Engineering Decision Methods

Size: px
Start display at page:

Download "Engineering Decision Methods"

Transcription

1 GSOE Maximin and minimax regret 1 2 Indifference; equal preference 3 Graphing decisin prblems 4 Dminance

2 The Maximin principle Maximin and minimax Regret are similar principles: ne cnsiders riginal values and the ther regrets The Maximin criteria is the main decisin methd used under cmplete uncertainty We ve seen Maximin and minimax Regret n decisin tables, but what abut mre cmplex decisin prblems (e.g., multiple decisin pints)? Multi-stage decisins Example (Prduct develpment) Yu head the R&D department f a small manufacturing cmpany which is cnsidering develping a new prduct. The cmpany must decide whether t prceed with prttype develpment and, if develpment is successful, subsequently determine the prductin scale (i.e., the size f the factry) based n prjected demand fr the prduct. Questins What des Maximin r minimax Regret mean in this prblem? Is there a decisin-table representatin?

3 Multi-stage decisins Eliminating uncertainty L S h l h L S 4 l 4 5 h 5 l 8 L 4 What is Maximin mean in a tree? Maximin eliminates branches in chance ndes (i.e., prunes the tree) Reduces prblem t that f certainty S 5 5

4 Outline 1 2 Indifference; equal preference 3 Graphing decisin prblems 4 Dminance Prblem representatin: decisin tables u F D v A ($0) B ($30) C ( $10) Observatin: Each actin and state uniquely determine an utcme Mdel as a binary functin: ω : A S Ω Represented as a table: A ω F D Decisin tables: S A A B C rw = actin clumn = state Interpretatin: B = ω(d, ) means B is the utcme f actin D in state ;

5 Trees and tables u F D A ($0) v B ($30) C ( $10) F $0 $0 D $30 $10 u F D w v A A B C Multiple trees may crrespnd t the same table Ging frm tables (nrmal frm) t trees (extensive frm) is straight frward, but the cnverse can be tricky Which representatin is better: trees r tables? Which representatin facilitates decisin analysis mst? Multi-stage decisins

6 Multi-stage decisins Example (Prduct develpment) Yu head the R&D department f a small manufacturing cmpany which is cnsidering develping a new prduct. The cmpany must decide whether t prceed with prttype develpment and, if develpment is successful, subsequently determine the prductin scale (i.e., the size f the factry) based n prjected demand fr the prduct. Questins What des Maximin r minimax Regret mean in this prblem? Is there a decisin-table representatin? Actins t strategies In a decisin tree: Recall that a decisin table is a representatin f the utcme mapping ω : A S Ω Observatin: fllwing a path frm the rt t a leaf leads t a unique utcme Therefre: A state cnsists f all the cnditins alng this path An actin cnsists f all the chices alng the path Definitin (Strategy) A strategy (r plicy r plan) is a prcedure that specifies the selectin f an actin at every reachable decisin pint.

7 States: s 1 s 2 s 3 s, h s, l f A strategy must specify an actin at each reachable decisin pint; e.g., Authrise develpment (Au), if develpment succeeds (s), then build large factry (L) encded Au;s/L Encding: α/a says: Example: Au;s/S: At the decisin nde reached via path α chse actin A. After authrising develpment (Au), in the event that develpment succeeds (s), chse t build a small factry (S). Strategies fr this prblem: A 1 Au;s/L Au;s/S A 2 A 3 Ab

8 Cde fc pc lp mp be ldc sat dis sq Descriptin full capacity partial capacity large prfits mderate prfits break even lse dev. csts demand satisfied dissatisfactin status qu s, h s, l f Au;s/L fc,lp,sat pc,be,sat ldc Au;s/S fc,mp,dis fc,mp,sat ldc Ab sq sq sq Value functin: ω V fc,lp,sat 10 pc,be,sat 4 ldc 1 fc,mp,dis 5 fc,mp,sat 8 sq 0 Decisin table: s, h s, l f Au;s/L Au;s/S Ab Exercises What are the Maximin and minimax Regret strategies fr this prblem?

9 Outline Indifference; equal preference 1 2 Indifference; equal preference 3 Graphing decisin prblems 4 Dminance Indifference; equal preference Indifference: equal preference Which actin belw is preferred abve under Maximin? s 1 s 2 A 1 0 B 0 1 Definitin (Indifference) If tw actins A and B are equally preferred then the agent is said t be indifferent between A and B. Definitin (Weak preference) Actin A is weakly preferred t B iff it A preferred t B r the tw are indifferent; i.e., the agent prefers A at least as much as B.

10 Indifference classes Indifference; equal preference Definitin (Indifference class) An indifference class is a nn-empty set f all actins/utcmes between which an agent is indifferent. Fr a given actin A A, the indifference class f A is given by I(A) = {a A V (a) = V (A)} Different agents will have different preferences ver utcmes/actins, hence different indifference classes Different decisin rules will prduce different indifference classes Outline Graphing decisin prblems 1 2 Indifference; equal preference 3 Graphing decisin prblems 4 Dminance

11 Visualisatin Graphing decisin prblems s 1 s 2 A 2 3 B 4 0 C 3 3 D 5 2 E 3 5 Let v i (a) = v(a, s i ) be the value f actin a in state s i. Each actin a crrespnds t a pint (v 1, v 2 ), where v i = v(a, s i ). v 2 5 (3, 5) 4 A C 3 (2, 3) (3, 3) D 2 1 B (4, 0) E (5, 2) v 1 Graphing decisin prblems Indifference curves: Maximin Fr the pure actins belw: s 1 s 2 A 2 3 B 4 0 C 3 3 D 5 2 E 3 5 Cnsider the curves f all pints which represent actins with the same Maximin value; i.e., the Maximin indifference curves. v 2 5 E 4 3 A C 2 I(A) D v 1

