Source side Dependency Tree Reordering Models with Subtree Movements and Constraints
|
|
|
- Carmella Stevens
- 5 years ago
- Views:
Transcription
1 Source sde Dependency Tree Reorderng Models wth Subtree Movements nd Constrnts Nguyen Bch, Qn Go nd Stephn Vogel Crnege Mellon Unversty 1
2 Overvew We ntroduce source sde dependency tree reorderng models Inspred by lexclzed reorderng model (Koehn et. l 2005), herrchcl dependency trnslton (Shen et. l, 2008) nd cohesve decodng (Cherry, 2008) We model reorderng events o phrses ssocted wth source sde dependency trees Insde/Outsde subtree movements ecently cpture the sttstcl dstrbuton o the subtree to subtree trnstons n trnng dt Utlze subtree movements drectly t the decodng tme longsde wth cohesve constrnts to gude the serch process Improvements re shown n Englsh Spnsh nd Englsh Irq tsks 2
3 Outlne Bckground & Motvtons Source sde dependency tree reorderng models Modelng Trnng Decodng Experments & Anlyss Conclusons 3
4 Bckground o Reorderng Models Explctly model phrse reorderng dstnces Put syntctc nlyss o the trget lnguge nto both modelng nd decodng Use source lnguge syntx 4
5 Explctly model phrse reorderng dstnces Put syntctc nlyss o the trget lnguge nto both modelng nd decodng Use source lnguge syntx Dstnce bsed (Och, 2002; Koehn et.l., 2003) Lexclzed phrse (Tllmnn, 2004; Koehn, et.l., 2005; Al Onzn nd Ppnen, 2006) Herrchcl phrse (Glley nd Mnnng, 2008) MxEnt clsser (Zens nd Ney, 2006; Xong, et.l., 2006; Chng, et. l., 2009) Drect model trget lnguge consttuents movement n ether consttuency trees (Ymd nd Knght, 2001; Glley et.l., 2006; Zollmnn et.l., 2008) or dependency trees (Qurk, et.l., 2005) Herrchcl phrse bsed (Chng, 2005; Shen et. l., 2008) Preprocessng wth syntctc reorderng rules (X nd McCord, 2004; Collns et.l., 2005; Rottmnn nd Vogel, 2007; Wng et.l., 2007; Xu et.l. 2009) Use syntctcl nlyss to provde multple source sentence reorderng optons through word lttces (Zhng et.l., 2007; L et.l., 2007; Elmng, 2008). 5
6 Explctly model phrse reorderng dstnces Put syntctc nlyss o the trget lnguge nto both modelng nd decodng Use source lnguge syntx Dstnce bsed (Och, 2002; Koehn et.l., 2003) Lexclzed phrse (Tllmnn, 2004; Koehn, et.l., 2005; Al Onzn nd Ppnen, 2006) Herrchcl phrse (Glley nd Mnnng, 2008) MxEnt clsser (Zens nd Ney, 2006; Xong, et.l., 2006; Chng, et. l., 2009) Drect modelng o trget lnguge consttuents movement n ether consttuency trees (Ymd nd Knght, 2001; Glley et.l., 2006; Zollmnn et.l., 2008) or dependency trees (Qurk, et.l., 2005) Herrchcl phrse bsed (Chng, 2005; Shen et. l., 2008) Preprocessng wth syntctc reorderng rules (X nd McCord, 2004; Collns et.l., 2005; Rottmnn nd Vogel, 2007; Wng et.l., 2007; Xu et.l. 2009) Source sde Dependency Tree Reorderng Models wth Subtree Movements nd Constrnts Use syntctcl nlyss to provde multple source sentence reorderng optons through word lttces (Zhng et.l., 2007; L et.l., 2007; Elmng, 2008). 6
7 Wht re the derences? Insted o usng lt word structures to extrct reorderng events, utlze source sde dependency structures Provde more lngustc cues or reorderng events Insted o usng pre dened reorderng ptterns, lern reorderng eture dstrbutons rom trnng dt Cpture reorderng events rom rel dt Insted o preprocessng the dt, dscrmntvely trn the reorderng model v MERT Tghter ntegrton wth the decoder 7
8 Cohesve Decodng A cohesve decodng (Cherry, 08; Bch et. l., 09) s orcng the cohesve constrnt: When the decoder begns trnslton ny prt o source subtree, t must cover ll words under tht subtree beore t cn trnslte nythng outsde. Source sde dependency tree reorderng models Ecently cpture the sttstcl dstrbuton o the subtree to subtree trnstons n trnng dt. Drectly utlze t t the decodng tme to gude the serch process. 8
9 Outlne Bckground o Reorderng Models Source sde dependency tree reorderng models Modelng Trnng Decodng Experments & Anlyss Conclusons 9
10 Lexclzed Reorderng Models (Tllmnn, 2004; Koehn, et.l., 2005; Al Onzn & Ppnen, 2006) p( O e, ) = n = 1 p( o e,, 1, ) where s the nput sentence; e = ( e 1,..., e = (,..., 1 n n ) s the trget lnguge phrses; ) s phrse lgnments; s source phrse whch hs trnslted phrse e O s orentton phrse sequence; ech o dened by n lgnment hs vlue over 3 possbles ( M, S,D); ; 10
11
12 quser 2 tnto 1 lo 0 Por
13 pedrle 3 quser Dscontnuous 2 tnto 1 lo 0 Por
14 Swp 5 nuevmente 4 pedrle 3 quser Dscontnuous 2 tnto 1 lo 0 Por
15 Dscontnuous 10 que 9 de 8 encrgue 7 se Swp 6 que 5 nuevmente 4 Pedrle 3 quser Dscontnuous 2 tnto 1 lo 0 Por
16 16 neerlndés 15 cnl 14 Un 13 tmbén 12 ver 11 podmos Dscontnuous Monotone 10 que 9 de 8 encrgue 7 se Swp 6 que 5 nuevmente 4 Pedrle 3 quser Dscontnuous 2 tnto 1 lo 0 Por
