Meet the editor

Abdo Abou Jaoudé has been teaching for many years and has a passion for researching and teaching mathematics. He is currently an Associate Professor of Mathematics and Statistics at Notre Dame University-Louaizé (NDU), Lebanon. He holds a BSc and an MSc in Computer Science from NDU, and three Ph.D.'s in Applied Mathematics, Computer Science, and Applied Statistics and Probability, all from Bircham International University

through a distance learning program. He also holds two PhDs in Mathematics and Prognostics from the Lebanese University, Lebanon, and Aix-Marseille University, France. Dr. Jaoudé's broad research interests are in the field of applied mathematics. He has published twenty-three international journal articles and six contributions to conference proceedings, in addition to seven books on prognostics, applied mathematics, and computer science.

Contents

*by Abdo Abou Jaoudé*

*by Abdo Abou Jaoudé*

Theoretic Particles

for Radiotherapy

Appropriation Algorithm *by Maher Abdelghani*

*by Alison Wells and Chad L. Pope*

*by Tokunbo Ogunfunmi and Manas Deb*

Monte Carlo and Medical Physics

**Preface XI**

**Chapter 1 1**

**Chapter 2 45**

**Chapter 3 117**

**Chapter 4 133**

**Chapter 5 155**

**Chapter 6 177**

**Chapter 7 199**

**Chapter 8 211**

The Paradigm of Complex Probability and Thomas Bayes' Theorem

The Paradigm of Complex Probability and Isaac Newton's Classical

Flooding Fragility Model Development Using Bayesian Regression

Markov Chain Monte Carlo in a Dynamical System of Information

*by Omaima Essaad Belhaj, Hamid Boukhal and El Mahjoub Chakir*

Reliability and Comparison of Some GEANT4-DNA Processes and Models for Proton Transportation: An Ultra-Thin Layer Study *by Gabriela Hoff, Raquel S. Thomaz, Leandro I. Gutierres, Sven Muller,* 

Applications of Simulation Codes Based on Monte Carlo Method

Physical Only Modes Identification Using the Stochastic Modal

*by Iury Mergen Knoll, Ana Quevedo and Mirko Salomón Alva Sánchez*

*Viviana Fanti, Elaine E. Streck and Ricardo M. Papaleo*

Mechanics: On the Foundation of Statistical Physics

## Contents


Preface

illustrates the famous Monte Carlo methods and the computer simulation of random experiments in different areas of science. As such, the book will be of interest to all scholars, researchers, and undergraduate and graduate students in mathematics and

*The Monte Carlo Methods - Recent Advances, New Perspectives and Applications*

In applied mathematics, the name Monte Carlo is given to the method of solving problems by means of experiments with random numbers. This name, after the casino at Monaco, was first applied around 1944 to the method of solving deterministic problems by reformulating them in terms of a problem with random elements, which could then be solved by large-scale sampling. But, by extension, the term has come to

The development and proliferation of computers has led to the widespread use of Monte Carlo methods in virtually all branches of science, ranging from nuclear physics (where computer-aided Monte Carlo was first applied) to astrophysics, biology, engineering, medicine, operations research, and the social sciences.

The Monte Carlo method of solving problems by using random numbers in a computer, either by direct simulation of physical or statistical problems or by reformulating deterministic problems in terms of one incorporating randomness, has become one of the most important tools of applied mathematics and computer science. A significant proportion of articles in technical journals in such fields as physics, chemistry, and statistics contain articles reporting results of Monte Carlo simulations or suggestions on how they might be applied. Some journals are devoted almost entirely to Monte Carlo problems in their fields. Studies in the formation of the universe or of stars and their planetary systems use Monte Carlo techniques. Studies in genetics, the biochemistry of DNA, and the random configuration and knotting of biological molecules are studied by Monte Carlo methods. In number theory, Monte Carlo methods play an important role in determining primality or factoring of very large integers far beyond the range of deterministic methods. Several important new statistical techniques such as "bootstrapping" and "jackknifing" are based on Monte

Hence, the role of Monte Carlo methods and simulation in all the sciences has increased in importance during the past several years. These methods play a central role in the rapidly developing subdisciplines of the computational physical sciences, computational life sciences, and other computational sciences. Therefore, the growing power of computers and evolving simulation methodology has led to the recognition of computation as a third approach for advancing the natural sciences, together with theory and traditional experimentation. Knowing that at the kernel

Moreover, the book develops methods for simulating simple or complicated

processes or phenomena. If the computer can be made to imitate an experiment or a process, then by repeating the computer simulation with different data, we can draw

of Monte Carlo simulation is random number generation.

mean any simulation that uses random numbers.

science in general.

Carlo methods.
