Sequential Allocation with Minimal Switching

Size: px
Start display at page:

Download "Sequential Allocation with Minimal Switching"

Transcription

1 In Cmputing Science and Statistics 28 (1996), pp Sequential Allcatin with Minimal Switching Quentin F. Stut 1 Janis Hardwick 1 EECS Dept., University f Michigan Statistics Dept., Purdue University Abstract This paper describes algrithms fr the design f sequential experiments where extensive switching is undesirable. Given an bjective functin t minimize by sampling between Bernulli ppulatins, tw different mdels are cnsidered. The cnstraint mdel ptimizes the tradeff f the maximum number f switches vs. the bjective functin, while the cst mdel ptimizes the tradeff fr the expected number f switches. Fr each mdel, an algrithm is develped which prduces the ptimal sequential experiment. The algrithms are quite general, and give users flexibility in incrprating practical cnsideratins in the design f experiments. T shw the usability f these algrithms, they are applied t a bandit prblem and an estimatin prblem. It is bserved that the expected number f switches grws apprximately as the square rt f the sample size, fr sample sizes up t a few hundred. It is als bserved that ne can dramatically reduce the number f switches withut substantially affecting the expected value f the bjective functin. Thus ne need sacrifice nly a small amunt f statistical bjective in rder t achieve significant gains in practicality. Keywrds: adaptive sampling, switching csts, cnstraints, bandit, estimatin, dynamic prgramming, ptimal tradeffs 1 Intrductin In situatins where data is cllected ver time, adaptive sampling r allcatin, in which decisins are made based n accruing data, is mre efficient than fixed sampling, where all decisins are made in advance. Adaptive allcatins can reduce csts r time, r imprve the results fr a given sample size. Hwever, fully adaptive designs are rarely used, due t varius cncerns ver their design, analysis, and implementatin. In sme settings, ne cncern is that sequential designs switch repeatedly between the alternatives, a design attribute that may be cstly r impssible [6]. Fr example, in an industrial setting, ne may need t recnfigure fixtures each time a switch ccurs. In a clinical setting, similar setup r 1 Research supprted in part by Natinal Science Fundatin under grants DMS and DMS training csts may be required t switch between treatment alternatives. Imprtant alternatives fr mdeling the ill effects f switching include: 1. Yu have setup cst ff i t change t ppulatin i, and incur incremental cst fi i fr each bservatin as lng as yu stay n that ppulatin, where ff i fl fi i. 2. Yu have t make up a treatment in batches, r need t set up fixtures t cnduct several identical tests at the same time, s when yu decide that the next m bservatins are n ppulatin i yu incur a cst ff i + fi i m. Here yu must specify m in advance. 3. Yu can switch at mst S times. Fr example, yu may need t use a special apparatus t which yu have nly S accesses. Such cst structures are quite imprtant, althugh rarely directly incrprated in designs. One exceptin is in cntrl thery, where the cst structure is as in 1 (see [1] and the references therein). Unfrtunately, their results apply nly when a gemetric discunt structure is used with an infinite hrizn and n terminal bjective. Anther analysis f switching csts appears in [2], where the setting is quite specialized with ne arm having a knwn prbability f success and the bjective is t minimize the expected number f failures. Nne f this prir wrk applies t the fairly general sequential prblems we have in mind, which allws fr an arbitrary bjective functin, finite hrizn, and flexible methds fr incrprating switching cnsideratins. In Sectin 2, basic definitins are given. In Sectin 3 a cnstraint mdel is defined, crrespnding t alternative 3 abve, and an algrithm is given that determines the ptimal sequential design fr this mdel. In Sectin 4 a cst mdel is defined, generalizing alternative 1. There it is shwn that this mdel determines the ptimal tradeff f expected switches vs. bjective, and an algrithm that determines the ptimal sequential design is given. The algrithms in Sectins 3 and 4 are based n dynamic prgramming, and the crux f the cmputatinal prblem is t determine a minimal state space and manner f evaluatin fr these mdels that makes the cmputatins feasible. In Sectin 5 the algrithms are applied t a bandit prblem and an estimatin prblem, and the switching

