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Chapter 1 Measurement What is physics? jearl walker Answer: Measurements ... and relationships among measurements. Measurements are numbers. Chapter 1 Measurement Chapter 1, #31 A vertical container with base area measuring 14.0 cm by 17.0 cm is being filled with identical pieces of candy, each with a volume of 50.00 mm3 and a mass of 0.0200 g. Assume that the volume of the empty spaces between the candies is negligible. If the height of the candies in the container increases at the rate of 0.250 cm/s, at what rate (kg/minute) does the mass of the candies in the container increase? 14.0 cm 17.0 cm 50.00 mm3 0.0200 g 0.250 cm/s at what rate (kg/minute) Chapter 1 Measurement Chapter 1, #31 A vertical container with base area measuring 14.0 cm by 17.0 cm is being filled with identical pieces of candy, each with a volume of 50.00 mm3 and a mass of 0.0200 g. Assume that the volume of the empty spaces between the candies is negligible. If the height of the candies in the container increases at the rate of 0.250 cm/s, at what rate (kg/minute) does the mass of the candies in the container increase? 14.0 cm 17.0 cm 50.00 mm3 0.0200 g 0.250 cm/s at what rate (kg/minute) 10.0 mm = 1 cm Chapter 1 Measurement Chapter 1, #31 A vertical container with base area measuring 14.0 cm by 17.0 cm is being filled with identical pieces of candy, each with a volume of 50.00 mm3 and a mass of 0.0200 g. Assume that the volume of the empty spaces between the candies is negligible. If the height of the candies in the container increases at the rate of 0.250 cm/s, at what rate (kg/minute) does the mass of the candies in the container increase? 14.0 cm 17.0 cm 50.00 mm3 0.0200 g 0.250 cm/s at what rate (kg/minute) 10.0 mm = 1 cm 1000 g = 1 kg Chapter 1 Measurement Chapter 1, #31 A vertical container with base area measuring 14.0 cm by 17.0 cm is being filled with identical pieces of candy, each with a volume of 50.00 mm3 and a mass of 0.0200 g. Assume that the volume of the empty spaces between the candies is negligible. If the height of the candies in the container increases at the rate of 0.250 cm/s, at what rate (kg/minute) does the mass of the candies in the container increase? 14.0 cm 17.0 cm 50.00 mm3 0.0200 g 0.250 cm/s at what rate (kg/minute) 10.0 mm = 1 cm 1000 g = 1 kg 60 s = 1 minute Chapter 1 Measurement Chapter 1, #31 10.0 mm = 1 cm 1000 g = 1 kg 60 s = 1 minute A vertical container with base area measuring 14.0 cm by 17.0 cm is being filled with identical pieces of candy, each with a volume of 50.00 mm3 and a mass of 0.0200 g. Assume that the volume of the empty spaces between the candies is negligible. If the height of the candies in the container increases at the rate of 0.250 cm/s, at what rate (kg/minute) does the mass of the candies in the container increase? Height of candies increases at 15.0 cm 0.250 cm cm sec 60 = 15 min sec min 17.0 cm 14.0 cm volume = 15 14 17 = 3570 cm 3 Chapter 1 Measurement Chapter 1, #31 10.0 mm = 1 cm 1000 g = 1 kg 60 s = 1 minute Each candy has volume 50.00 mm3 and mass of 0.0200 g. At what rate (kg/minute) does the mass of the candies in the container increase? Height of candies increases at 15.0 cm cm cm sec 0.250 60 = 15 min sec min volume = 15 14 17 = 3570 cm 3 10 mm 3570 cm 1 cm 3 3 17.0 cm 14.0 cm = 3, 570, 000 mm 3 0.02 g 71, 400 candies = 1428 g candy ...in one minute, or 1.428 kg/minute 3, 570, 000 mm 3 = 71, 400 candies 3 50 mm / candy Chapter 1 Measurement Chapter 2, #13 Chapter 2, #43 Chapter 2, #63 Chapter 3, #31 Chapter 1 Measurement Example of a measurement: length The Metre Convention of 1875 mandated the establishment of a permanent International Bureau of Weights and Measures to be located in S vres, France. This organisation created a new