Database design and implementation CMPSCI 645. Lecture 14: Data Provenance
|
|
- Roberta York
- 5 years ago
- Views:
Transcription
1 Databas dsign and implmntation CMPSCI 645 Lctur 14: Data Provnanc 1
2 Provnanc provnanc, n. Th fact of coming from som particular sourc or quartr; origin, drivation [Oxford English Dictionary] } Data provnanc / linag } [BunmanKhannaTan01]: aims to xplain how a particular rsult was drivd. } Data-intnsiv scinc } Worry about provnanc 2
3 Motivation } Data intgration [WangMadnick90, LBrssanMadnick98] } Data Warhousing [CuiWidonWinr00] } Scintific Data Managmnt [BunmanKhannaTan01] } Dtrmins trust on rsults } Ensur rliability, quality of data } Rpatability/vrifiability } Avoid ffort duplication } Undrstanding transport of annotations 3
4 Exampl of data provnanc } A typical qustion: } For a givn databas qury Q, a databas D and a tupl t in th output of Q(D), which parts of D contribut to t? R Emp Dpt John D01 Susan D02 Anna D04 S Did D01 D02 D03 Mgr Mary Kn Ed Q = slct r.a, r.b, s.c from R r, S s whr r.b = s.b } Th qustion can b applid to attribut valus, tabls, tc. Q Emp Dpt Mgr John D01 Mary Susan D02 Kn 4
5 Timlin A Polygn Modl for Htrognous Databas Systms: Th Sourc Tagging Prspctiv. Y. R. Wang and S. E. Madnick. VLDB Supporting Fin-graind Data Linag in a Databas Visualization Environmnt. A. Woodruff and M. Stonbrakr. ICDE Tracing th Linag of Viw Data in a Warhousing Environmnt. Y. Cui, J. Widom and J. L. Winr. TODS Why and Whr: A Charactrization of Data Provnanc. P. Bunman, S. Khanna, Tan. ICDT On Propagation of Dltions and Annotations through Viws. P. Bunman, S. Khanna, Tan. PODS Containmnt of Rlational Quris with Annotation Propagation. Tan. DBPL
6 Timlin An Annotation Managmnt Systm for Rlational Databass. D. Bhagwat, L. Chiticariu, Tan, G. Vijayvargiya. VLDB 2004, VLDB Journal MONDRIAN: Annotating and Qurying Databass through Colors and Blocks. ICDE Provnanc in Curatd Databass. P. Bunman, A. Chapman and J. Chny. SIGMOD Annotation propagation rvisitd for ky prsrving viws. Gao Cong, Wnfi Fan, Floris Grts. CIKM ULDBs: Databass with Uncrtainty and Linag. O. Bnjlloun, A.D. Sarma, A. Y. Halvy, and J. Widom. VLDB Dbugging Schma Mappings with Routs. L. Chiticariu and Tan. VLDB On th Exprssivnss of Implicit Provnanc in Qury and Updat Languags. P. Bunman, J. Chny and S. Vansummrn. ICDT Intntional Associations Btwn Data and Mtadata. D. Srivastava and Y. Vlgrakis. SIGMOD Provnanc Smirings. T. J. Grn, G. Karvounarakis and V. Tannn. PODS Annotatd XML: Quris and Provnanc: J. N. Fostr, T. J. Grn, V. Tannn. PODS Containmnt of Conjunctiv Quris on Annotatd Rlations: T. J. Grn, ICDT
7 Two approachs } Eagr or annotation-basd } Changs th transformation from Q to Q to carry xtra information } Sourc data not ndd aftr transformation } Lazy or non-annotation basd } Q is unchangd } Good whn xtra storag is an issu } Rcomputation and accss to sourc rquird Annotation-basd Q Q Extra information 7
8 Typs of provnanc } Why } What DB tupls contribut to th prsnc of ach rsult tupl?! } How } By what procss is ach output tupl producd from th DB instanc?! } Whr } Whr (from what attribut of what tupl) dos ach output tupl valu com from?! 8
9 Why-provnanc xampl Agncis nam basd in phon t 1 : San Francisco t 2 : Santa Cruz ExtrnalTours nam dstination typ pric t 3 : San Francisco cabl car $50 t 4 : Santa Cruz bus $100 t 5 : Santa Cruz boat $250 t 6 : Montry boat $400 t 7 : Montry boat $200 t 8 : Carml train $90 Q: SELECT dstination, a.nam, a.phon a.phon FROM Agncis a, ExtrnalTours WHERE a.nam =.nam AND.typ= boat Rsult of Q 1 : nam phon
10 Linag } Linag for an output tupl t is a subst of th input tupls which ar rlvant to th output tupl Agncis nam basd in phon t 1 : San Francisco t 2 : Santa Cruz ExtrnalTours nam dstination typ pric t 3 : San Francisco cabl car $50 t 4 : Santa Cruz bus $100 t 5 : Santa Cruz boat $250 t 6 : Montry boat $400 t 7 : Montry boat $200 t 8 : Carml train $90 Q: SELECT dstination, DISTINCT a.nam, a.phon a.phon FROM Agncis a, ExtrnalTours WHERE a.nam =.nam AND.typ= boat Rsult of Q 1 : nam phon Linag: {t1, t5, t6} Problm: Not vry prcis..g. linag abov dos not spcify that t5 and t6 do not both nd to xist. 10
11 Why provnanc Agncis nam basd in phon t 1 : San Francisco t 2 : Santa Cruz ExtrnalTours nam dstination typ pric t 3 : San Francisco cabl car $50 t 4 : Santa Cruz bus $100 t 5 : Santa Cruz boat $250 t 6 : Montry boat $400 t 7 : Montry boat $200 t 8 : Carml train $90 Q: SELECT dstination, DISTINCT a.nam, a.phon a.phon FROM Agncis a, ExtrnalTours WHERE a.nam =.nam AND.typ= boat Witnss of t: Any subst of th databas sufficint to rconstruct tupl t in th qury rsult. Witnss basis: Lavs of th proof tr showing how rsult tupl t is gnratd Rsult of Q 1 : nam phon Linag: {t1, t5, t6} {t1, t5} {t1, t6} {t1, t2, t6, t8} {{t1, t5}, {t1, t6}} 11
