AlphaGo Overview. Overview. Digression: Zero sum, alternating move games. Original AlphaGo approach. Recent AlphaGo Zero approach 10/24/17
|
|
- Dwight Blankenship
- 5 years ago
- Views:
Transcription
1 AlphGo Overview Ron Prr CompSci Duke Univerity Overview Digreion: Zero um, lternting move gme Originl AlphGo pproch Recent AlphGo Zero pproch 1
2 2 Alternting move, zero-um, 2-plyer gme Ordinry bellmn eqution Two plyer å + = ' ', ', mx V P R V g å + = ' min mx ', ', mx V P R V g å + = ' mx min ', ', min V P R V g V min nd V mx Vmin i, by definition, the negtive of Vmx No need to tore two eprte vlue function Cn tore jut one nd flip the ign bed upon who i plying
3 Originl AlphGo Ingredient Policy network trined by upervied lerning Policy network trined by policy grdient Vlue function network Monte Crlo Tree Serch MCTS 3
4 Supervied Policy Network Similr to neuro-gmmon jut tried to mimic humn move CNN with oftmx output lyer Trined on 30 million expert move 57% ccurcy on held out tet et Seem low, but keep in mind tht thi not binry prediction problem, o thi i wy better thn flipping coin Alo trined fter rollout network tht got 24% ccurcy ued thi for ft rollout RL policy network Ued me network tructure upervied network Initilized to me weight upervied network Trined uing policy grdient Trined initilly gint upervied network, then gint previou verion of the RL policy network with ome rndomiztion I thi correct? NO! Still worked very well! 80% win rte gint upervied network 85% win rte gint Pchi, very trong MCTS progrm t the time 2 mteur dn Surpriing tht it plyed thi well with no lookhed 4
5 Vlue network Should predict probbility of win given bord poition Auming both plyer ply the me policy I thi reonble thing to ume? Tried trining on the humn dtbe, but thi didn t do well No ingle policy ued? Reltively mll mount of trining dt, o overfit Pper mention correltion, but not cler Trined on dt generted from the RL policy network Did reonbly well: MSE Did not overfit bdly MCTS Doe MCTS with explortion bonu The firt time new node i encountered: Evluted by the vlue network, AND A rollout uing the ft, upervied policy network for ech ction Initilize Q-vlue etimte for ech ction Weight explortion bonue by prior probbilitie = policy network ditribution Reult mixed uing voodoo contnt When time i up done erching Algorithm chooe the mot viited node from the root Ignore the vlue of the root, though mot viited node will tend to hve high vlue 5
6 Obervtion Supervied lerning network trined on humn move w better for rollout thn RL network, even though RL network produced tronger plyer Why? Author rgue tht upervied network covered the pce more, but tht not rigorou rgument Performnce On ingle CPU, AlphGo ignificntly outperformed ll vilble computer plyer ee figure 4 in pper Rollout, the vlue network, nd the policy network were ll individully pretty trong Combining them mde them tronger Ditributed verion bet the bet Europen go plyer 6
7 Comprion with Deep Blue Deep Blue bet computer che plyer Deep blue ued little/no mchine lerning Evluted more bord poition more brute force Supervied nd reinforcement lerning reduce erch pce Lerned vlue function nd rollout initilize new leve w/reonble vlue Le time pend on exhutive erch AlphGo Hitory Nture pper publihed in Jnury 2016 Plyed bet living humn go plyer, Lee Sedol, poibly one of the tronget go plyer ever in Mrch 2016 Ued between 1K nd 2K CPU, GPU, nd poibly Google new TPU not cler if thee were counted GPU Won 4/5 gme Subequently reveled tht Vlue network w tuned by elf ply Ued bigger NN nd 48 TPU Ply w decribed urpriing nd originl Mde move tht were unexpected t firt, but mde ene in hindight 7
8 AlphGo Hitory II Plyed the current bet go plyer Ke Jie in My 2017 Won 3/3 gme Livetrem w cenored in Chin: Surpriing thing bout AlphGo Rollout with ft, upervied policy better thn rollout with RL policy enble more erching? RL policy ued only indirectly to trin vlue function Serchle ply w urpriingly good for both RL policy nd V Contrt with che: Serch eem eentil for reonble che ply Rollout le helpful Deep blue w hrdwre triumph AlphGo i n AI/ML triumph 8
9 Originl AlphGo Zero Wht i AlphGo Zero Announced in mid October 2017 with much hype Lern to ply with zero humn knowledge No obviou reltionhip to Coke Zero 9
10 Difference from AlphGo Clic I Ue ingle convolutionl network to propoe ction oftmx nd produce vlue etimte Firt time node i viited: NN ign vlue nd probbilitie of ction me clic? No hndcrfted feture were thee previouly dicued? No rollout Ued Jut ingle mchine with 4 TPU Difference from AlphGo Clic II Exploit rottion nd reflection invrince did clic do thi? When gme end: Neurl network i trined to mximize imilrity between predicted nd ctul outcome for ech tte in the gme Network i lo trined to mke ction probbilitie conitent with MCTS ction election probbilitie 10