prototype bar in 1889 at the first General Conference on Weights and Measures, establishing the International Prototype Metre as the distance between two lines on a standard bar of an alloy of ninety percent platinum and ten percent iridium, measured at the melting point of ice. from Wikipedia organisation or organization metre or meter meter, or yard, or foot, or ... Length: English: International Prototype Metre bar, made of an alloy of platinum and iridium, that was the standard from 1889 to 1960. Chapter 1 Measurement 1983 Forget the metre bar in S vres! The meter is the distance light goes in 1/299,792,458 of one second One second is the time taken by 9,192,631,770 oscillations of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. Chapter 1 Measurement It is the year 1889 You visit the International Bureau of Weights and Measures in S vres You suggest that the new platinum/iridium bar be thrown out, and that the meter be, from now on, defined as the distance a car can go in one second! They object that different cars go at different speeds. You say, Oops, right. Sorry! Let s say, instead, the DISTANCE light goes in the vacuum in 1/299792458 seconds! They say: Forget it! Light goes different distances in 1/299792458 seconds, depending on the time of year! Remember, the Earth is moving at about 30 km/s around the Sun! Chapter 1 Measurement The difference in speeds is only 1/100 of 1% not much! start end start end Chapter 1 Measurement An experimental test of non local realism Anton Zeilinger NATURE 2007 April 19 Most working scientists hold fast to the concept of realism a viewpoint according to which an external reality exists independent of observation. Here we show by both theory and experiment ...... Our result suggests that giving up the concept of locality is not sufficient to be consistent with quantum experiments, unless certain intuitive features of realism are abandoned. Chapter 1 Measurement 1925: Discovery of Quantum Mechanics: According to Sir James Jeans: the stream of knowledge is heading towards a non mechanical reality; the Universe begins to look more like a great thought than like a great machine. Mind no longer appears to be an accidental intruder into the realm of matter ... we ought rather hail it as the creator and governor of the realm of matter. According to Sir Arthur Stanley Eddington: It is difficult for the matter of fact physicist to accept the view that the substratum of everything is of mental character. Chapter 1 Measurement Chapter One discusses: length, time, mass, density Conversion from one unit of mass (the atomic mass units, u) to another unit of mass (kilogram, kg): 1 u = 1.66053886 10 27 kg u and kg are independent units: we don t accurately know precisely how many amu are in one kg Chapter 1 Measurement Next, length Yard of beer at end! Conversion from one unit of length (yard) to another unit of length (meter, m): 1 yard = 0.9144 m yard and m are NOT independent units: we do know precisely how many yards are in one meter Chapter 1 Measurement OK, done mass, length, time...which leaves density. (I have no real idea why Jearl chose density!) c a b m m density = = = V a b c A grey glow on the sky: N photons cm 2 s 1sr 1 1 (In fact, once, people liked expressing I ergs cm 2 s 1sr 1 Hz 1 ) surface brightnesses as Suppose you wanted to express this, instead, in units of ergs cm 2 s 1sr 1 Hz 1 E = h ergs photon 1 c ccm s 1 = cm Hz = N photons cm s sr 2 1 1 1 hc hc 1 E = h = ergs photon = ergs photon 1 cm 10 8 hc N hc 1 ergs photon = ergs cm 2 s 1sr 1 1 10 8 10 8 So far, so good! But, the next bit is somewhat tricky! c = = c 1 d = d c 1 = c 2 d ( ) d = d c 1 = c 2 d ( ) Hz Hz c c = cm = cm cm cm If = 1 the passband width is c Hz cm N h c ergs cm 2 s 1sr 1 N h c ergs cm 2 s 1sr 1 = 8 c 10 1 10 8 Hz cm N h cm N hc 2 1 1 1 = ergs cm s sr Hz = 8 ergs cm 2 s 1sr 1 Hz 1 10 8 10 N hc = 8 ergs cm 2 s 1sr 1 Hz 1 10 h c 6.625 10 27 3 1010 1 8 = = 1.9875 10 ; 8 8 10 10 5 10 7 So! N photons cm s sr 2 1 1 1 N > ergs cm 2 s 1sr 1 Hz 1 5 10 7 If N is independent of frequency (a flat spectrum), then for constant b b b N photons cm s sr 2 1 1 d 1 = N ergs cm 2 s 1sr 1 Hz 1d 5 10 7 N N N N b b = ln = ln (b ) ln ) = ln = ln b 7 7( 7 7 5 10 5 10 5 10 5 10 ...which is a constant. There is equal energy per factor b in frequency b 1 e = 2.718.. 