12 Why: qury rwriting R Q(I),Q 0 (I) t1 t t2 t3 Q(x, y) : R(x, y) Q 0 (x, y) : R(x, y),r(x, z) Why(Q, I, t): {{t1}} Why(Q, I, t): {{t1}, {t1, t2}} Minimal witnss basis: Minimal witnsss in th witnss basis 12
13 Th viw dltion problm } D a databas instanc and V=Q(D) a viw dfind ovr D. } Find a st of tupls ΔD to rmov from D so that a spcific tupl t is rmovd from th viw } Minimiz th numbr of sid-ffcts in th viw } Viw sid-ffct problm Hard: quris with joins and projction or union PTIME: th rst } Minimiz th numbr of tupls dltd from D } Sourc sid-ffct problm Sam dichotomy [BunmanKhannaTan. PODS02] 13
14 How provnanc } Idntifis witnss tupls and th oprations prformd on thm to produc ach rsult tupl } Exprsss oprations using provnanc smirings } MERGE (+): union or projction } JOIN (): joins 14
15 Propagating annotations R A B C a b c p Join (on B) R S A B C D E a b c d p r S D B E d b r Th annotation p r mans joint us of th data annotatd by p and th data annotatd by r 15
16 Propagating annotations (2) R A B C a b c p Union R S A B C a b c p + r S A B C a b c r Th annotation p + r mans altrnativ us of th data annotatd by p and th data annotatd by r 16
17 Propagating Annotations (3) R A B C π AB R A B a b c 1 p Projct a b a b c 2 r p + r + s a b c 3 s + dnots altrnativ us of data 17
18 An xampl (SPJU) R A B C a b c d b f g p r s Q = σ C= π AC (π AB R π BC R π AC R π BC R) A C a a d d f c c (p p + p p) 0 p r 1 r p 0 (r r + r s + r r) 1 (s s + s r + s s) 1 For slction, multiply with annotation 0 and 1. 18
19 Exampl Agncis nam basd in phon t 1 : San Francisco t 2 : Santa Cruz ExtrnalTours nam dstination typ pric t 3 : San Francisco cabl car $50 t 4 : Santa Cruz bus $100 t 5 : Santa Cruz boat $250 t 6 : Montry boat $400 t 7 : Montry boat $200 t 8 : Carml train $90 Q: SELECT dstination, a.phon FROM Agncis a, (SELECT nam, basd in AS dstination FROM Agncis a UNION SELECT nam, dstination FROM ExtrnalTours) WHERE a.nam =.nam 19
20 Exampl Agncis nam basd in phon t 1 : San Francisco t 2 : Santa Cruz nam dstination ExtrnalTours nam dstination typ pric t 3 : San Francisco cabl car $50 t 4 : Santa Cruz bus $100 t 5 : Santa Cruz boat $250 t 6 : Montry boat $400 t 7 : Montry boat $200 t 8 : Carml train $90 Q: SELECT dstination, a.phon FROM Agncis a, (SELECT nam, basd in AS dstination FROM Agncis a UNION SELECT nam, dstination FROM ExtrnalTours) WHERE a.nam =.nam 20
21 Exampl Agncis nam basd in phon t 1 : San Francisco t 2 : Santa Cruz t 1 + t 3 t 4 + t 5 t 6 t 7 t 8 t 2 nam dstination San Francisco Santa Cruz Montry Montry Carml Santa Cruz Q: SELECT dstination, a.phon FROM Agncis a, (SELECT nam, basd in AS dstination FROM Agncis a UNION SELECT nam, dstination FROM ExtrnalTours) WHERE a.nam =.nam ExtrnalTours nam dstination typ pric t 3 : San Francisco cabl car $50 t 4 : Santa Cruz bus $100 t 5 : Santa Cruz boat $250 t 6 : Montry boat $400 t 7 : Montry boat $200 t 8 : Carml train $90 21
22 Exampl Agncis nam basd in phon t 1 : San Francisco t 2 : Santa Cruz t 1 + t 3 t 4 + t 5 t 6 t 7 t 8 t 2 nam dstination San Francisco Santa Cruz Montry Montry Carml Santa Cruz Q: SELECT dstination, a.phon FROM Agncis a, (SELECT nam, basd in AS dstination FROM Agncis a UNION SELECT nam, dstination FROM ExtrnalTours) WHERE a.nam =.nam ExtrnalTours nam dstination typ pric t 3 : San Francisco cabl car $50 t 4 : Santa Cruz bus $100 t 5 : Santa Cruz boat $250 t 6 : Montry boat $400 t 7 : Montry boat $200 t 8 : Carml train $90 22
23 Exampl Agncis nam basd in phon t 1 : San Francisco t 2 : Santa Cruz t 1 + t 3 t 4 + t 5 t 6 t 7 t 8 t 2 nam dstination San Francisco Santa Cruz Montry Montry Carml Santa Cruz Q: SELECT dstination, a.phon FROM Agncis a, (SELECT nam, basd in AS dstination FROM Agncis a UNION SELECT nam, dstination FROM ExtrnalTours) WHERE a.nam =.nam RESULT dstination phon 23
24 Exampl Agncis nam basd in phon t 1 : San Francisco t 2 : Santa Cruz t 1 + t 3 t 4 + t 5 t 6 t 7 t 8 t 2 nam dstination San Francisco Santa Cruz Montry Montry Carml Santa Cruz Q: SELECT dstination, a.phon FROM Agncis a, (SELECT nam, basd in AS dstination FROM Agncis a UNION SELECT nam, dstination FROM ExtrnalTours) WHERE a.nam =.nam RESULT dstination phon San Francisco
25 Exampl Agncis nam basd in phon t 1 : San Francisco t 2 : Santa Cruz t 1 + t 3 t 4 + t 5 t 6 t 7 t 8 t 2 nam dstination San Francisco Santa Cruz Montry Montry Carml Santa Cruz Q: SELECT dstination, a.phon FROM Agncis a, (SELECT nam, basd in AS dstination FROM Agncis a UNION SELECT nam, dstination FROM ExtrnalTours) WHERE a.nam =.nam RESULT dstination phon San Francisco t 1 (t 1 + t 3 ) 25
26 Exampl Agncis nam basd in phon t 1 : San Francisco t 2 : Santa Cruz t 1 + t 3 t 4 + t 5 t 6 t 7 t 8 t 2 nam dstination San Francisco Santa Cruz Montry Montry Carml Santa Cruz Q: SELECT dstination, a.phon FROM Agncis a, (SELECT nam, basd in AS dstination FROM Agncis a UNION SELECT nam, dstination FROM ExtrnalTours) WHERE a.nam =.nam RESULT dstination phon San Francisco t 1 (t 1 + t 3 ) Santa Cruz