12 Graphing regret Graphing decisin prblems Cnsider three actins: v 2 s 1 s 2 A 2 4 B 4 1 C 5 3 Regret values and indifference curves fr minimax Regret shwn in blue A B C A C B v 1 Outline Dminance 1 2 Indifference; equal preference 3 Graphing decisin prblems 4 Dminance

13 River example Dminance X A B C Example (River lgistics) Alice s cmpany has a warehuse situated at X n a river that flws dwn-stream frm C t A. Her cmpany delivers gds t a client at C via mtr bats. On sme days a (free) gds ferry perates, travelling up the river, stpping at A then B and C, but nt at X. The fuel required t reach C frm each starting pint: A X B C T C frm: Alice wants t minimise fuel cnsumptin (in litres). River example Dminance X A B C f f A 4 0 B 3 1 C 1 1 Alice cnsiders three pssible ways t get t C (frm starting pint X): A : via A, by flating dwn the river B : via B, by travelling up-stream t B C : by travelling all the way t C Outcmes are measured in litres left in a fur-litre tank. Exercise Let w : Ω R dente fuel cnsumptin in litres. What transfrmatin f : R R is respnsible fr the values v : Ω R in the decisin table?

14 River example Dminance The axes crrespnd t the payffs in each f the tw states; i.e., payff v 1 in state s 1 = f and v 2 in s 2 = f The actins are graphed belw: v 2 2 B 1 C A v 1 Clearly ptin C will nt be a better respnse than either f the ther tw under any circumstances (i.e., in any state) Actin C can be disregarded Generalised dminance Dminance Definitin (Strict dminance) Actin A strictly dminates B iff every utcme f A is strictly preferred ver the crrespnding utcme f B. Definitin (Weak dminance) Actin A weakly dminates B iff every utcme f A is weakly preferred ver the crrespnding utcme f B, and sme utcme is strictly preferred. s 1 s 2 s 3 Exercise A Which actins in the decisin table B shwn are dminated? C 5 6 3

15 Dminance Dminance and best respnse Crllary An actin A strictly dminates B iff A is a better respnse than B in each pssible state. Crllary An actin A weakly dminates B iff A is a better respnse than B in sme pssible state and B is nt a better respnse than A in any state. Dminance principle A ratinal agent shuld never chse a dminated actin. Admissibile actins Dminance s 1 s 2 A 4 A 0 4 C 3 D B B C D 1 2 v v 1 Definitin (Admissible) An actin is admissible iff it is nt dminated by any ther actin. The set f all admissible actins is called the admissible frntier. Exercises Which actins abve are admissible?

16 Dminance Dminance: MaxiMax and Maximin Definitin (Dminance eliminatin) s 1 s 2 M m A B C A decisin rule is said t satisfy (strict/weak) dminance eliminatin if it always eliminates actins that are (strictly/weakly) dminated. Dminated actins can be discarded under any rule that satisfies dminance eliminatin Dminance summary Dminance Rules that satisfy strict/weak dminance eliminatin. Rule Strict Weak MaxiMax Maximin Hurwicz s minimax Regret Laplace s Exercise Verify the prperties abve.

You need to be able to define the following terms and answer basic questions about them:

You need to be able to define the following terms and answer basic questions about them: CS440/ECE448 Sectin Q Fall 2017 Midterm Review Yu need t be able t define the fllwing terms and answer basic questins abut them: Intr t AI, agents and envirnments Pssible definitins f AI, prs and cns f

More information

CHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India

CHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India CHAPTER 3 INEQUALITIES Cpyright -The Institute f Chartered Accuntants f India INEQUALITIES LEARNING OBJECTIVES One f the widely used decisin making prblems, nwadays, is t decide n the ptimal mix f scarce

More information

Administrativia. Assignment 1 due thursday 9/23/2004 BEFORE midnight. Midterm exam 10/07/2003 in class. CS 460, Sessions 8-9 1

Administrativia. Assignment 1 due thursday 9/23/2004 BEFORE midnight. Midterm exam 10/07/2003 in class. CS 460, Sessions 8-9 1 Administrativia Assignment 1 due thursday 9/23/2004 BEFORE midnight Midterm eam 10/07/2003 in class CS 460, Sessins 8-9 1 Last time: search strategies Uninfrmed: Use nly infrmatin available in the prblem

More information

Section 6-2: Simplex Method: Maximization with Problem Constraints of the Form ~

Section 6-2: Simplex Method: Maximization with Problem Constraints of the Form ~ Sectin 6-2: Simplex Methd: Maximizatin with Prblem Cnstraints f the Frm ~ Nte: This methd was develped by Gerge B. Dantzig in 1947 while n assignment t the U.S. Department f the Air Frce. Definitin: Standard

More information

Five Whys How To Do It Better

Five Whys How To Do It Better Five Whys Definitin. As explained in the previus article, we define rt cause as simply the uncvering f hw the current prblem came int being. Fr a simple causal chain, it is the entire chain. Fr a cmplex

More information

Department of Economics, University of California, Davis Ecn 200C Micro Theory Professor Giacomo Bonanno. Insurance Markets

Department of Economics, University of California, Davis Ecn 200C Micro Theory Professor Giacomo Bonanno. Insurance Markets Department f Ecnmics, University f alifrnia, Davis Ecn 200 Micr Thery Prfessr Giacm Bnann Insurance Markets nsider an individual wh has an initial wealth f. ith sme prbability p he faces a lss f x (0

