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Rutgers - 790 - 104
Ten ways to help us all makethe most of these 80 minutes1. Arrive in class on time and remain attentive andengaged until you are dismissed.2. Sit as close to the front as you can.3. Use the restroom before, not during class.4. Do not talk to your ne
Rutgers - 790 - 104
Today in Comparative Politics Culture and the Evolution of Democracy Do we need a civic culture for democracy to takehold and thrive? Is there a best religion for encouraging democraticdevelopment? Are some religions incompatible with democracy? Tr
Rutgers - 790 - 104
Today in Comparative Politics Democratic Transitions Collective Action True?How do democratic transitions occur? External imposition: external forces imposedemocracy Bottom-up transition: people rise up tooverthrow an authoritarian regime Top-dow
Rutgers - 790 - 104
Today in Comparative Politics Rutgers-Ritsumeikan program onenvironmental politics Top-down transitions Democratization as an equilibrium outcome of agame of incomplete information Democracy: What difference does it make?Top-Down TransitionsSome t
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Africa and Middle East geography quiz today Notes and booksclosed Electronic devicesoff and stowed Pencil or pen onlyon your deskToday in Comparative Politics Democracy and majority ruleVoting rules with two alternatives n individuals 2 alterna
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Today in Comparative Politics Majority rule Single peakedness Median voter theorem Chaos in multidimensional problems Non-cycling voting methodsPreference notation xRiyx is at least as good as y for voter i xPiyx is strictly preferred to y by vo
Rutgers - 790 - 104
Today in Comparative Politics Geography quiz: Eastern Europe Elections and Electoral SystemsThe growing popularity of elections Virtually every independent country in the worldhas held elections at one time or another. Only 6 countries had not held
Rutgers - 790 - 104
Today in Comparative Politics Political parties Social cleavages, electoral rules,and party systemsPolitical Parties Organizations that include Officeholders Those who help get and keep them therePurposes of political parties1. Frame the politica
Rutgers - 790 - 104
Today in Comparative Politics Institutional Veto Players Federalism Bicameral legislatures Constitutionalism Veto Player TheoryLooking aheadNot in Scott 123!Final ExamCollege Avenue Gym AnnexThursday, December 168 to 11 amVeto power under non-
Rutgers - 790 - 104
Today in Comparative Politics Parliamentary, Presidential and MixedDemocracies Two Visions of Democracy:Implications for Democratic InstitutionsLooking aheadFinal ExamCollege Avenue Gym AnnexThursday, December 16Not in Scott 123!8 to 11 amFinal
Rutgers - 790 - 104
Today in Comparative Politics Consequences of democratic politicalinstitutions: income redistribution Where to from here? Preparing for the exam Course evaluationsFinal ExamCollege Avenue Gym AnnexThursday, December 16Not in Scott 123!8 to 11 am
Rutgers - 790 - 373
1 Sets and Searching1.1 Introduction to SetsA set is a collection of objects. We say that the objects in a set are elements of the set. Or we may saythat they belong to the set or we may say that they are in the set or we may say that they aremembers
Rutgers - 790 - 373
Detecting disease outbreaksusing searchingThe mathematics of itSearch logs Google (and others, we suppose) Maintain logs of searches Break them down geographically (IPaddresses) Track the trends over time Shows what topics are hot Sports celebr
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1. Estimating Search Result Sizes using ProbabilityWe can use some basic facts about probability, and use some terms that are "likelyto be independent" to estimate the size of the Iinternet. Actually, it is not the size ofthe Internet that we will esti
Rutgers - 790 - 373
1 Practical Remarks: the problem of near duplicates orexact duplicatesWe are making some changes in the way that we ask you to evaluate systems, for yourterm paper, this Semester. These changes are intended to recognize the fact that a searchengine ma