27 Exampl Agncis nam basd in phon t 1 : San Francisco t 2 : Santa Cruz t 1 + t 3 t 4 + t 5 t 6 t 7 t 8 t 2 nam dstination San Francisco Santa Cruz Montry Montry Carml Santa Cruz Q: SELECT dstination, a.phon FROM Agncis a, (SELECT nam, basd in AS dstination FROM Agncis a UNION SELECT nam, dstination FROM ExtrnalTours) WHERE a.nam =.nam RESULT dstination phon San Francisco t 1 (t 1 + t 3 ) Santa Cruz t 1 (t 4 + t 5 ) 27
28 Exampl Agncis nam basd in phon t 1 : San Francisco t 2 : Santa Cruz t 1 + t 3 t 4 + t 5 t 6 t 7 t 8 t 2 nam dstination San Francisco Santa Cruz Montry Montry Carml Santa Cruz Q: SELECT dstination, a.phon FROM Agncis a, (SELECT nam, basd in AS dstination FROM Agncis a UNION SELECT nam, dstination FROM ExtrnalTours) WHERE a.nam =.nam RESULT dstination phon San Francisco t 1 (t 1 + t 3 ) Santa Cruz t 1 (t 4 + t 5 ) Montry t 1 t 6 Montry t 2 t 7 Carml t 2 t 8 Santa Cruz t
29 Back to xampl R A B C a b c d b f g p r s Q A C a c a d c (p p + p p) 0 p r 1 r p 0 d (r r + r s + r r) 1 f (s s + s r + s s) 1 32
30 Applying th laws: polynomials R A B C a b c p Q A C a pr d b r d 2r 2 + rs f g s f rs + 2s 2 Polynomials with cofficints in N and annotation tokns as indtrminats p, r, s captur a vry gnral form of provnanc 33
31 How to rad this provnanc R A B C a b c p Q A C a pr d b r d 2r 2 + rs f g s f rs + 2s 2 3 ways to driv (d ) 2 of th ways us only r, but thy us it twic th 3 rd uss r onc and s onc 34
32 Dltion Propagation R A B C a b c p Q A C a pr Q A C a 0 Q A C f 2s 2 d b r d 2r 2 + rs d 0 f g s f rs + 2s 2 f 2s 2 Dlt (d b ) from R St r to 0! 35
33 Som usful commutativ smirings (B,,, fals, tru) St Smantics (N, +,, 0, 1) Bag Smantics (P ( ),,,, ) Probabilistic vnts (A, min, max, 0,P) A = P<C<S<T<0 Accss Control Public Top Scrt 36
34 Provnanc hirarchy most informativ 2x 2 y + xy + 5y 2 + z N[X] x 2 y + xy + y 2 + z B[X] 3xy + 5y + z T rio(x) W hy(x) xy + y + z last informativ Lin(X) xyz P osbool(x) y + z 38
35 Exampl: distrust scors } Smiring: (R +, min, +,, 0) } Tokns: X={p,r,s} } Assignmnt function f : X! K f(p) =0,f(r) =1.5, f(s) = h(2r 2 + rs) =h(r r + r r + r s) = min(f(r)+f(r),f(r)+f(r),f(r)+f(s)) = min( , , )=
36 Exampl: accss control (A, min, max, 0,P) whr A = P<C<S<T<0 a c 2p 2 a b c d b f g p=p, r=s, s=t p r s q a d d f c pr pr 2r 2 +rs 2s 2 +rs a b c d b f g P S T q a a d d c c P S S S Evaluat with p=p, r=s, s=t using min for +, max for f T Usr with scrt claranc 40
37 Whr provnanc } Idntifis witnss clls } Important for annotations SELECT * FROM R WHERE A <> 5 UNION SELECT A, 7 AS B FROM R WHERE A= 5 UPDATE R SET B=7 WHERE A=5 R A B ? A B
38 Color algbra [Grts, Kmntsitsidis, Milano 06] A B P[Q] A B Q = SELECT * FROM R WHERE A <> 5 UNION SELECT A, 7 AS B FROM R WHERE A= 5 42
39 Color algbra A B P[Q] A B Q = UPDATE R SET B=7 WHERE A=5 43
40 Whr provnanc and smirings R u A x B y C 1 a 1 b 1 c 1 p S v B 1 C 1 b z c 1 m π AC (π AB R (π BC R S)) A 1 C 1 a 1 c 1 u 2 p 2 xy 2 + uvpmxyz 1 is a nutral annotation, usd whn w don t bothr to track data 44
41 Diffrnt annotations à Diffrnt tupls R A B C a b c d b z f g w p r s π C σ C= π AC (π AB R π BC R) C z w pr+r 2 s 2 45
42 Wrap up: issus and dirctions } Archiving } Comprssion } Gnralizations } Program Slicing [Chny07] } Ngativ Provnanc } Why Not? [SIGMOD09], Artmis [PVLDB09] } Causality 46
Database Design and Implementation
Database Design and Implementation CS 645 Data provenance Provenance provenance, n. The fact of coming from some particular source or quarter; origin, derivation [Oxford English Dictionary] Data provenance
More informationRoadmap. XML Indexing. DataGuide example. DataGuides. Strong DataGuides. Multiple DataGuides for same data. CPS Topics in Database Systems
Roadmap XML Indxing CPS 296.1 Topics in Databas Systms Indx fabric Coopr t al. A Fast Indx for Smistructurd Data. VLDB, 2001 DataGuid Goldman and Widom. DataGuids: Enabling Qury Formulation and Optimization
More informationAbstract Interpretation: concrete and abstract semantics
Abstract Intrprtation: concrt and abstract smantics Concrt smantics W considr a vry tiny languag that manags arithmtic oprations on intgrs valus. Th (concrt) smantics of th languags cab b dfind by th funzcion
More informationCS 6353 Compiler Construction, Homework #1. 1. Write regular expressions for the following informally described languages:
CS 6353 Compilr Construction, Homwork #1 1. Writ rgular xprssions for th following informally dscribd languags: a. All strings of 0 s and 1 s with th substring 01*1. Answr: (0 1)*01*1(0 1)* b. All strings
More informationTwo Products Manufacturer s Production Decisions with Carbon Constraint
Managmnt Scinc and Enginring Vol 7 No 3 pp 3-34 DOI:3968/jms9335X374 ISSN 93-34 [Print] ISSN 93-35X [Onlin] wwwcscanadant wwwcscanadaorg Two Products Manufacturr s Production Dcisions with Carbon Constraint
More informationChemical Physics II. More Stat. Thermo Kinetics Protein Folding...
