Fusion of Retrieval Models at CLEF 2008 Ad-Hoc Persian Track
|
|
- Duane Cook
- 5 years ago
- Views:
Transcription
1 Fusio of Rtrival Modls at CLEF 008 Ad-Hoc Prsia rack Zahra Aghazad*, Nazai Dhghai* Lili Farzivash* Razih Rahimi* Abolfazl AlAhmad* Hadi Amiri Farhad Oroumchia** * Dpartmt of ECE, Uivrsity of hra {z.aghazadh,.dhghay, l.farzivash, r.rahimi}@c.ut.ac.ir ** Uivrsity of Wollogog i Dubai FarhadO@uow.du.au Abstract Mtasarch gis submit th usr qury to svral udrlyig sarch gis ad th mrg thir rtrivd rsults to grat a sigl list that is mor ffctiv to th usrs iformatio ds. Accordig to th ida bhid mtasarch gis, it sms that mrgig th rsults rtrivd from diffrt rtrival modls will improv th sarch covrag ad prcisio. I this study, w hav ivstigatd th ffct of fusio of diffrt rtrival tchiqus o th prformac of Prsia rtrival. W us a xtsio of Ordrd Wightd Avrag (OWA) oprator calld IOWA ad a wightig schma, NOWA for mrgig th rsults. Our xprimtal rsults show that mrgig by OWA oprators producs bttr prcisio. Catgoris ad Subjct Dscriptors Iformatio Sarch ad Rtrival, Rtrival Modls. Kywords Iformatio Rtrival, Iformatio Fusio, Prsia xt Rtrival.. Itroductio With th rapid growth of th volum of th data, improvig th ffctivss of iformatio rtrival systms is sstial. May approachs ad mthods hav dvlopd to xhibit bttr rtrival gis []. I this study, w try to us th ida bhid mtasarch gis i ordr to improv th rsults of Prsia iformatio rtrival. W cosidr ach rtrival modl as a dcisio makr ad th fus thir dcisios with a OWA oprator i ordr to icras th ffctivss. his work has b do as our first participatio i th CLEF valuatio campaig. For th Ad-Hoc Prsia track w submittd lv xprimts (rus): UNLPDB3BB, UNLPDB3BM5, UNLPDB3DFR, UNLPDB3IFB, UNLPDB3INEXPB, UNLPDB3INEXPC, UNLPDB3INL, UNLPDB3PL, UNLPDB3FIDF, UNLPDB3NOWA ad UNLPDB3OWA. Our mai goal was to study th ffct of fusio oprators ad whthr fusig rtrival modls ca brig additioal prformac improvmts. h collctio that is usd i this study is a stadard tst collctio of Prsia txt which is calld Hamshahri ad was mad availabl to CLEF by Uivrsity of hra [], [3]. I sctio two, w prst a brif dscriptio of th rtrival mthods that hav b usd i our xprimts. Prvious xprimts hav dmostratd that ths mthods hav good prformac o Prsia rtrival. I sctio thr, OWA oprator ad its xtsios that ar usd for mrgig th rsults ar dscribd. O ky poit i th OWA oprator is to dtrmi its associatd wights. I this study, w us a wightig modl which is basd o Normal distributio ad a IOWA xtsio. hr ar two approachs to fus th rtrivd lists: Combi th rsults of distict rtrival mthods. Combi th rsults of th sam mthod but with diffrt typs of toks Rus that submittd to CLEF 008 us th first approach ad rsults show that usig this approach dos ot ld itslf to a sigificat improvmt. It sms although th rtrival mthods ar diffrt but thir prformac ad rsult st is similar. I aothr word, thos rtrival mthods provid th sam visio of th data. Aftr
2 CLEF rsults wr publishd, w trid th scod approach ad w wr abl to improv th ffctivss up to 5.67% ad rachd th 45.% avrag prcisio o tst st. Sctio four dscribs th xprimts ad thir rsults.. Rtrival Mthods I this work, for th purpos of fusio, w dd diffrt rtrival mthods. Aftr studyig diffrt rtrival toolkits, fially w choos rrir [4]. Diffrt mthods hav b implmtd i rrir toolkit. Amog ths mthods, w slctd i of thm. h wightig modls ad a brif dscriptio of thm (from [5]) ar illustratd i tabl. Wightig Modl BB abl A dscriptio of rtrival mthods Dscriptio Bos-Eisti modl for radomss, th ratio of two Broulli's procsss for first ormalizatio, ad Normalizatio for trm frqucy ormalizatio BM5 h BM5 probabilistic modl DFR_BM5 IFB I_xpB I_xpC IL PL F_IDF h DFR vrsio of BM5 Ivrs rm Frqucy modl for radomss, th ratio of two Broulli's procsss for first ormalizatio, ad Normalizatio for trm frqucy ormalizatio Ivrs xpctd documt frqucy modl for radomss, th ratio of two Broulli's procsss for first ormalizatio, ad Normalizatio for trm frqucy ormalizatio Ivrs xpctd documt frqucy modl for radomss, th ratio of two Broulli's procsss for first ormalizatio, ad Normalizatio for trm frqucy ormalizatio with atural logarithm Ivrs documt frqucy modl for radomss, Laplac succssio for first ormalizatio, ad Normalizatio for trm frqucy ormalizatio Poisso stimatio for radomss, Laplac succssio for first ormalizatio, ad Normalizatio for trm frqucy ormalizatio h tf*idf wightig fuctio, whr tf is giv by Robrtso's tf ad idf is giv by th stadard Sparck Jos' idf abl dpicts th rsult obtaid from ruig th abov i mthods dscribd i abl o th traiig st of quris.
