Searching: Deterministic single-agent
|
|
|
- Delilah Peters
- 5 years ago
- Views:
Transcription
1 Sing: Dtministi singl-gnt Anw W. Moo Posso Sool o Comut Sin Cngi Mllon Univsity wm@s.mu.u ot to ot ts n uss o ts slis. Anw woul ligt i you oun tis sou mtil usul in giving you own ltus. Fl to us ts slis vtim, o to moiy tm to it you own ns. PowPoint oiginls vill. I you mk us o signiint otion o ts slis in you own ltu, ls inlu tis mssg, o t ollowing link to t sou ositoy o Anw s tutoils: tt:// Commnts n otions gtully iv. Sli Ovviw Dtministi, singl-gnt, s olms Bt Fist S Otimlity, Comltnss, Tim n S omlxity S Ts Dt Fist S Ittiv Dning Bst Fist Gy S Sli
2 A s olm How o w gt om S to G? An wt s t smllst ossil num o tnsitions? Sli Fomlizing s olm A s olm s iv omonnts: Q, S, G, sus, ost Q is init st o stts. S Q is non-mty st o stt stts. G Q is non-mty st o gol stts. sus : Q P(Q) is untion wi tks stt s inut n tuns st o stts s outut. sus(s) mns t st o stts you n om s in on st. ost : Q, Q Positiv um is untion wi tks two stts, s n s, s inut. It tuns t on-st ost o tvling om s to s. T ost untion is only in wn s is susso stt o s. Sli
3 Ou S Polm Q = {,,,,,,,,,,, } S = { } G = { } sus() = { } sus() = {, } sus() = ULL t. ost(s,s ) = o ll tnsitions Sli Ou S Polm Q = {,,,,,,,,,,, } S = { } G = { } sus() = { } sus() = {, } sus() = ULL t. ost(s,s ) = o ll tnsitions Wy o w? Wt olms lik tis? Sli 6
4 S Polms Sli 7 Mo S Polms Suling 8-Quns Wt nxt? Sli 8
5 Mo S Polms But t lnty o tings wi w nomlly ll s olms tt on t it ou Suling igi inition A s olm s iv omonnts: Q, S, G, sus, ost 8-Quns Q is init st o stts. S Q is non-mty st o stt stts. G Q is non-mty st o gol stts. sus : Q P(Q) is untion wi tks stt s inut n tuns st o stts s outut. sus(s) mns t st o stts you n om s in on st. ost : Q, Q Positiv um is untion wi tks two stts, s n s, s inut. It tuns t on-st ost o tvling om Wt snxt? to s. T ost untion is only in wn s is susso stt o s. Cn you tink o xmls? Sli Ou inition xlus Sli 0
6 Gm ginst vsy Ou inition xlus Cn Hin Stt Continuum (ininit num) o stts All o t ov, lus istiut tm ontol Sli Bt Fist S Ll ll stts tt l om S in st ut n t l in lss tn st. Tn ll ll stts tt l om S in sts ut n t l in lss tn sts. Tn ll ll stts tt l om S in sts ut n t l in lss tn sts. Et until Gol stt. Sli 6
7 Bt-ist S 0 sts om stt Sli st om stt Bt-ist S 0 sts om stt Sli 7
8 st om stt Bt-ist S 0 sts om stt sts om stt Sli st om stt Bt-ist S 0 sts om stt sts om stt sts om stt Sli 6 8
9 st om stt Bt-ist S sts om stt 0 sts om stt sts om stt sts om stt Sli 7 Rmm t t! Also, wn you ll stt, o t sso stt. Tis o is ll koint. T istoy o ssos is us to gnt t solution t, on you v oun t gol: I v got to t gol. I s I ws t o tis. An I ws t o I ws t. An I ws. so solution t is S G Sli 8
10 st om stt Bkoints sts om stt 0 sts om stt sts om stt sts om stt Sli st om stt Bkoints sts om stt 0 sts om stt sts om stt sts om stt Sli 0 0
11 Stting Bt Fist S Fo ny stt s tt w v ll, w ll mm: vious(s) s t vious stt on sotst t om stt to s. On t kt ittion o t lgoitm w ll gin wit V k in s t st o tos stts o wi t sotst t om t stt osts xtly k sts Tn, uing tt ittion, w ll omut V k+, in s t st o tos stts o wi t sotst t om t stt osts xtly k+ sts W gin wit k = 0, V 0 = {} n w ll in, vious() = ULL Tn w ll in tings on st om t into V. An w ll k going. Sli V 0 Sli
12 V 0 V Sli V 0 V V Sli
13 V V 0 V V Sli V V V 0 V V Sli 6
14 Bt Fist S V 0 := S (t st o stt stts) vious() := IL k := 0 wil (no gol stt is in V k n V k is not mty) o V k+ := mty st Fo stt s in V k Fo stt s in sus(s) I s s not ly n ll St vious(s ) := s A s into V k+ k := k+ I V k is mty signl FAILURE Els uil t solution t tus: Lt S i t it stt in t sotst t. Din S k =, n oll i <= k, in S i- = vious(s i ). Sli 7 V V 0 Suos you s s onvnintly llow you to otin ssos(stt). Cn you tink o int wy to o? An woul you l to voi stoing somting tt w viously to sto? V V V Sli 8
15 Anot wy: Wok k Ll ll stts tt n G in st ut n t it in lss tn st. Ll ll stts tt n G in sts ut n t it in lss tn sts. Et. until stt is. num o sts to gol lls tmin t sotst t. Don t n xt ookking ino. Sli Bt Fist Dtils It is in o t to mo tn on gol stt. It is in o t to mo tn on stt stt. Tis lgoitm woks ows om t stt. Any lgoitm wi woks ows om t stt is si to ow ining. ou n lso wok kws om t gol. Tis lgoitm is vy simil to Dijkst s lgoitm. Any lgoitm wi woks kws om t gol is si to kw ining. Bkw vsus ow. Wi is tt? Sli 0
16 Costs on tnsitions 8 oti tt ins t sotst t in tms o num o tnsitions. It os not in t lst-ost t. W will uikly viw n lgoitm wi os in t lst-ost t. On t kt ittion, o ny stt S, wit g(s) s t lst-ost t to S in k o w sts. Sli Lst Cost Bt Fist V k = t st o stts wi n in xtly k sts, n o wi t lstost k-st t is lss ost tn ny t o lngt lss tn k. In ot wos, V k = t st o stts wos vlus ng on t vious ittion. V 0 := S (t st o stt stts) vious() := IL g() = 0 k := 0 wil (V k is not mty) o V k+ := mty st Fo stt s in V k Fo stt s in sus(s) I s s not ly n ll OR i g(s) + Cost(s,s ) < g(s ) St vious(s ) := s St g(s ) := g(s) + Cost(s,s ) A s into V k+ k := k+ I not ll, xit signling FAILURE Els uil t solution t tus: Lt S k t kt stt in t sotst t. Din S k =, n oll i <= k, in S i- = vious(s i ). Sli 6
17 Uniom-Cost S A ontully siml o wn t osts on tnsitions It uss ioity uus Sli Pioity Quu Rs A ioity uu is t stutu in wi you n inst n tiv (ting, vlu) is wit t ollowing otions: Init-PiQuu(PQ) Inst-PiQuu(PQ, ting, vlu) Po-lst(PQ) initilizs t PQ to mty. insts (ting, vlu) into t uu. tuns t (ting, vlu) i wit t lowst vlu, n movs it om t uu. Sli 7