Rutgers - 790 - 373
Note: this material was developed by Prof. Endre Boros, Director of theOperations Research Center, RUTCOR, for a guest lecture in 2008.An example for a linear programming problemDescriptionGiapettos woodcarving shop manufactures two types of wooden to
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1. Speaking MathematicsToday's class is going to begin with a very very very important digression from themainstream of learning about the mathematics of searching.As you know, from time to time we wander around the class looking over yours houlders t
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Euler CycleA cycle (path that starts and ends at the same node) which traverses each edge exactly once.Bridges of Konigsberg(http:/en.wikipedia.org/wiki/Seven_Bridges_of_Konigsberg):Sufficient and Necessary condition: all nodes have an even degreeInt
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How probability relates tosearch enginesPaul KantorWhat thesystemseesRealinformationNeedQuery: flyinglessons HawaiiThe whole webTheindexSet Retrieval processRanking processMore likelyVeryverylargeRetrievedsetLess likelyThe system ca
Rutgers - 790 - 373
ITI 1111/28/2011Lecture 4 notesMathematical InductionSummation N otationThe mathematical notation of infinite sums is often done using big sigma notation. The variable that ischanging is written beneath the sigma, usually with it s starting value. I
Rutgers - 790 - 373
Lecture Notes 1The Internet: A QuantitativeApproachITI 111sakai.rutgers.eduProf. Paul Kantorkantor@scils.rutgers.eduCharlie Filechasfile@rutgers.eduSpring 2011 We will race through these slides so thatwe can begin doing something interestingof
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1 Language modelsProbabilities also enter in the very important activity of ranking results that are retrievedby search engines. This is done using a kind of computation which has a number ofdifferent theoretical justifications but one of the most inte
Rutgers - 790 - 373
1 Latent SemanticsWe recall that we were able to express the huge matrix that relates words (terms) todocuments by introducing a matrix that relates words to concepts, and doing a matrixmultiplication.Terms x DocumentsTopics x TermsTopics x Document
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Proceedings of the 44th Hawaii International Conference on System Sciences - 2011Third Party Application Forensics on Apple Mobile DevicesAlex LevinsonRochester Institute ofTechnologyalex.levinson@mail.rit.eduBill StackpoleRochester Institute ofTe
Rutgers - 790 - 373
11.1Mathematical inductionA conjecture about Sums of odd numbersLet s recall that the i-th Odd number is given by the expression 2 i-1. So we can make a table whosecolumns are labeled by i, and show the odd nu mb ers and their sums.IOdd n umberRun
Rutgers - 790 - 373
Today we are going to move from vectors to some concepts that are very important f orsearching and other things that computers can do with texts. These things are calledstems or roots of words, and they are the first step towards having computers recogn
Rutgers - 790 - 373
Basiswalkwalkswalkedwalkingrunranrunning||1010101001010 |1 |D1|||||||D21100110#VALUE!0ab15535-23-6 15 14ba135-235 140 |0 |0 |0 |4 |0 |0 |
Rutgers - 790 - 373
The ITI 111 Term Paperand How to Ace ItSpring 2011Paul KantorKantor - Spring 20101Title PageInclude either as a separate page, or if you want to savepaper, on the top of your first page:Your Titleby Jane SmithITI 111 / Professor KantorDate2R
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1 Permutations And Combinations: Proof by InductionWe have the relation expressed by the arrows can be written mathematically as: n 1 n n k k 1 k We could also derive this formula by considering the definition of n choose k as thenumber of subsets
Rutgers - 790 - 373