3 abl Compariso btw diffrt wightig modls Wightig Modl Avrag Prcisio R-Prcisio BB BM DFR_BM IFB I_xpB I_xpC IL PL F_IDF OWA Fuzzy Oprator his sctio dscribs th Ordr Wightd Avrag (OWA) oprator, ormal distributio-basd wightig ad IOWA xtsio. 3.. OWA Dfiitio A OWA oprator of dimsio is a mappig, OWA: w = ( w w,..., w, ) such that w j [0,] ad Whr w j =. Furthrmor, OWA ( a, a,..., a ) = R R, that has a associatd vctor b j w j b j is th j th largst lmt of th collctio of th aggrgatd objcts 3.. IOWA A IOWA oprator is dfid as follows: IOWA( u =, a, u, a,..., u, a ) w j = j b j, that w j =, 0 w j ad b j is th a i valu of th OWA pair a, a,..., a [6]. w = ( w, w,..., w ) whr is a wightig vctor, such u i, ai havig th j th largst u i, ad u i i u i, a i is rfrrd to as th ordr iducig variabl ad a i as th argumt variabl. It is assumd that ai is a xact umrical valu whil ui ca b draw from ay ordial st Ω [7] NOWA Suppos that w wat to fus prfrc valus providd by diffrt idividuals. Som idividuals may assig uduly high or uduly low prfrc valus to thir prfrrd or rpugat objcts. I such a cas, w shall assig vry low wights to ths fals or biasd opiios, that is to say, th closr a prfrc valu (argumt) is to th mid o(s), th mor th wight it will rciv; covrsly, th furthr a prfrc valu is from th mid o(s), th lss th wight it will hav [8]. Lt w = ( w, w,..., w ) b th wight vctor of th OWA oprator; th w dfi th followig:. [( i µ ) ] σ w i =, i =,,..., πσ Whr µ is th ma of th collctio of,,...,, ad σ ( σ > 0) is th stadard dviatio of th collctio of,,...,. µ adσ ar obtaid by th followig formulas, rspctivly:
4 Cosidr that w j w µ σ ( + ) + = = = i= = ad 0 w j th w hav: i = πσ πσ i µ ) σ ] j µ ) σ ] = ( i µ ) i µ ) σ ] j µ ) σ ], i =,,..., 4. Exprimt For th xprimts, CLEF has obtaid th stadard Prsia tst collctio which is calld Hamshahri. Hamshahri collctio is th largst tst collctio of Prsia txt. his collctio is prpard ad distributd by Uivrsity of hra. h third vrsio of Hamshahri collctio is 600MB i siz ad cotais mor tha 60,000 distict txtual ws articls i Prsia [9]. hr wr 50 traiig quris with thir rlvac judgmts ad 50 tst quris prpard for th Prsia ad-hoc track. For th CLEF, w choos i mthods of documt rtrival dscribd abov ad fus th top hudrd rtrivd rsults from ach of thm. W us OWA oprator basd o ormal distributio wightig for mrgig th lists. I this problm, w hav i dcisio makrs, so th wightig vctor is as th followig: = 9, µ 0 9 = 5, σ 9 =, ors( w) = 0.5, disp( w) =.95, 3 w = (0.0506,0.0855,0.43,0.557,0.678,0.557,0.43,0.0855,0.0506) h prcisio-rcall diagram obtaid aftr submittig th OWA ru to CLEF is illustratd i figur. Figur - h rsult of ruig NOWA publishd by CLEF 008 IOWA xtsio was also tstd. W usd 50 traiig quris i ordr to calculat th wightig vctor for this mthod. W ra th i slctd rtrival mthods o th collctio. h followig wightig vctor is obtaid by usig th avrag prcisio of ach mthod as its wight: {0.467/3.8409, /3.8409, /3.8409, 0.438/3.8409, 0.439/3.8409, 0.446/3.8409, 0.4/3.8409, /3.8409, 0.40/3.8409} ( is th sum of th obtaid avrag prcisios) Figur illustrats th prcisio-rcall diagram of IOWA ru with th abov wightig vctor.
5 Figur - h rsult of ruig IOWA publishd by CLEF Aalyzig th Rsults ad Mor Exprimts W submittd top hudrd rtrivd documts for our rus to CLEF, whil CLEF valuats th rsults by top thousad documts which dcrasd avrag prcisio about 0% i avrag. hrfor, i futur w itd to calculat our Prcisio-Rcall charts ad othr masurmts basd th top thousad rtrivd documts. h rsults publishd by CLEF for our fusio rus show that usig fusio tchiqus o ths mthods dos ot yild to improvd rsults ovr th idividual mthods. By aalyzig th lists obtaid from th rtrival mthods, w obsrvd that ths rsult lists for ths i diffrt mthods hav high ovrlap amog thm. O th othr had, fusio mthods work wll wh thr ar sigificat diffrcs btw dcisio makrs. hrfor, w hav cocludd that although th mthods ar diffrt thy ar ot sigificatly diffrt from ach othr ad basically thy provid th sam viw of th collctio. Aftr th CLEF rsults wr publishd, w dcidd to ivstigat th scod approach for fusio ad look ito th ffct of diffrt toks i rtrival. For this purpos w chos a vctor spac modl ad ra it o th traiig st thr tims with thr diffrt typs of toks amly 4-grams, stmmd sigl trms ad ustmmd sigl trms. o obtaiig bst rsults, w ra PL mthod of trrir toolkit o 4gram trms, idri of lmur toolkit [0] o stmmd trms ad F_IDF of trrir toolkit o ustmmd trms. h w applid th abov OWA mthods ad as show i tabl 3, w obtaid 9.97% improvmts ovr idividual rus. abl 3 Rsults of applyig fusio mthods o traiig st Rtrival Mthod Avrag Prcisio R-Prcisio Dif F_IDF with ustmmd sigl trms PL with 4gram trms Idri with stmmd trms IOWA NOWA Aftr that, w cotiud this approach ad did mor xprimts with th CLEF tst st. O th tst st, this approach lad oly to 5.67% improvmts o th avrag prcisio ovr idividual rus usig NOWA mthod ad 5.6% usig IOWA mthod. abl 4, figur 3 ad figur 4 dmostrat th obtaid rsults. abl 4 Rsults of applyig fusio mthods o tst st Rtrival Mthod Avrag Prcisio R-Prcisio Dif F_IDF with ustmmd sigl trms PL with 4gram trms Idri with stmmd trms IOWA NOWA
6 Figur 3 Compariso of prcisio btw NOWA ad idividual mthods. Figur 4 - Compariso of prcisio at top rtrivd documts btw NOWA ad idividual mthods. 6. Coclusio Our motivatio for participatio i th Ad-Hoc Prsia track of CLEF was ivstigatig th ifluc of fusio tchiqus o th ffctivss of Prsia rtrival mthods. First w us i rtrival mthods ad th fus th rsults by NOWA ad IOWA. h obtaid rsults showd that fuctioality of ths mthods hav high ovrlap ad thr wr o cosidrabl improvmt by applyig fusio tchiqus. I th scod stag, w chagd our approach to us diffrt vrsios of a sam mthod. o rach this goal, w focusd o workig with diffrt trms istad of diffrt mthods. Rsults idicats fusio tchiqus works wll o th circumstacs which th dcisio makrs hav diffrt viws.