18 Pioity Quu Rs A ioity uu is t stutu in wi you n inst n tiv (ting, vlu) is wit t ollowing otions: Fo mo tils, s Knut o Sgwik o silly ny ook wit t wo lgoitms ominntly ing in t titl. Init-PiQuu(PQ) Inst-PiQuu(PQ, ting, vlu) Po-lst(PQ) initilizs t PQ to mty. insts (ting, vlu) into t uu. tuns t (ting, vlu) i wit t lowst vlu, n movs it om t uu. Pioity Quus n imlmnt in su wy tt t ost o t inst n o otions O(log(num o tings in ioity uu)) Vy (toug not solutly, inily!) Sli Uniom-Cost S A ontully siml o wn t osts on tnsitions It uss ioity uu PQ = St o stts tt v n xn o witing xnsion Pioity o stt s = g(s) = ost o gtting to s using t imli y koints. Sli 6 8
19 Stting UCS 8 PQ = { (S,0) } Sli 7 UCS Ittions PQ = { (S,0) } 8 Ittion:. Po lst-ost stt om PQ. A sussos Sli 8
20 UCS Ittions 8 PQ = { (,), (,), (,) } Ittion:. Po lst-ost stt om PQ. A sussos Sli UCS Ittions PQ = { (,), (,), (,6) } 8 Ittion:. Po lst-ost stt om PQ. A sussos Sli 0 0
21 UCS Ittions 8 PQ = { (,), (,), (,), (,6) } Ittion:. Po lst-ost stt om PQ. A sussos Sli UCS Ittions PQ = { (,), (,), (,), (,6) } 8 ot wt n : liz tt gtting to vi ws tt tn t viously st-known wy to gt to Ittion:. Po lst-ost stt om PQ. A sussos Sli n so s ioity ws ng
22 UCS Ittions 8 PQ = { (,), (,6), (,), (,6) } Ittion:. Po lst-ost stt om PQ. A sussos Sli UCS Ittions PQ = { (,6),(,6),(,),(,),(,6) } 8 Ittion:. Po lst-ost stt om PQ. A sussos Sli
23 UCS Ittions 8 PQ = { (,6),(,),(,),(,6) } Ittion:. Po lst-ost stt om PQ. A sussos Sli UCS Ittions PQ = { (,0), (,),(,) } 8 Ittion:. Po lst-ost stt om PQ. A sussos Sli 6
24 UCS Ittions ot wt n : oun nw wy to gt to PQ = { (,0), (,),(,) } ut it ws mo ostly tn t st known wy n so s ioity ws unng 8 Ittion:. Po lst-ost stt om PQ. A sussos Sli 7 UCS Ittions PQ = { (,),(,) } 8 Ittion:. Po lst-ost stt om PQ. A sussos Sli 8
25 UCS Ittions PQ = { (,) } 8 Ittion:. Po lst-ost stt om PQ. A sussos Sli UCS Ittions PQ = { (,8) } 8 Ittion:. Po lst-ost stt om PQ. A sussos Sli 0
26 UCS Ittions PQ = { (G,) } 8 Ittion:. Po lst-ost stt om PQ. A sussos Sli UCS Ittions Qustion: Is tmint s soon s you isov t gol t igt stoing ition? PQ = { (G,) } 8 Ittion:. Po lst-ost stt om PQ. A sussos Sli 6
27 UCS tmints PQ = { } 8 Tmint only on t gol is o om t ioity uu. Els w my miss sot t. Ittion:. Po lst-ost stt om PQ. A sussos Sli Juging s lgoitm Comltnss: is t lgoitm gunt to in solution i solution xists? Gunt to in otiml? (will it in t lst ost t?) Algoitmi tim omlxity S omlxity (mmoy us) Vils: B L num o stts in t olm t vg ning to (t vg num o sussos) (B>) t lngt o t t om stt to gol wit t sotst num o sts How woul w jug ou lgoitms? Sli 7
28 Juging s lgoitm B L Q num o stts in t olm t vg ning to (t vg num o sussos) (B>) t lngt o t t om stt to gol wit t sotst num o sts t vg siz o t ioity uu Algoitm LC Lst Cost UCS Bt Fist S Uniom Cost S Com Otiml Tim lt i ll tnsitions sm ost O(log(Q) * min(,b L )) S Sli Juging s lgoitm B L Q num o stts in t olm t vg ning to (t vg num o sussos) (B>) t lngt o t t om stt to gol wit t sotst num o sts t vg siz o t ioity uu Algoitm UCS Bt Fist S LC Lst Cost Uniom Cost S Com Otiml Tim lt i ll tnsitions sm ost O(log(Q) * min(,b L )) S Sli 6 8
29 S T Rsnttion Wt o o w go toug t s t wit? Sli 7 Dt Fist S 8 An ltntiv to. Alwys xn om t mostntly-xn no, i it s ny unti sussos. Els ku to t vious no on t unt t. Sli 8
30 DFS in tion Sli DFS S t tvsl Cn you w in t o in wi t s-t nos visit? Sli 60 0
31 DFS Algoitm W us t stutu w ll ll Pt to snt t,, t om t to t unt stt. E.G. Pt P = <,,, > Along wit no on t t, w must mm wi sussos w still v vill to xn. E.G. t t ollowing oint, w ll v P = < (xn=, ), (xn = ULL), (xn = ), (xn = ) > Sli 6 DFS Algoitm Lt P = < (xn = sus())> Wil (P not mty n to(p) not gol) i xn o to(p) is mty tn mov to(p) ( o t stk ) ls lt s mm o xn o to(p) mov s om xn o to(p) mk nw itm on t to o t P: s (xn = sus(s)) I P is mty tun FAILURE Els tun t t onsisting o stts in P Tis lgoitm n wittn ntly wit usion, i.. using t ogm stk to imlmnt P. Sli 6
32 Juging s lgoitm B L Q num o stts in t olm t vg ning to (t vg num o sussos) (B>) t lngt o t t om stt to gol wit t sotst num o sts t vg siz o t ioity uu Algoitm UCS DFS Bt Fist S LC Lst Cost Uniom Cost S Dt Fist S Com Otiml Tim lt i ll tnsitions sm ost O(log(Q) * min(,b L )) /A S /A Sli 6 Juging s lgoitm B L Q num o stts in t olm t vg ning to (t vg num o sussos) (B>) t lngt o t t om stt to gol wit t sotst num o sts t vg siz o t ioity uu Algoitm UCS DFS Bt Fist S LC Lst Cost Uniom Cost S Dt Fist S Com Otiml Tim lt i ll tnsitions sm ost O(log(Q) * min(,b L )) /A S /A Sli 6
33 Juging s lgoitm B L LMAX Q num o stts in t olm t vg ning to (t vg num o sussos) (B>) t lngt o t t om stt to gol wit t sotst num o sts Lngt o longst t om stt to nyw t vg siz o t ioity uu Algoitm UCS DFS** Bt Fist S LC Lst Cost Uniom Cost S Dt Fist S Com Otiml Tim lt i ll tnsitions sm ost Assuming Ayli S S O(log(Q) * min(,b L )) O(B LMAX ) S O(LMAX) Sli 6 Juging s lgoitm B L LMAX Q num o stts in t olm t vg ning to (t vg num o sussos) (B>) t lngt o t t om stt to gol wit t sotst num o sts Lngt o longst t om stt to nyw t vg siz o t ioity uu Algoitm UCS DFS** Bt Fist S LC Lst Cost Uniom Cost S Dt Fist S Com Otiml Tim lt i ll tnsitions sm ost Assuming Ayli S S O(log(Q) * min(,b L )) O(B LMAX ) S O(LMAX) Sli 66
