PDF-Commutativity Theorems Examples in Search of Algorithm

edu dedicated to the memory of John Hunter 1 Introduction Commutativity theorems are part of the study of polyno mial identities in noncommutative rings They are theo rems which assert that under certain conditions the ring at hand must be commutativ. AS if for every trajectory we have as implies is the unique equilibrium point system is locally asymptotically stable LAS near or at if there is an R st 0 k as Basic Lyapunov theory 122 brPage 3br often we change coordinates so that 0 ie we use a 1 0 n 0 Error between 64257lter output and a desired signal Change the 64257lter parameters according to 1 57525u 1 Normalized LMS Algorithm Modify at time the parameter vector from to 1 ful64257lling the constraint 1 with the least modi6425 brPage 1br brPage 2br Examples Examples brPage 3br 27 Examples Examples 18 brPage 4br 15 15 729 16 brPage 5br 12 12 12 12 brPage 6br 16 18 18 Represented Theorems. Sara . Billey. University . of . Washington. Reproducibility in Computational and Experimental Math. ICERM. December 13, 2012. The Standard Inquiry. “Do you know anything about the following math problem?”. NoSQL Databases Table of Contents ApplicApplications:ations: Examples:Examples: ApplicApplications:ations: Examples:Examples: ApplicApplications:ations: Examples:Examples: TAKEAWAYS TAKEAWAYS TAKEAWAY L.R. . Rabiner. and M.R. . Sambur. The Bell System Technical Journal. , Vol. 54, No. 2, Feb. 1975, pp. 297-315. Outline. Intro to problem. Solution. Algorithm. Summary. Motivation. Word recognition needs to detect word boundaries in speech. Commutativity. Rule: Designing Scalable Software for Multicore Processors. Austin T. Clements, M. . Frans. . Kaashoek. , . Nickolai. . Zeldovich. , Robert T. Morris, and Eddie Kohler. MIT CSAIL and Harvard University. By: Pau . Thang. Theorem, and. Counterexample. Conjectures. an opinion or conclusion formed on the basis of incomplete information. Conjectures -. In other words, conjectures are . It is the use of . Convergence & Divergence Theorems. Convergence & Divergence Theorems. Convergence & Divergence Theorems. Convergence & Divergence Theorems. . Theorems. m. example. Write a proof.. Given. : . Prove. : . . Statements Reason. . 1.. ___________________ _______________________. . 2.. ___________________ _______________________. . 3.. ___________________ _______________________. Focus: developing algorithms . abstractly. Independent of programming . language, data types, etc.. Think of a stack or queue: not specific to C , but can be implemented when needed. Addressed in depth during COSC 320. Assorted minutiae. HW1P1 due tonight at midnight. HW1P2 due Friday at midnight. HW2 out tonight. Second Java review session: . Friday 10:30 – ARC 147. Today’s Schedu. le. Algorithm Analysis, cont.. Objectives. Determine the running time of simple algorithms. Best case. Average case. Worst case. Profile algorithms. Understand O notation's mathematical basis. Use O notation to measure running time. often, something learned experientially and recalled when needed. Heuristic Function - function applied to a state in a search space to indicate a likelihood of success if that state is selected. heuristic search methods are known as “weak methods” because of their generality and because they do not apply a great deal of knowledge .