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Re75: Gradients and Partial Derivatives Part 6 (AIMA4e pp. 119-122)

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Can we please just place an airport?

Air date: Friday, 9th Dec. 2022, 11:00 PM Eastern/US.

We're focusing on the math and code of AIMA4e^1 right now, December 2022. This is in service of our plan to deep-dive the book from Jan.-Jun., 2023. DISCLAIMER: The below mathematics cannot be trusted; it's a student's attempt, not an expert's.

A guess for our airport^2 location (deliberately off-straight-line). ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

PIC ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Our coordinates and a set:

Fagaras cFa = (14,13) B ucharest cBu = (19,6) 1stairport locationguess x1 = (18,11) The set of cities whose C = {c ,c } closestairportisx1: x1 Fa Bu

<-This y is red because it corresponds to the single-airport version of our objective function. During the livestream I incorrectly said it should be blue.

Calculating the objective function value for our first guess state x:Toil: mundane, repetitive operational work providing no enduring value, which scales linearly with service growth. --Beyer et al. (2016) p. 23

A little inaccuracy sometimes saves tons of explanation. --H. H. Munro, quoted in Knowles (1999) p. 764:7.

our objective 3 fufoncrmtiuonla (for f(x) = f(x1,y1,x2,y2,x3,y3) = \sum \sum (xi- xc)2 + (yi- yc)2 threeairports) i=1 c(-Ci 1 oneairport f(x1) = f(x1 = 18,y1 = 11) = (xi- xc)2 + (yi- yc)2 \sumi=1 c\sum(-Ci 2ndsum unnecessary f(18,11) = \sum (xi- xc)2 + (yi- yc)2 c(-Ci plug-insetalgebra f(18,11) = (x - x)2 + (y - y)2 c\sum(-Cx 1 c 1 c 1 plug-inairportcoordinates f(18,11) = \sum (18- xc)2 + (11 - yc)2 c(-Cx1 exciptieansdalsgeumbraof f(18,11) = (18- xcFa)2 + (11 - ycFa)2 2 2 + (18 - xcBu) + (11 - ycBu) 2 2 plug-incitycoordinates f(18,11) = (18 - 14) + (11 - 13) + (18 - 19)2 + (11 - 6)2 dosubtraction f(18,11) = (4)2 + (- 2)2 + (- 1)2 + (5)2 flatten f(18,11) = (4)2+ (- 2)2 + (- 1)2+(5)2 squares f(18,11) = (16)+(4) + (1)+ (25) f(18,11) = 46

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References

Beyer, B., Jones, C., Petoff, J., & Murphy, N. (2016). Site Reliability Engineering: How Google Runs Production Systems. O'Reilly Media. ISBN: 978-1491929124. https://sre.google/sre-book/table-of-contents/ Searches: https://www.amazon.com/s?k=9781491929124 https://www.google.com/search?q=isbn+9781491929124 https://lccn.loc.gov/2017304248

Knowles, E. (Ed.) (1999). The Oxford Dictionary of Quotations. Oxford University Press, 5th ed. ISBN: 0198601735. Searches: https://www.amazon.com/s?k=0198601735 https://www.google.com/search?q=isbn+0198601735 https://lccn.loc.gov/99012096

Russell, S., & Norvig, P. (2020). Artificial Intelligence: A Modern Approach. Pearson, 4th ed. ISBN: 978-0134610993. Searches: https://www.amazon.com/s?k=978-0134610993 https://www.google.com/search?q=isbn+978-0134610993 https://lccn.loc.gov/2019047498

Footnotes

^1 Russell & Norvig (2020).

^2 Russell & Norvig (2020) p. 120.