34 Qustions to on How woul you vnt DFS om looing? How oul you o it to giv n otiml solution? Sli 67 Qustions to on How woul you vnt DFS om looing? How oul you o it to giv n otiml solution? Answ : PC-DFS (Pt Cking DFS): Don t us on stt i tt stt is ly in t unt t Answ : MEMDFS (Mmoizing DFS): Rmm ll stts xn so. v xn nyting twi. Sli 68
35 Qustions to on How woul you vnt DFS om looing? How oul you o it to giv n otiml solution? Answ : PC-DFS (Pt Cking DFS): Don t us on stt i tt stt is ly in t unt t Answ : MEMDFS (Mmoizing DFS): Rmm ll stts xn so. v xn nyting twi. Sli 6 Qustions to on How woul you vnt DFS om looing? A t osions wn PCDFS is tt tn MEMDFS? How oul you o it to giv n otiml solution? A t osions wn MEMDFS is tt tn PCDFS? Answ : PC-DFS (Pt Cking DFS): Don t us on stt i tt stt is ly in t unt t Answ : MEMDFS (Mmoizing DFS): Rmm ll stts xn so. v xn nyting twi. Sli 70
36 Juging s lgoitm B L LMAX Q num o stts in t olm t vg ning to (t vg num o sussos) (B>) t lngt o t t om stt to gol wit t sotst num o sts Lngt o longst yl- t om stt to nyw t vg siz o t ioity uu Algoitm UCS Bt Fist S LC Lst Cost Uniom Cost S PCDFS Pt Ck DFS MEMDFS Mmoizing DFS Com Otiml Tim lt i ll tnsitions sm ost O(log(Q) * min(,b L )) O(B LMAX ) O(min(,B LMAX )) S O(LMAX) O(min(,B LMAX )) Sli 7 Juging s lgoitm B L LMAX Q num o stts in t olm t vg ning to (t vg num o sussos) (B>) t lngt o t t om stt to gol wit t sotst num o sts Lngt o longst yl- t om stt to nyw t vg siz o t ioity uu Algoitm UCS Bt Fist S LC Lst Cost Uniom Cost S PCDFS Pt Ck DFS MEMDFS Mmoizing DFS Com Otiml Tim lt i ll tnsitions sm ost O(log(Q) * min(,b L )) O(B LMAX ) O(min(,B LMAX )) S O(LMAX) O(min(,B LMAX )) Sli 7 6
37 Juging s lgoitm B L LMAX Q num o stts in t olm t vg ning to (t vg num o sussos) (B>) t lngt o t t om stt to gol wit t sotst num o sts Lngt o longst yl- t om stt to nyw t vg siz o t ioity uu Algoitm UCS Bt Fist S LC Lst Cost Uniom Cost S PCDFS Pt Ck DFS MEMDFS Mmoizing DFS Com Otiml Tim lt i ll tnsitions sm ost O(log(Q) * min(,b L )) O(B LMAX ) O(min(,B LMAX )) S O(LMAX) O(min(,B LMAX )) Sli 7 Mz xml Imgin stts lls in mz, you n mov, E, S, W. Wt woul lin DFS o, ssuming it lwys xn t E susso ist, tn, tn W, tn S? G Exnsion o E,, W, S S Ot ustions: Wt woul o? Wt woul PCDFS o? Wt woul MEMDFS o? Sli 7 7
38 Two ot DFS xmls G O:, E, S, W? S G O:, E, S, W wit loos vnt S Sli 7 Fow DFS o Bkw DFS I you v ssos() untion s wll s sussos() untion you n gin t t gol n t-ist-s kws until you it stt. Wy/Wn migt tis goo i? Sli 76 8
39 Invnt An Algoitm Tim! H s wy to mtilly s osts somtims. Biitionl S. Cn you guss wt tis lgoitm is, n wy it n ug ost-sv? Sli 77 B L LMAX Q num o stts in t olm t vg ning to (t vg num o sussos) (B>) t lngt o t t om stt to gol wit t sotst num o sts Lngt o longst yl- t om stt to nyw t vg siz o t ioity uu Algoitm UCS MEMDFS Mmoizing DFS BI Bt Fist S LC Lst Cost Uniom Cost S PCDFS Pt Ck DFS Biition BF S Com Otiml Tim lt i ll tnsitions sm ost O(log(Q) * min(,b L )) O(B LMAX ) O(min(,B LMAX )) O(min(,B L/ )) S O(LMAX) O(min(,B LMAX )) O(min(,B L/ )) Sli 78
40 B L LMAX Q num o stts in t olm t vg ning to (t vg num o sussos) (B>) t lngt o t t om stt to gol wit t sotst num o sts Lngt o longst yl- t om stt to nyw t vg siz o t ioity uu Algoitm UCS Bt Fist S LC Lst Cost Uniom Cost S PCDFS Pt Ck DFS MEMDFS Mmoizing DFS BI Biition BF S Com Otiml Tim lt i ll tnsitions sm ost All tns sm ost O(log(Q) * min(,b L )) O(B LMAX ) O(min(,B LMAX )) O(min(,B L/ )) S O(LMAX) O(min(,B LMAX )) O(min(,B L/ )) Sli 7 Ittiv Dning Ittiv ning is siml lgoitm wi uss DFS s suoutin:. Do DFS wi only ss o ts o lngt o lss. (DFS givs u ny t o lngt ). I il, o DFS wi only ss ts o lngt o lss.. I il, o DFS wi only ss ts o lngt o lss..n so on until suss Cost is O( L ) = O( L ) Cn mu tt tn gul DFS. But ost n mu gt tn t num o stts. Sli 80 0
41 Mz xml Imgin stts lls in mz, you n mov, E, S, W. Wt woul Ittiv Dning o, ssuming it lwys xn t E susso ist, tn, tn W, tn S? G S Exnsion o E,, W, S Sli 8 B L LMAX Q num o stts in t olm t vg ning to (t vg num o sussos) (B>) t lngt o t t om stt to gol wit t sotst num o sts Lngt o longst yl- t om stt to nyw t vg siz o t ioity uu Algoitm UCS Bt Fist S LC Lst Cost Uniom Cost S PCDFS Pt Ck DFS MEMDFS Mmoizing DFS BI Biition BF S Ittiv ID Dning Com Otiml Tim lt i ll tnsitions sm ost All tns sm ost i ll tnsitions sm ost O(log(Q) * min(,b L )) O(B LMAX ) O(min(,B LMAX )) O(min(,B L/ )) O(B L ) S O(LMAX) O(min(,B LMAX )) O(min(,B L/ )) O(L) Sli 8
42 B L LMAX Q num o stts in t olm t vg ning to (t vg num o sussos) (B>) t lngt o t t om stt to gol wit t sotst num o sts Lngt o longst yl- t om stt to nyw t vg siz o t ioity uu Algoitm UCS Bt Fist S LC Lst Cost Uniom Cost S PCDFS Pt Ck DFS MEMDFS Mmoizing DFS BI Biition BF S Ittiv ID Dning Com Otiml Tim lt i ll tnsitions sm ost All tns sm ost i ll tnsitions sm ost O(log(Q) * min(,b L )) O(B LMAX ) O(min(,B LMAX )) O(min(,B L/ )) O(B L ) S O(LMAX) O(min(,B LMAX )) O(min(,B L/ )) O(L) Sli 8 Bst Fist Gy S s uisti. A uisti untion ms stt onto n stimt o t ost to t gol om tt stt. Cn you tink o xmls o uistis? E.G. o t 8-uzzl? E.G. o lnning t toug mz? Dnot t uisti y untion (s) om stts to ost vlu. Sli 8
43 Huisti S Suos in ition to t stn s siition w lso v uisti. A uisti untion ms stt onto n stimt o t ost to t gol om tt stt. Cn you tink o xmls o uistis? E.G. o t 8-uzzl? E.G. o lnning t toug mz? Dnot t uisti y untion (s) om stts to ost vlu. Sli 8 Euliin Huisti = = =8 8 = = =8 = =6 = =0 = =6 Sli 86