Chmical Physics II Mor Stat. Thrmo Kintics Protin Folding... http://www.nmc.ctc.com/imags/projct/proj15thumb.jpg http://nuclarwaponarchiv.org/usa/tsts/ukgrabl2.jpg http://www.photolib.noaa.gov/corps/imags/big/corp1417.jpg
More informationDealing with quantitative data and problem solving life is a story problem! Attacking Quantitative Problems
Daling with quantitati data and problm soling lif is a story problm! A larg portion of scinc inols quantitati data that has both alu and units. Units can sa your butt! Nd handl on mtric prfixs Dimnsional
More informationECE602 Exam 1 April 5, You must show ALL of your work for full credit.
ECE62 Exam April 5, 27 Nam: Solution Scor: / This xam is closd-book. You must show ALL of your work for full crdit. Plas rad th qustions carfully. Plas chck your answrs carfully. Calculators may NOT b
More informationEEO 401 Digital Signal Processing Prof. Mark Fowler
EEO 401 Digital Signal Procssing Prof. Mark Fowlr Dtails of th ot St #19 Rading Assignmnt: Sct. 7.1.2, 7.1.3, & 7.2 of Proakis & Manolakis Dfinition of th So Givn signal data points x[n] for n = 0,, -1
More informationCS 361 Meeting 12 10/3/18
CS 36 Mting 2 /3/8 Announcmnts. Homwork 4 is du Friday. If Friday is Mountain Day, homwork should b turnd in at my offic or th dpartmnt offic bfor 4. 2. Homwork 5 will b availabl ovr th wknd. 3. Our midtrm
More information1 Minimum Cut Problem
CS 6 Lctur 6 Min Cut and argr s Algorithm Scribs: Png Hui How (05), Virginia Dat: May 4, 06 Minimum Cut Problm Today, w introduc th minimum cut problm. This problm has many motivations, on of which coms
More informationAssociation (Part II)
Association (Part II) nanopoulos@ismll.d Outlin Improving Apriori (FP Growth, ECLAT) Qustioning confidnc masur Qustioning support masur 2 1 FP growth Algorithm Us a comprssd rprsntation of th dtb databas
More informationProbability Translation Guide
Quick Guid to Translation for th inbuilt SWARM Calculator If you s information looking lik this: Us this statmnt or any variant* (not th backticks) And this is what you ll s whn you prss Calculat Th chancs
More informationClassical Magnetic Dipole
Lctur 18 1 Classical Magntic Dipol In gnral, a particl of mass m and charg q (not ncssarily a point charg), w hav q g L m whr g is calld th gyromagntic ratio, which accounts for th ffcts of non-point charg
More information1973 AP Calculus AB: Section I
97 AP Calculus AB: Sction I 9 Minuts No Calculator Not: In this amination, ln dnots th natural logarithm of (that is, logarithm to th bas ).. ( ) d= + C 6 + C + C + C + C. If f ( ) = + + + and ( ), g=
More informationph People Grade Level: basic Duration: minutes Setting: classroom or field site
ph Popl Adaptd from: Whr Ar th Frogs? in Projct WET: Curriculum & Activity Guid. Bozman: Th Watrcours and th Council for Environmntal Education, 1995. ph Grad Lvl: basic Duration: 10 15 minuts Stting:
More informationUNTYPED LAMBDA CALCULUS (II)
1 UNTYPED LAMBDA CALCULUS (II) RECALL: CALL-BY-VALUE O.S. Basic rul Sarch ruls: (\x.) v [v/x] 1 1 1 1 v v CALL-BY-VALUE EVALUATION EXAMPLE (\x. x x) (\y. y) x x [\y. y / x] = (\y. y) (\y. y) y [\y. y /
More informationThat is, we start with a general matrix: And end with a simpler matrix:
DIAGON ALIZATION OF THE STR ESS TEN SOR INTRO DUCTIO N By th us of Cauchy s thorm w ar abl to rduc th numbr of strss componnts in th strss tnsor to only nin valus. An additional simplification of th strss
More informationObjective Mathematics
x. Lt 'P' b a point on th curv y and tangnt x drawn at P to th curv has gratst slop in magnitud, thn point 'P' is,, (0, 0),. Th quation of common tangnt to th curvs y = 6 x x and xy = x + is : x y = 8
More informationFrom Elimination to Belief Propagation
School of omputr Scinc Th lif Propagation (Sum-Product lgorithm Probabilistic Graphical Modls (10-708 Lctur 5, Sp 31, 2007 Rcptor Kinas Rcptor Kinas Kinas X 5 ric Xing Gn G T X 6 X 7 Gn H X 8 Rading: J-hap
More informationAs the matrix of operator B is Hermitian so its eigenvalues must be real. It only remains to diagonalize the minor M 11 of matrix B.
