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COMPUTATION OF ALGEBRAIC SYSTEM FROM SELF-ASSEMBLY
by
Qing Luo
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(COMPUTER SCIENCE)
December 2007
Copyright 2007 Qing Luo
Object Description
| Title | Computation of algebraic system from self-assembly |
| Author | Luo, Qing |
| Author email | qingluo@usc.edu |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Computer Science |
| School | Viterbi School of Engineering |
| Date defended/completed | 2007-09-21 |
| Date submitted | 2007 |
| Restricted until | Unrestricted |
| Date published | 2007-11-20 |
| Advisor (committee chair) | Huang, Ming-Deh |
| Advisor (committee member) |
Proskurowski, Wlodek Kempe, David Nakano, Aiichiro |
| Abstract | We are interested in finding real positive solutions to posynomial systems of the form: [equation] with a_sj set R and pi_j, c_3 set R_>0. These systems arise in the study of algorithmic self-assembly. A positive solution of p=(p_1,...,p_m) to such a system corresponds to an equilibrium of a reversible self-assembly system. It has been proven that the real positive solution to such a system is unique when the underlying polytope: [equation] has a real positive point.; Existing methods can solve some special cases of this system. The Iterative Proportional Scaling (IPS) method, for instance, can solve the system with constraints that all the elements in the last row of matrix A are 1 and that the elements in matrix A are nonnegative. Another method called Improved Iterative Scaling (IIS) solves the system (1) with all constraints relaxed except for the requirement that A be nonnegative.; This thesis proposes a method to solve the system (1) in full generality without constraints. The work starts with exploring the geometric properties of these systems. Based on that, we then extend IPS to find positive solutions to system (1). Numerical analysis related to the computational problems, such as global convergence, convergence rate, and sensitivity analysis, are also discussed in this thesis. |
| Keyword | maximum entropy; iterative proportional scaling |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Type | texts |
| Legacy record ID | usctheses-m935 |
| Rights | Luo, Qing |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Luo-20071120 |
| Archival file | uscthesesreloadpub_Volume35/etd-Luo-20071120.pdf |
Description
| Title | Page 1 |
| Full text | COMPUTATION OF ALGEBRAIC SYSTEM FROM SELF-ASSEMBLY by Qing Luo A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (COMPUTER SCIENCE) December 2007 Copyright 2007 Qing Luo |
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