17 Pros Pros & Cons o Lexclzed Reorderng Models ntutvely model lt word movements well dened or phrse bsed rmework Cons No lngustcs structures Need lgnment mtrx to determne movements 17
18 Completed/Open subtrees A completed subtree g b d c e All words under node hve been trnslted then we cll completed subtree 18
19 Completed/Open subtrees An open subtree g b d c e A subtree tht hs begun trnslton but not yet complete, n open subtree 19
20 Insde/Outsde subtree movements c s movng nsde subtree rooted t b g A structure s movng nsde subtree t helps the subtree to be completed or less open b d c e Insde 20
21 Insde/Outsde subtree movements Outsde b g d A structure s movng outsde subtree t leves the subtree to be open c e d e s movng outsde subtree rooted t b 21
22 Source sde Dependency Tree (SDT) Reorderng Models p( D e, ) = n = 1 p( d e,,, s 1, s ) where s the nput sentence; e = ( e 1,..., e = (,..., 1 n n ) s the trget lnguge phrses; ) s phrse lgnments ; s source phrse whch hs trnslte d phrse e dened by n lgnment ; s nd s- 1 re dependency structures o source phrses nd - ; 1 D represents the sequence o syntctc phrse movements over source dependency tree; ech d = {I, O} ; 22
23 would I thereore once sk more ensure get you to tht we chnnel s Dutch well neerlndés cnl un tmbén ver podmos que de encrgue se que nuevmente Pedrle quser tnto lo Por 23
24 would I thereore once sk more ensure get you to tht we chnnel s Dutch well neerlndés cnl un tmbén ver podmos que de encrgue se que nuevmente Pedrle quser tnto lo Por 24
25 would I thereore once sk more ensure get Insde you to tht we chnnel s Dutch well neerlndés cnl un tmbén ver podmos que de encrgue se que nuevmente Pedrle quser Dscontnuous tnto lo Por 25
26 would I thereore once sk more ensure get Insde Outsde you to tht we chnnel s Dutch well neerlndés cnl un tmbén ver podmos que de Swp encrgue se que nuevmente Pedrle quser Dscontnuous tnto lo Por 26
27 27 neerlndés cnl un tmbén ver podmos que de encrgue se que nuevmente Pedrle quser tnto lo Por sk more once would get chnnel tht we thereore I ensure you to s Dutch well Dscontnuous Insde Swp Outsde Dscontnuous Insde
28 28 neerlndés cnl un tmbén ver podmos que de encrgue se que nuevmente Pedrle quser tnto lo Por sk more once would get chnnel tht we thereore I ensure you to s Dutch well Dscontnuous Insde Swp Outsde Dscontnuous Insde Monotone Insde
29 would Insde I thereore once sk more ensure get Insde Outsde you to tht we chnnel s Insde Dutch well neerlndés cnl Monotone un tmbén Source-sde Dependency Tree R.M. Dscontnuous ver podmos que Insde Outsde Insde Insde de Swp encrgue se que Lexclzed R.M. nuevmente Pedrle Dscontnuous Swp Dscontnuous Monotone quser Dscontnuous tnto lo Por 29
30 Extended Source sde Dependency Tree (SDT) Reorderng Models p( D e, ) = where s the nput sentence; e = ( e nd 1,..., e = (,..., s 1 ) s phrse lgnments ; n = 1 ) s the trget lnguge phrses; p(( o _ s source phrse whch hs trnslte d phrse s -1 re dependency structures o source phrses ech (o_d) n n e d) nd ; e, dened by n lgnment -1, ;, {M_I, S_I, D_I, M_O, S_O, D_O} ; 1, s 1, s ) D represents the sequence o syntctc phrse movements over source dependency tree; = 30
31 Extended Source sde Dependency Tree (SDT) Reorderng Models p( D e, ) = where s the nput sentence; e = ( e nd 1,..., e = (,..., s D 1 ) s phrse lgnments ; re dependency structures n ) s the trget lnguge phrses; p(( o s source phrse whch hs trnslte d phrse s -1 n n _ d) e, Insde Outsde Insde Insde = 1 o source e phrses represents the sequence o over source dependency tree; ech (o_d) = nd ;, dened by n lgnment -1 ;, Dscontnuous Swp Dscontnuous Monotone D_I S_O D_I M_I {M_I, S_I, D_I, M_O, S_O, D_O} ; 1, s 1, s ) syntctc phrse movements 31
32 Trnng Obtn dependency prse o the source sde Gven sentence pr nd the source sde dependency tree Phrse extrcton: lso extrct source dependency structures o phrse prs Identy Insde/Outsde movement by usng Interrupton Check Algorthms (Bch et.l., 2009) 32
33 Trnng = k j k j k j k j k j d o count d o count d o e d o p ) ) _ ( ( ) _ ( ),,, ) _ (( γ γ + + = k k j k j k k j d o count d o count d e d o p ) ) _ ( ( ) _ ( ),, ) _ (( γ γ + + = j k j k j j k j d o count d o count o e d o p ) ) _ ( ( ) _ ( ),, ) _ (( γ γ DO: jont probblty o subtree movements nd lexclzed orenttons DOD: condtoned on subtree movements DOO: condtoned on lexclzed orenttons
34 Decodng Wthout cohesve constrnts Hvng no normton bout the source dependency tree normton durng the decodng tme Consder both subtree movements, nd dd them up to the trnslton model costs Wth cohesve constrnts The source dependency tree s vlble durng the decodng tme Only consder ether nsde or outsde movement, dependng on the output o the nterrupton check lgorthm 34