10 ln(b) 0 1 2.303.. In the past, people often used units I ergs cm s sr Hz 2 1 1 1 Suppose a spectrum were flat in those units. b I ergs cm s sr 2 1 1 Hz d = I = I (b ) = I (b 1) 1 b This says that for a spectrum that is flat in these units, the amount of energy per factor b in frequency increases linearly with frequency! So the spectrum looks flat, but there is really much more energy at the high frequency end, than at the low frequency end. Not a very satisfactory way to display a spectrum! Recall that N photons cm s sr 2 1 1 1 N > ergs cm 2 s 1sr 1 Hz 1 5 10 7 and that if N is independent of frequency (flat spectrum) we proved there is equal energy per factor b in frequency (which we like). N 2 1 1 1 ergs cm s sr Hz Let I = 7 5 10 Form the quantity with N constant N N 2 1 1 1 I = ( Hz ) ergs cm s sr Hz = ergs cm 2 s 1sr 1 5 10 7 5 10 7 Since N is independent of frequency, so is this. I This technique is often used (unfortunately) to display spectra. I I photons cm 2 s 1sr 1 1 All the spectra shown have equal energy per factor b in frequency Chapter 1
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Path: Canterbury >> PHYS >> 113 Spring, 2008
Description: Department of Physics and Astronomy University of Canterbury PHYS113-08S2 Homework #4, 2008 Due 15th August Attempt all questions in writing before you come to the tutorial. All problems will be discussed with your tutor in group sessions in the tuto...
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Path: Canterbury >> PHYS >> 113 Spring, 2008
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Path: Canterbury >> PHYS >> 113 Spring, 2008
Description: Department of Physics and Astronomy University of Canterbury PHYS113-08S2 Homework #2, 2008 Due 1st August Attempt all questions in writing before you come to the tutorial. All problems will be discussed with your tutor in group sessions in the tutor...
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Path: Canterbury >> PHYS >> 113 Spring, 2008
Description: Department of Physics and Astronomy University of Canterbury PHYS113-08S2 Homework #6, 2008 Due 12 September Attempt all questions in writing before you come to the tutorial. All problems will be discussed with your tutor in group sessions in the tut...
PHYS113_homework#8
Path: Canterbury >> PHYS >> 113 Spring, 2008
Description: Department of Physics and Astronomy University of Canterbury PHYS113-08S2 Homework #8, 2008 (for week of September 22-26) Attempt all questions in writing before you come to the tutorial. All problems will be discussed with your tutor in group sessio...
PHYS113_homework#7
Path: Canterbury >> PHYS >> 113 Spring, 2008
Description: Department of Physics and Astronomy University of Canterbury PHYS113-08S2 Homework #7, 2008 (for week of Sept 15-19) Attempt all questions in writing before you come to the tutorial. All problems will be discussed with your tutor in group sessions in...
PHYS113_homework#1
Path: Canterbury >> PHYS >> 113 Spring, 2008
Description: Department of Physics and Astronomy University of Canterbury PHYS113-08S2 Homework #1, 2008 Attempt all questions in writing before you come to the tutorial. All problems will be discussed with your tutor in group sessions in the tutorials. Hand in y...