7 I futur, w will ivstigat th ffcts of diffrt tok typs ad rtrival gis o Prsia rtrival ad will try to fi tu a gi basd o fusio. Rfrcs [] Ia H. Witt, Alistair Moffat ad imothy C. Bll. Maagig Gigabyts: Comprssig ad Idxig Documts ad Imags. Morga Kaufma Publishrs, Los Altos, USA, 999 [] Oroumchia F, Darrudi E. Exprimts with Prsia xt Comprssio for Wb. WWW 004. [3] [4] [5] [6] Yagr RR. O ordrd wightd avragig aggrgatio oprators i multicritria dcisio makig. IEEE ras Syst Ma Cybr 988; 8: [7] Yagr RR, Filv D.P. Iducd ordrd wightd avragig oprators. IEEE rasactios o Systms, Ma, ad Cybrtics Part B 9 (999) [8] Xu Z. Iducd ucrtai liguistic OWA oprators applid to group dcisio makig. Itratioal Joural of Itlligt Systms, Vol. 0, (005). [9] Amiri H, Alahmad A, Oroumchia F, Lucas C, Rahgozar M. Usig OWA Fuzzy Oprator to Mrg Rtrival Systm Rsults, 007 [0]
APPENDIX: STATISTICAL TOOLS
I. Nots o radom samplig Why do you d to sampl radomly? APPENDI: STATISTICAL TOOLS I ordr to masur som valu o a populatio of orgaisms, you usually caot masur all orgaisms, so you sampl a subst of th populatio.
More informationSolution to 1223 The Evil Warden.
Solutio to 1 Th Evil Ward. This is o of thos vry rar PoWs (I caot thik of aothr cas) that o o solvd. About 10 of you submittd th basic approach, which givs a probability of 47%. I was shockd wh I foud
More information1985 AP Calculus BC: Section I
985 AP Calculus BC: Sctio I 9 Miuts No Calculator Nots: () I this amiatio, l dots th atural logarithm of (that is, logarithm to th bas ). () Ulss othrwis spcifid, th domai of a fuctio f is assumd to b
More informationz 1+ 3 z = Π n =1 z f() z = n e - z = ( 1-z) e z e n z z 1- n = ( 1-z/2) 1+ 2n z e 2n e n -1 ( 1-z )/2 e 2n-1 1-2n -1 1 () z
Sris Expasio of Rciprocal of Gamma Fuctio. Fuctios with Itgrs as Roots Fuctio f with gativ itgrs as roots ca b dscribd as follows. f() Howvr, this ifiit product divrgs. That is, such a fuctio caot xist
More informationChapter (8) Estimation and Confedence Intervals Examples
Chaptr (8) Estimatio ad Cofdc Itrvals Exampls Typs of stimatio: i. Poit stimatio: Exampl (1): Cosidr th sampl obsrvatios, 17,3,5,1,18,6,16,10 8 X i i1 17 3 5 118 6 16 10 116 X 14.5 8 8 8 14.5 is a poit
More informationFolding of Hyperbolic Manifolds
It. J. Cotmp. Math. Scics, Vol. 7, 0, o. 6, 79-799 Foldig of Hyprbolic Maifolds H. I. Attiya Basic Scic Dpartmt, Collg of Idustrial Educatio BANE - SUEF Uivrsity, Egypt hala_attiya005@yahoo.com Abstract
More informationOn the approximation of the constant of Napier
Stud. Uiv. Babş-Bolyai Math. 560, No., 609 64 O th approximatio of th costat of Napir Adri Vrscu Abstract. Startig from som oldr idas of [] ad [6], w show w facts cocrig th approximatio of th costat of
More informationLectures 9 IIR Systems: First Order System
EE3054 Sigals ad Systms Lcturs 9 IIR Systms: First Ordr Systm Yao Wag Polytchic Uivrsity Som slids icludd ar xtractd from lctur prstatios prpard by McCllla ad Schafr Lics Ifo for SPFirst Slids This work
More informationDiscrete Fourier Transform. Nuno Vasconcelos UCSD
Discrt Fourir Trasform uo Vascoclos UCSD Liar Shift Ivariat (LSI) systms o of th most importat cocpts i liar systms thory is that of a LSI systm Dfiitio: a systm T that maps [ ito y[ is LSI if ad oly if
More informationDTFT Properties. Example - Determine the DTFT Y ( e ) of n. Let. We can therefore write. From Table 3.1, the DTFT of x[n] is given by 1
DTFT Proprtis Exampl - Dtrmi th DTFT Y of y α µ, α < Lt x α µ, α < W ca thrfor writ y x x From Tabl 3., th DTFT of x is giv by ω X ω α ω Copyright, S. K. Mitra Copyright, S. K. Mitra DTFT Proprtis DTFT
More informationINTRODUCTION TO SAMPLING DISTRIBUTIONS
http://wiki.stat.ucla.du/socr/id.php/socr_courss_2008_thomso_econ261 INTRODUCTION TO SAMPLING DISTRIBUTIONS By Grac Thomso INTRODUCTION TO SAMPLING DISTRIBUTIONS Itro to Samplig 2 I this chaptr w will
More informationProbability & Statistics,
Probability & Statistics, BITS Pilai K K Birla Goa Campus Dr. Jajati Kshari Sahoo Dpartmt of Mathmatics BITS Pilai, K K Birla Goa Campus Poisso Distributio Poisso Distributio: A radom variabl X is said
More informationOn a problem of J. de Graaf connected with algebras of unbounded operators de Bruijn, N.G.