44 Euliin Huisti = = =8 =8 8 = = Anot ioity uu lgoitm. But tis tim, ioity is t uisti vlu. = = =6 =6 =0 = Sli 87 Bst Fist Gy S Init-PiQuu(PQ) Inst-PiQuu(PQ,,()) wil (PQ is not mty n PQ os not ontin gol stt) (s, ) := Po-lst(PQ) o s in sus(s) i s is not ly in PQ n s nv viously n visit Inst-PiQuu(PQ,s,(s )) Algoitm BstFS Bst Fist S Com Otiml Tim lt O(min(,B LMAX )) S O(min(,B LMAX )) A w imovmnts to tis lgoitm n mk tings mu tt. It s littl ting w lik to ll: A*. to ontinu! Sli 88
45 Wt you soul know Tooug unstning o, LC, UCS. PCDFS, MEMDFS Unstn t onts o wt s is omlt, otiml, its tim n s omlxity Unstn t is in ittiv ning n iitionl s B l to isuss t oktil tis t os n ons o t ov ss Sli 8
A search problem. Formalizing a search problem. Our Search Problem. Our Search Problem. Overview
Sing: Dtministi singl-gnt Atully, tis is otimiztion ov tim wit ist vils Anw W. Moo Posso Sool o Comut Sin Cngi Mllon Univsity www.s.mu.u/~wm wm@s.mu.u -6-7 ot to ot ts n uss o ts slis. Anw woul ligt i
CS 188: Artificial Intelligence Fall Announcements
C 188: Atiiil Intllign Fll 007 Ltu : Quu-Bs 8/31/007 Dn Klin UC Bkly Mny slis om it tut Russll o Anw Moo Announmnts Nxt wk Nw oom is 105 Not Gt, stts Tusy Ck w g o stions (nw oming) L Fiy 10m to 5m in
CS 188: Artificial Intelligence Spring Announcements
C 188: Atiiil Intllign ing 2006 Ltu 2: Quu-Bs 8/31/2006 Dn Klin UC Bkly Mny slis om it tut Russll o Anw Moo Announmnts L Fiy 1-5m in o 275 Ln Pyton tt on Pojt 1.1: Mzwol Com o wtv tims you lik No stions
Announcements. CS 188: Artificial Intelligence Fall Today. Reflex Agents. Goal Based Agents. Search Problems
C 88: Atiiil Intllign Fll 009 Ltu : Quu-Bs 9//009 Dn Klin UC Bkly Multil slis om tut Russll, Anw Moo Announmnts Pojt 0: Pyton Tutoil Du tomoow! T is l tomoow om m-3m in o 75 T l tim is otionl, ut P0 itsl
CS 188: Artificial Intelligence Fall Announcements
C 188: Atiiil Intllign Fll 2009 Ltu 2: Quu-Bs 9/1/2009 Dn Klin UC Bkly Multil slis om tut Russll, Anw Moo Announmnts Pojt 0: Pyton Tutoil Du tomoow! T is l tomoow om 1m-3m in o 275 T l tim is otionl, ut
Announcements. CS 188: Artificial Intelligence Spring More Announcements. Today. From Last Time: Reflex Agents.
C 88: Atiiil Intllign ing 009 Ltu : Quu-Bs //008 Jon DNo UC Bkly Mny slis om Dn Klin, tut Russll o Anw Moo Announmnts Pojt 0: Pyton Tutoil Post onlin now Du nxt Wnsy, Jn 8 T is l toy om m-3m in o 75 T
Announcements. CS 188: Artificial Intelligence Fall Reflex Agents. Today. Goal Based Agents. Search Problems
Announmnts Pojt 0: Pyton Tutoil Du tomoow! T is l Wnsy om 3m-5m in o 75 T l tim is otionl, ut P0 itsl is not On sumit, you soul gt mil om t utog Pojt : On t w toy tt ly n sk ustions. It s long tn most!
CS 188: Artificial Intelligence Spring 2009
C 188: Atiiil Intllign ing 009 Ltu : Quu-Bs 1//008 Jon DNo UC Bkly Mny slis om Dn Klin, tut Russll o Anw Moo Announmnts Pojt 0: Pyton Tutoil Post onlin now Du nxt Wnsy, Jn 8 T is l toy om 1m-3m in o 75
Outline. CSE 473: Artificial Intelligence Spring Types of Agents
9/9/7 CE 7: Atiiil Intllign ing 07 Polms Outlin Polm s & Dit Fox Uninom Mtos Dt-Fist Bt-Fist Uniom-Cost Wit slis om Dn Wl, Pit Al, Dn Klin, tut Russll, Anw Moo, Luk Zttlmoy Agnt vs. Envionmnt Tys o Agnts
CS 188: Artificial Intelligence Fall 2011
Announmnts Pojt 0: Pyton Tutoil Du tomoow! T is l Wnsy om 3m-5m in o 275 T l tim is otionl, ut P0 itsl is not On sumit, you soul gt mil om t utog Pojt 1: On t w toy tt ly n sk ustions. It s long tn most!
CS 188: Artificial Intelligence Spring Announcements
CS 188: Atiiil Intllign Sing 2011 Ltu 2: Quu-Bs S 1/24/2010 Pit Al UC Bkly Mny slis om Dn Klin Announmnts Pojt 0: Pyton Tutoil Du Fiy 5m. L sssion Wnsy 3-5m in 271 So T l tim is otionl, ut P0 itsl is not
CS 188: Artificial Intelligence Spring Announcements
C 188: Atiiil Intllign ing 2010 Ltu 2: Quu-Bs 1/21/2010 Pit Al UC Bkly Mny slis om Dn Klin Announmnts Pojt 0: Pyton Tutoil Out toy. Du nxt wk Tusy. L sssions in 271 o: Mony 2-3m Wnsy 4-5m T l tim is otionl,
Today. CS 232: Ar)ficial Intelligence. Search. Agents that Plan. September 3 rd, 2015 Search Problems. Uninformed Search Methods
1 C 232: A)iil Intllign Toy tm 3, 2015 Agnts tt Pln A Polms Uninom Mtos Dt- Fist Bt- Fist Uniom- Cost [Ts slis w t y Dn Klin n Pit Al o C188 Into to AI t UC Bkly. All C188 mtils vill t M://i.kly.u.] Agnts
CS 188: Artificial Intelligence
C 188: Atiiil Intllign Toy Agnts tt Pln A Polms Instuto: Mo Alvz Univsity o Ro Isln (Ts slis w t/moii y Dn Klin, Pit Al, An Dgn o C188 t UC Bkly) Uninom Mtos Dt-Fist Bt-Fist Uniom-Cost Agnts tt Pln Rlx
Reminder. CS 188: Artificial Intelligence. A reflex agent for pacman. Reflex Agent. A reflex agent for pacman (3) A reflex agent for pacman (2)
C 88: Atiiil Intllign Ltus n : Rmin Only vy smll tion o AI is out mking omuts ly gms intlligntly Rll: omut vision, ntul lngug, ootis, min lning, omuttionl iology, t. Pit Al UC Bkly Mny slis om Dn Klin
CSE 573: Artificial Intelligence Autumn Search thru a. Goal Based Agents 9/28/2012. Agent vs. Environment. Example: N Queens
CE 573: Atiiil Intllign Autumn 0 Intoution & Dn Wl Wit slis om Dn Klin, tut Russll, Anw Moo, Luk Zttlmoy Agnt vs. Envionmnt An gnt is n ntity tt ivs n ts. A tionl gnt slts tions tt mximiz its utility untion.