HW ILR
Path: Cornell >> ILRST >> 2100 Fall, 2007
Description: Chapter 8 (SDM) Linear Regression 2) Regression Equations x 30 100 4 6 sx 4 18 0.8 1.2 y 18 60 50 18 sy 6 10 15 4 r -0.2 0.9 0.8 -0.6 = bo + b1x = 27 0.3x = 10 + 0.5x = -10 + 15x = 30- 2x a) b1 = rsy/sx = (-0.2)(6)/(4) = b1 =-0.3 = bo +...
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Path: Cornell >> ILRST >> 2100 Fall, 2007
Description: Note: Here are the question options for the Final Examination. As before, there will be five questions on the actual exam selected from a set of 10 questions circulated beforehand. 1. a. Utilizing one neighborhood planning, architecture, and transpor...
prelim 2 notes part 2
Path: Cornell >> ILRST >> 2100 Fall, 2007
Description: Probability- The proportion of the time an event would occur in a very long sequence of repetitions. Any probability is a number from zero up to one that describes the long run relative frequency of a particular outcome. A probability of zero connote...
Stats
Path: Cornell >> ILRST >> 2100 Fall, 2007
Description: Stats Chapter 18 6. 500 candies 12%= green p= 0.12 np = 500 (0.12) = 60 >10 nq = 500 (0.88) = 487 > 10 SD = pq/n = (0.12)(0.88) / (500) = 0.0167 N(0.12, 0.167) This is a not a large proportion because the proportion falls within one standard deviati...
HW Ch 19-20
Path: Cornell >> ILRST >> 2100 Fall, 2007
Description: Chapter 19 SDM Confidence Intervals for Proportions 2. Margin of Error The margin of error means that the medical researcher believes the proportion is within 3% of his estimate, with some 95% (probably) degree of confidence. 4. More Conditions a) Po...
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Path: Cornell >> ILRST >> 2100 Fall, 2007
Description: Chapter 11 (Active Stats) Randomness ACT-1 Studies of Random Behavior 1. Data was collected to estimate the proportion of the bar that was red. Red was the higher probably, being selected 58% of the time 2. After 100 trials, I was able to be reasonab...
Notes 9.9.08
Path: ASU >> MCO >> 460 Fall, 2008
Description: MCO 460 9.9.08 How do mass media affect our ideas and attitudes about race, ethnicity, gender and culture? It is maintained, and changed by media. What is mass communication? - Mass communication is a process in which information, ideas and symbols a...
Notes 9.16.08
Path: ASU >> MCO >> 460 Fall, 2008
Description: MCO 460 9.16.08 Stereotypes What is a stereotype? A schema (mind structure) that contains our knowledge, beliefs. Stereotypes are so pervasive in the media iand in our interation with others they become well learned When we encounter people form a pa...
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Path: ASU >> MCO >> 460 Fall, 2008
Description: ALL ON POWERPOINT MCO 460 9.18.08 Evolution of media stereotypes: From live stage to TV 1) historical social factors influenced media development and use of racial stereotypes 2) media AHANA stereotypes have roots in racists attitudes in society 3) n...
Notes 9.11.08
Path: ASU >> MCO >> 460 Fall, 2008
Description: MCO 460 9.11.08 Social Cognitive Theory - Focuses on how we are socialized by what we learn from media - Developed by Albert Bandura - Suggest media (TV & Movies), have the potential to impact our beliefs, attitudes and behaviors by providing models ...
Notes 9.23.08
Path: ASU >> MCO >> 460 Fall, 2008
Description: MCO 460 9.23.2008 All in the family producer Good times Norman Leer *Bill COSBY First interracial friendship show I SPY* ...
ACC 382 Chapter 3 The Accounting Equation Data
Path: ASU >> ACC >> 382 Fall, 2008
Description: The Accounting Equation Assets = Liabilities + Owners (Stockholder) Equity T Account Explanation Account Title _+_ _ Left Side | Right Side DEBIT | CREDIT | | | Rules of Debit/Credit Balance Sheet Accounts Assets = Liabilities + Capital Sto...