More information

NUMBERS, MATHEMATICS AND EQUATIONS

NUMBERS, MATHEMATICS AND EQUATIONS AUSTRALIAN CURRICULUM PHYSICS GETTING STARTED WITH PHYSICS NUMBERS, MATHEMATICS AND EQUATIONS An integral part t the understanding f ur physical wrld is the use f mathematical mdels which can be used t

More information

Name: Block: Date: Science 10: The Great Geyser Experiment A controlled experiment

Name: Block: Date: Science 10: The Great Geyser Experiment A controlled experiment Science 10: The Great Geyser Experiment A cntrlled experiment Yu will prduce a GEYSER by drpping Ments int a bttle f diet pp Sme questins t think abut are: What are yu ging t test? What are yu ging t measure?

More information

CHM112 Lab Graphing with Excel Grading Rubric

CHM112 Lab Graphing with Excel Grading Rubric Name CHM112 Lab Graphing with Excel Grading Rubric Criteria Pints pssible Pints earned Graphs crrectly pltted and adhere t all guidelines (including descriptive title, prperly frmatted axes, trendline

More information

Experiment #3. Graphing with Excel

Experiment #3. Graphing with Excel Experiment #3. Graphing with Excel Study the "Graphing with Excel" instructins that have been prvided. Additinal help with learning t use Excel can be fund n several web sites, including http://www.ncsu.edu/labwrite/res/gt/gt-

More information

Differentiation Applications 1: Related Rates

Differentiation Applications 1: Related Rates Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm

More information

Lab 1 The Scientific Method

Lab 1 The Scientific Method INTRODUCTION The fllwing labratry exercise is designed t give yu, the student, an pprtunity t explre unknwn systems, r universes, and hypthesize pssible rules which may gvern the behavir within them. Scientific

More information

Pattern Recognition 2014 Support Vector Machines

Pattern Recognition 2014 Support Vector Machines Pattern Recgnitin 2014 Supprt Vectr Machines Ad Feelders Universiteit Utrecht Ad Feelders ( Universiteit Utrecht ) Pattern Recgnitin 1 / 55 Overview 1 Separable Case 2 Kernel Functins 3 Allwing Errrs (Sft

More information

AP Statistics Notes Unit Two: The Normal Distributions

AP Statistics Notes Unit Two: The Normal Distributions AP Statistics Ntes Unit Tw: The Nrmal Distributins Syllabus Objectives: 1.5 The student will summarize distributins f data measuring the psitin using quartiles, percentiles, and standardized scres (z-scres).

More information

Revision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax

Revision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax .7.4: Direct frequency dmain circuit analysis Revisin: August 9, 00 5 E Main Suite D Pullman, WA 9963 (509) 334 6306 ice and Fax Overview n chapter.7., we determined the steadystate respnse f electrical

More information

Tree Structured Classifier

Tree Structured Classifier Tree Structured Classifier Reference: Classificatin and Regressin Trees by L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stne, Chapman & Hall, 98. A Medical Eample (CART): Predict high risk patients

More information

GSOE9210 Engineering Decisions

GSOE9210 Engineering Decisions Sutdent ID: Name: Signature: The University of New South Wales Session 2, 2017 GSOE9210 Engineering Decisions Sample mid-term test Instructions: Time allowed: 1 hour Reading time: 5 minutes This examination

More information

Admin. MDP Search Trees. Optimal Quantities. Reinforcement Learning

Admin. MDP Search Trees. Optimal Quantities. Reinforcement Learning Admin Reinfrcement Learning Cntent adapted frm Berkeley CS188 MDP Search Trees Each MDP state prjects an expectimax-like search tree Optimal Quantities The value (utility) f a state s: V*(s) = expected

More information

Determining Optimum Path in Synthesis of Organic Compounds using Branch and Bound Algorithm

Determining Optimum Path in Synthesis of Organic Compounds using Branch and Bound Algorithm Determining Optimum Path in Synthesis f Organic Cmpunds using Branch and Bund Algrithm Diastuti Utami 13514071 Prgram Studi Teknik Infrmatika Seklah Teknik Elektr dan Infrmatika Institut Teknlgi Bandung,

More information

Medium Scale Integrated (MSI) devices [Sections 2.9 and 2.10]

Medium Scale Integrated (MSI) devices [Sections 2.9 and 2.10] EECS 270, Winter 2017, Lecture 3 Page 1 f 6 Medium Scale Integrated (MSI) devices [Sectins 2.9 and 2.10] As we ve seen, it s smetimes nt reasnable t d all the design wrk at the gate-level smetimes we just

More information

Computational modeling techniques

Computational modeling techniques Cmputatinal mdeling techniques Lecture 4: Mdel checing fr ODE mdels In Petre Department f IT, Åb Aademi http://www.users.ab.fi/ipetre/cmpmd/ Cntent Stichimetric matrix Calculating the mass cnservatin relatins

More information

A new Type of Fuzzy Functions in Fuzzy Topological Spaces

A new Type of Fuzzy Functions in Fuzzy Topological Spaces IOSR Jurnal f Mathematics (IOSR-JM e-issn: 78-578, p-issn: 39-765X Vlume, Issue 5 Ver I (Sep - Oct06, PP 8-4 wwwisrjurnalsrg A new Type f Fuzzy Functins in Fuzzy Tplgical Spaces Assist Prf Dr Munir Abdul

More information

Compressibility Effects

Compressibility Effects Definitin f Cmpressibility All real substances are cmpressible t sme greater r lesser extent; that is, when yu squeeze r press n them, their density will change The amunt by which a substance can be cmpressed

More information

Part a: Writing the nodal equations and solving for v o gives the magnitude and phase response: tan ( 0.25 )

Part a: Writing the nodal equations and solving for v o gives the magnitude and phase response: tan ( 0.25 ) + - Hmewrk 0 Slutin ) In the circuit belw: a. Find the magnitude and phase respnse. b. What kind f filter is it? c. At what frequency is the respnse 0.707 if the generatr has a ltage f? d. What is the

More information

Lim f (x) e. Find the largest possible domain and its discontinuity points. Why is it discontinuous at those points (if any)?