Announcements. CS 188: Artificial Intelligence Fall Office hours, Section. Today. DFS and BFS. Recap: Search. Lecture 3: A* Search 9/3/2009
C 88: Atiicil Intllignc Fll 009 Lctu : A* ch 9//009 Pit Al UC Bkly Mny slids om Dn Klin Announcmnts Assignmnts: Pojct 0 (Python tutoil): du Thusdy /8 Wittn (ch): du Thusdy /8 Pojct (ch): to lsd tody, du
Exam 2 Solutions. Jonathan Turner 4/2/2012. CS 542 Advanced Data Structures and Algorithms
CS 542 Avn Dt Stutu n Alotm Exm 2 Soluton Jontn Tun 4/2/202. (5 ont) Con n oton on t tton t tutu n w t n t 2 no. Wt t mllt num o no tt t tton t tutu oul ontn. Exln you nw. Sn n mut n you o u t n t, t n
Self-Adjusting Top Trees
Th Polm Sl-jsting Top Ts ynmi ts: ol: mintin n n-tx ost tht hngs o tim. link(,w): ts n g twn tis n w. t(,w): lts g (,w). pplition-spii t ssoit with gs n/o tis. ont xmpls: in minimm-wight g in th pth twn
Course Logistics Textbook: Artificial Intelligence: A Modern Approach, Russell and Norvig (3 rd ed) Topics
CE 573: Atiiil Intllign Autumn 0 Intoution & Dn Wl Wit slis om Dn Klin, tut Russll, Anw Moo, Luk Zttlmoy Cous Logistis Txtook: Atiiil Intllign: A Mon Ao, Russll n Novig (3 ) Puisits: Dt tutus (CE 36 o
T h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
10.3 The Quadratic Formula
. Te Qudti Fomul We mentioned in te lst setion tt ompleting te sque n e used to solve ny qudti eqution. So we n use it to solve 0. We poeed s follows 0 0 Te lst line of tis we ll te qudti fomul. Te Qudti
Announcements. CS 188: Artificial Intelligence. Costs on Actions. Recap: Search. Lecture 3: A* Search
Announcmnts Pojcts: Looking fo ojct tns? --- Com to font ft lctu. Ty i ogmming, not divid-nd-conu Account foms vill u font duing k nd ft lctu Assignmnts Looking fo studnts to wok on ssignmnts with? ---
(2) If we multiplied a row of B by λ, then the value is also multiplied by λ(here lambda could be 0). namely
. DETERMINANT.. Dtrminnt. Introution:I you think row vtor o mtrix s oorint o vtors in sp, thn th gomtri mning o th rnk o th mtrix is th imnsion o th prlllppi spnn y thm. But w r not only r out th imnsion,
CS 103 BFS Alorithm. Mark Redekopp
CS 3 BFS Aloritm Mrk Rkopp Brt-First Sr (BFS) HIGHLIGHTED ALGORITHM 3 Pt Plnnin W'v sn BFS in t ontxt o inin t sortst pt trou mz? S?? 4 Pt Plnnin W xplor t 4 niors s on irtion 3 3 3 S 3 3 3 3 3 F I you
P a g e 3 6 of R e p o r t P B 4 / 0 9
P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J
Weighted Graphs. Weighted graphs may be either directed or undirected.
1 In mny ppltons, o rp s n ssot numrl vlu, ll wt. Usully, t wts r nonntv ntrs. Wt rps my tr rt or unrt. T wt o n s otn rrr to s t "ost" o t. In ppltons, t wt my msur o t lnt o rout, t pty o ln, t nry rqur
Tangram Fractions Overview: Students will analyze standard and nonstandard
ACTIVITY 1 Mtrils: Stunt opis o tnrm mstrs trnsprnis o tnrm mstrs sissors PROCEDURE Skills: Dsriin n nmin polyons Stuyin onrun Comprin rtions Tnrm Frtions Ovrviw: Stunts will nlyz stnr n nonstnr tnrms
Easy Steps to build a part number... Tri-Start Series III CF P
ulti-l i Oti iul ( oto) ow to O ol os sy ts to uil t u... i-tt is 1. 2 3 4. 5. 6. oto y til iis ll tyl ll iz- st t ott y & y/ ywy ositio 50 9 0 17-08 ol ulti-l i oti otos o us wit ulti-o sil o tii o y
Problem solving by search
Prolm solving y srh Tomáš voo Dprtmnt o Cyrntis, Vision or Roots n Autonomous ystms Mrh 5, 208 / 3 Outlin rh prolm. tt sp grphs. rh trs. trtgis, whih tr rnhs to hoos? trtgy/algorithm proprtis? Progrmming
d e c b a d c b a d e c b a a c a d c c e b
FLAT PEYOTE STITCH Bin y mkin stoppr -- sw trou n pull it lon t tr until it is out 6 rom t n. Sw trou t in witout splittin t tr. You soul l to sli it up n own t tr ut it will sty in pl wn lt lon. Evn-Count
P a g e 5 1 of R e p o r t P B 4 / 0 9
P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e
An undirected graph G = (V, E) V a set of vertices E a set of unordered edges (v,w) where v, w in V
Unirt Grphs An unirt grph G = (V, E) V st o vrtis E st o unorr gs (v,w) whr v, w in V USE: to mol symmtri rltionships twn ntitis vrtis v n w r jnt i thr is n g (v,w) [or (w,v)] th g (v,w) is inint upon
CSE 373: AVL trees. Warmup: Warmup. Interlude: Exploring the balance invariant. AVL Trees: Invariants. AVL tree invariants review
rmup CSE 7: AVL trs rmup: ht is n invrint? Mihl L Friy, Jn 9, 0 ht r th AVL tr invrints, xtly? Disuss with your nighor. AVL Trs: Invrints Intrlu: Exploring th ln invrint Cor i: xtr invrint to BSTs tht
Lecture 20: Minimum Spanning Trees (CLRS 23)
Ltur 0: Mnmum Spnnn Trs (CLRS 3) Jun, 00 Grps Lst tm w n (wt) rps (unrt/rt) n ntrou s rp voulry (vrtx,, r, pt, onnt omponnts,... ) W lso suss jny lst n jny mtrx rprsntton W wll us jny lst rprsntton unlss
OpenMx Matrices and Operators
OpnMx Mtris n Oprtors Sr Mln Mtris: t uilin loks Mny typs? Dnots r lmnt mxmtrix( typ= Zro", nrow=, nol=, nm="" ) mxmtrix( typ= Unit", nrow=, nol=, nm="" ) mxmtrix( typ= Int", nrow=, nol=, nm="" ) mxmtrix(
16.unified Introduction to Computers and Programming. SOLUTIONS to Examination 4/30/04 9:05am - 10:00am
16.unii Introution to Computrs n Prormmin SOLUTIONS to Exmintion /30/0 9:05m - 10:00m Pro. I. Kristin Lunqvist Sprin 00 Grin Stion: Qustion 1 (5) Qustion (15) Qustion 3 (10) Qustion (35) Qustion 5 (10)
CSE 373. Graphs 1: Concepts, Depth/Breadth-First Search reading: Weiss Ch. 9. slides created by Marty Stepp
CSE 373 Grphs 1: Conpts, Dpth/Brth-First Srh ring: Wiss Ch. 9 slis rt y Mrty Stpp http://www.s.wshington.u/373/ Univrsity o Wshington, ll rights rsrv. 1 Wht is grph? 56 Tokyo Sttl Soul 128 16 30 181 140
Using the Printable Sticker Function. Using the Edit Screen. Computer. Tablet. ScanNCutCanvas
