Dan Jurafsky ˆ = Nc P(c) N Training count(w, c) +1 ˆ P(w| c) = count(c)+ | V | Priors: P(f)= 3 4 1 P(g)= 4 Test Doc Words Class 1 fish smoked fish f 2 fish line f 3 fish haul smoked f 4 guitar jazz line g 5 line guitar jazz jazz V = {fish, smoked, line, haul, guitar, jazz} ? Choosing a class: P(f|d5)  3/4 * 2/14 * (1/14)2 * 1/14 ≈ 0.00003 25 Conditional Probabilities: (1+1) / (8+6) = 2/14 P(line|f) = P(guitar|f) = (0+1) / (8+6) = 1/14 P(jazz|f) = (0+1) / (8+6) = 1/14 P(line|g) = (1+1) / (3+6) = 2/9 P(guitar|g) = (1+1) / (3+6) = 2/9 P(jazz|g) = (1+1) / (3+6) = 2/9 P(g|d5)  1/4 * 2/9 * (2/9)2 * 2/9 ≈ 0.0006
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Universal Turing Machines (cont.)  A Universal Turing Machine (UTM) is capable of simulating an arbitrary Turing Machine M on an arbitrary input word w.  One possible UTM is a two-tape TM that may be described as:    The UTM simulates M by locating on the program tape the appropriate transition given the current state of M and the symbol on the work tape being scanned by its head When the transition is located, the UTM carries out the operation on the work tape There is a standard UTM equivalent to this two-tape UTM w    work tape Control Unit (M)    program tape
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A Matrix Organization Functional authority Project authority President President Farm FarmMachinery Machinery Division Division Production Production department department Legal Legal department department Engineering Engineering department department Accounting Accounting department department Project Project Alpha Alpha manager manager Production Production support support group group Legal Legal support support group group Engineering Engineering support support group group Accounting Accounting support support group group Project Project Beta Beta manager manager Production Production support support group group Legal Legal support support group group Engineering Engineering support support group group Accounting Accounting support support group group Project Project Gamma Gamma manager manager Production Production support support group group Legal Legal support support group group Engineering Engineering support support group group Accounting Accounting support support group group
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Jazz Idiom Students who complete a minor in jazz idiom will develop competency in music theory, an awareness of the historical, social, and musical relevance of jazz, and will attain performance fluency in both jazz improvisation and jazz arranging. QuickTime™ and aGIF decompressorare needed
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Example 3: Buying Online Question: Suppose Charlie values 4 disposable DVDs (Gladiator, …) at $3 each, suppose it costs Blockbuster $1 to provide each DVD, and suppose Blockbuster sells DVDs for $2 each. Should Blockbuster send the first DVD to Charlie? • If the first DVD is sent, Charlie (C) faces a decision: steal the DVD and terminate the relationship; or, send $2 for the first DVD. • If the first $2 is sent, Blockbuster (B) faces a decision: take the $2 and terminate the relationship; or, send the second DVD to C. • If the second DVD is sent, C faces a decision: steal the DVD and terminate the relationship; or, send $2 for the second DVD. • If the second $2 is sent, B faces a decision: take the $2 and terminate the relationship; or, send the third DVD to C. • And so on. • If the fourth DVD is sent, C faces a decision: steal the DVD and terminate the relationship; or, send $2 for the fourth DVD. Are there mutual gains from cooperation? Can Charlie trust Blockbuster to cooperate? Can Blockbuster trust Charlie to cooperate? BA 445 Lesson B.7 Repeated Dilemmas 21
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Example 3: Buying Online Centipede Game: Should Blockbuster send the first DVD to Charlie? In the rollback solution, Charlie will steal the first DVD and terminate the relationship. So Blockbuster should not send the first DVD. There are mutual gains if, say, Charlie always pays and Blockbuster sends every DVD. But Blockbuster cannot trust Charlie to cooperate because Charlie paying for the fourth DVD is not a best response to Blockbuster sending every DVD. BA 445 Lesson B.7 Repeated Dilemmas 31
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Example 3: Buying Online Centipede Game: Should Blockbuster send the first DVD to Charlie? In the rollback solution, Charlie will steal the first DVD and terminate the relationship. So Blockbuster should not send the first DVD. There are mutual gains if, say, Charlie pays for every DVD and Blockbuster sends every DVD. But Blockbuster cannot trust Charlie to cooperate because Charlie paying for every DVD, including the last DVD, is not a best response to Blockbuster sending every DVD. BA 210 Lesson II.7 Repeated Dilemmas 27
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Fine Arts: Music • Courses Offered – – – – – – – Music Theory I & II Music Appreciation History of Jazz Music History Jazz Improvisation History of Jazz Jazz Arranging
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Choreographer Auditions • Pick dances based on the 30 second audition, teaching style, and need of the show 1. Beg/Int Contemporary 2. Beg/Int Contemporary 3. Int. Contemporary 4. Int. Contemporary 5. Int/Adv Contemporary 6. Int/Adv Contempoary 7. Advanced Contemporary 8. Advanced Contemporary 9. Beg/Int Hip Hop 10.Beg/Int Hip Hop 11.Int. Hip Hop 12.Int. Hip Hop 13.Int/Adv Hip Hop 14. Int/Adv Hip Hop 15. Advanced Hip Hop 16. Advanced Hip Hop 17. Spanish Styled 18. Irish 19. Beg/Int Tap 20. Int/Adv Tap 21. Beg/Int Jazz 22. Int. Jazz 23. Int/Adv Jazz 24. Adv Jazz 25. Kickline 26. Musical Theater
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