Lim f (x) e. Find the largest possible domain and its discontinuity points. Why is it discontinuous at those points (if any)? THESE ARE SAMPLE QUESTIONS FOR EACH OF THE STUDENT LEARNING OUTCOMES (SLO) SET FOR THIS COURSE. SLO 1: Understand and use the cncept f the limit f a functin i. Use prperties f limits and ther techniques,

More information

Sections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.

Sections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic. Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage

More information

Chapter Summary. Mathematical Induction Strong Induction Recursive Definitions Structural Induction Recursive Algorithms

Chapter Summary. Mathematical Induction Strong Induction Recursive Definitions Structural Induction Recursive Algorithms Chapter 5 1 Chapter Summary Mathematical Inductin Strng Inductin Recursive Definitins Structural Inductin Recursive Algrithms Sectin 5.1 3 Sectin Summary Mathematical Inductin Examples f Prf by Mathematical

More information

Dispersion Ref Feynman Vol-I, Ch-31

Dispersion Ref Feynman Vol-I, Ch-31 Dispersin Ref Feynman Vl-I, Ch-31 n () = 1 + q N q /m 2 2 2 0 i ( b/m) We have learned that the index f refractin is nt just a simple number, but a quantity that varies with the frequency f the light.

More information

Thermodynamics and Equilibrium

Thermodynamics and Equilibrium Thermdynamics and Equilibrium Thermdynamics Thermdynamics is the study f the relatinship between heat and ther frms f energy in a chemical r physical prcess. We intrduced the thermdynamic prperty f enthalpy,

More information

ChE 471: LECTURE 4 Fall 2003

ChE 471: LECTURE 4 Fall 2003 ChE 47: LECTURE 4 Fall 003 IDEL RECTORS One f the key gals f chemical reactin engineering is t quantify the relatinship between prductin rate, reactr size, reactin kinetics and selected perating cnditins.

More information

ANSWER KEY FOR MATH 10 SAMPLE EXAMINATION. Instructions: If asked to label the axes please use real world (contextual) labels

ANSWER KEY FOR MATH 10 SAMPLE EXAMINATION. Instructions: If asked to label the axes please use real world (contextual) labels ANSWER KEY FOR MATH 10 SAMPLE EXAMINATION Instructins: If asked t label the axes please use real wrld (cntextual) labels Multiple Chice Answers: 0 questins x 1.5 = 30 Pints ttal Questin Answer Number 1

More information

Review Problems 3. Four FIR Filter Types

Review Problems 3. Four FIR Filter Types Review Prblems 3 Fur FIR Filter Types Fur types f FIR linear phase digital filters have cefficients h(n fr 0 n M. They are defined as fllws: Type I: h(n = h(m-n and M even. Type II: h(n = h(m-n and M dd.

More information

Hypothesis Tests for One Population Mean

Hypothesis Tests for One Population Mean Hypthesis Tests fr One Ppulatin Mean Chapter 9 Ala Abdelbaki Objective Objective: T estimate the value f ne ppulatin mean Inferential statistics using statistics in rder t estimate parameters We will be

More information

Math Foundations 20 Work Plan

Math Foundations 20 Work Plan Math Fundatins 20 Wrk Plan Units / Tpics 20.8 Demnstrate understanding f systems f linear inequalities in tw variables. Time Frame December 1-3 weeks 6-10 Majr Learning Indicatrs Identify situatins relevant

More information

AP Statistics Practice Test Unit Three Exploring Relationships Between Variables. Name Period Date

AP Statistics Practice Test Unit Three Exploring Relationships Between Variables. Name Period Date AP Statistics Practice Test Unit Three Explring Relatinships Between Variables Name Perid Date True r False: 1. Crrelatin and regressin require explanatry and respnse variables. 1. 2. Every least squares

More information

Kinetics of Particles. Chapter 3

Kinetics of Particles. Chapter 3 Kinetics f Particles Chapter 3 1 Kinetics f Particles It is the study f the relatins existing between the frces acting n bdy, the mass f the bdy, and the mtin f the bdy. It is the study f the relatin between

More information

Building to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems.