SnNCutCnvs Using th Printl Stikr Funtion On-o--kin stikrs n sily rt y using your inkjt printr n th Dirt Cut untion o th SnNCut mhin. For inormtion on si oprtions o th SnNCutCnvs, rr to th Hlp. To viw th
Who is this Great Team? Nickname. Strangest Gift/Friend. Hometown. Best Teacher. Hobby. Travel Destination. 8 G People, Places & Possibilities
Who i thi Gt Tm? Exi Sh th foowing i of infomtion bot of with o tb o tm mt. Yo o not hv to wit n of it own. Yo wi b givn on 5 mint to omih thi tk. Stngt Gift/Fin Niknm Homtown Bt Th Hobb Tv Dtintion Robt
KEB INVERTER L1 L2 L3 FLC - RELAY 1 COMMON I1 - APPROACH CLOSE 0V - DIGITAL COMMON FLA - RELAY 1 N.O. AN1+ - ANALOG 1 (+) CRF - +10V OUTPUT
XT SSMLY MOL 00 (O FS) 00 (I- PT) 00 (SIGL SLI) WG O 0 0-0 0-0-0 0.0. 0 0-0 0-0-0 0 0-0 0-0-0 VOLTG F.L...0..0..0.0..0 IIG POW FOM US SUPPLI ISOT (S TL) US OP OUTOS T T 0 O HIGH H IUIT POTTIO OT: H IUIT
Spanning Trees. BFS, DFS spanning tree Minimum spanning tree. March 28, 2018 Cinda Heeren / Geoffrey Tien 1
Spnnn Trs BFS, DFS spnnn tr Mnmum spnnn tr Mr 28, 2018 Cn Hrn / Gory Tn 1 Dpt-rst sr Vsts vrts lon snl pt s r s t n o, n tn ktrks to t rst junton n rsums own notr pt Mr 28, 2018 Cn Hrn / Gory Tn 2 Dpt-rst
Series III, TV Breakaway Fail-Safe Connectors Quick-Disconnect with an Axial Pull of Lanyard
is, wy il- otos Qui-isot wit xil ull o y ulo ss quo mol i-tt wy il- otos ovi uqul om i viomts quii istt ismt. wy il- oto mily os wi o ltil mil tus: stt ouli m stio omltly itmtl wit st tls (/20 /2) vtoy
Trade Patterns, Production networks, and Trade and employment in the Asia-US region
Trade Patterns, Production networks, and Trade and employment in the Asia-U region atoshi Inomata Institute of Developing Economies ETRO Development of cross-national production linkages, 1985-2005 1985
Chapter 6 Perturbation theory
Ct 6 Ptutio to 6. Ti-iddt odgt tutio to i o tutio sst is giv to fid solutios of λ ' ; : iltoi of si stt : igvlus of : otool igfutios of ; δ ii Rlig-Södig tutio to ' λ..6. ; : gl iltoi ': tutio λ : sll
Classical Theory of Fourier Series : Demystified and Generalised VIVEK V. RANE. The Institute of Science, 15, Madam Cama Road, Mumbai
Clssil Thoy o Foi Sis : Dmystii Glis VIVEK V RANE Th Istitt o Si 5 Mm Cm Ro Mmbi-4 3 -mil ss : v_v_@yhoooi Abstt : Fo Rim itgbl tio o itvl o poit thi w i Foi Sis t th poit o th itvl big ot how wh th tio
1 Introduction to Modulo 7 Arithmetic
1 Introution to Moulo 7 Arithmti Bor w try our hn t solvin som hr Moulr KnKns, lt s tk los look t on moulr rithmti, mo 7 rithmti. You ll s in this sminr tht rithmti moulo prim is quit irnt rom th ons w
Module graph.py. 1 Introduction. 2 Graph basics. 3 Module graph.py. 3.1 Objects. CS 231 Naomi Nishimura
Moul grph.py CS 231 Nomi Nishimur 1 Introution Just lik th Python list n th Python itionry provi wys of storing, ssing, n moifying t, grph n viw s wy of storing, ssing, n moifying t. Bus Python os not
Math 166 Week in Review 2 Sections 1.1b, 1.2, 1.3, & 1.4
Mt 166 WIR, Sprin 2012, Bnjmin urisp Mt 166 Wk in Rviw 2 Stions 1.1, 1.2, 1.3, & 1.4 1. S t pproprit rions in Vnn irm tt orrspon to o t ollowin sts. () (B ) B () ( ) B B () (B ) B 1 Mt 166 WIR, Sprin 2012,
4.1 Interval Scheduling. Chapter 4. Greedy Algorithms. Interval Scheduling: Greedy Algorithms. Interval Scheduling. Interval scheduling.
Cptr 4 4 Intrvl Suln Gry Alortms Sls y Kvn Wyn Copyrt 005 Prson-Ason Wsly All rts rsrv Intrvl Suln Intrvl Suln: Gry Alortms Intrvl suln! Jo strts t s n nss t! Two os omptl ty on't ovrlp! Gol: n mxmum sust
Language Processors F29LP2, Lecture 5
Lnguge Pocessos F29LP2, Lectue 5 Jmie Gy Feuy 2, 2014 1 / 1 Nondeteministic Finite Automt (NFA) NFA genelise deteministic finite utomt (DFA). They llow sevel (0, 1, o moe thn 1) outgoing tnsitions with
(Minimum) Spanning Trees
(Mnmum) Spnnn Trs Spnnn trs Kruskl's lortm Novmr 23, 2017 Cn Hrn / Gory Tn 1 Spnnn trs Gvn G = V, E, spnnn tr o G s onnt surp o G wt xtly V 1 s mnml sust o s tt onnts ll t vrts o G G = Spnnn trs Novmr
Planar Upward Drawings
C.S. 252 Pro. Rorto Tmssi Computtionl Gomtry Sm. II, 1992 1993 Dt: My 3, 1993 Sri: Shmsi Moussvi Plnr Upwr Drwings 1 Thorm: G is yli i n only i it hs upwr rwing. Proo: 1. An upwr rwing is yli. Follow th
ENGO 431 Analytical Photogrammetry
EGO Altil Phtgmmt Fll 00 LAB : SIGLE PHOTO RESECTIO u t: vm 00 Ojtiv: tmi th Eti Oitti Pmts EOP f sigl ht usig lst squs justmt u. Giv:. Iti Oitti Pmts IOP f th m fm th Cm Cliti Ctifit CCC; Clit fl lgth
CSE 373: More on graphs; DFS and BFS. Michael Lee Wednesday, Feb 14, 2018
CSE 373: Mor on grphs; DFS n BFS Mihl L Wnsy, F 14, 2018 1 Wrmup Wrmup: Disuss with your nighor: Rmin your nighor: wht is simpl grph? Suppos w hv simpl, irt grph with x nos. Wht is th mximum numr of gs
Convergence tests for the cluster DFT calculations
Covgc ss o h clus DF clculos. Covgc wh spc o bss s. s clculos o bss s covgc hv b po usg h PBE ucol o 7 os gg h-b. A s o h Guss bss ss wh csg s usss hs b us clug h -G -G** - ++G(p). A l sc o. Å h c bw h
NUCON NRNON CONRNC ON CURRN RN N CHNOOGY, 011 oo uul o w ul x ol volv y y oll. y ov,., - o lo ll vy ul o Mo l u v ul (G) v Gl vlu oll. u 3- [11]. 000
![NUCON NRNON CONRNC ON CURRN RN N CHNOOGY, 011 oo uul o w ul x ol volv y y oll. y ov,., - o lo ll vy ul o Mo l u v ul (G) v Gl vlu oll. u 3- [11]. 000](/thumbs/93/113547584.jpg "NUCON NRNON CONRNC ON CURRN RN N CHNOOGY, 011 oo uul o w ul x ol volv y y oll. y ov,., - o lo ll vy ul o Mo l u v ul (G) v Gl vlu oll. u 3- [11]. 000")
NU O HMB NRM UNVRY, HNOOGY, C 8 0 81, 8 3-1 01 CMBR, 0 1 1 l oll oll ov ll lvly lu ul uu oll ul. w o lo u uol u z. ul l u oll ul. quk, oll, vl l, lk lo, - ul o u v (G) v Gl o oll. ul l u vlu oll ul uj
176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s
A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps
Paths. Connectivity. Euler and Hamilton Paths. Planar graphs.