O a problm of J. d Graaf coctd with algbras of uboudd oprators d Bruij, N.G. Publishd: 01/01/1984 Documt Vrsio Publishr s PDF, also kow as Vrsio of Rcord (icluds fial pag, issu ad volum umbrs) Plas chck
More informationThe Interplay between l-max, l-min, p-max and p-min Stable Distributions
DOI: 0.545/mjis.05.4006 Th Itrplay btw lma lmi pma ad pmi Stabl Distributios S Ravi ad TS Mavitha Dpartmt of Studis i Statistics Uivrsity of Mysor Maasagagotri Mysuru 570006 Idia. Email:ravi@statistics.uimysor.ac.i
More informationFigure 2-18 Thevenin Equivalent Circuit of a Noisy Resistor
.8 NOISE.8. Th Nyquist Nois Thorm W ow wat to tur our atttio to ois. W will start with th basic dfiitio of ois as usd i radar thory ad th discuss ois figur. Th typ of ois of itrst i radar thory is trmd
More informationStatistics 3858 : Likelihood Ratio for Exponential Distribution
Statistics 3858 : Liklihood Ratio for Expotial Distributio I ths two xampl th rjctio rjctio rgio is of th form {x : 2 log (Λ(x)) > c} for a appropriat costat c. For a siz α tst, usig Thorm 9.5A w obtai
More informationFurther Results on Pair Sum Graphs
Applid Mathmatis, 0,, 67-75 http://dx.doi.org/0.46/am.0.04 Publishd Oli Marh 0 (http://www.sirp.org/joural/am) Furthr Rsults o Pair Sum Graphs Raja Poraj, Jyaraj Vijaya Xavir Parthipa, Rukhmoi Kala Dpartmt
More informationDerivation of a Predictor of Combination #1 and the MSE for a Predictor of a Position in Two Stage Sampling with Response Error.
Drivatio of a Prdictor of Cobiatio # ad th SE for a Prdictor of a Positio i Two Stag Saplig with Rspos Error troductio Ed Stak W driv th prdictor ad its SE of a prdictor for a rado fuctio corrspodig to
More informationSession : Plasmas in Equilibrium
Sssio : Plasmas i Equilibrium Ioizatio ad Coductio i a High-prssur Plasma A ormal gas at T < 3000 K is a good lctrical isulator, bcaus thr ar almost o fr lctros i it. For prssurs > 0.1 atm, collisio amog
More informationDigital Signal Processing, Fall 2006
Digital Sigal Procssig, Fall 6 Lctur 9: Th Discrt Fourir Trasfor Zhg-Hua Ta Dpartt of Elctroic Systs Aalborg Uivrsity, Dar zt@o.aau.d Digital Sigal Procssig, I, Zhg-Hua Ta, 6 Cours at a glac MM Discrt-ti
More informationWorksheet: Taylor Series, Lagrange Error Bound ilearnmath.net
Taylor s Thorm & Lagrag Error Bouds Actual Error This is th ral amout o rror, ot th rror boud (worst cas scario). It is th dirc btw th actual () ad th polyomial. Stps:. Plug -valu ito () to gt a valu.
More informationAvailable online at Energy Procedia 4 (2011) Energy Procedia 00 (2010) GHGT-10
Availabl oli at www.scicdirct.com Ergy Procdia 4 (01 170 177 Ergy Procdia 00 (010) 000 000 Ergy Procdia www.lsvir.com/locat/procdia www.lsvir.com/locat/xxx GHGT-10 Exprimtal Studis of CO ad CH 4 Diffusio
More informationNEW VERSION OF SZEGED INDEX AND ITS COMPUTATION FOR SOME NANOTUBES
Digst Joural of Naomatrials ad Biostructurs Vol 4, No, March 009, p 67-76 NEW VERSION OF SZEGED INDEX AND ITS COMPUTATION FOR SOME NANOTUBES A IRANMANESH a*, O KHORMALI b, I NAJAFI KHALILSARAEE c, B SOLEIMANI
More informationA Simple Proof that e is Irrational
Two of th most bautiful ad sigificat umbrs i mathmatics ar π ad. π (approximatly qual to 3.459) rprsts th ratio of th circumfrc of a circl to its diamtr. (approximatly qual to.788) is th bas of th atural
More informationChapter 2 Infinite Series Page 1 of 11. Chapter 2 : Infinite Series
Chatr Ifiit Sris Pag of Sctio F Itgral Tst Chatr : Ifiit Sris By th d of this sctio you will b abl to valuat imror itgrals tst a sris for covrgc by alyig th itgral tst aly th itgral tst to rov th -sris
More informationJournal of Modern Applied Statistical Methods
Joural of Modr Applid Statistical Mthods Volum Issu Articl 6 --03 O Som Proprtis of a Htrogous Trasfr Fuctio Ivolvig Symmtric Saturatd Liar (SATLINS) with Hyprbolic Tagt (TANH) Trasfr Fuctios Christophr
More informationThey must have different numbers of electrons orbiting their nuclei. They must have the same number of neutrons in their nuclei.