35 Outlne Bckground o Reorderng Models Source sde dependency tree reorderng models Modelng Trnng Decodng Experments & Anlyss Concluson 35
36 Experments setups Bselne: phrse bsed MT wth lexclzed reorderng model Coh: usng cohesve constrnts DO / DOD / DOO: usng source sde dependency tree (SDT) reorderng model wth derent prmeter estmtons DO+Coh / DOD+Coh / DOO+Coh: decodng wth both SDT reorderng model nd cohesve constrnts. 36
37 Englsh Spnsh (Europrl) Englsh Spnsh: nc test2007 Englsh Spnsh: news test BLEU 33.2 BLEU Source sde dependency tree reorderng models nd cohesve constrnts obtned mprovements over the lexclzed reorderng models. 37
38 Englsh Irq (TrnsTc) Englsh Irq: june2008 Englsh Irq: nov BLEU BLEU Decodng wth both source sde dependency tree reorderng models nd cohesve constrnts oten obtn the best perormnce. 38
39 Where re mprovements comng rom? 39
40 Test set brekdown Dvde the test sets nto three portons bsed on sentence level TER o the bselne system μ nd σ re men nd stndrd devton o the whole test set Hed, Tl nd Md s the sentence whose score s lower thn μ 1/2 σ, hgher thn μ+1/2 σ nd the rest 40
41 Englsh Spnsh: nc test2007 Englsh Spnsh: news test BLEU tl md hed BLEU tl md hed Englsh Irq: june 2008 Englsh Irq: nov 2008 BLEU tl md hed BLEU tl md hed june 08 nov 08 nc test2007 news test2008 Hed Md Tl
42 Wht s the most sgncnt eect the sourcetree reorderng models contrbute? 42
43 Numbers o Reorderngs nc test2007 news test2008 june 2008 nov 2008 Bselne Coh DO DO+Coh DOD DOD+Coh DOO DOO+Coh More reorderngs cn be generted wthout losng perormnce. The source tree reorderng models provde more dscrmntve mechnsm to estmte reorderng events. Reorderng s more lnguge specc thn generl trnslton models, nd the condtons or reorderng event to hppen vry mong lnguges. 43
44 Outlne Bckground & Motvtons Source sde dependency tree reorderng models Modelng Trnng Decodng Experments & Anlyss Conclusons 44
45 Conclusons & Future Work Conclusons Source sde dependency tree reorderng models re helpul Model reorderng event wth Insde/Outsde subtree movements The eectveness ws shown when comprng wth strong reorderng model Obtned mprovements wth 2 lnguge prs nd lso covered trnng corpus szes, rngng rom 500K up to 1.3M sentence prs Future work A herrchcl source sde dependency reorderng model: extend Glley&Mnnng (2008). Pcked orest dependency tree reorderng models 45
46 Bck up 46
47 A completed subtree g An open subtree g b d b d c e c e c s movng nsde subtree rooted t b g Outsde g b d b d c e c e Insde d e s movng outsde subtree rooted t b 47
48 Outsde g Outsde g b d b d c e c e Insde g g b d b d c e c Insde e 48
49 Wht do you men by ntroducng Insde/Outsde notons? The movement o the subtree nsde or outsde source subtree cn be vewed s the decoder s levng rom the prevous source stte to the current source stte. Trckng cts bout the subtree to subtree trnstons observed n the source sde o wordlgned trnng dt. 49
50 Lexclzed Source tree sk you # pedrle ds swp D_I * sk you # pedrle mono mono M_I sk you # pedrle mono mono M_O once more # nuevmente swp ds S_O * once more # nuevmente ds swp D_O once more # nuevmente que swp ds S_O nsde nd outsde probbltes or phrse sk you - pedrle ccordng to three prmeter estmton methods M_I S_I D_I M_O S_O D_O DO DOD DOO
51 Dstrbutons o Reorderng Events En Es M_I S_I D_I M_O S_O D_O En Ir M_I S_I D_I M_O S_O D_O Observed monotone & nsde (M_I) movements more oten thn other ctegores 51
52 Explctly model phrse reorderng dstnces Put syntctc nlyss o the trget lnguge nto both modelng nd decodng Use source lnguge syntx Dstnce bsed (Och, 2002; Koehn et.l., 2003) Lexclzed phrse (Tllmnn, 2004; Koehn, et.l., 2005; Al Onzn nd Ppnen, 2006) Herrchcl phrse (Glley nd Mnnng, 2008) MxEnt clsser (Zens nd Ney, 2006; Xong, et.l., 2006; Chng, et. l., 2009) 52
53 Explctly model phrse reorderng dstnces Put syntctc nlyss o the trget lnguge nto both modelng nd decodng Use source lnguge syntx Dstnce bsed (Och, 2002; Koehn et.l., 2003) Lexclzed phrse (Tllmnn, 2004; Koehn, et.l., 2005; Al Onzn nd Ppnen, 2006) Herrchcl phrse (Glley nd Mnnng, 2008) MxEnt clsser (Zens nd Ney, 2006; Xong, et.l., 2006; Chng, et. l., 2009) Drect model trget lnguge consttuents movement n ether consttuency trees (Ymd nd Knght, 2001; Glley et.l., 2006; Zollmnn et.l., 2008) or dependency trees (Qurk, et.l., 2005) Herrchcl phrse bsed (Chng, 2005; Shen et. l., 2008) 53
Variable time amplitude amplification and quantum algorithms for linear algebra. Andris Ambainis University of Latvia
Vrble tme mpltude mplfcton nd quntum lgorthms for lner lgebr Andrs Ambns Unversty of Ltv Tlk outlne. ew verson of mpltude mplfcton;. Quntum lgorthm for testng f A s sngulr; 3. Quntum lgorthm for solvng
Remember: Project Proposals are due April 11.