Pths.. Eulr n Hmilton Pths.. Pth D. A pth rom s to t is squn o gs {x 0, x 1 }, {x 1, x 2 },... {x n 1, x n }, whr x 0 = s, n x n = t. D. Th lngth o pth is th numr o gs in it. {, } {, } {, } {, } {, } {,
Outline. 1 Introduction. 2 Min-Cost Spanning Trees. 4 Example
Outlin Computr Sin 33 Computtion o Minimum-Cost Spnnin Trs Prim's Alorithm Introution Mik Joson Dprtmnt o Computr Sin Univrsity o Clry Ltur #33 3 Alorithm Gnrl Constrution Mik Joson (Univrsity o Clry)
The University of Sydney MATH 2009
T Unvrsty o Syny MATH 2009 APH THEOY Tutorl 7 Solutons 2004 1. Lt t sonnt plnr rp sown. Drw ts ul, n t ul o t ul ( ). Sow tt s sonnt plnr rp, tn s onnt. Du tt ( ) s not somorp to. ( ) A onnt rp s on n
Math 61 : Discrete Structures Final Exam Instructor: Ciprian Manolescu. You have 180 minutes.
Nm: UCA ID Numr: Stion lttr: th 61 : Disrt Struturs Finl Exm Instrutor: Ciprin nolsu You hv 180 minuts. No ooks, nots or lultors r llow. Do not us your own srth ppr. 1. (2 points h) Tru/Fls: Cirl th right
L...,,...lllM" l)-""" Si_...,...
> 1 122005 14:8 S BF 0tt n FC DRE RE FOR C YER 2004 80?8 P01/ Rc t > uc s cttm tsus H D11) Rqc(tdk ;) wm1111t 4 (d m D m jud: US
Stable Matching for Spectrum Market with Guaranteed Minimum Requirement
Sl g Spum Gun mum Rqumn Yno n T S Ky Sw ngg ompu Sool Wun Uny nyno@wuun Yuxun Xong T S Ky Sw ngg ompu Sool Wun Uny xongyx@mlluun Qn Wng ompu Sool Wun Uny qnwng@wuun STRT Xoyn Y Sool mon Tlogy ow Uny X
( ) ( ) ( ) 0. Conservation of Energy & Poynting Theorem. From Maxwell s equations we have. M t. From above it can be shown (HW)
8 Conson o n & Ponn To Fo wll s quons w D B σ σ Fo bo n b sown (W) o s W w bo on o s l us n su su ul ow ns [W/ ] [W] su P su B W W 4 444 s W A A s V A A : W W R o n o so n n: [/s W] W W 4 44 9 W : W F
LWC 434 East First Street 4440 Garwood Place
//0 :: UI IXTUS TO US IIT TOS O T IST UTU I TOY IST OW - ITIO UTUS IST I TSIS. I ST (O, ZU). cui (, ZU). TOTO (OI, O). SO (ZU, Y). TUO (SO, ZU). TOTO (O US). IS (OSOIT, U). UST (ST WIIS, ZU). Y (T&S SS,
Problem 1. Solution: = show that for a constant number of particles: c and V. a) Using the definitions of P
rol. Using t dfinitions of nd nd t first lw of trodynis nd t driv t gnrl rltion: wr nd r t sifi t itis t onstnt rssur nd volu rstivly nd nd r t intrnl nrgy nd volu of ol. first lw rlts d dq d t onstnt
Appendix. In the absence of default risk, the benefit of the tax shield due to debt financing by the firm is 1 C E C
nx. Dvon o h n wh In h sn o ul sk h n o h x shl u o nnng y h m s s h ol ouon s h num o ssus s h oo nom x s h sonl nom x n s h v x on quy whh s wgh vg o vn n l gns x s. In hs s h o sonl nom xs on h x shl
COMP 250. Lecture 29. graph traversal. Nov. 15/16, 2017
COMP 250 Ltur 29 rp trvrsl Nov. 15/16, 2017 1 Toy Rursv rp trvrsl pt rst Non-rursv rp trvrsl pt rst rt rst 2 Hs up! Tr wr w mstks n t sls or S. 001 or toy s ltur. So you r ollown t ltur rorns n usn ts
Functions and Graphs 1. (a) (b) (c) (f) (e) (d) 2. (a) (b) (c) (d)
Functions nd Grps. () () (c) - - - O - - - O - - - O - - - - (d) () (f) - - O - 7 6 - - O - -7-6 - - - - - O. () () (c) (d) - - - O - O - O - - O - -. () G() f() + f( ), G(-) f( ) + f(), G() G( ) nd G()
ECE COMBINATIONAL BUILDING BLOCKS - INVEST 13 DECODERS AND ENCODERS
C 24 - COMBINATIONAL BUILDING BLOCKS - INVST 3 DCODS AND NCODS FALL 23 AP FLZ To o "wll" on this invstition you must not only t th riht nswrs ut must lso o nt, omplt n onis writups tht mk ovious wht h
Nefertiti. Echoes of. Regal components evoke visions of the past MULTIPLE STITCHES. designed by Helena Tang-Lim
MULTIPLE STITCHES Nrtiti Ehos o Rgl omponnts vok visions o th pst sign y Hln Tng-Lim Us vrity o stiths to rt this rgl yt wrl sign. Prt sping llows squr s to mk roun omponnts tht rp utiully. FCT-SC-030617-07
Housing Market Monitor
M O O D Y È S A N A L Y T I C S H o u s i n g M a r k e t M o n i t o r I N C O R P O R A T I N G D A T A A S O F N O V E M B E R İ Ī Ĭ Ĭ E x e c u t i v e S u m m a r y E x e c u t i v e S u m m a r y
Beechwood Music Department Staff
Beechwood Music Department Staff MRS SARAH KERSHAW - HEAD OF MUSIC S a ra h K e rs h a w t r a i n e d a t t h e R oy a l We ls h C o l le g e of M u s i c a n d D ra m a w h e re s h e ob t a i n e d
The local orthonormal basis set (r,θ,φ) is related to the Cartesian system by:
TIS in Sica Cooinats As not in t ast ct, an of t otntias tat w wi a wit a cnta otntias, aning tat t a jst fnctions of t istanc btwn a atic an so oint of oigin. In tis cas tn, (,, z as a t Coob otntia an
Solutions for HW11. Exercise 34. (a) Use the recurrence relation t(g) = t(g e) + t(g/e) to count the number of spanning trees of v 1
Solutions for HW Exris. () Us th rurrn rltion t(g) = t(g ) + t(g/) to ount th numr of spnning trs of v v v u u u Rmmr to kp multipl gs!! First rrw G so tht non of th gs ross: v u v Rursing on = (v, u ):
learning objectives learn what graphs are in mathematical terms learn how to represent graphs in computers learn about typical graph algorithms
rp loritms lrnin ojtivs loritms your sotwr systm sotwr rwr lrn wt rps r in mtmtil trms lrn ow to rprsnt rps in omputrs lrn out typil rp loritms wy rps? intuitivly, rp is orm y vrtis n s twn vrtis rps r
PLAYGROUND SALE Take up to 40% off. Plus FREE equipment * with select purchase DETAILS INSIDE
PLYROUND SL Tk up t 40% ff Plu FR quipnt * with lct puch DTILS INSID T BONUS QUIPMNT FR! T BONUS QUIPMNT FR * Mk qulifing $10K, $0K $30K puch f thi ORDR $10K ORDR $0K ORDR $30K T ON FR* T TO FR* T THR
Ash Wednesday. First Introit thing. * Dómi- nos. di- di- nos, tú- ré- spi- Ps. ne. Dó- mi- Sál- vum. intra-vé-runt. Gló- ri-
sh Wdsdy 7 gn mult- tú- st Frst Intrt thng X-áud m. ns ní- m-sr-cór- Ps. -qu Ptr - m- Sál- vum m * usqu 1 d fc á-rum sp- m-sr-t- ó- num Gló- r- Fí- l- Sp-rí- : quó-n- m ntr-vé-runt á- n-mm c * m- quó-n-
Improving Union. Implementation. Union-by-size Code. Union-by-Size Find Analysis. Path Compression! Improving Find find(e)
POW CSE 36: Dt Struturs Top #10 T Dynm (Equvln) Duo: Unon-y-Sz & Pt Comprsson Wk!! Luk MDowll Summr Qurtr 003 M! ZING Wt s Goo Mz? Mz Construton lortm Gvn: ollton o rooms V Conntons twn t rooms (ntlly
Three Phase Asymmetrical Load Flow for Four-Wire Distribution Networks
T Aytl Lo Flow o Fou-W Dtuto Ntwo M. Mo *, A. M. Dy. M. A Dtt o Eltl E, A Uvty o Toloy Hz Av., T 59, I * El: o8@yoo.o Att-- Mjoty o tuto two ul u to ul lo, yty to l two l ut. T tt o tuto yt ult y o ovt
7 ACM FOR FRAME 2SET 6 FRAME 2SET 5 ACM FOR MAIN FRAME 2SET 4 MAIN FRAME 2SET 3 POLE ASSLY 1 2 CROWN STRUCTURE ASSLY 1 1 CROWN ASSLY 1
7 M OR RM 2ST 6 RM 2ST 5 M OR MIN RM 2ST 4 MIN RM 2ST 3 POL SSLY 1 2 ROWN STRUTUR SSLY 1 1 ROWN SSLY 1 SR.NO. SRIPTION QTY. a LL IMNSIONS R IN mm I N MT Pi IOLMI 1'NTION LT. Tm: XPLO VIW OR POL MOUNT MLM
Multicast routing algorithm based on Extended Simulated Annealing Algorithm
7t WSEAS Int. Con. on MATHEMATICAL METHODS n COMPUTATIONAL TECHNIQUES IN ELECTRICAL ENGINEERING, Soi, 27-29/10/05 (pp129-133) Multist outing lgoitm s on Extn Simult Annling Algoitm Jin-Ku Jong*, Sung-Ok
A L A BA M A L A W R E V IE W
A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N
C-Curves. An alternative to the use of hyperbolic decline curves S E R A F I M. Prepared by: Serafim Ltd. P. +44 (0)
An ltntiv to th us of hypolic dclin cuvs Ppd y: Sfim Ltd S E R A F I M info@sfimltd.com P. +44 (02890 4206 www.sfimltd.com Contnts Contnts... i Intoduction... Initil ssumptions... Solving fo cumultiv...