37 1 How may utros ar i a uclus of th uclid l? 20 37 54 2 crtai lmt has svral isotops. Which statmt about ths isotops is corrct? Thy must hav diffrt umbrs of lctros orbitig thir ucli. Thy must hav th sam
More informationSOME IDENTITIES FOR THE GENERALIZED POLY-GENOCCHI POLYNOMIALS WITH THE PARAMETERS A, B AND C
Joural of Mathatical Aalysis ISSN: 2217-3412, URL: www.ilirias.co/ja Volu 8 Issu 1 2017, Pags 156-163 SOME IDENTITIES FOR THE GENERALIZED POLY-GENOCCHI POLYNOMIALS WITH THE PARAMETERS A, B AND C BURAK
More information5.1 The Nuclear Atom
Sav My Exams! Th Hom of Rvisio For mor awsom GSE ad lvl rsourcs, visit us at www.savmyxams.co.uk/ 5.1 Th Nuclar tom Qustio Papr Lvl IGSE Subjct Physics (0625) Exam oard Topic Sub Topic ooklt ambridg Itratioal
More informationA Novel Approach to Recovering Depth from Defocus
Ssors & Trasducrs 03 by IFSA http://www.ssorsportal.com A Novl Approach to Rcovrig Dpth from Dfocus H Zhipa Liu Zhzhog Wu Qiufg ad Fu Lifag Collg of Egirig Northast Agricultural Uivrsity 50030 Harbi Chia
More informationTime : 1 hr. Test Paper 08 Date 04/01/15 Batch - R Marks : 120
Tim : hr. Tst Papr 8 D 4//5 Bch - R Marks : SINGLE CORRECT CHOICE TYPE [4, ]. If th compl umbr z sisfis th coditio z 3, th th last valu of z is qual to : z (A) 5/3 (B) 8/3 (C) /3 (D) o of ths 5 4. Th itgral,
More information07 - SEQUENCES AND SERIES Page 1 ( Answers at he end of all questions ) b, z = n
07 - SEQUENCES AND SERIES Pag ( Aswrs at h d of all qustios ) ( ) If = a, y = b, z = c, whr a, b, c ar i A.P. ad = 0 = 0 = 0 l a l
More informationH2 Mathematics Arithmetic & Geometric Series ( )
H Mathmatics Arithmtic & Gomtric Sris (08 09) Basic Mastry Qustios Arithmtic Progrssio ad Sris. Th rth trm of a squc is 4r 7. (i) Stat th first four trms ad th 0th trm. (ii) Show that th squc is a arithmtic
More information2617 Mark Scheme June 2005 Mark Scheme 2617 June 2005
Mark Schm 67 Ju 5 GENERAL INSTRUCTIONS Marks i th mark schm ar plicitly dsigatd as M, A, B, E or G. M marks ("mthod" ar for a attmpt to us a corrct mthod (ot mrly for statig th mthod. A marks ("accuracy"
More informationBlackbody Radiation. All bodies at a temperature T emit and absorb thermal electromagnetic radiation. How is blackbody radiation absorbed and emitted?
All bodis at a tmpratur T mit ad absorb thrmal lctromagtic radiatio Blackbody radiatio I thrmal quilibrium, th powr mittd quals th powr absorbd How is blackbody radiatio absorbd ad mittd? 1 2 A blackbody
More informationSolution of Assignment #2
olution of Assignmnt #2 Instructor: Alirza imchi Qustion #: For simplicity, assum that th distribution function of T is continuous. Th distribution function of R is: F R ( r = P( R r = P( log ( T r = P(log
More informationProblem Value Score Earned No/Wrong Rec -3 Total
GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING ECE6 Fall Quiz # Writt Eam Novmr, NAME: Solutio Kys GT Usram: LAST FIRST.g., gtiit Rcitatio Sctio: Circl t dat & tim w your Rcitatio
More informationOption 3. b) xe dx = and therefore the series is convergent. 12 a) Divergent b) Convergent Proof 15 For. p = 1 1so the series diverges.
Optio Chaptr Ercis. Covrgs to Covrgs to Covrgs to Divrgs Covrgs to Covrgs to Divrgs 8 Divrgs Covrgs to Covrgs to Divrgs Covrgs to Covrgs to Covrgs to Covrgs to 8 Proof Covrgs to π l 8 l a b Divrgt π Divrgt
More informationData Assimilation 1. Alan O Neill National Centre for Earth Observation UK
Data Assimilation 1 Alan O Nill National Cntr for Earth Obsrvation UK Plan Motivation & basic idas Univariat (scalar) data assimilation Multivariat (vctor) data assimilation 3d-Variational Mthod (& optimal
More informationLinear Algebra Existence of the determinant. Expansion according to a row.
Lir Algbr 2270 1 Existc of th dtrmit. Expsio ccordig to row. W dfi th dtrmit for 1 1 mtrics s dt([]) = (1) It is sy chck tht it stisfis D1)-D3). For y othr w dfi th dtrmit s follows. Assumig th dtrmit
More informationEmpirical Study in Finite Correlation Coefficient in Two Phase Estimation
M. Khoshvisa Griffith Uivrsity Griffith Busiss School Australia F. Kaymarm Massachustts Istitut of Tchology Dpartmt of Mchaical girig USA H. P. Sigh R. Sigh Vikram Uivrsity Dpartmt of Mathmatics ad Statistics
More informationIntroduction to Quantum Information Processing. Overview. A classical randomised algorithm. q 3,3 00 0,0. p 0,0. Lecture 10.