Building to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. Building t Transfrmatins n Crdinate Axis Grade 5: Gemetry Graph pints n the crdinate plane t slve real-wrld and mathematical prblems. 5.G.1. Use a pair f perpendicular number lines, called axes, t define

More information

COMP 551 Applied Machine Learning Lecture 11: Support Vector Machines

COMP 551 Applied Machine Learning Lecture 11: Support Vector Machines COMP 551 Applied Machine Learning Lecture 11: Supprt Vectr Machines Instructr: (jpineau@cs.mcgill.ca) Class web page: www.cs.mcgill.ca/~jpineau/cmp551 Unless therwise nted, all material psted fr this curse

More information

CONSTRUCTING STATECHART DIAGRAMS

CONSTRUCTING STATECHART DIAGRAMS CONSTRUCTING STATECHART DIAGRAMS The fllwing checklist shws the necessary steps fr cnstructing the statechart diagrams f a class. Subsequently, we will explain the individual steps further. Checklist 4.6

More information

Turing Machines. Human-aware Robotics. 2017/10/17 & 19 Chapter 3.2 & 3.3 in Sipser Ø Announcement:

Turing Machines. Human-aware Robotics. 2017/10/17 & 19 Chapter 3.2 & 3.3 in Sipser Ø Announcement: Turing Machines Human-aware Rbtics 2017/10/17 & 19 Chapter 3.2 & 3.3 in Sipser Ø Annuncement: q q q q Slides fr this lecture are here: http://www.public.asu.edu/~yzhan442/teaching/cse355/lectures/tm-ii.pdf

More information

ENSC Discrete Time Systems. Project Outline. Semester

ENSC Discrete Time Systems. Project Outline. Semester ENSC 49 - iscrete Time Systems Prject Outline Semester 006-1. Objectives The gal f the prject is t design a channel fading simulatr. Upn successful cmpletin f the prject, yu will reinfrce yur understanding

More information

CHEM Thermodynamics. Change in Gibbs Free Energy, G. Review. Gibbs Free Energy, G. Review

CHEM Thermodynamics. Change in Gibbs Free Energy, G. Review. Gibbs Free Energy, G. Review Review Accrding t the nd law f Thermdynamics, a prcess is spntaneus if S universe = S system + S surrundings > 0 Even thugh S system

More information

Weathering. Title: Chemical and Mechanical Weathering. Grade Level: Subject/Content: Earth and Space Science

Weathering. Title: Chemical and Mechanical Weathering. Grade Level: Subject/Content: Earth and Space Science Weathering Title: Chemical and Mechanical Weathering Grade Level: 9-12 Subject/Cntent: Earth and Space Science Summary f Lessn: Students will test hw chemical and mechanical weathering can affect a rck

More information

Determining the Accuracy of Modal Parameter Estimation Methods

Determining the Accuracy of Modal Parameter Estimation Methods Determining the Accuracy f Mdal Parameter Estimatin Methds by Michael Lee Ph.D., P.E. & Mar Richardsn Ph.D. Structural Measurement Systems Milpitas, CA Abstract The mst cmmn type f mdal testing system

More information

CAUSAL INFERENCE. Technical Track Session I. Phillippe Leite. The World Bank

CAUSAL INFERENCE. Technical Track Session I. Phillippe Leite. The World Bank CAUSAL INFERENCE Technical Track Sessin I Phillippe Leite The Wrld Bank These slides were develped by Christel Vermeersch and mdified by Phillippe Leite fr the purpse f this wrkshp Plicy questins are causal

More information

The steps of the engineering design process are to:

The steps of the engineering design process are to: The engineering design prcess is a series f steps that engineers fllw t cme up with a slutin t a prblem. Many times the slutin invlves designing a prduct (like a machine r cmputer cde) that meets certain

More information

Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018

Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018 Michael Faraday lived in the Lndn area frm 1791 t 1867. He was 29 years ld when Hand Oersted, in 1820, accidentally discvered that electric current creates magnetic field. Thrugh empirical bservatin and

More information

Product authorisation in case of in situ generation

Product authorisation in case of in situ generation Prduct authrisatin in case f in situ generatin Intrductin At the 74 th CA meeting (27-29 September 2017), Aqua Eurpa and ECA Cnsrtium presented their cncerns and prpsals n the management f the prduct authrisatin

More information

ENG2410 Digital Design Sequential Circuits: Part B

ENG2410 Digital Design Sequential Circuits: Part B ENG24 Digital Design Sequential Circuits: Part B Fall 27 S. Areibi Schl f Engineering University f Guelph Analysis f Sequential Circuits Earlier we learned hw t analyze cmbinatinal circuits We will extend

More information

TEST 3A AP Statistics Name: Directions: Work on these sheets. A standard normal table is attached.

TEST 3A AP Statistics Name: Directions: Work on these sheets. A standard normal table is attached. TEST 3A AP Statistics Name: Directins: Wrk n these sheets. A standard nrmal table is attached. Part 1: Multiple Chice. Circle the letter crrespnding t the best answer. 1. In a statistics curse, a linear

More information

SPH3U1 Lesson 06 Kinematics

SPH3U1 Lesson 06 Kinematics PROJECTILE MOTION LEARNING GOALS Students will: Describe the mtin f an bject thrwn at arbitrary angles thrugh the air. Describe the hrizntal and vertical mtins f a prjectile. Slve prjectile mtin prblems.

More information

, which yields. where z1. and z2

, which yields. where z1. and z2 The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin

More information

CHAPTER 2 Algebraic Expressions and Fundamental Operations

CHAPTER 2 Algebraic Expressions and Fundamental Operations CHAPTER Algebraic Expressins and Fundamental Operatins OBJECTIVES: 1. Algebraic Expressins. Terms. Degree. Gruping 5. Additin 6. Subtractin 7. Multiplicatin 8. Divisin Algebraic Expressin An algebraic

More information

LHS Mathematics Department Honors Pre-Calculus Final Exam 2002 Answers

LHS Mathematics Department Honors Pre-Calculus Final Exam 2002 Answers LHS Mathematics Department Hnrs Pre-alculus Final Eam nswers Part Shrt Prblems The table at the right gives the ppulatin f Massachusetts ver the past several decades Using an epnential mdel, predict the

More information

Preparation work for A2 Mathematics [2017]