Bonformtcs ecture Notes Announcements Remember: Project Proposls re due Aprl. Clss 22 Aprl 4, 2002 A. Hdden Mrov Models. Defntons Emple - Consder the emple we tled bout n clss lst tme wth the cons. However,
Dynamic Power Management in a Mobile Multimedia System with Guaranteed Quality-of-Service
Dynmc Power Mngement n Moble Multmed System wth Gurnteed Qulty-of-Servce Qnru Qu, Qng Wu, nd Mssoud Pedrm Dept. of Electrcl Engneerng-Systems Unversty of Southern Clforn Los Angeles CA 90089 Outlne! Introducton
In this Chapter. Chap. 3 Markov chains and hidden Markov models. Probabilistic Models. Example: CpG Islands
In ths Chpter Chp. 3 Mrov chns nd hdden Mrov models Bontellgence bortory School of Computer Sc. & Eng. Seoul Ntonl Unversty Seoul 5-74, Kore The probblstc model for sequence nlyss HMM (hdden Mrov model)
The Schur-Cohn Algorithm
Modelng, Estmton nd Otml Flterng n Sgnl Processng Mohmed Njm Coyrght 8, ISTE Ltd. Aendx F The Schur-Cohn Algorthm In ths endx, our m s to resent the Schur-Cohn lgorthm [] whch s often used s crteron for
Rank One Update And the Google Matrix by Al Bernstein Signal Science, LLC
Introducton Rnk One Updte And the Google Mtrx y Al Bernsten Sgnl Scence, LLC www.sgnlscence.net here re two dfferent wys to perform mtrx multplctons. he frst uses dot product formulton nd the second uses
Chapter Newton-Raphson Method of Solving a Nonlinear Equation
Chpter 0.04 Newton-Rphson Method o Solvng Nonlner Equton Ater redng ths chpter, you should be ble to:. derve the Newton-Rphson method ormul,. develop the lgorthm o the Newton-Rphson method,. use the Newton-Rphson
Previously on GLT. Basic technologies. Lexical analysis. Basic technologies ASF+SDF. Concepts of programming languages
Prevously on GLT Generc Lnguge Technology: Bsc technologes Pro.dr. Mrk vn den Brnd ASF+SDF syntx descrptons semntc descrptons: type checkng nlyss trnsormtons t so to s Concepts o progrmmng lnguges syntctc
Principle Component Analysis
Prncple Component Anlyss Jng Go SUNY Bufflo Why Dmensonlty Reducton? We hve too mny dmensons o reson bout or obtn nsghts from o vsulze oo much nose n the dt Need to reduce them to smller set of fctors
Dennis Bricker, 2001 Dept of Industrial Engineering The University of Iowa. MDP: Taxi page 1
Denns Brcker, 2001 Dept of Industrl Engneerng The Unversty of Iow MDP: Tx pge 1 A tx serves three djcent towns: A, B, nd C. Ech tme the tx dschrges pssenger, the drver must choose from three possble ctons:
Model Fitting and Robust Regression Methods
Dertment o Comuter Engneerng Unverst o Clorn t Snt Cruz Model Fttng nd Robust Regresson Methods CMPE 64: Imge Anlss nd Comuter Vson H o Fttng lnes nd ellses to mge dt Dertment o Comuter Engneerng Unverst
Introduction to Numerical Integration Part II
Introducton to umercl Integrton Prt II CS 75/Mth 75 Brn T. Smth, UM, CS Dept. Sprng, 998 4/9/998 qud_ Intro to Gussn Qudrture s eore, the generl tretment chnges the ntegrton prolem to ndng the ntegrl w
3/6/00. Reading Assignments. Outline. Hidden Markov Models: Explanation and Model Learning
3/6/ Hdden Mrkov Models: Explnton nd Model Lernng Brn C. Wllms 6.4/6.43 Sesson 2 9/3/ courtesy of JPL copyrght Brn Wllms, 2 Brn C. Wllms, copyrght 2 Redng Assgnments AIMA (Russell nd Norvg) Ch 5.-.3, 2.3
4. Eccentric axial loading, cross-section core
. Eccentrc xl lodng, cross-secton core Introducton We re strtng to consder more generl cse when the xl force nd bxl bendng ct smultneousl n the cross-secton of the br. B vrtue of Snt-Vennt s prncple we
Proof that if Voting is Perfect in One Dimension, then the First. Eigenvector Extracted from the Double-Centered Transformed
Proof tht f Votng s Perfect n One Dmenson, then the Frst Egenvector Extrcted from the Doule-Centered Trnsformed Agreement Score Mtrx hs the Sme Rn Orderng s the True Dt Keth T Poole Unversty of Houston
FABER Formal Languages, Automata and Models of Computation
DVA337 FABER Forml Lnguges, Automt nd Models of Computtion Lecture 5 chool of Innovtion, Design nd Engineering Mälrdlen University 2015 1 Recp of lecture 4 y definition suset construction DFA NFA stte
UNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS. M.Sc. in Economics MICROECONOMIC THEORY I. Problem Set II
Mcroeconomc Theory I UNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS MSc n Economcs MICROECONOMIC THEORY I Techng: A Lptns (Note: The number of ndctes exercse s dffculty level) ()True or flse? If V( y )
Applied Statistics Qualifier Examination
Appled Sttstcs Qulfer Exmnton Qul_june_8 Fll 8 Instructons: () The exmnton contns 4 Questons. You re to nswer 3 out of 4 of them. () You my use ny books nd clss notes tht you mght fnd helpful n solvng
Definition of Tracking
Trckng Defnton of Trckng Trckng: Generte some conclusons bout the moton of the scene, objects, or the cmer, gven sequence of mges. Knowng ths moton, predct where thngs re gong to project n the net mge,
Partially Observable Systems. 1 Partially Observable Markov Decision Process (POMDP) Formalism
CS294-40 Lernng for Rootcs nd Control Lecture 10-9/30/2008 Lecturer: Peter Aeel Prtlly Oservle Systems Scre: Dvd Nchum Lecture outlne POMDP formlsm Pont-sed vlue terton Glol methods: polytree, enumerton,
Bayesian Networks: Approximate Inference
pproches to inference yesin Networks: pproximte Inference xct inference Vrillimintion Join tree lgorithm pproximte inference Simplify the structure of the network to mkxct inferencfficient (vritionl methods,
5.2 Exponent Properties Involving Quotients