Itroductio to Quatum Iformatio Procssig Lctur Michl Mosca Ovrviw! Classical Radomizd vs. Quatum Computig! Dutsch-Jozsa ad Brsti- Vazirai algorithms! Th quatum Fourir trasform ad phas stimatio A classical
More informationNew Sixteenth-Order Derivative-Free Methods for Solving Nonlinear Equations
Amrica Joural o Computatioal ad Applid Mathmatics 0 (: -8 DOI: 0.59/j.ajcam.000.08 Nw Sixtth-Ordr Drivativ-Fr Mthods or Solvig Noliar Equatios R. Thukral Padé Rsarch Ctr 9 Daswood Hill Lds Wst Yorkshir
More informationPURE MATHEMATICS A-LEVEL PAPER 1
-AL P MATH PAPER HONG KONG EXAMINATIONS AUTHORITY HONG KONG ADVANCED LEVEL EXAMINATION PURE MATHEMATICS A-LEVEL PAPER 8 am am ( hours) This papr must b aswrd i Eglish This papr cosists of Sctio A ad Sctio
More informationEinstein Equations for Tetrad Fields
Apiron, Vol 13, No, Octobr 006 6 Einstin Equations for Ttrad Filds Ali Rıza ŞAHİN, R T L Istanbul (Turky) Evry mtric tnsor can b xprssd by th innr product of ttrad filds W prov that Einstin quations for
More informationTechnical Support Document Bias of the Minimum Statistic
Tchical Support Documt Bias o th Miimum Stattic Itroductio Th papr pla how to driv th bias o th miimum stattic i a radom sampl o siz rom dtributios with a shit paramtr (also kow as thrshold paramtr. Ths
More informationDETECTION OF RELIABLE SOFTWARE USING SPRT ON TIME DOMAIN DATA
Itratioal Joural of Computr Scic, Egirig ad Applicatios (IJCSEA Vol., No.4, August DETECTION OF RELIABLE SOFTWARE USING SRT ON TIME DOMAIN DATA G.Krisha Moha ad Dr. Satya rasad Ravi Radr, Dpt. of Computr
More informationA Propagating Wave Packet Group Velocity Dispersion
Lctur 8 Phys 375 A Propagating Wav Packt Group Vlocity Disprsion Ovrviw and Motivation: In th last lctur w lookd at a localizd solution t) to th 1D fr-particl Schrödingr quation (SE) that corrsponds to
More informationWashington State University
he 3 Ktics ad Ractor Dsig Sprg, 00 Washgto Stat Uivrsity Dpartmt of hmical Egrg Richard L. Zollars Exam # You will hav o hour (60 muts) to complt this xam which cosists of four (4) problms. You may us
More informationInternational Journal of Advanced and Applied Sciences
Itratioal Joural of Advacd ad Applid Scics x(x) xxxx Pags: xx xx Cotts lists availabl at Scic Gat Itratioal Joural of Advacd ad Applid Scics Joural hompag: http://wwwscic gatcom/ijaashtml Symmtric Fuctios
More informationNarayana IIT Academy
INDIA Sc: LT-IIT-SPARK Dat: 9--8 6_P Max.Mars: 86 KEY SHEET PHYSIS A 5 D 6 7 A,B 8 B,D 9 A,B A,,D A,B, A,B B, A,B 5 A 6 D 7 8 A HEMISTRY 9 A B D B B 5 A,B,,D 6 A,,D 7 B,,D 8 A,B,,D 9 A,B, A,B, A,B,,D A,B,
More informationMotivation. We talk today for a more flexible approach for modeling the conditional probabilities.
Baysia Ntworks Motivatio Th coditioal idpdc assuptio ad by aïv Bays classifirs ay s too rigid spcially for classificatio probls i which th attributs ar sowhat corrlatd. W talk today for a or flibl approach
More informationThomas J. Osler. 1. INTRODUCTION. This paper gives another proof for the remarkable simple
5/24/5 A PROOF OF THE CONTINUED FRACTION EXPANSION OF / Thomas J Oslr INTRODUCTION This ar givs aothr roof for th rmarkabl siml cotiud fractio = 3 5 / Hr is ay ositiv umbr W us th otatio x= [ a; a, a2,
More information10. Joint Moments and Joint Characteristic Functions
0 Joit Momts ad Joit Charactristic Fctios Followig sctio 6 i this sctio w shall itrodc varios paramtrs to compactly rprst th iformatio cotaid i th joit pdf of two rvs Giv two rvs ad ad a fctio g x y dfi
More informationComparison of Simple Indicator Kriging, DMPE, Full MV Approach for Categorical Random Variable Simulation
Papr 17, CCG Aual Rport 11, 29 ( 29) Compariso of Simpl Idicator rigig, DMPE, Full MV Approach for Catgorical Radom Variabl Simulatio Yupg Li ad Clayto V. Dutsch Ifrc of coditioal probabilitis at usampld
More informationDiscrete Fourier Transform. Discrete Fourier Transform. Discrete Fourier Transform. Discrete Fourier Transform. Discrete Fourier Transform
Discrt Fourir Trasform Dfiitio - T simplst rlatio btw a lt- squc x dfid for ω ad its DTFT X ( ) is ω obtaid by uiformly sampli X ( ) o t ω-axis btw ω < at ω From t dfiitio of t DTFT w tus av X X( ω ) ω
More informationOutline. Ionizing Radiation. Introduction. Ionizing radiation
Outli Ioizig Radiatio Chaptr F.A. Attix, Itroductio to Radiological Physics ad Radiatio Dosimtry Radiological physics ad radiatio dosimtry Typs ad sourcs of ioizig radiatio Dscriptio of ioizig radiatio
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 informationln x = n e = 20 (nearest integer)
H JC Prlim Solutios 6 a + b y a + b / / dy a b 3/ d dy a b at, d Giv quatio of ormal at is y dy ad y wh. d a b () (,) is o th curv a+ b () y.9958 Qustio Solvig () ad (), w hav a, b. Qustio d.77 d d d.77
More informationTriple Play: From De Morgan to Stirling To Euler to Maclaurin to Stirling
Tripl Play: From D Morga to Stirlig To Eulr to Maclauri to Stirlig Augustus D Morga (186-1871) was a sigificat Victoria Mathmaticia who mad cotributios to Mathmatics History, Mathmatical Rcratios, 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 Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with A Gestation Period for Interaction
Int. J. Opn Problms Compt. Math., Vol., o., Jun 008 A Pry-Prdator Modl with an Altrnativ Food for th Prdator, Harvsting of Both th Spcis and with A Gstation Priod for Intraction K. L. arayan and. CH. P.
