algebra and basic hypergeometric functions .. 89 IV. su2 and Krawtchouk polynomials .. . 93 V. e2 and Lommel polynomials . . 101 Chapter 6 Nilpotent and solvable algebras I. Heisenberg algebras . .. 113 II. Type-H Lie algebras .. 118 Vll III. Upper-triangular matrices .. . 125 IV. Affine and Euclidean algebras . . 127 Chapter 7 Hermitian symmetric spaces I. Basic structures . 131 II. Space of rectangular matrices . . 133 III. Space of skew-symmetric matrices . . 136 IV. Space of symmetric matrices . 143 Chapter 8 Properties of matrix elements I. Addition formulas .. . 147 II. Recurrences . .. 148 III. Quotient representations and summation formulas .. 149 Chapter 9 Symbolic computations I. Computing the pi-matrices . . 153 II. Adjoint group .. 154 III. Recursive computation of matrix elements .

Economics of Information Security applies economics not to generate breakthroughs in theoretical economics, but rather breakthroughs in understanding the problems of security. Security, privacy and trusted computing are examined distinctly, using the tools of economics, and as elements of a larger dynamic system.