NASA Scientific and Technical Aerospace Reports

partners, they tend to be involved in the same biological process. We used this finding to predict the functions of 81
un-annotated proteins in yeast.
Derived from text
Applications of Mathematics; Genome; Genetics
20040068180 NASA Ames Research Center, Moffett Field, CA, USA
Deriving Laws from Ordering Relations
Knuth, Kevin H.; [2004]; 32 pp.; In English; No Copyright; Avail: CASI; A03, Hardcopy
The effect of Richard T. Cox’s contribution to probability theory was to generalize Boolean implication among logical
statements to degrees of implication, which are manipulated using rules derived from consistency with Boolean algebra. These
rules are known as the sum rule, the product rule and Bayes Theorem, and the measure resulting from this generalization is
probability. In this paper, I will describe how Cox s technique can be further generalized to include other algebras and hence
other problems in science and mathematics. The result is a methodology that can be used to generalize an algebra to a calculus
by relying on consistency with order theory to derive the laws of the calculus. My goals are to clear up the mysteries as to
why the same basic structure found in probability theory appears in other contexts, to better understand the foundations of
probability theory, and to extend these ideas to other areas by developing new mathematics and new physics. The relevance
of this methodology will be demonstrated using examples from probability theory, number theory, geometry, information
theory, and quantum mechanics.
Author
Bayes Theorem; Boolean Algebra; Probability Theory; Sum Rules; Algebra
20040073531 Princeton Univ., NJ
A High Efficiency Algorithm for Combinatorial Synthesis: Maximum Utilization of Minimal Libraries
Rabitz, Herschel; Jan. 15, 2003; 6 pp.; In English
Contract(s)/Grant(s): F49620-00-1-0297
Report No.(s): AD-A413449; AF-6773-3; AFRL-SR-AR-TR-03-0161; No Copyright; Avail: CASI; A02, Hardcopy
This research addressed the common mathematical characteristics of a broad variety of science and engineering
applications having large numbers of input variables for exploration. A family of High Dimensional Model Representation
(HDMR) techniques was developed to provide efficient and accurate input-output maps for such problems. HDMR operates
by breaking down the original high dimensional map into a hierarchy of interrelated lower dimensional components. The
mathematical and numerical foundations of HDMR were developed along with demonstrations of its capabilities in selected
chemistry, physics, and engineering applications.
DTIC
Algorithms; Combinatorial Analysis; Libraries
20040073676 Utah Univ., Salt Lake City, UT
Engineered Photonic Materials for Nanoscale Optical Logic Devices
Blair, Steve; Feb. 24, 2004; 7 pp.; In English
Contract(s)/Grant(s): DAAD19-00-1-0556
Report No.(s): AD-A422569; ARO-41374.6-PH-YIP; No Copyright; Avail: CASI; A02, Hardcopy
Two major activities of this grant were to develop a generalized approach to the enhancement of nonlinear optical effects
based upon slow-light propagation in artificial resonators and the study of nonlinear self-focusing in periodic arrays of
photonic microcavities, thereby providing a mechanism for the formation of very narrow (i.e. wavelength scale) spatial
solitons at very low powers.
DTIC
Optical Equipment; Wave Propagation
20040073696 Air Force Inst. of Tech., Wright-Patterson AFB, OH
Optimal Design of Generalized Multiple Model Adaptive Controllers
Brehm, Thomas E.; Mar. 2004; 298 pp.; In English; Original contains color illustrations
Report No.(s): AD-A422596; AFIT/DS/ENG/04-01; No Copyright; Avail: CASI; A13, Hardcopy
Advanced analysis and optimal design techniques that achieve performance improvement for multiple model adaptive
control (MMAC) and multiple model adaptive estimation (MMAE) based control are developed and tested for this dissertation
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