More informationMONTGOMERY COLLEGE Department of Mathematics Rockville Campus. 6x dx a. b. cos 2x dx ( ) 7. arctan x dx e. cos 2x dx. 2 cos3x dx
MONTGOMERY COLLEGE Dpartmt of Mathmatics Rockvill Campus MATH 8 - REVIEW PROBLEMS. Stat whthr ach of th followig ca b itgratd by partial fractios (PF), itgratio by parts (PI), u-substitutio (U), or o of
More informationAn Introduction to Asymptotic Expansions
A Itroductio to Asmptotic Expasios R. Shaar Subramaia Asmptotic xpasios ar usd i aalsis to dscrib th bhavior of a fuctio i a limitig situatio. Wh a fuctio ( x, dpds o a small paramtr, ad th solutio of
More informationFunction Spaces. a x 3. (Letting x = 1 =)) a(0) + b + c (1) = 0. Row reducing the matrix. b 1. e 4 3. e 9. >: (x = 1 =)) a(0) + b + c (1) = 0
unction Spacs Prrquisit: Sction 4.7, Coordinatization n this sction, w apply th tchniqus of Chaptr 4 to vctor spacs whos lmnts ar functions. Th vctor spacs P n and P ar familiar xampls of such spacs. Othr
More informationCDS 101: Lecture 5.1 Reachability and State Space Feedback
CDS, Lctur 5. CDS : Lctur 5. Rachability ad Stat Spac Fdback Richard M. Murray ad Hido Mabuchi 5 Octobr 4 Goals: Di rachability o a cotrol systm Giv tsts or rachability o liar systms ad apply to ampls
More informationChapter Taylor Theorem Revisited
Captr 0.07 Taylor Torm Rvisitd Atr radig tis captr, you sould b abl to. udrstad t basics o Taylor s torm,. writ trascdtal ad trigoomtric uctios as Taylor s polyomial,. us Taylor s torm to id t valus o
More informationANOVA- Analyisis of Variance
ANOVA- Aalii of Variac CS 700 Comparig altrativ Comparig two altrativ u cofidc itrval Comparig mor tha two altrativ ANOVA Aali of Variac Comparig Mor Tha Two Altrativ Naïv approach Compar cofidc itrval
More informationECE594I Notes set 6: Thermal Noise
C594I ots, M. odwll, copyrightd C594I Nots st 6: Thrmal Nois Mark odwll Uivrsity of Califoria, ata Barbara rodwll@c.ucsb.du 805-893-344, 805-893-36 fax frcs ad Citatios: C594I ots, M. odwll, copyrightd
More informationBayesian Test for Lifetime Performance Index of Exponential Distribution under Symmetric Entropy Loss Function
Mathmatics ttrs 08; 4(): 0-4 http://www.scicpublishiggroup.com/j/ml doi: 0.648/j.ml.08040.5 ISSN: 575-503X (Prit); ISSN: 575-5056 (Oli) aysia Tst for iftim Prformac Idx of Expotial Distributio udr Symmtric
More informationCDS 101: Lecture 5.1 Reachability and State Space Feedback
CDS, Lctur 5. CDS : Lctur 5. Rachability ad Stat Spac Fdback Richard M. Murray 7 Octobr 3 Goals: Di rachability o a cotrol systm Giv tsts or rachability o liar systms ad apply to ampls Dscrib th dsig o
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 informationSupplemental Material for "Automated Estimation of Vector Error Correction Models"
Supplmtal Matrial for "Automatd Estimatio of Vctor Error Corrctio Modls" ipg Liao Ptr C. B. Pillips y Tis Vrsio: Sptmbr 23 Abstract Tis supplmt icluds two sctios. Sctio cotais t proofs of som auxiliary
More information(Reference: sections in Silberberg 5 th ed.)
ALE. Atomic Structur Nam HEM K. Marr Tam No. Sctio What is a atom? What is th structur of a atom? Th Modl th structur of a atom (Rfrc: sctios.4 -. i Silbrbrg 5 th d.) Th subatomic articls that chmists
More informationNET/JRF, GATE, IIT JAM, JEST, TIFR
Istitut for NET/JRF, GATE, IIT JAM, JEST, TIFR ad GRE i PHYSICAL SCIENCES Mathmatical Physics JEST-6 Q. Giv th coditio φ, th solutio of th quatio ψ φ φ is giv by k. kφ kφ lφ kφ lφ (a) ψ (b) ψ kφ (c) ψ
More informationRestricted Factorial And A Remark On The Reduced Residue Classes
Applid Mathmatics E-Nots, 162016, 244-250 c ISSN 1607-2510 Availabl fr at mirror sits of http://www.math.thu.du.tw/ am/ Rstrictd Factorial Ad A Rmark O Th Rducd Rsidu Classs Mhdi Hassai Rcivd 26 March
More informationDiscrete Fourier Transform (DFT)
Discrt Fourir Trasorm DFT Major: All Egirig Majors Authors: Duc guy http://umricalmthods.g.us.du umrical Mthods or STEM udrgraduats 8/3/29 http://umricalmthods.g.us.du Discrt Fourir Trasorm Rcalld th xpotial
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 informationFUZZY ACCEPTANCE SAMPLING AND CHARACTERISTIC CURVES
Itratioal Joural of Computatioal Itlligc Systms, Vol. 5, No. 1 (Fbruary, 2012), 13-29 FUZZY ACCEPTANCE SAMPLING AND CHARACTERISTIC CURVES Ebru Turaoğlu Slçu Uivrsity, Dpartmt of Idustrial Egirig, 42075,
More informationOrdinary Differential Equations
Basi Nomlatur MAE 0 all 005 Egirig Aalsis Ltur Nots o: Ordiar Diffrtial Equatios Author: Profssor Albrt Y. Tog Tpist: Sakurako Takahashi Cosidr a gral O. D. E. with t as th idpdt variabl, ad th dpdt variabl.