11 Trining Million of gme of elf-ply 64 GPU, 19 CPU Surped the verion tht defeted Lee Sedol fter jut 36 hour of trining After ~30 dy, urped AlphGo Mter verion tht hd been beting top humn mter 60-0 online See figure 6 Remrkble thing bout AlphGo Zero Compre w/td gmmon TD gmmon did pretty well without expert feture Needed expert feture to excel AlphGo Zero ued rw bord poition eentilly imge Advntge of convolutionl network? Independently lerned expert level knowledge of importnt bord/end gme configurtion Developed new pproche to known Go problem Simpler nd clener lgorithm thn clic Reduced computtionl reource t execution time 11
12 Why thi mtter Previouly viewed chllenge problem for AI Previou chllenge problem were olved uing: Simple lgorithm nd mive hrdwre Deep blue Specil purpoe hrdwre nd lgorithm utonomou driving AlphGo Zero ue lmot no domin pecific humn knowledge: Rule of the gme Symmetrie I thi wterhed event for AI/ML? Could be Some quetion tht need to be nwered: MCTS help for other domin, but eem like prticulrly big win for Go Cn MCTS + RL be big of win for other domin? Humn Go bility leverged humn pttern recognition prowe W humn Go dominnce n rtifct of vnihing edge humn hd in pttern recognition? Are humn the right benchmrk Cn thi be done with le reource thn Google-like firm? Wht doe thi y bout generl intelligence? 12
CS321 Languages and Compiler Design I. Winter 2012 Lecture 5
CS321 Lnguges nd Compiler Design I Winter 2012 Lecture 5 1 FINITE AUTOMATA A non-deterministic finite utomton (NFA) consists of: An input lphet Σ, e.g. Σ =,. A set of sttes S, e.g. S = {1, 3, 5, 7, 11,
More informationWhat do all those bits mean now? Number Systems and Arithmetic. Introduction to Binary Numbers. Questions About Numbers
Wht do ll those bits men now? bits (...) Number Systems nd Arithmetic or Computers go to elementry school instruction R-formt I-formt... integer dt number text chrs... floting point signed unsigned single
More informationQuestions About Numbers. Number Systems and Arithmetic. Introduction to Binary Numbers. Negative Numbers?
Questions About Numbers Number Systems nd Arithmetic or Computers go to elementry school How do you represent negtive numbers? frctions? relly lrge numbers? relly smll numbers? How do you do rithmetic?
More informationSlides for Data Mining by I. H. Witten and E. Frank
Slides for Dt Mining y I. H. Witten nd E. Frnk Simplicity first Simple lgorithms often work very well! There re mny kinds of simple structure, eg: One ttriute does ll the work All ttriutes contriute eqully
More informationGiving credit where credit is due
JEP 84H Foundtion of omputer tem Proceor rchitecture II: ogic eign r. teve Goddrd goddrd@ce.unl.edu Giving credit where credit i due Mot of lide for thi lecture re ed on lide creted r. rnt, rnegie Mellon
More informationAnnouncements. CS 188: Artificial Intelligence Fall Recap: Search. Today. Example: Pancake Problem. Example: Pancake Problem
Announcements Project : erch It s live! Due 9/. trt erly nd sk questions. It s longer thn most! Need prtner? Come up fter clss or try Pizz ections: cn go to ny, ut hve priority in your own C 88: Artificil
More informationLecture 14: Minimum Spanning Tree I
COMPSCI 0: Deign and Analyi of Algorithm October 4, 07 Lecture 4: Minimum Spanning Tree I Lecturer: Rong Ge Scribe: Fred Zhang Overview Thi lecture we finih our dicuion of the hortet path problem and introduce
More informationA Comparison of the Discretization Approach for CST and Discretization Approach for VDM
Interntionl Journl of Innovtive Reserch in Advnced Engineering (IJIRAE) Volume1 Issue1 (Mrch 2014) A Comprison of the Discretiztion Approch for CST nd Discretiztion Approch for VDM Omr A. A. Shib Fculty
More informationBall. Player X. Player O. X Goal. O Goal
Generlizing Adversril Reinforcement Lerning Willim T. B. Uther nd Mnuel M. Veloso Computer Science Deprtment Crnegie Mellon University Pittsburgh, PA 15213 futher,velosog@cs.cmu.edu Abstrct Reinforcement
More informationGeneric Traverse. CS 362, Lecture 19. DFS and BFS. Today s Outline
Generic Travere CS 62, Lecture 9 Jared Saia Univerity of New Mexico Travere(){ put (nil,) in bag; while (the bag i not empty){ take ome edge (p,v) from the bag if (v i unmarked) mark v; parent(v) = p;
More informationDQL: A New Updating Strategy for Reinforcement Learning Based on Q-Learning
DQL: A New Updting Strtegy for Reinforcement Lerning Bsed on Q-Lerning Crlos E. Mrino 1 nd Edurdo F. Morles 2 1 Instituto Mexicno de Tecnologí del Agu, Pseo Cuhunáhuc 8532, Jiutepec, Morelos, 6255, MEXICO
More informationWhat do all those bits mean now? Number Systems and Arithmetic. Introduction to Binary Numbers. Questions About Numbers
Wht do ll those bits men now? bits (...) Number Systems nd Arithmetic or Computers go to elementry school instruction R-formt I-formt... integer dt number text chrs... floting point signed unsigned single
More informationUnit 5 Vocabulary. A function is a special relationship where each input has a single output.