5. Eponent Properties Involving Quotients Lerning Objectives Use the quotient of powers property. Use the power of quotient property. Simplify epressions involving quotient properties of eponents. Use
Substitution Matrices and Alignment Statistics. Substitution Matrices
Susttuton Mtrces nd Algnment Sttstcs BMI/CS 776 www.ostt.wsc.edu/~crven/776.html Mrk Crven crven@ostt.wsc.edu Ferur 2002 Susttuton Mtrces two oulr sets of mtrces for roten seuences PAM mtrces [Dhoff et
Lecture 4: Piecewise Cubic Interpolation
Lecture notes on Vrtonl nd Approxmte Methods n Appled Mthemtcs - A Perce UBC Lecture 4: Pecewse Cubc Interpolton Compled 6 August 7 In ths lecture we consder pecewse cubc nterpolton n whch cubc polynoml
DCDM BUSINESS SCHOOL NUMERICAL METHODS (COS 233-8) Solutions to Assignment 3. x f(x)
DCDM BUSINESS SCHOOL NUMEICAL METHODS (COS -8) Solutons to Assgnment Queston Consder the followng dt: 5 f() 8 7 5 () Set up dfference tble through fourth dfferences. (b) Wht s the mnmum degree tht n nterpoltng
Name: SID: Discussion Session:
Nme: SID: Dscusson Sesson: hemcl Engneerng hermodynmcs -- Fll 008 uesdy, Octoer, 008 Merm I - 70 mnutes 00 onts otl losed Book nd Notes (5 ponts). onsder n del gs wth constnt het cpctes. Indcte whether
Chapter 3 The Schrödinger Equation and a Particle in a Box
Chpter 3 The Schrödinger Eqution nd Prticle in Bo Bckground: We re finlly ble to introduce the Schrödinger eqution nd the first quntum mechnicl model prticle in bo. This eqution is the bsis of quntum mechnics
M/G/1/GD/ / System. ! Pollaczek-Khinchin (PK) Equation. ! Steady-state probabilities. ! Finding L, W q, W. ! π 0 = 1 ρ
M/G//GD/ / System! Pollcze-Khnchn (PK) Equton L q 2 2 λ σ s 2( + ρ ρ! Stedy-stte probbltes! π 0 ρ! Fndng L, q, ) 2 2 M/M/R/GD/K/K System! Drw the trnston dgrm! Derve the stedy-stte probbltes:! Fnd L,L
University of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2014
Lecture 16 8/4/14 Unversty o Washngton Department o Chemstry Chemstry 452/456 Summer Quarter 214. Real Vapors and Fugacty Henry s Law accounts or the propertes o extremely dlute soluton. s shown n Fgure
Chapter 2 Finite Automata
Chpter 2 Finite Automt 28 2.1 Introduction Finite utomt: first model of the notion of effective procedure. (They lso hve mny other pplictions). The concept of finite utomton cn e derived y exmining wht
Chapter Newton-Raphson Method of Solving a Nonlinear Equation
Chpter.4 Newton-Rphson Method of Solvng Nonlner Equton After redng ths chpter, you should be ble to:. derve the Newton-Rphson method formul,. develop the lgorthm of the Newton-Rphson method,. use the Newton-Rphson
The graphs of Rational Functions
Lecture 4 5A: The its of Rtionl Functions s x nd s x + The grphs of Rtionl Functions The grphs of rtionl functions hve severl differences compred to power functions. One of the differences is the behvior
Force = F Piston area = A
CHAPTER III Ths chapter s an mportant transton between the propertes o pure substances and the most mportant chapter whch s: the rst law o thermodynamcs In ths chapter, we wll ntroduce the notons o heat,
A Family of Multivariate Abel Series Distributions. of Order k
Appled Mthemtcl Scences, Vol. 2, 2008, no. 45, 2239-2246 A Fmly of Multvrte Abel Seres Dstrbutons of Order k Rupk Gupt & Kshore K. Ds 2 Fculty of Scence & Technology, The Icf Unversty, Agrtl, Trpur, Ind
n f(x i ) x. i=1 In section 4.2, we defined the definite integral of f from x = a to x = b as n f(x i ) x; f(x) dx = lim i=1
The Fundmentl Theorem of Clculus As we continue to study the re problem, let s think bck to wht we know bout computing res of regions enclosed by curves. If we wnt to find the re of the region below the
4 7x =250; 5 3x =500; Read section 3.3, 3.4 Announcements: Bell Ringer: Use your calculator to solve
Dte: 3/14/13 Objective: SWBAT pply properties of exponentil functions nd will pply properties of rithms. Bell Ringer: Use your clcultor to solve 4 7x =250; 5 3x =500; HW Requests: Properties of Log Equtions
Graph Theory. Dr. Saad El-Zanati, Faculty Mentor Ryan Bunge Graduate Assistant Illinois State University REU. Graph Theory
Grph Theory Gibson, Ngel, Stnley, Zle Specil Types of Bckground Motivtion Grph Theory Dniel Gibson, Concordi University Jckelyn Ngel, Dominicn University Benjmin Stnley, New Mexico Stte University Allison
First Midterm Examination
24-25 Fll Semester First Midterm Exmintion ) Give the stte digrm of DFA tht recognizes the lnguge A over lphet Σ = {, } where A = {w w contins or } 2) The following DFA recognizes the lnguge B over lphet
SVMs for regression Non-parametric/instance based classification method
S 75 Mchne ernng ecture Mos Huskrecht mos@cs.ptt.edu 539 Sennott Squre SVMs for regresson Non-prmetrc/nstnce sed cssfcton method S 75 Mchne ernng Soft-mrgn SVM Aos some fet on crossng the seprtng hperpne
Bi-level models for OD matrix estimation
TNK084 Trffc Theory seres Vol.4, number. My 2008 B-level models for OD mtrx estmton Hn Zhng, Quyng Meng Abstrct- Ths pper ntroduces two types of O/D mtrx estmton model: ME2 nd Grdent. ME2 s mxmum-entropy
E-Companion: Mathematical Proofs
E-omnon: Mthemtcl Poo Poo o emm : Pt DS Sytem y denton o t ey to vey tht t ncee n wth d ncee n We dene } ] : [ { M whee / We let the ttegy et o ech etle n DS e ]} [ ] [ : { M w whee M lge otve nume oth
ANALOG CIRCUIT SIMULATION BY STATE VARIABLE METHOD
U.P.B. Sc. Bull., Seres C, Vol. 77, Iss., 25 ISSN 226-5 ANAOG CIRCUIT SIMUATION BY STATE VARIABE METHOD Rodc VOICUESCU, Mh IORDACHE 22 An nlog crcut smulton method, bsed on the stte euton pproch, s presented.