Preparation work for A2 Mathematics [2017] Preparatin wrk fr A2 Mathematics [2017] The wrk studied in Y12 after the return frm study leave is frm the Cre 3 mdule f the A2 Mathematics curse. This wrk will nly be reviewed during Year 13, it will

More information

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents WRITING THE REPORT Organizing the reprt Mst reprts shuld be rganized in the fllwing manner. Smetime there is a valid reasn t include extra chapters in within the bdy f the reprt. 1. Title page 2. Executive

More information

Floating Point Method for Solving Transportation. Problems with Additional Constraints

Floating Point Method for Solving Transportation. Problems with Additional Constraints Internatinal Mathematical Frum, Vl. 6, 20, n. 40, 983-992 Flating Pint Methd fr Slving Transprtatin Prblems with Additinal Cnstraints P. Pandian and D. Anuradha Department f Mathematics, Schl f Advanced

More information

Technical Bulletin. Generation Interconnection Procedures. Revisions to Cluster 4, Phase 1 Study Methodology

Technical Bulletin. Generation Interconnection Procedures. Revisions to Cluster 4, Phase 1 Study Methodology Technical Bulletin Generatin Intercnnectin Prcedures Revisins t Cluster 4, Phase 1 Study Methdlgy Release Date: Octber 20, 2011 (Finalizatin f the Draft Technical Bulletin released n September 19, 2011)

More information

Kinematic transformation of mechanical behavior Neville Hogan

Kinematic transformation of mechanical behavior Neville Hogan inematic transfrmatin f mechanical behavir Neville Hgan Generalized crdinates are fundamental If we assume that a linkage may accurately be described as a cllectin f linked rigid bdies, their generalized

More information

COMP 551 Applied Machine Learning Lecture 5: Generative models for linear classification

COMP 551 Applied Machine Learning Lecture 5: Generative models for linear classification COMP 551 Applied Machine Learning Lecture 5: Generative mdels fr linear classificatin Instructr: Herke van Hf (herke.vanhf@mail.mcgill.ca) Slides mstly by: Jelle Pineau Class web page: www.cs.mcgill.ca/~hvanh2/cmp551

More information

MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b

MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b . REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but

More information

Chapter 3 Kinematics in Two Dimensions; Vectors

Chapter 3 Kinematics in Two Dimensions; Vectors Chapter 3 Kinematics in Tw Dimensins; Vectrs Vectrs and Scalars Additin f Vectrs Graphical Methds (One and Tw- Dimensin) Multiplicatin f a Vectr b a Scalar Subtractin f Vectrs Graphical Methds Adding Vectrs

More information

T Algorithmic methods for data mining. Slide set 6: dimensionality reduction

T Algorithmic methods for data mining. Slide set 6: dimensionality reduction T-61.5060 Algrithmic methds fr data mining Slide set 6: dimensinality reductin reading assignment LRU bk: 11.1 11.3 PCA tutrial in mycurses (ptinal) ptinal: An Elementary Prf f a Therem f Jhnsn and Lindenstrauss,

More information

Thermodynamics Partial Outline of Topics

Thermodynamics Partial Outline of Topics Thermdynamics Partial Outline f Tpics I. The secnd law f thermdynamics addresses the issue f spntaneity and invlves a functin called entrpy (S): If a prcess is spntaneus, then Suniverse > 0 (2 nd Law!)

More information

Interference is when two (or more) sets of waves meet and combine to produce a new pattern.

Interference is when two (or more) sets of waves meet and combine to produce a new pattern. Interference Interference is when tw (r mre) sets f waves meet and cmbine t prduce a new pattern. This pattern can vary depending n the riginal wave directin, wavelength, amplitude, etc. The tw mst extreme

More information

Physical Layer: Outline

Physical Layer: Outline 18-: Intrductin t Telecmmunicatin Netwrks Lectures : Physical Layer Peter Steenkiste Spring 01 www.cs.cmu.edu/~prs/nets-ece Physical Layer: Outline Digital Representatin f Infrmatin Characterizatin f Cmmunicatin

More information

COMP 551 Applied Machine Learning Lecture 9: Support Vector Machines (cont d)

COMP 551 Applied Machine Learning Lecture 9: Support Vector Machines (cont d) COMP 551 Applied Machine Learning Lecture 9: Supprt Vectr Machines (cnt d) Instructr: Herke van Hf (herke.vanhf@mail.mcgill.ca) Slides mstly by: Class web page: www.cs.mcgill.ca/~hvanh2/cmp551 Unless therwise

More information

Strategy and Game Theory: Practice Exercises with Answers, Errata in First Edition, Prepared on December 13 th 2016

Strategy and Game Theory: Practice Exercises with Answers, Errata in First Edition, Prepared on December 13 th 2016 Strategy and Game Thery: Practice Exercises with Answers, by Felix Munz-Garcia and Daniel Tr-Gnzalez Springer-Verlag, August 06 Errata in First Editin, Prepared n December th 06 Chapter Dminance Slvable

More information

Resampling Methods. Chapter 5. Chapter 5 1 / 52

Resampling Methods. Chapter 5. Chapter 5 1 / 52 Resampling Methds Chapter 5 Chapter 5 1 / 52 1 51 Validatin set apprach 2 52 Crss validatin 3 53 Btstrap Chapter 5 2 / 52 Abut Resampling An imprtant statistical tl Pretending the data as ppulatin and

More information

[COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t o m a k e s u r e y o u a r e r e a d y )

[COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t o m a k e s u r e y o u a r e r e a d y ) (Abut the final) [COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t m a k e s u r e y u a r e r e a d y ) The department writes the final exam s I dn't really knw what's n it and I can't very well