MODULE 3 Terms Definition Picture/Exmple/Nottion 1 Function Nottion Function nottion is n efficient nd effective wy to write functions of ll types. This nottion llows you to identify the input vlue with
More informationCS481: Bioinformatics Algorithms
CS481: Bioinformtics Algorithms Cn Alkn EA509 clkn@cs.ilkent.edu.tr http://www.cs.ilkent.edu.tr/~clkn/teching/cs481/ EXACT STRING MATCHING Fingerprint ide Assume: We cn compute fingerprint f(p) of P in
More informationCOMBINATORIAL PATTERN MATCHING
COMBINATORIAL PATTERN MATCHING Genomic Repets Exmple of repets: ATGGTCTAGGTCCTAGTGGTC Motivtion to find them: Genomic rerrngements re often ssocited with repets Trce evolutionry secrets Mny tumors re chrcterized
More informationCHAPTER III IMAGE DEWARPING (CALIBRATION) PROCEDURE
CHAPTER III IMAGE DEWARPING (CALIBRATION) PROCEDURE 3.1 Scheimpflug Configurtion nd Perspective Distortion Scheimpflug criterion were found out to be the best lyout configurtion for Stereoscopic PIV, becuse
More informationA New Learning Algorithm for the MAXQ Hierarchical Reinforcement Learning Method
A New Lerning Algorithm for the MAXQ Hierrchicl Reinforcement Lerning Method Frzneh Mirzzdeh 1, Bbk Behsz 2, nd Hmid Beigy 1 1 Deprtment of Computer Engineering, Shrif University of Technology, Tehrn,
More informationLaboratory Exercise 6
Laboratory Exercie 6 Adder, Subtractor, and Multiplier The purpoe of thi exercie i to examine arithmetic circuit that add, ubtract, and multiply number. Each type of circuit will be implemented in two
More informationEssential Question What are some of the characteristics of the graph of a rational function?
8. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS A..A A..G A..H A..K Grphing Rtionl Functions Essentil Question Wht re some of the chrcteristics of the grph of rtionl function? The prent function for rtionl functions
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationMIPS I/O and Interrupt
MIPS I/O nd Interrupt Review Floting point instructions re crried out on seprte chip clled coprocessor 1 You hve to move dt to/from coprocessor 1 to do most common opertions such s printing, clling functions,
More informationDigital Design. Chapter 1: Introduction. Digital Design. Copyright 2006 Frank Vahid
Chpter : Introduction Copyright 6 Why Study?. Look under the hood of computers Solid understnding --> confidence, insight, even better progrmmer when wre of hrdwre resource issues Electronic devices becoming
More informationVery sad code. Abstraction, List, & Cons. CS61A Lecture 7. Happier Code. Goals. Constructors. Constructors 6/29/2011. Selectors.
6/9/ Abstrction, List, & Cons CS6A Lecture 7-6-9 Colleen Lewis Very sd code (define (totl hnd) (if (empty? hnd) (+ (butlst (lst hnd)) (totl (butlst hnd))))) STk> (totl (h c d)) 7 STk> (totl (h ks d)) ;;;EEEK!