Lecture 5 Single factor design and analysis
Lectue 5 Sngle fcto desgn nd nlss Completel ndomzed desgn (CRD Completel ndomzed desgn In the desgn of expements, completel ndomzed desgns e fo studng the effects of one pm fcto wthout the need to tke
CS 331 DESIGN AND ANALYSIS OF ALGORITHMS DYNAMIC PROGRAMMING. Dr. Daisy Tang
CS DESIGN ND NLYSIS OF LGORITHMS DYNMIC PROGRMMING Dr. Dasy Tang Dynamc Programmng Idea: Problems can be dvded nto stages Soluton s a sequence o decsons and the decson at the current stage s based on the
CSC 473 Automata, Grammars & Languages 11/9/10
CSC 473 utomt, Grmmrs & Lnguges 11/9/10 utomt, Grmmrs nd Lnguges Discourse 06 Decidbility nd Undecidbility Decidble Problems for Regulr Lnguges Theorem 4.1: (embership/cceptnce Prob. for DFs) = {, w is
Bases for Vector Spaces
Bses for Vector Spces 2-26-25 A set is independent if, roughly speking, there is no redundncy in the set: You cn t uild ny vector in the set s liner comintion of the others A set spns if you cn uild everything
Quiz: Experimental Physics Lab-I
Mxmum Mrks: 18 Totl tme llowed: 35 mn Quz: Expermentl Physcs Lb-I Nme: Roll no: Attempt ll questons. 1. In n experment, bll of mss 100 g s dropped from heght of 65 cm nto the snd contner, the mpct s clled
Chapters 18 & 19: Themodynamics review. All macroscopic (i.e., human scale) quantities must ultimately be explained on the microscopic scale.
Chapters 18 & 19: Themodynamcs revew ll macroscopc (.e., human scale) quanttes must ultmately be explaned on the mcroscopc scale. Chapter 18: Thermodynamcs Thermodynamcs s the study o the thermal energy
CS 275 Automata and Formal Language Theory
CS 275 Automt nd Forml Lnguge Theory Course Notes Prt II: The Recognition Problem (II) Chpter II.5.: Properties of Context Free Grmmrs (14) Anton Setzer (Bsed on book drft by J. V. Tucker nd K. Stephenson)
ESCI 342 Atmospheric Dynamics I Lesson 1 Vectors and Vector Calculus
ESI 34 tmospherc Dnmcs I Lesson 1 Vectors nd Vector lculus Reference: Schum s Outlne Seres: Mthemtcl Hndbook of Formuls nd Tbles Suggested Redng: Mrtn Secton 1 OORDINTE SYSTEMS n orthonorml coordnte sstem
Read section 3.3, 3.4 Announcements:
Dte: 3/1/13 Objective: SWBAT pply properties of exponentil functions nd will pply properties of rithms. Bell Ringer: 1. f x = 3x 6, find the inverse, f 1 x., Using your grphing clcultor, Grph 1. f x,f
Generalized Fano and non-fano networks
Generlized Fno nd non-fno networks Nildri Ds nd Brijesh Kumr Ri Deprtment of Electronics nd Electricl Engineering Indin Institute of Technology Guwhti, Guwhti, Assm, Indi Emil: {d.nildri, bkri}@iitg.ernet.in
GAUSS ELIMINATION. Consider the following system of algebraic linear equations
Numercl Anlyss for Engneers Germn Jordnn Unversty GAUSS ELIMINATION Consder the followng system of lgebrc lner equtons To solve the bove system usng clsscl methods, equton () s subtrcted from equton ()
523 P a g e. is measured through p. should be slower for lesser values of p and faster for greater values of p. If we set p*
R. Smpth Kumr, R. Kruthk, R. Rdhkrshnn / Interntonl Journl of Engneerng Reserch nd Applctons (IJERA) ISSN: 48-96 www.jer.com Vol., Issue 4, July-August 0, pp.5-58 Constructon Of Mxed Smplng Plns Indexed
We partition C into n small arcs by forming a partition of [a, b] by picking s i as follows: a = s 0 < s 1 < < s n = b.
![We partition C into n small arcs by forming a partition of [a, b] by picking s i as follows: a = s 0 < s 1 < < s n = b.](/thumbs/93/114277851.jpg "We partition C into n small arcs by forming a partition of [a, b] by picking s i as follows: a = s 0 < s 1 < < s n = b.")
Mth 255 - Vector lculus II Notes 4.2 Pth nd Line Integrls We begin with discussion of pth integrls (the book clls them sclr line integrls). We will do this for function of two vribles, but these ides cn
Electrochemical Thermodynamics. Interfaces and Energy Conversion
CHE465/865, 2006-3, Lecture 6, 18 th Sep., 2006 Electrochemcl Thermodynmcs Interfces nd Energy Converson Where does the energy contrbuton F zϕ dn come from? Frst lw of thermodynmcs (conservton of energy):
CHI-SQUARE DIVERGENCE AND MINIMIZATION PROBLEM
CHI-SQUARE DIVERGENCE AND MINIMIZATION PROBLEM PRANESH KUMAR AND INDER JEET TANEJA Abstrct The mnmum dcrmnton nformton prncple for the Kullbck-Lebler cross-entropy well known n the lterture In th pper
8. INVERSE Z-TRANSFORM
8. INVERSE Z-TRANSFORM The proce by whch Z-trnform of tme ere, nmely X(), returned to the tme domn clled the nvere Z-trnform. The nvere Z-trnform defned by: Computer tudy Z X M-fle trn.m ued to fnd nvere