More information

Root locus ( )( ) The given TFs are: 1. Using Matlab: >> rlocus(g) >> Gp1=tf(1,poly([0-1 -2])) Transfer function: s^3 + 3 s^2 + 2 s

Root locus ( )( ) The given TFs are: 1. Using Matlab: >> rlocus(g) >> Gp1=tf(1,poly([0-1 -2])) Transfer function: s^3 + 3 s^2 + 2 s The given TFs are: 1 1() s = s s + 1 s + G p, () s ( )( ) >> Gp1=tf(1,ply([0-1 -])) Transfer functin: 1 ----------------- s^ + s^ + s Rt lcus G 1 = p ( s + 0.8 + j)( s + 0.8 j) >> Gp=tf(1,ply([-0.8-*i

More information

ENGI 4430 Parametric Vector Functions Page 2-01

ENGI 4430 Parametric Vector Functions Page 2-01 ENGI 4430 Parametric Vectr Functins Page -01. Parametric Vectr Functins (cntinued) Any nn-zer vectr r can be decmpsed int its magnitude r and its directin: r rrˆ, where r r 0 Tangent Vectr: dx dy dz dr

More information

A New Evaluation Measure. J. Joiner and L. Werner. The problems of evaluation and the needed criteria of evaluation

A New Evaluation Measure. J. Joiner and L. Werner. The problems of evaluation and the needed criteria of evaluation III-l III. A New Evaluatin Measure J. Jiner and L. Werner Abstract The prblems f evaluatin and the needed criteria f evaluatin measures in the SMART system f infrmatin retrieval are reviewed and discussed.

More information

Unit Project Descriptio

Unit Project Descriptio Unit Prject Descriptin: Using Newtn s Laws f Mtin and the scientific methd, create a catapult r trebuchet that will sht a marshmallw at least eight feet. After building and testing yur machine at hme,

More information

UNIT 6 DETERMINATION OF FLASH AND FIRE POINT OF A LUBRICATING OIL BY OPEN CUP AND CLOSED CUP METHODS

UNIT 6 DETERMINATION OF FLASH AND FIRE POINT OF A LUBRICATING OIL BY OPEN CUP AND CLOSED CUP METHODS UNIT 6 DETERMINATION OF FLASH AND FIRE POINT OF A LUBRICATING OIL BY OPEN CUP AND CLOSED CUP METHODS Determinatin f Flash and Fire Pint f a Cup and Clsed Cup Structure 6. Intrductin Objectives 6. Experiment

More information

If (IV) is (increased, decreased, changed), then (DV) will (increase, decrease, change) because (reason based on prior research).

If (IV) is (increased, decreased, changed), then (DV) will (increase, decrease, change) because (reason based on prior research). Science Fair Prject Set Up Instructins 1) Hypthesis Statement 2) Materials List 3) Prcedures 4) Safety Instructins 5) Data Table 1) Hw t write a HYPOTHESIS STATEMENT Use the fllwing frmat: If (IV) is (increased,

More information

x x

x x Mdeling the Dynamics f Life: Calculus and Prbability fr Life Scientists Frederick R. Adler cfrederick R. Adler, Department f Mathematics and Department f Bilgy, University f Utah, Salt Lake City, Utah

More information

Trigonometric Ratios Unit 5 Tentative TEST date

Trigonometric Ratios Unit 5 Tentative TEST date 1 U n i t 5 11U Date: Name: Trignmetric Ratis Unit 5 Tentative TEST date Big idea/learning Gals In this unit yu will extend yur knwledge f SOH CAH TOA t wrk with btuse and reflex angles. This extensin

More information

Pre-Calculus Individual Test 2017 February Regional

Pre-Calculus Individual Test 2017 February Regional The abbreviatin NOTA means Nne f the Abve answers and shuld be chsen if chices A, B, C and D are nt crrect. N calculatr is allwed n this test. Arcfunctins (such as y = Arcsin( ) ) have traditinal restricted

More information

1. What is the difference between complementary and supplementary angles?

1. What is the difference between complementary and supplementary angles? Name 1 Date Angles Intrductin t Angles Part 1 Independent Practice 1. What is the difference between cmplementary and supplementary angles? 2. Suppse m TOK = 49. Part A: What is the measure f the angle

More information

1 The limitations of Hartree Fock approximation

1 The limitations of Hartree Fock approximation Chapter: Pst-Hartree Fck Methds - I The limitatins f Hartree Fck apprximatin The n electrn single determinant Hartree Fck wave functin is the variatinal best amng all pssible n electrn single determinants

More information

Lecture 02 CSE 40547/60547 Computing at the Nanoscale

Lecture 02 CSE 40547/60547 Computing at the Nanoscale PN Junctin Ntes: Lecture 02 CSE 40547/60547 Cmputing at the Nanscale Letʼs start with a (very) shrt review f semi-cnducting materials: - N-type material: Obtained by adding impurity with 5 valence elements

More information

We can see from the graph above that the intersection is, i.e., [ ).