More information1 ( = 80 points) 50 min. LOAD INI I <= 0; J <= 1; LSA <= 1; DONE. COMP Compare M[I] with PREV
Spring 203 EE457 Intructor: Gndhi Puvvd Quiz (~ 0%) Dte: 2/22/203, Fridy in THH20 Clcultor nd Epern Verilog Guide re llowed; Time: 09:5AM-:45AM (2 Hour 30 Min) Cloed-book/Cloed-note Exm Totl point: 246
More informationOn String Matching in Chunked Texts
On String Mtching in Chunked Texts Hnnu Peltol nd Jorm Trhio {hpeltol, trhio}@cs.hut.fi Deprtment of Computer Science nd Engineering Helsinki University of Technology P.O. Box 5400, FI-02015 HUT, Finlnd
More informationStained Glass Design. Teaching Goals:
Stined Glss Design Time required 45-90 minutes Teching Gols: 1. Students pply grphic methods to design vrious shpes on the plne.. Students pply geometric trnsformtions of grphs of functions in order to
More informationEXPONENTIAL & POWER GRAPHS
Eponentil & Power Grphs EXPONENTIAL & POWER GRAPHS www.mthletics.com.u Eponentil EXPONENTIAL & Power & Grphs POWER GRAPHS These re grphs which result from equtions tht re not liner or qudrtic. The eponentil
More informationOrthogonal line segment intersection
Computtionl Geometry [csci 3250] Line segment intersection The prolem (wht) Computtionl Geometry [csci 3250] Orthogonl line segment intersection Applictions (why) Algorithms (how) A specil cse: Orthogonl
More informationShortest Paths Problem. CS 362, Lecture 20. Today s Outline. Negative Weights
Shortet Path Problem CS 6, Lecture Jared Saia Univerity of New Mexico Another intereting problem for graph i that of finding hortet path Aume we are given a weighted directed graph G = (V, E) with two
More informationMATH 25 CLASS 5 NOTES, SEP
MATH 25 CLASS 5 NOTES, SEP 30 2011 Contents 1. A brief diversion: reltively prime numbers 1 2. Lest common multiples 3 3. Finding ll solutions to x + by = c 4 Quick links to definitions/theorems Euclid
More informationCOMP 423 lecture 11 Jan. 28, 2008
COMP 423 lecture 11 Jn. 28, 2008 Up to now, we hve looked t how some symols in n lphet occur more frequently thn others nd how we cn sve its y using code such tht the codewords for more frequently occuring
More informationToday. CS 188: Artificial Intelligence Fall Recap: Search. Example: Pancake Problem. Example: Pancake Problem. General Tree Search.
CS 88: Artificil Intelligence Fll 00 Lecture : A* Serch 9//00 A* Serch rph Serch Tody Heuristic Design Dn Klein UC Berkeley Multiple slides from Sturt Russell or Andrew Moore Recp: Serch Exmple: Pncke
More informationOn the Detection of Step Edges in Algorithms Based on Gradient Vector Analysis
On the Detection of Step Edges in Algorithms Bsed on Grdient Vector Anlysis A. Lrr6, E. Montseny Computer Engineering Dept. Universitt Rovir i Virgili Crreter de Slou sin 43006 Trrgon, Spin Emil: lrre@etse.urv.es
More informationAlgorithm Design (5) Text Search
Algorithm Design (5) Text Serch Tkshi Chikym School of Engineering The University of Tokyo Text Serch Find sustring tht mtches the given key string in text dt of lrge mount Key string: chr x[m] Text Dt:
More informationL. Yaroslavsky. Fundamentals of Digital Image Processing. Course
L. Yroslvsky. Fundmentls of Digitl Imge Processing. Course 0555.330 Lecture. Imge enhncement.. Imge enhncement s n imge processing tsk. Clssifiction of imge enhncement methods Imge enhncement is processing
More informationToday s Outline. CS 561, Lecture 23. Negative Weights. Shortest Paths Problem. The presence of a negative cycle might mean that there is
Today Outline CS 56, Lecture Jared Saia Univerity of New Mexico The path that can be trodden i not the enduring and unchanging Path. The name that can be named i not the enduring and unchanging Name. -
More informationToday. Search Problems. Uninformed Search Methods. Depth-First Search Breadth-First Search Uniform-Cost Search
Uninformed Serch [These slides were creted by Dn Klein nd Pieter Abbeel for CS188 Intro to AI t UC Berkeley. All CS188 mterils re vilble t http://i.berkeley.edu.] Tody Serch Problems Uninformed Serch Methods
More informationTHE USE OF ARTIFICIAL INTELLIGENCE IN CONTROLLING A 6DOF MOTION PLATFORM
THE USE OF ARTIFICIAL INTELLIGENCE IN CONTROLLING A 6DOF MOTION PLATFORM Webjørn Rekdlbkken Intitute of Technology nd Nuticl Science Aleund Univerity College 605 Aleund, Norwy E-mil: wr@hil.no KEYWORDS
More informationECE 468/573 Midterm 1 September 28, 2012
ECE 468/573 Midterm 1 September 28, 2012 Nme:! Purdue emil:! Plese sign the following: I ffirm tht the nswers given on this test re mine nd mine lone. I did not receive help from ny person or mteril (other
More informationUSING HOUGH TRANSFORM IN LINE EXTRACTION
Stylinidis, Efstrtios USING HOUGH TRANSFORM IN LINE EXTRACTION Efstrtios STYLIANIDIS, Petros PATIAS The Aristotle University of Thessloniki, Deprtment of Cdstre Photogrmmetry nd Crtogrphy Univ. Box 473,