7636S ADVANCED QUANTUM MECHANICS Solutions Spring. Considr a thr dimnsional kt spac. If a crtain st of orthonormal kts, say, and 3 ar usd as th bas kts, thn th oprators A and B ar rprsntd by a b A a and
More informationLecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields
Lctur 37 (Schrödingr Equation) Physics 6-01 Spring 018 Douglas Filds Rducd Mass OK, so th Bohr modl of th atom givs nrgy lvls: E n 1 k m n 4 But, this has on problm it was dvlopd assuming th acclration
More informationMiddle East Technical University Department of Mechanical Engineering ME 413 Introduction to Finite Element Analysis
Middl East Tchnical Univrsity Dpartmnt of Mchanical Enginring ME 43 Introduction to Finit Elmnt Analysis Chaptr 3 Computr Implmntation of D FEM Ths nots ar prpard by Dr. Cünyt Srt http://www.m.mtu.du.tr/popl/cunyt
More informationComputing and Communications -- Network Coding
89 90 98 00 Computing and Communications -- Ntwork Coding Dr. Zhiyong Chn Institut of Wirlss Communications Tchnology Shanghai Jiao Tong Univrsity China Lctur 5- Nov. 05 0 Classical Information Thory Sourc
More informationEstimation of apparent fraction defective: A mathematical approach
Availabl onlin at www.plagiarsarchlibrary.com Plagia Rsarch Library Advancs in Applid Scinc Rsarch, 011, (): 84-89 ISSN: 0976-8610 CODEN (USA): AASRFC Estimation of apparnt fraction dfctiv: A mathmatical
More informationSearch sequence databases 3 10/25/2016
Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an
More informationA False History of True Concurrency
A Fals History of Tru Concurrncy Javir Esparza Sofwar Rliability and Scurity Group Institut for Formal Mthods in Computr Scinc Univrsity of Stuttgart. Th arly 6s. 2 Abstract Modls of Computation in th
More information1997 AP Calculus AB: Section I, Part A
997 AP Calculus AB: Sction I, Part A 50 Minuts No Calculator Not: Unlss othrwis spcifid, th domain of a function f is assumd to b th st of all ral numbrs for which f () is a ral numbr.. (4 6 ) d= 4 6 6
More informationLecture 4: Parsing. Administrivia
Adminitrivia Lctur 4: Paring If you do not hav a group, pla pot a rqut on Piazzza ( th Form projct tam... itm. B ur to updat your pot if you find on. W will aign orphan to group randomly in a fw day. Programming
More informationHydrogen Atom and One Electron Ions
Hydrogn Atom and On Elctron Ions Th Schrödingr quation for this two-body problm starts out th sam as th gnral two-body Schrödingr quation. First w sparat out th motion of th cntr of mass. Th intrnal potntial
More informationLearning Spherical Convolution for Fast Features from 360 Imagery
Larning Sphrical Convolution for Fast Faturs from 36 Imagry Anonymous Author(s) 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 3 3 33 34 35 In this fil w provid additional dtails to supplmnt th main papr
More informationProblem Statement. Definitions, Equations and Helpful Hints BEAUTIFUL HOMEWORK 6 ENGR 323 PROBLEM 3-79 WOOLSEY
Problm Statmnt Suppos small arriv at a crtain airport according to Poisson procss with rat α pr hour, so that th numbr of arrivals during a tim priod of t hours is a Poisson rv with paramtr t (a) What
More informationLecture 2: Discrete-Time Signals & Systems. Reza Mohammadkhani, Digital Signal Processing, 2015 University of Kurdistan eng.uok.ac.
Lctur 2: Discrt-Tim Signals & Systms Rza Mohammadkhani, Digital Signal Procssing, 2015 Univrsity of Kurdistan ng.uok.ac.ir/mohammadkhani 1 Signal Dfinition and Exampls 2 Signal: any physical quantity that
More informationBrief Introduction to Statistical Mechanics
Brif Introduction to Statistical Mchanics. Purpos: Ths nots ar intndd to provid a vry quick introduction to Statistical Mchanics. Th fild is of cours far mor vast than could b containd in ths fw pags.
More informationExercise 1. Sketch the graph of the following function. (x 2
Writtn tst: Fbruary 9th, 06 Exrcis. Sktch th graph of th following function fx = x + x, spcifying: domain, possibl asymptots, monotonicity, continuity, local and global maxima or minima, and non-drivability
More informationRelational completeness of query languages for annotated databases
Relational completeness of query languages for annotated databases Floris Geerts 1,2 and Jan Van den Bussche 1 1 Hasselt University/Transnational University Limburg 2 University of Edinburgh Abstract.
More informationThus, because if either [G : H] or [H : K] is infinite, then [G : K] is infinite, then [G : K] = [G : H][H : K] for all infinite cases.
Homwork 5 M 373K Solutions Mark Lindbrg and Travis Schdlr 1. Prov that th ring Z/mZ (for m 0) is a fild if and only if m is prim. ( ) Proof by Contrapositiv: Hr, thr ar thr cass for m not prim. m 0: Whn
More informationIntroduction to Arithmetic Geometry Fall 2013 Lecture #20 11/14/2013
18.782 Introduction to Arithmtic Gomtry Fall 2013 Lctur #20 11/14/2013 20.1 Dgr thorm for morphisms of curvs Lt us rstat th thorm givn at th nd of th last lctur, which w will now prov. Thorm 20.1. Lt φ:
More informationMCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17)
MCB37: Physical Biology of th Cll Spring 207 Homwork 6: Ligand binding and th MWC modl of allostry (Du 3/23/7) Hrnan G. Garcia March 2, 207 Simpl rprssion In class, w drivd a mathmatical modl of how simpl
More informationThere is an arbitrary overall complex phase that could be added to A, but since this makes no difference we set it to zero and choose A real.