TEST 5 (phy 240) 2. Show that the volume coefficient of thermal expansion for an ideal gas at constant pressure is temperature dependent and given by
ES 5 (phy 40). a) Wrte the zeroth law o thermodynamcs. b) What s thermal conductvty? c) Identyng all es, draw schematcally a P dagram o the arnot cycle. d) What s the ecency o an engne and what s the coecent
CS 275 Automata and Formal Language Theory
CS 275 utomt nd Forml Lnguge Theory Course Notes Prt II: The Recognition Prolem (II) Chpter II.5.: Properties of Context Free Grmmrs (14) nton Setzer (Bsed on ook drft y J. V. Tucker nd K. Stephenson)
Lecture 22: Logic Synthesis (1)
Lecture 22: Logc Synthess (1) Sldes courtesy o Demng Chen Some sldes Courtesy o Pro. J. Cong o UCLA Outlne Redng Synthess nd optmzton o dgtl crcuts, G. De Mchel, 1994, Secton 2.5-2.5.1 Overvew Boolen lgebr
CALIBRATION OF SMALL AREA ESTIMATES IN BUSINESS SURVEYS
CALIBRATION OF SMALL AREA ESTIMATES IN BUSINESS SURVES Rodolphe Prm, Ntle Shlomo Southmpton Sttstcl Scences Reserch Insttute Unverst of Southmpton Unted Kngdom SAE, August 20 The BLUE-ETS Project s fnnced
90 S.S. Drgomr nd (t b)du(t) =u()(b ) u(t)dt: If we dd the bove two equltes, we get (.) u()(b ) u(t)dt = p(; t)du(t) where p(; t) := for ll ; t [; b]:
![90 S.S. Drgomr nd (t b)du(t) =u()(b ) u(t)dt: If we dd the bove two equltes, we get (.) u()(b ) u(t)dt = p(; t)du(t) where p(; t) := for ll ; t [; b]:](/thumbs/77/75155737.jpg "90 S.S. Drgomr nd (t b)du(t) =u()(b ) u(t)dt: If we dd the bove two equltes, we get (.) u()(b ) u(t)dt = p(; t)du(t) where p(; t) := for ll ; t [; b]:")
RGMIA Reserch Report Collecton, Vol., No. 1, 1999 http://sc.vu.edu.u/οrgm ON THE OSTROWSKI INTEGRAL INEQUALITY FOR LIPSCHITZIAN MAPPINGS AND APPLICATIONS S.S. Drgomr Abstrct. A generlzton of Ostrowsk's
New Expansion and Infinite Series
Interntionl Mthemticl Forum, Vol. 9, 204, no. 22, 06-073 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/0.2988/imf.204.4502 New Expnsion nd Infinite Series Diyun Zhng College of Computer Nnjing University
KNOWLEDGE-BASED AGENTS INFERENCE
AGENTS THAT REASON LOGICALLY KNOWLEDGE-BASED AGENTS Two components: knowledge bse, nd n inference engine. Declrtive pproch to building n gent. We tell it wht it needs to know, nd It cn sk itself wht to
Course Review Introduction to Computer Methods
Course Revew Wht you hopefully hve lerned:. How to nvgte nsde MIT computer system: Athen, UNIX, emcs etc. (GCR). Generl des bout progrmmng (GCR): formultng the problem, codng n Englsh trnslton nto computer
Solubilities and Thermodynamic Properties of SO 2 in Ionic
Solubltes nd Therodync Propertes of SO n Ionc Lquds Men Jn, Yucu Hou, b Weze Wu, *, Shuhng Ren nd Shdong Tn, L Xo, nd Zhgng Le Stte Key Lbortory of Checl Resource Engneerng, Beng Unversty of Checl Technology,
Math Lecture 23
Mth 8 - Lecture 3 Dyln Zwick Fll 3 In our lst lecture we delt with solutions to the system: x = Ax where A is n n n mtrix with n distinct eigenvlues. As promised, tody we will del with the question of
v v at 1 2 d vit at v v 2a d
SPH3UW Unt. Accelerton n One Denon Pge o 9 Note Phyc Inventory Accelerton the rte o chnge o velocty. Averge ccelerton, ve the chnge n velocty dvded by the te ntervl, v v v ve. t t v dv Intntneou ccelerton
Support vector machines for regression
S 75 Mchne ernng ecture 5 Support vector mchnes for regresson Mos Huskrecht mos@cs.ptt.edu 539 Sennott Squre S 75 Mchne ernng he decson oundr: ˆ he decson: Support vector mchnes ˆ α SV ˆ sgn αˆ SV!!: Decson
( dg. ) 2 dt. + dt. dt j + dh. + dt. r(t) dt. Comparing this equation with the one listed above for the length of see that
Arc Length of Curves in Three Dimensionl Spce If the vector function r(t) f(t) i + g(t) j + h(t) k trces out the curve C s t vries, we cn mesure distnces long C using formul nerly identicl to one tht we
Convert the NFA into DFA
Convert the NF into F For ech NF we cn find F ccepting the sme lnguge. The numer of sttes of the F could e exponentil in the numer of sttes of the NF, ut in prctice this worst cse occurs rrely. lgorithm:
Finite Difference Method
7/0/07 Instructor r. Ramond Rump (9) 747 698 rcrump@utep.edu EE 337 Computatonal Electromagnetcs (CEM) Lecture #0 Fnte erence Method Lecture 0 These notes ma contan coprghted materal obtaned under ar use
Haddow s Experiment:
schemtc drwng of Hddow's expermentl set-up movng pston non-contctng moton sensor bems of sprng steel poston vres to djust frequences blocks of sold steel shker Hddow s Experment: terr frm Theoretcl nd
THE EXISTENCE-UNIQUENESS THEOREM FOR FIRST-ORDER DIFFERENTIAL EQUATIONS.