ACC 382 9.9.08
Path: ASU >> ACC >> 382 Fall, 2008
Description: ACC 382 ...
Exam 1 review
Path: ASU >> REA >> 380 Fall, 2008
Description: Exam #1 Review You are responsible for all assigned material in the text, the case and real estate forms and everything covered in class. There are exam questions from parts of the text not discussed in class. Syllabus Housing market overview Chapter...
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Path: ASU >> REA >> 380 Fall, 2008
Description: Public Limitations to Ownership Fee simple absolute owned completely. -Escheat -Property tax -Eminent Domain -Zoning Property Tax Rate -Assessor: all property on the tax roll Full cash value FCV (sec), bonds, special districts Limited property value...
REA 380 Exam 1 Study Guide
Path: ASU >> REA >> 380 Fall, 2008
Description: REA 380 Exam 1 Study Guide 50 questions Syllabus 2 questions Housing Market Overview - 4 questions Risky financing; subprime mortgages Reasons for price increases in 2004-2005 Housing was affordable Interest rates were low Stock market was dow...
exam questions
Path: ASU >> REA >> 380 Fall, 2008
Description: 1) A listing agreement whereby the seller reserves the right to sell the property without having to pay a commission but also allows a real estate agent to sell the property and earn a commission a _ listing? a) exclusive agency b) non-exclusive agen...
Price Theory HW5 answers
Path: SMU >> ECON >> 3301 Spring, 2008
Description: Skelton Eco 3301 Homework 5 Answers 1. A) Since capital is fixed at 10, then the short-run production function would be Q = 40L. This implies that for any level of output (Q), the number of labor teams hired will be L = Q/40. The total cost function...
Price Theory HW2 answers
Path: SMU >> ECON >> 3301 Spring, 2008
Description: Skelton Eco 3301 Homework 2 Answers 1. After the changes, you can still afford your original basket, so you must be better off after the changes. 2. No, he should not make the trade because the ratio of prices (for basketball tickets over movie tick...
Price Theory HW3
Path: SMU >> ECON >> 3301 Spring, 2008
Description: Skelton Eco 3301 Homework 3 1. The utility Martha Stewart derives from her purchase of bowls and stock tips is represented by the equation U(b,s) = b0.75s0.25, so that MUb = 0.75*b -0.25s0.25 and MUs = 0.25*s -0.75b0.75. A) What equation describes ...
Price Theory HW1
Path: SMU >> ECON >> 3301 Spring, 2008
Description: Skelton Eco 3301 Homework 1 1. If the demand curve for a good is given by the following equation: Q = 1,000 200*P And, the supply curve is given by: 300*P Calculate equilibrium price and quantity. A) Suppose an excise tax of $0.50 is placed on the ...
Price Theory HW1 answers
Path: SMU >> ECON >> 3301 Spring, 2008
Description: Skelton Eco 3301 Homework 1 Answers 1. Initial price = $2, quantity = 600 A) Supply: 300P 150; Demand: 1,000 200P; P = $2.30, posttax P = $1.80; Q = 540 B) Supply: 300P; Demand: 900 200P; P = $1.80; Q = 540 C) Supply: 300P 60; Demand: 940 200P;...
Price Theory HW4
Path: SMU >> ECON >> 3301 Spring, 2008
Description: Skelton Eco 3301 Homework 4 1. Which of the following might affect the price of a hamburger at Upton Sinclairs Jungle Bar & Grill? A) The price of meat rises. B) A new restaurant tax of $1 per hamburger is imposed. C) The restaurant is found to be i...
Price Theory HW5
Path: SMU >> ECON >> 3301 Spring, 2008
Description: Skelton Eco 3301 Homework 5 1. Assume that you manage a plant that mass produces engines by teams of workers using assembly machines. The technology is summarized by the production function Q = 4KL, where Q is the number of engines produced per week...