More informationNormal Form for Systems with Linear Part N 3(n)
Applid Mathmatics 64-647 http://dxdoiorg/46/am7 Publishd Oli ovmbr (http://wwwscirporg/joural/am) ormal Form or Systms with Liar Part () Grac Gachigua * David Maloza Johaa Sigy Dpartmt o Mathmatics Collg
More informationAddition of angular momentum
Addition of angular momntum April, 07 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat
More informationChapter 3 Fourier Series Representation of Periodic Signals
Chptr Fourir Sris Rprsttio of Priodic Sigls If ritrry sigl x(t or x[] is xprssd s lir comitio of som sic sigls th rspos of LI systm coms th sum of th idividul rsposs of thos sic sigls Such sic sigl must:
More informationIterative Methods of Order Four for Solving Nonlinear Equations
Itrativ Mods of Ordr Four for Solvig Noliar Equatios V.B. Kumar,Vatti, Shouri Domii ad Mouia,V Dpartmt of Egirig Mamatis, Formr Studt of Chmial Egirig Adhra Uivrsity Collg of Egirig A, Adhra Uivrsity Visakhapatam
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 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 informationNEW APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA
NE APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA Mirca I CÎRNU Ph Dp o Mathmatics III Faculty o Applid Scincs Univrsity Polithnica o Bucharst Cirnumirca @yahoocom Abstract In a rcnt papr [] 5 th indinit intgrals
More informationPPS (Pottial Path Spac) i y i l j Vij (2) H x PP (Pottial Path ra) (gravity-typ masur) i i i j1 cij (1) D j j c ij ij 4)7) 8), 9) D j V ij j i 198 1)1
1 2 3 1 (68-8552 4 11) E-mail: taimoto@ss.tottori-u.ac.jp 2 (68-8552 4 11) 3 (657-851 1-1) Ky Words: accssibility, public trasportatio plaig, rural aras, tim allocatio, spac-tim prism 197 Hady ad Nimir
More informationTraveling Salesperson Problem and Neural Networks. A Complete Algorithm in Matrix Form
Procdigs of th th WSEAS Itratioal Cofrc o COMPUTERS, Agios Nikolaos, Crt Islad, Grc, July 6-8, 7 47 Travlig Salsprso Problm ad Nural Ntworks A Complt Algorithm i Matrix Form NICOLAE POPOVICIU Faculty of
More informationNew Binary Complementary Codes Compressing a Pulse to a Width of Several Sub-pulses
Nw Biary Complmtary Cods Comprssig a Puls to a Width of Svral Sub-pulss Hiroshi TAKASE ad Masaori SHINRIKI Dpartmt of Computr ad Iformatio Egirig, Nippo Istitut of Tchology 4- Gakudai, Miyashiro, Saitama-k,
More informationUNIT 2: MATHEMATICAL ENVIRONMENT
UNIT : MATHEMATICAL ENVIRONMENT. Itroductio This uit itroducs som basic mathmatical cocpts ad rlats thm to th otatio usd i th cours. Wh ou hav workd through this uit ou should: apprciat that a mathmatical
More informationPartial Derivatives: Suppose that z = f(x, y) is a function of two variables.
Chaptr Functions o Two Variabls Applid Calculus 61 Sction : Calculus o Functions o Two Variabls Now that ou hav som amiliarit with unctions o two variabls it s tim to start appling calculus to hlp us solv
More information2.29 Numerical Fluid Mechanics Spring 2015 Lecture 12
REVIEW Lctur 11: Numrical Fluid Mchaics Sprig 2015 Lctur 12 Fiit Diffrcs basd Polyomial approximatios Obtai polyomial (i gral u-qually spacd), th diffrtiat as dd Nwto s itrpolatig polyomial formulas Triagular
More informationOn Deterministic Finite Automata and Syntactic Monoid Size, Continued
O Dtrmiistic Fiit Automata ad Sytactic Mooid Siz, Cotiud Markus Holzr ad Barbara Köig Istitut für Iformatik, Tchisch Uivrsität Müch, Boltzmastraß 3, D-85748 Garchig bi Müch, Grmay mail: {holzr,koigb}@iformatik.tu-much.d
More informationu 3 = u 3 (x 1, x 2, x 3 )
Lctur 23: Curvilinar Coordinats (RHB 8.0 It is oftn convnint to work with variabls othr than th Cartsian coordinats x i ( = x, y, z. For xampl in Lctur 5 w mt sphrical polar and cylindrical polar coordinats.
More informationPart B: Transform Methods. Professor E. Ambikairajah UNSW, Australia
Part B: Trasform Mthods Chaptr 3: Discrt-Tim Fourir Trasform (DTFT) 3. Discrt Tim Fourir Trasform (DTFT) 3. Proprtis of DTFT 3.3 Discrt Fourir Trasform (DFT) 3.4 Paddig with Zros ad frqucy Rsolutio 3.5
More informationKISS: A Bit Too Simple. Greg Rose
KI: A Bit Too impl Grg Ros ggr@qualcomm.com Outli KI radom umbr grator ubgrators Efficit attack N KI ad attack oclusio PAGE 2 O approach to PRNG scurity "A radom umbr grator is lik sx: Wh it's good, its
More informationω (argument or phase)
Imagiary uit: i ( i Complx umbr: z x+ i y Cartsia coordiats: x (ral part y (imagiary part Complx cougat: z x i y Absolut valu: r z x + y Polar coordiats: r (absolut valu or modulus ω (argumt or phas x
More informationPage 1. Before-After Control-Impact (BACI) Power Analysis For Several Related Populations (Variance Known) Richard A. Hinrichsen. September 24, 2010
Pag for-aftr Cotrol-Impact (ACI) Powr Aalysis For Svral Rlatd Populatios (Variac Kow) Richard A. Hirichs Sptmbr 4, Cavat: This primtal dsig tool is a idalizd powr aalysis built upo svral simplifyig assumptios
More informationChapter Five. More Dimensions. is simply the set of all ordered n-tuples of real numbers x = ( x 1
Chatr Fiv Mor Dimsios 51 Th Sac R W ar ow rard to mov o to sacs of dimsio gratr tha thr Ths sacs ar a straightforward gralizatio of our Euclida sac of thr dimsios Lt b a ositiv itgr Th -dimsioal Euclida
More information