Midtrm #, Physics 37A, Spring 07. Writ your rsponss blow or on xtra pags. Show your work, and tak car to xplain what you ar doing; partial crdit will b givn for incomplt answrs that dmonstrat som concptual
More informationOutline. Why speech processing? Speech signal processing. Advanced Multimedia Signal Processing #5:Speech Signal Processing 2 -Processing-
Outlin Advancd Multimdia Signal Procssing #5:Spch Signal Procssing -Procssing- Intllignt Elctronic Systms Group Dpt. of Elctronic Enginring, UEC Basis of Spch Procssing Nois Rmoval Spctral Subtraction
More informationAS 5850 Finite Element Analysis
AS 5850 Finit Elmnt Analysis Two-Dimnsional Linar Elasticity Instructor Prof. IIT Madras Equations of Plan Elasticity - 1 displacmnt fild strain- displacmnt rlations (infinitsimal strain) in matrix form
More informationSCHUR S THEOREM REU SUMMER 2005
SCHUR S THEOREM REU SUMMER 2005 1. Combinatorial aroach Prhas th first rsult in th subjct blongs to I. Schur and dats back to 1916. On of his motivation was to study th local vrsion of th famous quation
More informationFinite element discretization of Laplace and Poisson equations
Finit lmnt discrtization of Laplac and Poisson quations Yashwanth Tummala Tutor: Prof S.Mittal 1 Outlin Finit Elmnt Mthod for 1D Introduction to Poisson s and Laplac s Equations Finit Elmnt Mthod for 2D-Discrtization
More informationSource code. where each α ij is a terminal or nonterminal symbol. We say that. α 1 α m 1 Bα m+1 α n α 1 α m 1 β 1 β p α m+1 α n
Adminitrivia Lctur : Paring If you do not hav a group, pla pot a rqut on Piazzza ( th Form projct tam... itm. B ur to updat your pot if you find on. W will aign orphan to group randomly in a fw day. Programming
More information(Upside-Down o Direct Rotation) β - Numbers
Amrican Journal of Mathmatics and Statistics 014, 4(): 58-64 DOI: 10593/jajms0140400 (Upsid-Down o Dirct Rotation) β - Numbrs Ammar Sddiq Mahmood 1, Shukriyah Sabir Ali,* 1 Dpartmnt of Mathmatics, Collg
More informationPHA 5127 Answers Homework 2 Fall 2001
PH 5127 nswrs Homwork 2 Fall 2001 OK, bfor you rad th answrs, many of you spnt a lot of tim on this homwork. Plas, nxt tim if you hav qustions plas com talk/ask us. Thr is no nd to suffr (wll a littl suffring
More informationQuasi-Classical States of the Simple Harmonic Oscillator
Quasi-Classical Stats of th Simpl Harmonic Oscillator (Draft Vrsion) Introduction: Why Look for Eignstats of th Annihilation Oprator? Excpt for th ground stat, th corrspondnc btwn th quantum nrgy ignstats
More informationDifferentiation of Exponential Functions
Calculus Modul C Diffrntiation of Eponntial Functions Copyright This publication Th Northrn Albrta Institut of Tchnology 007. All Rights Rsrvd. LAST REVISED March, 009 Introduction to Diffrntiation of
More informationMA 262, Spring 2018, Final exam Version 01 (Green)
MA 262, Spring 218, Final xam Vrsion 1 (Grn) INSTRUCTIONS 1. Switch off your phon upon ntring th xam room. 2. Do not opn th xam booklt until you ar instructd to do so. 3. Bfor you opn th booklt, fill in
More informationThe second condition says that a node α of the tree has exactly n children if the arity of its label is n.
CS 6110 S14 Hanout 2 Proof of Conflunc 27 January 2014 In this supplmntary lctur w prov that th λ-calculus is conflunt. This is rsult is u to lonzo Church (1903 1995) an J. arkly Rossr (1907 1989) an is
More informationSara Godoy del Olmo Calculation of contaminated soil volumes : Geostatistics applied to a hydrocarbons spill Lac Megantic Case
wwwnvisol-canadaca Sara Godoy dl Olmo Calculation of contaminatd soil volums : Gostatistics applid to a hydrocarbons spill Lac Mgantic Cas Gostatistics: study of a PH contamination CONTEXT OF THE STUDY
More informationPair (and Triplet) Production Effect:
Pair (and riplt Production Effct: In both Pair and riplt production, a positron (anti-lctron and an lctron (or ngatron ar producd spontanously as a photon intracts with a strong lctric fild from ithr a
More informationInternational Journal of Scientific & Engineering Research, Volume 6, Issue 7, July ISSN
Intrnational Journal of Scintific & Enginring Rsarch, Volum 6, Issu 7, July-25 64 ISSN 2229-558 HARATERISTIS OF EDGE UTSET MATRIX OF PETERSON GRAPH WITH ALGEBRAI GRAPH THEORY Dr. G. Nirmala M. Murugan
More informationFourier Transforms and the Wave Equation. Key Mathematics: More Fourier transform theory, especially as applied to solving the wave equation.
Lur 7 Fourir Transforms and th Wav Euation Ovrviw and Motivation: W first discuss a fw faturs of th Fourir transform (FT), and thn w solv th initial-valu problm for th wav uation using th Fourir transform
More informationMor Tutorial at www.dumblittldoctor.com Work th problms without a calculator, but us a calculator to chck rsults. And try diffrntiating your answrs in part III as a usful chck. I. Applications of Intgration
More informationMaximizing Conjunctive Views in Deletion Propagation
Maximizing Conjunctiv Viws in Dltion Propagation Bnny Kimlfld Jan Vondrá Ryan Williams IBM Rsarch Almadn San Jos, CA 9510, USA {imlfld, jvondra, ryanwill}@us.ibm.com ABSTRACT In dltion propagation, tupls
More informationNetwork Congestion Games
Ntwork Congstion Gams Assistant Profssor Tas A&M Univrsity Collg Station, TX TX Dallas Collg Station Austin Houston Bst rout dpnds on othrs Ntwork Congstion Gams Travl tim incrass with congstion Highway
More informationChapter 6 Folding. Folding
Chaptr 6 Folding Wintr 1 Mokhtar Abolaz Folding Th folding transformation is usd to systmatically dtrmin th control circuits in DSP architctur whr multipl algorithm oprations ar tim-multiplxd to a singl
More information1 Isoparametric Concept
UNIVERSITY OF CALIFORNIA BERKELEY Dpartmnt of Civil Enginring Spring 06 Structural Enginring, Mchanics and Matrials Profssor: S. Govindj Nots on D isoparamtric lmnts Isoparamtric Concpt Th isoparamtric
More informationSec 2.3 Modeling with First Order Equations
Sc.3 Modling with First Ordr Equations Mathmatical modls charactriz physical systms, oftn using diffrntial quations. Modl Construction: Translating physical situation into mathmatical trms. Clarly stat
More informationA. Limits and Horizontal Asymptotes ( ) f x f x. f x. x "±# ( ).