PermutationsandCombinations_VFIN.docPermutations and Combinations or the Mathematics ofHugs and Kisses1. An apologyThis is a topic that I use to discuss much earlier in the course, because I had theimpression that it was very important in leading up
Rutgers - 790 - 373
Notes for class 7. ITI:111 Paul Kantor 2009W ere going to discuss three different topics today: the pigeon -hole principle, theprinciple of mathematical induction, and the concept of triangular numbers.1. The Pigeon-hole principleA pigeon-hole desk f
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Two Decks Of Cards [Revised]Full deckSpadesA2345678910JQKHeartsA2345678910JQKDiamondsA2345678910JQKClubsA2345678910JQKA2345678910JQK56789JQ789JCASTAWAY DECKSpadesHeartsDi
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ITI 111Mor Naaman, PhD and Paul KantorProbability Notes1. Probability1.1.Probability Intro and MotivationWikipedia:A way of expressing knowledge or belief that an event will occur or hasoccurredIf a fair coin is tossed, what is the probability of
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1 Added notes on conditional probability.These are further notes on conditional probability. Recall that we have in mind two decksof cards, the ordinary deck that contains 52 cards, and what we call the castaways deckwhich contains only 31 cards. When
Rutgers - 790 - 373
Section H of the Term Paper: How to compare search enginesSET THEORY METHODS1A000BC00DES20CB0GA0D00S3AG0FE00000Relevant items are marked A, B, C, D, E, F, GHow many pairs?6S1 + S2, S1 + S3, S1 + S4S2 + S3, S2+ S4S3
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ITI 1111/28/2011Lecture 4 notesSet ArithmeticReview of concepts5 +7 = 7 +53 x8 = 8 x3So we say multiplication and addition are commutative (7 + 5) + 3 = (3 + 5) + 7(7 x 2) x 3 = 7 x (2 x 3)So we say that multiplication i s associative 7 x (3 +
Rutgers - 790 - 373
1. Set TheoryThe first mathematical topic that we have to look at in order to understand how searchengines work is the topic of s ets . We need this because the first step that any searchengine does in trying to answer your question, is to identify a c
Rutgers - 790 - 373
Size of Google's indexoreorockfishPRODUCall 3wordsdividesquare root1.52E+071.13E+094.09E+087.02E+247.49E+049.38E+199.68E+09riversportteacher5.51E+081.20E+093.00E+08algebrabeehiveafghan1.98E+26364,0000.00E+005.45E+202.33E+10#DI
Rutgers - 790 - 373
Sizes of setsPaul Kantor1 Size of the Union of Two setsWe have shown that the size of the union of two sets can be expressed in terms of thesizes of the sets, and the size of the intersection of the two sets.1.1 Rigorous mathematical argumentWe did
Rutgers - 790 - 373
COS010203040506070809001.00000.98480.93970.86600.76600.64280.50000.34200.17360.000010.99980.98160.93360.85720.75470.62930.48480.32560.156420.99940.97810.92720.84800.74310.61570.46950.30900.139230.99860.97440.92
Rutgers - 790 - 373
Probabilities, Utilities and Decision Making1 Probabilities1.1 Example in this courseWe have encountered probability theory, and have seen how it takes the idea ofelementary events, counts them up, and produces measures called probability. We haveapp
Rutgers - 790 - 373
Exam 1 Review Answers1b2 a, d3d4a5 c, e6d8a9b10 a11 d12 f13 e14 b15 d16 b17 d18 i19 i20 i30 i31 i32 p33 d34 c35 e36 d37 f38 a39 f40 c41 f [the table is wrong]42 e43 d44 c45 d46 f [This equality is true, and is essential
Rutgers - 790 - 373
1 s qrt(4+16+9+36)=sqrt(65) ~ = 8.062. sqrt(0+4+1+25)=sqrt(30) ~= 5.483. 354. 35/(sqrt(65)*sqrt(30) ~ = 0.805. arccos(.8) ~ = 37 degrees6.B7. ET8. AA, AC, BA, BC, DB, DDT9. DD10. 011. C12. C13. 414. 415. 716. 1417. no18. yes19. A and D
Rutgers - 790 - 373
ITI 111 Spring 2011. Exam 2Vectors:a (2, 4, 3, 6)are as indicated, what are the values ofb (0, 2,1,5)If the vectors1. |a|a. 65 b. 6.86 c. 9 d. 4.342. |b|a. 5.39 b. 10 c. 29 d. 2.833. <a|b>a. 94 b. 16 c. - 1,440 d. 354. cos(angle between a and
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ITI 111 Spring 2011 Practice final ExamThere are 4 web pages in a small internet. Call them A,B,C,DEach has a representation using a basis of terms:PagePeoplelovehatewarABCDQ3012210412100410| P |21421320A user has entered