Planar convex hulls (I)
Covx Hu Covxty Gv st P o ots 2D, tr ovx u s t sst ovx oyo tt ots ots o P A oyo P s ovx or y, P, t st s try P. Pr ovx us (I) Coutto Gotry [s 3250] Lur To Bowo Co ovx o-ovx 1 2 3 Covx Hu Covx Hu Covx Hu
b. How many ternary words of length 23 with eight 0 s, nine 1 s and six 2 s?
MATH 3012 Finl Exm, My 4, 2006, WTT Stunt Nm n ID Numr 1. All our prts o this prolm r onrn with trnry strings o lngth n, i.., wors o lngth n with lttrs rom th lpht {0, 1, 2}.. How mny trnry wors o lngth
5/1/2018. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees
/1/018 W usully no strns y ssnn -lnt os to ll rtrs n t lpt (or mpl, 8-t on n ASCII). Howvr, rnt rtrs our wt rnt rquns, w n sv mmory n ru trnsmttl tm y usn vrl-lnt non. T s to ssn sortr os to rtrs tt our
SOUTH. Bus Map. From 25 October travelsouthyorkshire.com/sbp
SOUT SFFIL u Mp F Ocb 1 N Sff p vb f Tv Su Y If Sff vuc/sp Sff u Pp - v Sff Sff u Pp cu w pv u w: u p bu w b vu c f u-p v Fqu vc ub f u Fw u c bu w w f cc v w cv f? 3 f-p p Sff bu Ipv cu fc b up % 0,000
Search: Cost & Heuristics
9/9/ CSE 7: Artiiil Intelligene Autumn 0 Pizz? Announements Serh: Cost & Heuristis Dn Wel Projet : Serh online tomorrow ue Mony 0/ ue We / Strt! With slies rom Dn Klein, Sturt Russell, Anrew Moore, Luke
I N A C O M P L E X W O R L D
IS L A M I C E C O N O M I C S I N A C O M P L E X W O R L D E x p l o r a t i o n s i n A g-b eanste d S i m u l a t i o n S a m i A l-s u w a i l e m 1 4 2 9 H 2 0 0 8 I s l a m i c D e v e l o p m e
Econ 401A Three extra questions John Riley. Homework 3 Due Tuesday, Nov 28
Econ 40 ree etr uestions Jon Riley Homework Due uesdy, Nov 8 Finncil engineering in coconut economy ere re two risky ssets Plnttion s gross stte contingent return of z (60,80) e mrket vlue of tis lnttion
What are S M U s? SMU = Software Maintenance Upgrade Software patch del iv ery u nit wh ich once ins tal l ed and activ ated prov ides a point-fix for
SMU 101 2 0 0 7 C i s c o S y s t e m s, I n c. A l l r i g h t s r e s e r v e d. 1 What are S M U s? SMU = Software Maintenance Upgrade Software patch del iv ery u nit wh ich once ins tal l ed and activ
DUET WITH DIAMONDS COLOR SHIFTING BRACELET By Leslie Rogalski
Dut with Dimons Brlt DUET WITH DIAMONDS COLOR SHIFTING BRACELET By Lsli Roglski Photo y Anrw Wirth Supruo DUETS TM from BSmith rt olor shifting fft tht mks your work tk on lif of its own s you mov! This
Grade 7/8 Math Circles March 4/5, Graph Theory I- Solutions
ulty o Mtmtis Wtrloo, Ontrio N ntr or ution in Mtmtis n omputin r / Mt irls Mr /, 0 rp Tory - Solutions * inits lln qustion. Tr t ollowin wlks on t rp low. or on, stt wtr it is pt? ow o you know? () n
Pythagorean Theorem and Trigonometry
Ptgoren Teorem nd Trigonometr Te Ptgoren Teorem is nient, well-known, nd importnt. It s lrge numer of different proofs, inluding one disovered merin President Jmes. Grfield. Te we site ttp://www.ut-te-knot.org/ptgors/inde.stml
sin sin 1 d r d Ae r 2
Diffction k f c f Th Huygn-Fnl Pincil tt: Evy unobtuct oint of vfont, t givn intnt, v ouc of hicl cony vlt (ith th m funcy tht of th imy v. Th mlitu of th oticl fil t ny oint byon i th uoition of ll th
Chapter 5: Quantization of Radiation in Cavities and Free Space
Quu O f Ph Ol Fh R Cll vy Ch 5: Quz f R Cv F S 5 Cll ly 5 Cll Cvy ly Mxwll u f lg J 4 h lv l C fl vy W f h g f h vy Th vy u luly ll W l u h J Cvy F Mxwll u v h wv u Th v u lv h f h fu h vy I w wh h v l
Depth First Search. Yufei Tao. Department of Computer Science and Engineering Chinese University of Hong Kong
Dprtmnt o Computr Sn n Ennrn Cns Unvrsty o Hon Kon W v lry lrn rt rst sr (BFS). Toy, w wll suss ts sstr vrson : t pt rst sr (DFS) lortm. Our susson wll on n ous on rt rps, us t xtnson to unrt rps s strtorwr.
F102 1/4 AMP +240 VDC SEE FIGURE 5-14 FILAMENT AND OVEN CKTS BLU J811 BREAK-IN TB103 TO S103 TRANSMITTER ASSOCIATED CAL OFF FUNCTION NOTE 2 STANDBY
OWR OR F0 M NOT S0 RT OF FUNTI FL0 T0 OWR SULY SUSSIS T0 T0 WIR FOR 0 V OWR SULY SUSSIS T0 WIR FOR V 0 0 RT V0 RT V0. V RT V0 RT V0 NOT. V. V NOT +0 V 0 +0 V. V 0 FUNTI NOT L +0 V S FIUR - FILMNT N OVN