A. Limits and Horizontal Asymptots What you ar finding: You can b askd to find lim x "a H.A.) problm is asking you find lim x "# and lim x "$#. or lim x "±#. Typically, a horizontal asymptot algbraically,
More informationEXST Regression Techniques Page 1
EXST704 - Rgrssion Tchniqus Pag 1 Masurmnt rrors in X W hav assumd that all variation is in Y. Masurmnt rror in this variabl will not ffct th rsults, as long as thy ar uncorrlatd and unbiasd, sinc thy
More informationPropositional Logic. Combinatorial Problem Solving (CPS) Albert Oliveras Enric Rodríguez-Carbonell. May 17, 2018
Propositional Logic Combinatorial Problm Solving (CPS) Albrt Olivras Enric Rodríguz-Carbonll May 17, 2018 Ovrviw of th sssion Dfinition of Propositional Logic Gnral Concpts in Logic Rduction to SAT CNFs
More informationGradebook & Midterm & Office Hours
Your commnts So what do w do whn on of th r's is 0 in th quation GmM(1/r-1/r)? Do w nd to driv all of ths potntial nrgy formulas? I don't undrstand springs This was th first lctur I actually larnd somthing
More informationAP Calculus BC Problem Drill 16: Indeterminate Forms, L Hopital s Rule, & Improper Intergals
AP Calulus BC Problm Drill 6: Indtrminat Forms, L Hopital s Rul, & Impropr Intrgals Qustion No. of Instrutions: () Rad th problm and answr hois arfully () Work th problms on papr as ndd () Pik th answr
More informationDivision of Mechanics Lund University MULTIBODY DYNAMICS. Examination Name (write in block letters):.
Division of Mchanics Lund Univrsity MULTIBODY DYNMICS Examination 7033 Nam (writ in block lttrs):. Id.-numbr: Writtn xamination with fiv tasks. Plas chck that all tasks ar includd. clan copy of th solutions
More informationCalculus II Solutions review final problems
Calculus II Solutions rviw final problms MTH 5 Dcmbr 9, 007. B abl to utiliz all tchniqus of intgration to solv both dfinit and indfinit intgrals. Hr ar som intgrals for practic. Good luck stuing!!! (a)
More informationMathematics. Complex Number rectangular form. Quadratic equation. Quadratic equation. Complex number Functions: sinusoids. Differentiation Integration
Mathmatics Compl numbr Functions: sinusoids Sin function, cosin function Diffrntiation Intgration Quadratic quation Quadratic quations: a b c 0 Solution: b b 4ac a Eampl: 1 0 a= b=- c=1 4 1 1or 1 1 Quadratic
More informationECE 407 Computer Aided Design for Electronic Systems. Instructor: Maria K. Michael. Overview. CAD tools for multi-level logic synthesis:
407 Computr Aidd Dsign for Elctronic Systms Multi-lvl Logic Synthsis Instructor: Maria K. Michal 1 Ovrviw Major Synthsis Phass Logic Synthsis: 2-lvl Multi-lvl FSM CAD tools for multi-lvl logic synthsis:
More informationThe Transmission Line Wave Equation
1//5 Th Transmission Lin Wav Equation.doc 1/6 Th Transmission Lin Wav Equation Q: So, what functions I (z) and V (z) do satisfy both tlgraphr s quations?? A: To mak this asir, w will combin th tlgraphr
More informationWeek 3: Connected Subgraphs
Wk 3: Connctd Subgraphs Sptmbr 19, 2016 1 Connctd Graphs Path, Distanc: A path from a vrtx x to a vrtx y in a graph G is rfrrd to an xy-path. Lt X, Y V (G). An (X, Y )-path is an xy-path with x X and y
More information1997 AP Calculus AB: Section I, Part A
997 AP Calculus AB: Sction I, Part A 50 Minuts No Calculator Not: Unlss othrwis spcifid, th domain of a function f is assumd to b th st of all ral numbrs x for which f (x) is a ral numbr.. (4x 6 x) dx=
More informationCE 530 Molecular Simulation
CE 53 Molcular Simulation Lctur 8 Fr-nrgy calculations David A. Kofk Dpartmnt of Chmical Enginring SUNY Buffalo kofk@ng.buffalo.du 2 Fr-Enrgy Calculations Uss of fr nrgy Phas quilibria Raction quilibria
More informationWhy is a E&M nature of light not sufficient to explain experiments?
1 Th wird world of photons Why is a E&M natur of light not sufficint to xplain xprimnts? Do photons xist? Som quantum proprtis of photons 2 Black body radiation Stfan s law: Enrgy/ ara/ tim = Win s displacmnt
More informationEstimation of odds ratios in Logistic Regression models under different parameterizations and Design matrices
Advancs in Computational Intllignc, Man-Machin Systms and Cybrntics Estimation of odds ratios in Logistic Rgrssion modls undr diffrnt paramtrizations and Dsign matrics SURENDRA PRASAD SINHA*, LUIS NAVA
More informationMolecular Orbitals in Inorganic Chemistry
Outlin olcular Orbitals in Inorganic Chmistry Dr. P. Hunt p.hunt@imprial.ac.uk Rm 167 (Chmistry) http://www.ch.ic.ac.uk/hunt/ octahdral complxs forming th O diagram for Oh colour, slction ruls Δoct, spctrochmical
More informationThe pn junction: 2 Current vs Voltage (IV) characteristics
Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) by D. Klain Vrsion 207.0.05 Corrctions and commnts ar wlcom. Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix A A k I + A + k!
