Statistical learning for alloy design from electronic structure calculations

Abstract

APPENDIX: BACKGROUND INFORMATION 99 iv A.1 Mathematics of PCA 99 A.2 Mathematics of PLS 102 A.3 Schematic of Modeling the Density of States 104 A.4 Mathematics of Haydock's Recursion Method 108 REFERENCES 110 v ACKNOWLEDGMENTS I would like to express my deepest gratitude to my thesis advisor, Professor Krishna Rajan. He has provided me with numerous opportunities beyond what is normal for a graduate student, and his guidance has made this experience very productive. I would also like to thank my thesis committee members-Professors Vasant Honavar, Michael Kessler, Richard LeSar and Sriram Sundrarajan-for their insights. I have been fortunate to have collaborated with numerous excellent scientists. I would like to specifically mention Professor Shuichi Iwata and his laboratory members at the University of Tokyo for their hospitality during my visits and for their insights and ideas. I would also like to thank Professor Hafid Aourag at the Univeristy Abou Bekr Belkaid in Algeria for providing me numerous ideas and suggestions during the course of this work. He has been instrumental in the development of the work discussed in this thesis. I would also like to acknowledge my fellow group members for the numerous discussions we have had over the years. In particular, I would like to thank Dr. Changwon Suh for his advice and teachings during my beginning years in graduate school.