Price Theory HW3 answers
Path: SMU >> ECON >> 3301 Spring, 2008
Description: Skelton Eco 3301 Homework 3 Answers 1. The utility Martha Stewart derives from her purchase of bowls and stock tips is represented by the equation U(b,s) = b0.75s0.25, so that MUb = 0.75*b -0.25s0.25 and MUs = 0.25*s -0.75b0.75. A) Demand for stock...
Price Theory HW2
Path: SMU >> ECON >> 3301 Spring, 2008
Description: Skelton Eco 3301 Homework 2 1. Suppose you divide your income between cheese and other goods. Cheese costs $4 a pound and you buy 10 pounds a day. One day the price of cheese rises to $6 a pound and at the same time your income rises by $20 a day. D...
Price Theory HW4 answers
Path: SMU >> ECON >> 3301 Spring, 2008
Description: Skelton Eco 3301 Homework 4 Answers 1. A) This increases MC, so it will impact price. B) This is equivalent to part A; either one increases (marginal) production costs, so price is affected. C) This is a fixed cost, so it has no impact unless it dri...
Midterm2_CE351_WR06
Path: Cal Poly >> CE >> 351 Spring, 2008
Description: California Polytechnic State University Civil and Environmental Engineering Structural Analysis - Winter 2006 Professor Charles Chadwell CE351 Midterm 2 - Winter 2006 General Exam Notes: Attempt to do all the exam problems in the space provided. ...
Environmental law case review
Path: Cal Poly >> CRP >> 404 Spring, 2008
Description: 690 SIERRA CLUB v. WEST SIDE IRRIGATION DIST. 128 Cal.App.4th 690; 27 Cal.Rptr.3d 223 [Mar. 2005] [No. C044989. Third Dist. Mar. 22, 2005.] SIERRA CLUB, Plaintiff and Appellant, v. THE WEST SIDE IRRIGATION DISTRICT et al., Defendants and Respondent...
Important%20equations
Path: Cal Poly >> CE >> 381 Spring, 2008
Description: ...
StiffnessCoeffecients
Path: Cal Poly >> CE >> 351 Spring, 2008
Description: California Polytechnic State University Civil and Environmental Engineering Structural Analysis - Winter 2005 Professor Charles Chadwell Stiffness Coefficients 3EI - u 2 L u 3EI - u 3 L 3EI - u 3 L 4EI - u L 2EI - u L 6EI - u 2 L 3EI - u 2 L u 3E...
Final
Path: Cal Poly >> CRP >> 404 Spring, 2008
Description: Brian Fleck Page 1 Final CRP 404 10/2/2008 Part 1 Essay #2 Assuming that I am the U.S. Attorney for the Northern District of California, I would choose not to prosecute the company as a whole, and allow for private civil suits to be filed. In att...
Econ Final Review
Path: UVA >> ECON >> 421 Spring, 2007
Description: Econ Final Review Credit constraints can lead to under investment in both physical and human capital. Agricultural subsidies in the US and the EU do not reduce the incentive for LDCs to invest in manufacturing. Monopsony hiring practices may lea...
PLAP220 Midterm
Path: UVA >> PLAP >> 220 Spring, 2007
Description: Midterm Examination Question: What is classical budgeting and what happened to it? Consider incrementalism and the theories of budgeting that critiqued and followed it, taking into account actual changes in budgeting practices that reflected these th...
Stat 212 Final Review
Path: UVA >> STAT >> 212 Spring, 2007
Description: If we draw a random sample from a normal distribution population: The sample mean is not equal to the sample median The sample mean is not always equal to the population mean The sample variance is not always larger than the popul...
Study guide v.2
Path: UVA >> PLCP >> 212 Spring, 2007
Description: Theories of development, 1-16 Development means using the productive resources of society to improve the living conditions of the poorest people Differs from econ growth because pays attention to the conditions of production and social consequences E...