More informationIntegration. September 28, 2017
Integrtion September 8, 7 Introduction We hve lerned in previous chpter on how to do the differentition. It is conventionl in mthemtics tht we re supposed to lern bout the integrtion s well. As you my
More informationTilt-Sensing with Kionix MEMS Accelerometers
Tilt-Sensing with Kionix MEMS Accelerometers Introduction Tilt/Inclintion sensing is common ppliction for low-g ccelerometers. This ppliction note describes how to use Kionix MEMS low-g ccelerometers to
More informationP(r)dr = probability of generating a random number in the interval dr near r. For this probability idea to make sense we must have
Rndom Numers nd Monte Crlo Methods Rndom Numer Methods The integrtion methods discussed so fr ll re sed upon mking polynomil pproximtions to the integrnd. Another clss of numericl methods relies upon using
More informationThe Distributed Data Access Schemes in Lambda Grid Networks
The Distributed Dt Access Schemes in Lmbd Grid Networks Ryot Usui, Hiroyuki Miygi, Yutk Arkw, Storu Okmoto, nd Noki Ymnk Grdute School of Science for Open nd Environmentl Systems, Keio University, Jpn
More information4452 Mathematical Modeling Lecture 4: Lagrange Multipliers
Mth Modeling Lecture 4: Lgrnge Multipliers Pge 4452 Mthemticl Modeling Lecture 4: Lgrnge Multipliers Lgrnge multipliers re high powered mthemticl technique to find the mximum nd minimum of multidimensionl
More informationAlignment of Long Sequences. BMI/CS Spring 2012 Colin Dewey
Alignment of Long Sequences BMI/CS 776 www.biostt.wisc.edu/bmi776/ Spring 2012 Colin Dewey cdewey@biostt.wisc.edu Gols for Lecture the key concepts to understnd re the following how lrge-scle lignment
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationMinimum congestion spanning trees in bipartite and random graphs
Minimum congetion panning tree in bipartite and random graph M.I. Otrovkii Department of Mathematic and Computer Science St. John Univerity 8000 Utopia Parkway Queen, NY 11439, USA e-mail: otrovm@tjohn.edu
More informationDynamic Programming. Andreas Klappenecker. [partially based on slides by Prof. Welch] Monday, September 24, 2012
Dynmic Progrmming Andres Klppenecker [prtilly bsed on slides by Prof. Welch] 1 Dynmic Progrmming Optiml substructure An optiml solution to the problem contins within it optiml solutions to subproblems.
More informationImproper Integrals. October 4, 2017
Improper Integrls October 4, 7 Introduction We hve seen how to clculte definite integrl when the it is rel number. However, there re times when we re interested to compute the integrl sy for emple 3. Here
More informationSubband coding of image sequences using multiple vector quantizers. Emanuel Martins, Vitor Silva and Luís de Sá
Sund coding of imge sequences using multiple vector quntizers Emnuel Mrtins, Vitor Silv nd Luís de Sá Instituto de Telecomunicções, Deprtmento de Engenhri Electrotécnic Pólo II d Universidde de Coimr,
More informationLaboratory Exercise 6
Laboratory Exercie 6 Adder, Subtractor, and Multiplier The purpoe of thi exercie i to examine arithmetic circuit that add, ubtract, and multiply number. Each circuit will be decribed in VHL and implemented
More information1. SEQUENCES INVOLVING EXPONENTIAL GROWTH (GEOMETRIC SEQUENCES)
Numbers nd Opertions, Algebr, nd Functions 45. SEQUENCES INVOLVING EXPONENTIAL GROWTH (GEOMETRIC SEQUENCES) In sequence of terms involving eponentil growth, which the testing service lso clls geometric
More informationGENERATING ORTHOIMAGES FOR CLOSE-RANGE OBJECTS BY AUTOMATICALLY DETECTING BREAKLINES
GENEATING OTHOIMAGES FO CLOSE-ANGE OBJECTS BY AUTOMATICALLY DETECTING BEAKLINES Efstrtios Stylinidis 1, Lzros Sechidis 1, Petros Ptis 1, Spiros Sptls 2 Aristotle University of Thessloniki 1 Deprtment of
More informationDr. D.M. Akbar Hussain
Dr. D.M. Akr Hussin Lexicl Anlysis. Bsic Ide: Red the source code nd generte tokens, it is similr wht humns will do to red in; just tking on the input nd reking it down in pieces. Ech token is sequence
More informationAnnouncements. CSE332: Data Abstractions Lecture 19: Parallel Prefix and Sorting. The prefix-sum problem. Outline. Parallel prefix-sum
Announcement Homework 6 due Friday Feb 25 th at the BEGINNING o lecture CSE332: Data Abtraction Lecture 19: Parallel Preix and Sorting Project 3 the lat programming project! Verion 1 & 2 - Tue March 1,
More informationx )Scales are the reciprocal of each other. e
9. Reciprocls A Complete Slide Rule Mnul - eville W Young Chpter 9 Further Applictions of the LL scles The LL (e x ) scles nd the corresponding LL 0 (e -x or Exmple : 0.244 4.. Set the hir line over 4.