2 behavir f the ptimal allcatin prcedures is determined cmputatinally. Sectin 6 cncludes with remarks cncerning generalizatins and bservatins cncerning the results. While n wrk will be dne here n cst alternative 2, nte that it can be viewed as a staged-allcatin prblem, and can be ptimized by the techniques develped in [4]. 2 Definitins Thrughut, we assumethat thesample size N is fixed. This assumptin merely simplifies ur analyses and examples, and the algrithms can easily be adapted t include stpping rules. If ptinal stpping is desired (and it is quite natural t incrprate stpping rules in cst mdels), then N shuld be interpreted as the maximum pssible sample size. Often knwledge f the stpping rules can be used t significantly reduce the state space, but since this is quite applicatin-dependent we will mit such imprvements here and analyze nly the wrst case in which n stpping ccurs. There are P Bernulli ppulatins, and at any pint the nly decisin required is t chse which f these t bserve. We use a Bayesian apprach, where the success parameters f the ppulatins have independent prir distributins. Suppse that at sme pint we have bserved s i successes and f i failures n Ppulatin i. Then the vectr (s 1 ;f 1 ;:::;s P ;f P ) is a sufficient statistic, and frms a natural index fr the state space describing the experiment. States, dented as v, will be treated as vectrs s that ne can add bservatins in a natural manner. We use p i (v) t dente the prbability f success if the next bservatin is frm ppulatin i, given that the experiment is at state v. There is an bjective functin R Λ (v) which is the value f each final state v (i.e., states fr which jvj = N), and the gal is t minimize the expected value f R Λ.Theexpected value f allcatin A, dented R A, is the sum, ver all final states v, fr Λ (v) times the prbability that A reaches v. Fr an arbitrary state v,letr(v) dente the expected value f R Λ when starting at v and prceeding ptimally t the end. Then R(0) is the expected value f the ptimal sequential experiment, i.e., is R pt.theefficiency f allcatin prcedure A is R pt =R A. By using standard dynamic prgramming, R pt can be determined in (PN 2P =(2P )!) time since there are (N 2P =(2P )!) states, each requiring the evaluatin f P alternatives. Here, as in all f ur timing analyses, we assume that R Λ can be cmputed fr all terminal states in time prprtinal t the number f terminal states, and that fr each ppulatin i, p i can be determined fr all states in time prprtinal t the number f states. Even when R Λ r p i are cmplicated t cmpute fr a single state, ur assumptin typically hlds because ne can reuse parts f the calculatins fr ne state t assist thse fr ther states. N: samplesize P : number f ppulatins S: maximum number f switches pssible (cnstraint mdel) R Λ : terminal bjective functin R A : expected value f R fr allcatin A R(v): expected value f R Λ, starting at state v and prceeding ptimally (n cst cnsideratins) R pt : expected value f R fr ptimal sequential allcatin (i.e., R(0)) R i (v): expected value f bjective + switching csts btained by starting at state v, sampling frmppulatin i, and prceeding ptimally (cst mdel) R ff i (v): expected bjective btained by starting at state v, sampling frm pp. i, and prceeding ptimally using n mre than ff switches (cnstraint mdel) c(i; j): the cst f switching frm pp. i t pp. j C i (v): expected value f ttal switching csts btained by starting at state v, sampling frm ppulatin i, and prceeding ptimally (cst mdel) v: a state, that is, a vectr denting number f successes and failures bserved n each ppulatin jvj : the ttal number f bservatins at state v si; fi: vectrs denting 1 success r failure n pp. i p i (v): prbability f success n next bservatin f ppulatin i, when experiment is in state v Figure 1: Ntatin 3 Cnstraint Mdel In the cnstraint mdel, there is an upper bund S n the number f times that the ppulatins t be sampled can be switched (the initial sampling is nt cunted as a switch.) The gal is t minimize the expected value f the bjective functin, subject t this cnstraint. When S N 1, the prblem is equivalent t the standard ptimizatin prblem withut switching cnsideratins. Results fr k-stage allcatin immediately give a lwer bund n the efficiency btainable fr S =(P 1)k, since a k-stage allcatin can be scheduled by allcating all stage 1 bservatins n ppulatins 1 thrugh P,thenallstage2 bservatins n ppulatins P thrugh 1, etc. In particular,