PLCP 212 Final Review
Path: UVA >> PLCP >> 212 Spring, 2007
Description: PLCP 212 Final Review Major themes covered: Inequalities, Gender, and Ecology The Social Structure and the Problem of Social Equality Population, Women, and Development Development and Ecology The World Economy Development or Underdevelopment...
sol1
Path: Cornell >> CS >> 482 Spring, 2008
Description: Introduction to Algorithms CS 482, Spring 2008 Solution Set 1 (1) This problem can be solved using a greedy algorithm which always attempts to place the next cell phone tower as far east as possible without leaving a house uncovered. The algorithm ...
08 - The Ford-Fulkerson algorithm for maximum flow
Path: Cornell >> CS >> 482 Spring, 2008
Description: 18 2/25/08 - The Ford-Fulkerson algorith. reminders from Fri. Flow network is G = (V, E) directed with s, t V, ce 0 e Flow is f: E -> |R+ such that f(e) ce, n(v) = fout(v) (v s, t) Value of ow is v(f) = fout(s) Cut is a partition V = A A with s...
hw4_soln
Path: Cornell >> CS >> 478 Spring, 2008
Description: CS 478 Machine Learning: Homework 4 Suggested Solutions 1 The Na Bayes Independence Assumption ve P (X = (0, 1, 1, 1, 1) | Y = +1) P (X1 = 0, X2 = 1, X3 = 1, X4 = 1, X5 = 1 | Y = +1) P (X1 = 0, X2 = 1 | Y = +1) P (X1 = 0 | Y = +1)P (X2 = 1 | Y = +...
hw5_soln
Path: Cornell >> CS >> 478 Spring, 2008
Description: CS 478 Machine Learning: Homework 5 Suggested Solutions 1 The Viterbi Algorithm is (rain, rain, snow). skiing 0.00144 0.000432 0.000288 0.00216 (a) The most likely sequence of weather running programming sunny 0.12 0.0108 0.18 0.0108 rain cloudy ...
08 - Stable Matching, part 2.
Path: Cornell >> CS >> 482 Spring, 2008
Description: 4 1/23/08 - Stable Matching, part 2. Lecture: Stable matching, part 2. Gale-Shapley Algorithm /* Init. */ All men and women are free. /* main loop */ while a free man m Assert: there exists a woman w that m hasnt proposed to. Let w be the highest-r...
hw3_soln
Path: Cornell >> CS >> 478 Spring, 2008
Description: CS 478 Machine Learning: Homework 3 Suggested Solutions 1 SVM inside-out, the Primal (15 points) (a) It is easy to check that for the soft margin SVM, w = 0, = 1 is always a feasible solution. All the constraints are satised. (b) Consider the it...
08 - The preflow-push algorithm for maximum flow
Path: Cornell >> CS >> 482 Spring, 2008
Description: 20 2/29/08 - The preow-push algorithm. The Preow-Push Algorithm Def. A preow in a ow network is a function f: E -> + s.t. (i) 0 f(e) ce (ii) v s eIn(v)f(e) - eOut(v)f(e) =: ef(v) 0 excess at v Def. A labeling is a function h: V -> 0 . It is com...
08 - The Cook-Levin Theorem
Path: Cornell >> CS >> 482 Spring, 2008
Description: 26 3/14/08 - The Cook-Levin Theorem Today: The Cook-Levin Theorem (3SAT is NP-complete) Step 1: 4SAT p 3SAT p? 2SAT (no reduction to 2SAT) <- p Given 4SAT instance (x1 x2 x3 x4) (x2 x4 x5 x6) (x1 x2 z1) (z1 x3 x4) (x2 x4 z2) (z2 x5...
08 - NP-complete sequencing problems- Hamiltonian cycle, traveling salesman problem
Path: Cornell >> CS >> 482 Spring, 2008
Description: 27 3/24/08 - NP-complete sequencing pro. NP: problems whose solution can be eficiently (poly-time) veried. Ex: Compositeness: Given n-bit number x, in x composite? Hint: a pair y,z > 1 such that yz = x. NP-Complete: a problem X which is in NP and ev...