More informationComplete Coverage Path Planning of Mobile Robot Based on Dynamic Programming Algorithm Peng Zhou, Zhong-min Wang, Zhen-nan Li, Yang Li
2nd Interntionl Conference on Electronic & Mechnicl Engineering nd Informtion Technology (EMEIT-212) Complete Coverge Pth Plnning of Mobile Robot Bsed on Dynmic Progrmming Algorithm Peng Zhou, Zhong-min
More informationSolutions to Math 41 Final Exam December 12, 2011
Solutions to Mth Finl Em December,. ( points) Find ech of the following its, with justifiction. If there is n infinite it, then eplin whether it is or. ( ) / ln() () (5 points) First we compute the it:
More informationDelaunay Triangulation: Incremental Construction
Chapter 6 Delaunay Triangulation: Incremental Contruction In the lat lecture, we have learned about the Lawon ip algorithm that compute a Delaunay triangulation of a given n-point et P R 2 with O(n 2 )
More informationAnswer Key Lesson 6: Workshop: Angles and Lines
nswer Key esson 6: tudent Guide ngles nd ines Questions 1 3 (G p. 406) 1. 120 ; 360 2. hey re the sme. 3. 360 Here re four different ptterns tht re used to mke quilts. Work with your group. se your Power
More informationReducing Costs with Duck Typing. Structural
Reducing Costs with Duck Typing Structurl 1 Duck Typing In computer progrmming with object-oriented progrmming lnguges, duck typing is lyer of progrmming lnguge nd design rules on top of typing. Typing
More informationLecture 8: More Pipelining
Overview Lecture 8: More Pipelining David Black-Schaffer davidbb@tanford.edu EE8 Spring 00 Getting Started with Lab Jut get a ingle pixel calculating at one time Then look into filling your pipeline Multiplier
More informationCS 432 Fall Mike Lam, Professor a (bc)* Regular Expressions and Finite Automata
CS 432 Fll 2017 Mike Lm, Professor (c)* Regulr Expressions nd Finite Automt Compiltion Current focus "Bck end" Source code Tokens Syntx tree Mchine code chr dt[20]; int min() { flot x = 42.0; return 7;
More informationFig.1. Let a source of monochromatic light be incident on a slit of finite width a, as shown in Fig. 1.