THE EXISTENCE-UNIQUENESS THEOREM FOR FIRST-ORDER DIFFERENTIAL EQUATIONS RADON ROSBOROUGH https://intuitiveexplntionscom/picrd-lindelof-theorem/ This document is proof of the existence-uniqueness theorem
Lecture 1: Introduction to integration theory and bounded variation
Lecture 1: Introduction to integrtion theory nd bounded vrition Wht is this course bout? Integrtion theory. The first question you might hve is why there is nything you need to lern bout integrtion. You
f is a function that maps a structure (x, y) to a feature vector w is a parameter vector (also a member of R d )
Three Components of Globl Ler Models f is function tht mps structure (x, y) to feture vector f(x, y) R d 6.864 (Fll 2007) Globl Ler Models: Prt III GEN is function tht mps n put x to set of cndidtes GEN(x)
Statistics 423 Midterm Examination Winter 2009
Sttstcs 43 Mdterm Exmnton Wnter 009 Nme: e-ml: 1. Plese prnt your nme nd e-ml ddress n the bove spces.. Do not turn ths pge untl nstructed to do so. 3. Ths s closed book exmnton. You my hve your hnd clcultor
Exponentials - Grade 10 [CAPS] *
![Exponentials - Grade 10 [CAPS] *](/thumbs/88/115984632.jpg "Exponentials - Grade 10 [CAPS] *")
OpenStx-CNX module: m859 Exponentils - Grde 0 [CAPS] * Free High School Science Texts Project Bsed on Exponentils by Rory Adms Free High School Science Texts Project Mrk Horner Hether Willims This work
Computational Biology Lecture 8: Substitution matrices Saad Mneimneh
Computatonal Bology Lecture 8: Substtuton matrces Saad Mnemneh As we have ntroduced last tme, smple scorng schemes lke + or a match, - or a msmatch and -2 or a gap are not justable bologcally, especally
Fall 2012 Analysis of Experimental Measurements B. Eisenstein/rev. S. Errede
Fll Anlss of Epermentl Mesurements B. Esensten/rev. S. Errede Monte Crlo Methods/Technques: These re mong the most powerful tools for dt nlss nd smulton of eperments. The growth of ther mportnce s closel
Review of linear algebra. Nuno Vasconcelos UCSD
Revew of lner lgebr Nuno Vsconcelos UCSD Vector spces Defnton: vector spce s set H where ddton nd sclr multplcton re defned nd stsf: ) +( + ) (+ )+ 5) λ H 2) + + H 6) 3) H, + 7) λ(λ ) (λλ ) 4) H, - + 8)
Lecture 6 Regular Grammars
Lecture 6 Regulr Grmmrs COT 4420 Theory of Computtion Section 3.3 Grmmr A grmmr G is defined s qudruple G = (V, T, S, P) V is finite set of vribles T is finite set of terminl symbols S V is specil vrible
Riemann Sums and Riemann Integrals
Riemnn Sums nd Riemnn Integrls Jmes K. Peterson Deprtment of Biologicl Sciences nd Deprtment of Mthemticl Sciences Clemson University August 26, 203 Outline Riemnn Sums Riemnn Integrls Properties Abstrct
CS:4330 Theory of Computation Spring Regular Languages. Equivalences between Finite automata and REs. Haniel Barbosa
CS:4330 Theory of Computtion Spring 208 Regulr Lnguges Equivlences between Finite utomt nd REs Hniel Brbos Redings for this lecture Chpter of [Sipser 996], 3rd edition. Section.3. Finite utomt nd regulr
Endogenous timing in a mixed oligopoly consisting of a single public firm and foreign competitors. Abstract
Endogenous tmng n a mxed olgopoly consstng o a sngle publc rm and oregn compettors Yuanzhu Lu Chna Economcs and Management Academy, Central Unversty o Fnance and Economcs Abstract We nvestgate endogenous
CH 9 INTRO TO EQUATIONS
CH 9 INTRO TO EQUATIONS INTRODUCTION I m thinking of number. If I dd 10 to the number, the result is 5. Wht number ws I thinking of? R emember this question from Chpter 1? Now we re redy to formlize the
Chapter 3 Single Random Variables and Probability Distributions (Part 2)
Chpter 3 Single Rndom Vriles nd Proilit Distriutions (Prt ) Contents Wht is Rndom Vrile? Proilit Distriution Functions Cumultive Distriution Function Proilit Densit Function Common Rndom Vriles nd their
Strong Bisimulation. Overview. References. Actions Labeled transition system Transition semantics Simulation Bisimulation
Strong Bisimultion Overview Actions Lbeled trnsition system Trnsition semntics Simultion Bisimultion References Robin Milner, Communiction nd Concurrency Robin Milner, Communicting nd Mobil Systems 32
1 Linear Least Squares
Lest Squres Pge 1 1 Liner Lest Squres I will try to be consistent in nottion, with n being the number of dt points, nd m < n being the number of prmeters in model function. We re interested in solving
An Ising model on 2-D image
School o Coputer Scence Approte Inerence: Loopy Bele Propgton nd vrnts Prolstc Grphcl Models 0-708 Lecture 4, ov 7, 007 Receptor A Knse C Gene G Receptor B Knse D Knse E 3 4 5 TF F 6 Gene H 7 8 Hetunndn
ORDINARY DIFFERENTIAL EQUATIONS
6 ORDINARY DIFFERENTIAL EQUATIONS Introducton Runge-Kutt Metods Mult-step Metods Sstem o Equtons Boundr Vlue Problems Crcterstc Vlue Problems Cpter 6 Ordnr Derentl Equtons / 6. Introducton In mn engneerng
Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives
Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn
1.4 Nonregular Languages
74 1.4 Nonregulr Lnguges The number of forml lnguges over ny lphbet (= decision/recognition problems) is uncountble On the other hnd, the number of regulr expressions (= strings) is countble Hence, ll
along the vector 5 a) Find the plane s coordinate after 1 hour. b) Find the plane s coordinate after 2 hours. c) Find the plane s coordinate
L8 VECTOR EQUATIONS OF LINES HL Mth - Sntowski Vector eqution of line 1 A plne strts journey t the point (4,1) moves ech hour long the vector. ) Find the plne s coordinte fter 1 hour. b) Find the plne
GRADE 4. Division WORKSHEETS
GRADE Division WORKSHEETS Division division is shring nd grouping Division cn men shring or grouping. There re cndies shred mong kids. How mny re in ech shre? = 3 There re 6 pples nd go into ech bsket.
C. C^mpenu, K. Slom, S. Yu upper boun of mn. So our result is tight only for incomplete DF's. For restricte vlues of m n n we present exmples of DF's
Journl of utomt, Lnguges n Combintorics u (v) w, x{y c OttovonGuerickeUniversitt Mgeburg Tight lower boun for the stte complexity of shue of regulr lnguges Cezr C^mpenu, Ki Slom Computing n Informtion
CHAPTER IV RESEARCH FINDING AND DISCUSSIONS
CHAPTER IV RESEARCH FINDING AND DISCUSSIONS A. Descrpton of Research Fndng. The Implementaton of Learnng Havng ganed the whole needed data, the researcher then dd analyss whch refers to the statstcal data
Lesson 1: Quadratic Equations
Lesson 1: Qudrtic Equtions Qudrtic Eqution: The qudrtic eqution in form is. In this section, we will review 4 methods of qudrtic equtions, nd when it is most to use ech method. 1. 3.. 4. Method 1: Fctoring
Energy Bands Energy Bands and Band Gap. Phys463.nb Phenomenon
Phys463.nb 49 7 Energy Bnds Ref: textbook, Chpter 7 Q: Why re there insultors nd conductors? Q: Wht will hppen when n electron moves in crystl? In the previous chpter, we discussed free electron gses,