More informationMath 34A. Final Review
Math A Final Rviw 1) Us th graph of y10 to find approimat valus: a) 50 0. b) y (0.65) solution for part a) first writ an quation: 50 0. now tak th logarithm of both sids: log() log(50 0. ) pand th right
More informationCalculus Revision A2 Level
alculus Rvision A Lvl Tabl of drivativs a n sin cos tan d an sc n cos sin Fro AS * NB sc cos sc cos hain rul othrwis known as th function of a function or coposit rul. d d Eapl (i) (ii) Obtain th drivativ
More information11: Echo formation and spatial encoding
11: Echo formation and spatial ncoding 1. What maks th magntic rsonanc signal spatiall dpndnt? 2. How is th position of an R signal idntifid? Slic slction 3. What is cho formation and how is it achivd?
More informationHomework #3. 1 x. dx. It therefore follows that a sum of the
Danil Cannon CS 62 / Luan March 5, 2009 Homwork # 1. Th natural logarithm is dfind by ln n = n 1 dx. It thrfor follows that a sum of th 1 x sam addnd ovr th sam intrval should b both asymptotically uppr-
More informationSundials and Linear Algebra
Sundials and Linar Algbra M. Scot Swan July 2, 25 Most txts on crating sundials ar dirctd towards thos who ar solly intrstd in making and using sundials and usually assums minimal mathmatical background.
More informationAnnounce. ECE 2026 Summer LECTURE OBJECTIVES READING. LECTURE #3 Complex View of Sinusoids May 21, Complex Number Review
ECE 06 Summr 018 Announc HW1 du at bginning of your rcitation tomorrow Look at HW bfor rcitation Lab 1 is Thursday: Com prpard! Offic hours hav bn postd: LECTURE #3 Complx Viw of Sinusoids May 1, 018 READIG
More informationProvenance Semirings. Todd Green Grigoris Karvounarakis Val Tannen. presented by Clemens Ley
Provenance Semirings Todd Green Grigoris Karvounarakis Val Tannen presented by Clemens Ley place of origin Provenance Semirings Todd Green Grigoris Karvounarakis Val Tannen presented by Clemens Ley place
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) by Dan Klain Vrsion 28928 Corrctions and commnts ar wlcom Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix () A A k I + A + k!
More informationAdditional Math (4047) Paper 2 (100 marks) y x. 2 d. d d
Aitional Math (07) Prpar b Mr Ang, Nov 07 Fin th valu of th constant k for which is a solution of th quation k. [7] Givn that, Givn that k, Thrfor, k Topic : Papr (00 marks) Tim : hours 0 mins Nam : Aitional
More informationFirst derivative analysis
Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points
More informationInheritance Gains in Notional Defined Contributions Accounts (NDCs)
Company LOGO Actuarial Tachrs and Rsarchrs Confrnc Oxford 14-15 th July 211 Inhritanc Gains in Notional Dfind Contributions Accounts (NDCs) by Motivation of this papr In Financial Dfind Contribution (FDC)
More informationday month year documentname/initials 1
ECE 599/692 Dp Larning Lctur 10 Rgularizd AE and Cas Studis Hairong Qi, Gonzalz Family Profssor Elctrical Enginring and Computr Scinc Univrsity of Tnnss, Knovill http://www.cs.utk.du/faculty/qi Email:
More informationMATHEMATICS (B) 2 log (D) ( 1) = where z =
MATHEMATICS SECTION- I STRAIGHT OBJECTIVE TYPE This sction contains 9 multipl choic qustions numbrd to 9. Each qustion has choic (A), (B), (C) and (D), out of which ONLY-ONE is corrct. Lt I d + +, J +
More informationChapter 13 GMM for Linear Factor Models in Discount Factor form. GMM on the pricing errors gives a crosssectional
Chaptr 13 GMM for Linar Factor Modls in Discount Factor form GMM on th pricing rrors givs a crosssctional rgrssion h cas of xcss rturns Hors rac sting for charactristic sting for pricd factors: lambdas
More informationChapter 8: Electron Configurations and Periodicity
Elctron Spin & th Pauli Exclusion Principl Chaptr 8: Elctron Configurations and Priodicity 3 quantum numbrs (n, l, ml) dfin th nrgy, siz, shap, and spatial orintation of ach atomic orbital. To xplain how
More informationANALYSIS IN THE FREQUENCY DOMAIN
ANALYSIS IN THE FREQUENCY DOMAIN SPECTRAL DENSITY Dfinition Th spctral dnsit of a S.S.P. t also calld th spctrum of t is dfind as: + { γ }. jτ γ τ F τ τ In othr words, of th covarianc function. is dfind
More informationY 0. Standing Wave Interference between the incident & reflected waves Standing wave. A string with one end fixed on a wall
Staning Wav Intrfrnc btwn th incint & rflct wavs Staning wav A string with on n fix on a wall Incint: y, t) Y cos( t ) 1( Y 1 ( ) Y (St th incint wav s phas to b, i.., Y + ral & positiv.) Rflct: y, t)
More informationMAE4700/5700 Finite Element Analysis for Mechanical and Aerospace Design
MAE4700/5700 Finit Elmnt Analysis for Mchanical and Arospac Dsign Cornll Univrsity, Fall 2009 Nicholas Zabaras Matrials Procss Dsign and Control Laboratory Sibly School of Mchanical and Arospac Enginring
More informationCOHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim.
MTH rviw part b Lucian Mitroiu Th LOG and EXP functions Th ponntial function p : R, dfind as Proprtis: lim > lim p Eponntial function Y 8 6 - -8-6 - - X Th natural logarithm function ln in US- log: function
More information10. Limits involving infinity
. Limits involving infinity It is known from th it ruls for fundamntal arithmtic oprations (+,-,, ) that if two functions hav finit its at a (finit or infinit) point, that is, thy ar convrgnt, th it of
More informationHigher-Order Discrete Calculus Methods
Highr-Ordr Discrt Calculus Mthods J. Blair Prot V. Subramanian Ralistic Practical, Cost-ctiv, Physically Accurat Paralll, Moving Msh, Complx Gomtry, Slid 1 Contxt Discrt Calculus Mthods Finit Dirnc Mimtic
More information