Answer on Question #5692, Physics, Optics Stte slient fetures of single slit Frunhofer diffrction pttern. The slit is verticl nd illuminted by point source. Also, obtin n expression for intensity distribution
More informationChapter 1: Introduction
Chpter : Introduction Slides to ccompny the textbook, First Edition, by, John Wiley nd Sons Publishers, 7. http://www.ddvhid.com Copyright 7 Instructors of courses requiring Vhid's textbook (published
More information2014 Haskell January Test Regular Expressions and Finite Automata
0 Hskell Jnury Test Regulr Expressions nd Finite Automt This test comprises four prts nd the mximum mrk is 5. Prts I, II nd III re worth 3 of the 5 mrks vilble. The 0 Hskell Progrmming Prize will be wrded
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationCSCI1950 Z Computa4onal Methods for Biology Lecture 2. Ben Raphael January 26, hhp://cs.brown.edu/courses/csci1950 z/ Outline
CSCI1950 Z Comput4onl Methods for Biology Lecture 2 Ben Rphel Jnury 26, 2009 hhp://cs.brown.edu/courses/csci1950 z/ Outline Review of trees. Coun4ng fetures. Chrcter bsed phylogeny Mximum prsimony Mximum
More informationSpectral Analysis of MCDF Operations in Image Processing
Spectrl Anlysis of MCDF Opertions in Imge Processing ZHIQIANG MA 1,2 WANWU GUO 3 1 School of Computer Science, Northest Norml University Chngchun, Jilin, Chin 2 Deprtment of Computer Science, JilinUniversity
More informationEngineer To Engineer Note
Engineer To Engineer Note EE-188 Technicl Notes on using Anlog Devices' DSP components nd development tools Contct our technicl support by phone: (800) ANALOG-D or e-mil: dsp.support@nlog.com Or visit
More informationAn Efficient Divide and Conquer Algorithm for Exact Hazard Free Logic Minimization
An Efficient Divide nd Conquer Algorithm for Exct Hzrd Free Logic Minimiztion J.W.J.M. Rutten, M.R.C.M. Berkelr, C.A.J. vn Eijk, M.A.J. Kolsteren Eindhoven University of Technology Informtion nd Communiction
More informationCSCI 446: Artificial Intelligence
CSCI 446: Artificil Intelligence Serch Instructor: Michele Vn Dyne [These slides were creted by Dn Klein nd Pieter Abbeel for CS188 Intro to AI t UC Berkeley. All CS188 mterils re vilble t http://i.berkeley.edu.]
More informationModel-based Policy Gradient Reinforcement Learning
776 Model-bsed Policy Grdient Reinforcement Lerning Xin Wng WANGXI~CS.ORST.EDU Thoms G. Dietterlch TGD~CS.ORST.EDU Deprtment of Computer Science, Oregon Stte University, Derborn Hll 102, Corvllis, OR 97330
More informationstyle type="text/css".wpb_animate_when_almost_visible { opacity: 1; }/style
style type="text/css".wpb_nimte_when_lmost_vible { opcity: 1; }/style You cn chrome homepge for internet explorer quickly chrome homepge for internet explorer get chrome homepge for internet explorer every
More informationRepresentation of Numbers. Number Representation. Representation of Numbers. 32-bit Unsigned Integers 3/24/2014. Fixed point Integer Representation
Representtion of Numbers Number Representtion Computer represent ll numbers, other thn integers nd some frctions with imprecision. Numbers re stored in some pproximtion which cn be represented by fixed
More informationIntegration. October 25, 2016
Integrtion October 5, 6 Introduction We hve lerned in previous chpter on how to do the differentition. It is conventionl in mthemtics tht we re supposed to lern bout the integrtion s well. As you my hve
More informationEpson Projector Content Manager Operation Guide
Epson Projector Content Mnger Opertion Guide Contents 2 Introduction to the Epson Projector Content Mnger Softwre 3 Epson Projector Content Mnger Fetures... 4 Setting Up the Softwre for the First Time
More information10.5 Graphing Quadratic Functions
0.5 Grphing Qudrtic Functions Now tht we cn solve qudrtic equtions, we wnt to lern how to grph the function ssocited with the qudrtic eqution. We cll this the qudrtic function. Grphs of Qudrtic Functions
More informationUsing Ontrol MpBus Driver for Sedona on R-ION
Belimo MpBus Driver for R-ION Using Ontrol MpBus Driver for Sedon on R-ION 24 Vdc Supply Devices RS485 supervory system 1/7 Ontrol Belimo MpBus Driver for R-ION R-ION MPBus Connection 2/7 Ontrol Belimo
More informationUnit #9 : Definite Integral Properties, Fundamental Theorem of Calculus
Unit #9 : Definite Integrl Properties, Fundmentl Theorem of Clculus Gols: Identify properties of definite integrls Define odd nd even functions, nd reltionship to integrl vlues Introduce the Fundmentl
More informationStart Here. Remove all tape and lift display. Locate components
HP Photosmrt 2600/2700 series ll-in-one User Guide Strt Here 1 USB cle users: Do not connect the USB cle until this guide instructs you to or the softwre my not instll properly. Use this guide to set up
More information11/28/18 FIBONACCI NUMBERS GOLDEN RATIO, RECURRENCES. Announcements. Announcements. Announcements
Fiboncci (Leonrdo Pisno) 0-0? Sttue in Pis Itly FIBONACCI NUERS GOLDEN RATIO, RECURRENCES Lecture CS0 Fll 08 Announcements A: NO LATE DAYS. No need to put in time nd comments. We hve to grde quickly. No
More informationChapter Spline Method of Interpolation More Examples Electrical Engineering
Chpter. Spline Method of Interpoltion More Exmples Electricl Engineering Exmple Thermistors re used to mesure the temperture of bodies. Thermistors re bsed on mterils chnge in resistnce with temperture.