We can see from the graph above that the intersection is, i.e., [ ). MTH 111 Cllege Algebra Lecture Ntes July 2, 2014 Functin Arithmetic: With nt t much difficulty, we ntice that inputs f functins are numbers, and utputs f functins are numbers. S whatever we can d with

More information

AP Physics Kinematic Wrap Up

AP Physics Kinematic Wrap Up AP Physics Kinematic Wrap Up S what d yu need t knw abut this mtin in tw-dimensin stuff t get a gd scre n the ld AP Physics Test? First ff, here are the equatins that yu ll have t wrk with: v v at x x

More information

Computational modeling techniques

Computational modeling techniques Cmputatinal mdeling techniques Lecture 3: Mdeling change (2) Mdeling using prprtinality Mdeling using gemetric similarity In Petre Department f IT, Ab Akademi http://www.users.ab.fi/ipetre/cmpmd/ http://users.ab.fi/ipetre/cmpmd/

More information

Physics 212. Lecture 12. Today's Concept: Magnetic Force on moving charges. Physics 212 Lecture 12, Slide 1

Physics 212. Lecture 12. Today's Concept: Magnetic Force on moving charges. Physics 212 Lecture 12, Slide 1 Physics 1 Lecture 1 Tday's Cncept: Magnetic Frce n mving charges F qv Physics 1 Lecture 1, Slide 1 Music Wh is the Artist? A) The Meters ) The Neville rthers C) Trmbne Shrty D) Michael Franti E) Radiatrs

More information

CHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came.

CHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came. MATH 1342 Ch. 24 April 25 and 27, 2013 Page 1 f 5 CHAPTER 24: INFERENCE IN REGRESSION Chapters 4 and 5: Relatinships between tw quantitative variables. Be able t Make a graph (scatterplt) Summarize the

More information

Guide to Using the Rubric to Score the Klf4 PREBUILD Model for Science Olympiad National Competitions

Guide to Using the Rubric to Score the Klf4 PREBUILD Model for Science Olympiad National Competitions Guide t Using the Rubric t Scre the Klf4 PREBUILD Mdel fr Science Olympiad 2010-2011 Natinal Cmpetitins These instructins are t help the event supervisr and scring judges use the rubric develped by the

More information

MATCHING TECHNIQUES. Technical Track Session VI. Emanuela Galasso. The World Bank

MATCHING TECHNIQUES. Technical Track Session VI. Emanuela Galasso. The World Bank MATCHING TECHNIQUES Technical Track Sessin VI Emanuela Galass The Wrld Bank These slides were develped by Christel Vermeersch and mdified by Emanuela Galass fr the purpse f this wrkshp When can we use

More information

It is compulsory to submit the assignment before filling in the exam form.

It is compulsory to submit the assignment before filling in the exam form. OMT-101 ASSIGNMENT BOOKLET Bachelr's Preparatry Prgramme PREPARATORY COURSE IN GENERAL MATHEMATICS (This assignment is valid nly upt: 1 st December, 01 And Valid fr bth Jan 01 cycle and July 01 cycle)

More information

AP Literature and Composition. Summer Reading Packet. Instructions and Guidelines

AP Literature and Composition. Summer Reading Packet. Instructions and Guidelines AP Literature and Cmpsitin Summer Reading Packet Instructins and Guidelines Accrding t the Cllege Bard Advanced Placement prgram: "The AP English curse in Literature and Cmpsitin shuld engage students

More information

Building Consensus The Art of Getting to Yes

Building Consensus The Art of Getting to Yes Building Cnsensus The Art f Getting t Yes An interview with Michael Wilkinsn, Certified Master Facilitatr and authr f The Secrets f Facilitatin and The Secrets t Masterful Meetings Abut Michael: Mr. Wilkinsn

More information

Introduction to Models and Properties

Introduction to Models and Properties Intrductin t Mdels and Prperties Cmputer Science and Artificial Intelligence Labratry MIT Armand Slar-Lezama Nv 23, 2015 Nvember 23, 2015 1 Recap Prperties Prperties f variables Prperties at prgram pints

More information

Appendix I: Derivation of the Toy Model

Appendix I: Derivation of the Toy Model SPEA ET AL.: DYNAMICS AND THEMODYNAMICS OF MAGMA HYBIDIZATION Thermdynamic Parameters Appendix I: Derivatin f the Ty Mdel The ty mdel is based upn the thermdynamics f an isbaric twcmpnent (A and B) phase

More information

Activity Guide Loops and Random Numbers

Activity Guide Loops and Random Numbers Unit 3 Lessn 7 Name(s) Perid Date Activity Guide Lps and Randm Numbers CS Cntent Lps are a relatively straightfrward idea in prgramming - yu want a certain chunk f cde t run repeatedly - but it takes a

More information

Engineering Decisions

Engineering Decisions GSOE9 vicj@cse.unsw.edu.au www.cse.unsw.edu.au/~gs9 Outline Decision problem classes Decision problems can be classiied based on an agent s epistemic state: Decisions under certainty: the agent knows the

More information

Homology groups of disks with holes

Homology groups of disks with holes Hmlgy grups f disks with hles THEOREM. Let p 1,, p k } be a sequence f distinct pints in the interir unit disk D n where n 2, and suppse that fr all j the sets E j Int D n are clsed, pairwise disjint subdisks.

More information

Subject description processes

Subject description processes Subject representatin 6.1.2. Subject descriptin prcesses Overview Fur majr prcesses r areas f practice fr representing subjects are classificatin, subject catalging, indexing, and abstracting. The prcesses

More information

Lecture 6: Phase Space and Damped Oscillations

Lecture 6: Phase Space and Damped Oscillations Lecture 6: Phase Space and Damped Oscillatins Oscillatins in Multiple Dimensins The preius discussin was fine fr scillatin in a single dimensin In general, thugh, we want t deal with the situatin where:

More information

Equilibrium of Stress

Equilibrium of Stress Equilibrium f Stress Cnsider tw perpendicular planes passing thrugh a pint p. The stress cmpnents acting n these planes are as shwn in ig. 3.4.1a. These stresses are usuall shwn tgether acting n a small

More information