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ITI 111 Spring 2011 Practice final ExamThere are 4 web pages in a small internet. Call them A,B,C,DEach has a representation using a basis of terms:PagePeoplelovehatewarABCDQ30121210411210004100| P |214213202A user h
Rutgers - 790 - 373
Review for Exam 1. ITI 111. Spring 2011In questions 13, we run an experiment consisting of one tosswhose faces are labeled 1, 2, 3, and 4.of a 4-sided (tetrahedral) die,1. A possible outcome of this experiment is (select all that apply):a. 2b. cfw_2
Rutgers - 790 - 373
c/3 + d =aa/3 + c/3 = bb=c2a/3 + c/3 = da+b+c+d=10. Remove fractionsc+3d=3aa+c=3bb=c2a+c=3da+b+c+d=11. Express b in terms of cb=c2. Express a in terms of ca+c=3ba=3b- ca=3(c)- ca=2c3. Express d in terms of cc+3d=3a3d=3a- c3d=3(2c)- c
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Third Hourly Exam ITI 111 Spring 2011. I affirm that I have neither given nor received helpwhile taking this exam: Signature _Please print your name too:_ITI 111 Spring 2011 Practice final ExamThere are 4 web pages in a small internet. Call them A,B,
Rutgers - 790 - 373
Homework #2ITI 111Sets, Precision and RecallSets, Precision and RecallUnion and Intersection1. If we are given the information that |A|=200; |B|=400; and |A B|=100, what can wesay about |A B| ?a. it is less than 400 because the intersection is not
Rutgers - 790 - 373
ITI 111 Homework 8Dr. Paul KantorGraph Theory1. A Eulerian Circuit is:A. A path that crosses a bridge twice, once in each direction.B. A path that crosses all edges in a graph and returns to the original vertex where it startedwithout going over the
Rutgers - 790 - 373
ITI 111Fall 2010Homework #1SETSDue on Tuesday, September 7th at 11:30pm.NOTE: It is a good idea to print out this sheet, or keep it open in a second window, as theweb site simply gives multiple choices or True/False options, but does not repeat the
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ITI 111Dr. KantorHomework 3Homework: Exponentials and Mathematical Induction1. Suppose that each person who gets a message relays it to 5 other people, and thatthis takes 5 minutes. [Be careful: If we start at time 0 with only one personknowing, how
Rutgers - 790 - 373
ITI 111 Spring 2011Homework 10Reasoning about a rbitrary graphs1. Suppose we have 4 boxes:How many total different ways are there to put 4 beans in those 4 boxes?a. ( )b. ( )c. ( )d. ( )2. What does your answer to 1 evaluate to?a. 12870b. 35c.
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Practice exerciseGiven the vectorsa= (0,andb=( 3,2,- 1,4,- 1,2)5,6,2,- 2,- 2)You can work out these things for yourself, and then check the answers in the box belowVector a+bInner product <a|b>Length of a: |a|Length of b: |b|Cosine of
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ITI 111Dr. Paul KantorHomework 4ProbabilityIn questions 1-4, we run an experiment of tossing a fair coin twice. For notation we use,for example, HH if first and second tosses were Heads.1. The sample space for this experiment is:a. cfw_Heads, Tails
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ITI 111Homework 7Matrix Multiplication, VectorsA =||B=||C=||1. Lets say we want to find D such that AB = D. Matrix D:a.b.c.d.Is undefined since we cannot multiply A and B.Is a 2 x 3 matrixIs a 3 x 2 matrixIs a 2 x 2 matrix2. In order to
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ITI 111 Homework #5Result Set Sizes1. I do a search over my email messages for various terms and get the following results:love 1210 resultsbasketball 650 resultsorganic 250 resultsAssuming that these terms are independent, and that I have 10,000 em
Washington - CHEM 312 - CHEM 312
Helen YuzvyakFebruary 7, 2011Chemistry 410Identification and characterization of different compounds using X-Ray fluorescence spectroscopy,analyzed for element compositionAbstract:X-Ray Fluorescent Spectroscopy is a specific technique that measures
UMass (Amherst) - CEE - 240
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UMass (Amherst) - CEE - 240