More informationFunctor (1A) Young Won Lim 8/2/17
Copyright (c) 2016-2017 Young W. Lim. Permission is grnted to copy, distribute nd/or modify this document under the terms of the GNU Free Documenttion License, Version 1.2 or ny lter version published
More informationTowards the Formation of Comprehensive SLAs between Heterogeneous Wireless DiffServ Domains
Towrd the Formtion of Comprehenive SLA between Heterogeneou Wirele DiffServ Domin Mohin Iftikhr nd Born Lndfeldt School of Informtion Technologie Univerity of Sydney Sydney NSW Autrli mohinif@it.uyd.edu.u
More informationMid-term exam. Scores. Fall term 2012 KAIST EE209 Programming Structures for EE. Thursday Oct 25, Student's name: Student ID:
Fll term 2012 KAIST EE209 Progrmming Structures for EE Mid-term exm Thursdy Oct 25, 2012 Student's nme: Student ID: The exm is closed book nd notes. Red the questions crefully nd focus your nswers on wht
More informationNeural Networks and Tree Search
Mastering the Game of Go With Deep Neural Networks and Tree Search Nabiha Asghar 27 th May 2016 AlphaGo by Google DeepMind Go: ancient Chinese board game. Simple rules, but far more complicated than Chess
More informationbinary trees, expression trees
COMP 250 Lecture 21 binry trees, expression trees Oct. 27, 2017 1 Binry tree: ech node hs t most two children. 2 Mximum number of nodes in binry tree? Height h (e.g. 3) 3 Mximum number of nodes in binry
More informationComputing offsets of freeform curves using quadratic trigonometric splines
Computing offsets of freeform curves using qudrtic trigonometric splines JIULONG GU, JAE-DEUK YUN, YOONG-HO JUNG*, TAE-GYEONG KIM,JEONG-WOON LEE, BONG-JUN KIM School of Mechnicl Engineering Pusn Ntionl
More informationThe Reciprocal Function Family. Objectives To graph reciprocal functions To graph translations of reciprocal functions
- The Reciprocl Function Fmil Objectives To grph reciprocl functions To grph trnsltions of reciprocl functions Content Stndrds F.BF.3 Identif the effect on the grph of replcing f () b f() k, kf(), f(k),
More information1 Quad-Edge Construction Operators
CS48: Computer Grphics Hndout # Geometric Modeling Originl Hndout #5 Stnford University Tuesdy, 8 December 99 Originl Lecture #5: 9 November 99 Topics: Mnipultions with Qud-Edge Dt Structures Scribe: Mike
More informationSubtracting Fractions
Lerning Enhncement Tem Model Answers: Adding nd Subtrcting Frctions Adding nd Subtrcting Frctions study guide. When the frctions both hve the sme denomintor (bottom) you cn do them using just simple dding
More informationChapter 2 Sensitivity Analysis: Differential Calculus of Models
Chpter 2 Sensitivity Anlysis: Differentil Clculus of Models Abstrct Models in remote sensing nd in science nd engineering, in generl re, essentilly, functions of discrete model input prmeters, nd/or functionls
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationStack. A list whose end points are pointed by top and bottom
4. Stck Stck A list whose end points re pointed by top nd bottom Insertion nd deletion tke plce t the top (cf: Wht is the difference between Stck nd Arry?) Bottom is constnt, but top grows nd shrinks!
More informationInteger-Encoded Massively Parallel Processing of Fast-Learning Fuzzy ARTMAP Neural Networks
Integer-Encoded Mssively Prllel Processing of Fst-Lerning Fuzzy ARTMAP Neurl Networks Hubert A. Bhr, Ronld F. DeMr b, Michel N. Georgiopoulos b HQ STRICOM, AMSTI-ET, 2350 Reserch Boulevrd, Orlndo, FL 32826
More informationGeometric transformations
Geometric trnsformtions Computer Grphics Some slides re bsed on Shy Shlom slides from TAU mn n n m m T A,,,,,, 2 1 2 22 12 1 21 11 Rows become columns nd columns become rows nm n n m m A,,,,,, 1 1 2 22
More informationParallel Square and Cube Computations
Prllel Squre nd Cube Computtions Albert A. Liddicot nd Michel J. Flynn Computer Systems Lbortory, Deprtment of Electricl Engineering Stnford University Gtes Building 5 Serr Mll, Stnford, CA 945, USA liddicot@stnford.edu
More information1 The secretary problem
Thi i new material: if you ee error, pleae email jtyu at tanford dot edu 1 The ecretary problem We will tart by analyzing the expected runtime of an algorithm, a you will be expected to do on your homework.
More information