08 - NP-complete partitioning problems- 3-dimensional matching
Path: Cornell >> CS >> 482 Spring, 2008
Description: 28 3/26/08 - NP-complete partitioning pro. Reduction from 3SAT to HAM. CYCLE Theorem. HAM CYCLE is NP-Complete Proof. (1) Its in NP. Show me the cycle, and I can verify it in O(n) time. (2) The reduction runs in poly(n) time. Let b = length of each ...
08 - NP-complete coloring problems- 3-coloring
Path: Cornell >> CS >> 482 Spring, 2008
Description: 29 3/28/08 - NP-complete coloring proble. NP-complete problems 3SAT, k-SAT (k > 3) IND. SET CLIQUE VERTEX COVER HAMILTONIAN PATH/CYCLE TRAV. SALES. PROB. Reduce FROM . TO (e.g. set cover) if you could use set cover to solve trav salesman in poly tim...
08 - Divide and conquer algorithms in computational geometry- finding the closest pair of points
Path: Cornell >> CS >> 482 Spring, 2008
Description: 11 2/8/08 - Divide and conquer algorithms. Lecture: Divide and conquer algorithms in computational geometry: nding the closest pair of points Reading: Chapter 5.4 cs482-02-08-08-Audio.mp4 Closest pair of points Given n numbers x1, x2, . , xn Find i,...
hw2_soln
Path: Cornell >> CS >> 478 Spring, 2008
Description: CS 478 Machine Learning: Homework 2 Suggested Solutions 1 Separable or Not? (a) See the following tree: (b) If we draw a large enough sample, there would be at least two points on each of the four positions. Since there is no noise in the label,...
hw1_soln
Path: Cornell >> CS >> 478 Spring, 2008
Description: CS 478 Machine Learning: Homework 1 Suggested Solutions 1 kNN Decision Boundaries (a) (b) (c) It would be classied as circle. Adding one point is enough, say a cross at exactly (1,-1). (d) It would be classied as circle. The ve closest points ar...
08 - Computing RNA secondary structure
Path: Cornell >> CS >> 482 Spring, 2008
Description: 13 2/13/08 - Computing RNA secondary str. RNA: a single-stranded molecule made up of {A, C, G, U} Secondary structure: certain base pairs on same molecule match up Constraints: (i) A pairs only with U C pairs only with G U pairs only with A G pairs ...
sol9
Path: Cornell >> CS >> 482 Spring, 2008
Description: Introduction to Algorithms CS 482, Spring 2008 Solution Set 9 (1) Let T be the number of trucks used by the algorithm, and suppose the trucks are labeled 1, 2, . . . , T in the order that the algorithm loads them up. Observe that for i = 1, 2, . . ...
08 - NP-complete numerical problems- subset sum
Path: Cornell >> CS >> 482 Spring, 2008
Description: 30 3/31/08 - NP-complete numerical probl. NP-Complete Problems 3SAT Vtx Cover Indep. Set (even in deg 3) Clique Hamiltonian Path Set cover/packing Traveling salesman 3D matching Subset Sum. 3-D Matching Given sets X, Y, Z, with n elts each. Given 3...
08 - Case Theory; distribution of PRO
Path: Cornell >> LING >> 404 Spring, 2008
Description: 4 1/23/08 - Case Theory; distribution of PRO 4 levels of structure D structure move S-structure move LF PF For next week: read rst 2 chapters Londau D-Structure and S-structure connected by move-alpha Passive: _ was arrested John Johni was arrest...
08 - Binding Theory
Path: Cornell >> LING >> 404 Spring, 2008
Description: 5 1/28/08 - Binding Theory The binding theory divides into three types of things anaphors, pronouns, R-expressions The binding theory has three conditions. A. An anaphor must be bound in its governing category. C-Command condition: *Himselfi pinche...