3 wrk in [4] shws that fr P = 2, valuesfs as small as 3 will give very high efficiency n sme prblems, and this is bserved in Sectin 5. The bserved perfrmance with an average f k switches is significantly better than that f the k- stage rules, due t the increased adaptiveness f cst mdel 1 ver mdel 2. T determine the ptimal allcatin algrithm under the cnstraint mdel, there is a difficulty in that the natural state space des nt uniquely determine the number f switches that ccured in reaching that state (except in trivial cases), nr can ne determine if a switch ccurs when ging frm ne given state t its successr (again, except in trivial cases). T determine these, ne apparently needs t add infrmatin specifying the number f switches and the mst recent ppulatin sampled. There are several ways this can be dne. Here, the values Ri ff (v) are cmputed at each state, where Ri ff (v) is the expected value f the bjective functin if ne is at state v, bserves ppulatin i, and prceeds ptimally under the cnstraint that at mst ff mre switches ccur. This is equivalent t extending the state v t a cllectin f states (v; i; ff), with the abve interpretatins fr i and ff, andthen determining the value f the ptimal cntinuatin at each state. The ptimal expected value f a sequential allcatin prcedure satisfying the switching cnstraint is the minimum, ver all ppulatins i, fri S (0). The critical dynamic prgramming equatins determining the values f Ri ff (v) are based n nting that the successr states can nly be v + s i and v + f i, depending n whether a success r failure, respectively, ccurs. Upn reaching a successr state, either ppulatin i is sampled again, in which case the number f future switches pssible des nt change, r else a new ppulatin is sampled and the maximum number f switches remaining decreases by ne. The detailed equatins appear in Figure 2. Nte that if ff =0, then n further switches are pssible. Analyzing the time and space f the algrithm in Figure 2, ne arrives at the results in Therem 3.1. The space analysis assumes that space is reused fr each new value f m. Hwever, this requires that ne be careful with the rdering in which ne ges thrugh the states with jvj = m t make sure that values are nt verwritten befre all f their uses have ccurred. The wavefrnt dependencies can be satisfied by prceeding thrugh each cmpnent f v in increasing fashin, and prceeding thrugh the number f switches in decreasing rder. The rdering f the ppulatins is irrelevant. Therem 3.1 The value f the ptimal experiment f N bservatins with P Bernulli ppulatins, with an bjective functin and a cnstraint f at mst S switches, can be determined in (SP 2 N 2P =(2P )!) time and (SPN 2P 1 =(2P 1)!) space by the algrithm in Figure 2. 2 In practice ne wuld usually stre the Ri ff (v) values in a single array. In Frtran, it is best t d this as the array fr all terminal states v (i.e., states where jvj = N) fr all ppulatins i 2f1;:::;Pg fr all switches ff 2f0;:::;Sg initialize R ff i (v) =RΛ (v) fr m = n 1 dwnt 0 fr all states v with jvj = m fr all switches ff 2f0;:::;Sg fr all ppulatins i 2f1;:::;Pg r suc = R ff i (v + s i) r fail = R ff i (v + f i) if ff>0 then r suc = minfr suc ; minfr ff 1 j (v + si) :j 6= igg (v + fi) :j 6= igg r fail = minfr fail ; minfr ff 1 j Ri ff (v) =p i(v) r suc +(1 p i (v)) r fail Expected value = minfri S (0) :i 2f1;:::;Pgg Figure 2: Optimal Experiment fr Cnstraint Mdel R(i; ff; v), since there are multiple innermst lps (the minimum peratins) that run thrugh the ppulatins fr fixed values f ff and v. Figure 2 shws nly hw t cmpute the values f Ri S (0), nt what the allcatin algrithm is that achieves these values. T determine the algrithm, ne needs t recrd the value f j that achieves the minimum in each place where a minimum peratin is perfrmed. Then ne can fllw the standard prcedure f recnstructing the ptimal slutin frm the beginning f the experiment twards the end by fllwing these pinters. Nte that the algrithm actually finds the value f the ptimal experiments crrespnding t all cnstraints less than r equal t S, nt just the ptimal experiment fr S. This is quite useful, since it allws ne t examine the range f tradeffs between maximum switches vs. expected bjective functin all frm a single run. In general the mst interesting cases are thse in which S is quite small, and hence reductins in the effective value f S have a large percentage change in the runtime r space required. Fr example, Ri 0 (v) can ften be determined algebraically, and thus it need nt be stred. Fr ff = S, there have nly been bservatins n a single ppulatin, and hence mst states cannt ccur. There are nly apprximately PN 2 =2 states that can ccur, as ppsed t the apprximately PN 2P =(2P )! ttal states, s the time and space requirements fr determining Ri S can be significantly reduced. 4 Cst Mdel In the cst mdel, if the last ppulatin sampled was i, and we nw sample j,thenwepayacstc(i; j) (if the first bservatin is n i, thenwepayc(i; i)). The gal is t minimize

4 the expected value f the terminal bjective plus csts. This is a flexible mdel that includes cst alternative 1 f Sectin 1 as a special case. A particularly imprtant special case ccurs when c(i; i) = 0 and c(i; j) = ff, i 6= j, fr then the cst cmpnent is prprtinal t the number f switches. Let R ff dente the ptimal value btained using this cst functin (where value is nw terminal bjective plus cst), and let C ff dente the expected cst f the allcatin prcedure achieving R ff.thenr ff C ff is the ptimal expected value f the bjective functin, under the cnstraint that the expected cst is n mre than C ff, i.e., under the cnstraint that the average number f switches is n mre than C ff =ff. Thus the cst mdel achieves ptimal bjective functin vs. expected number f switches tradeffs, but des s thrugh an indirect cntrl parameter (ff). T investigate a specific expected number f switches, ne must search thrugh ff, thugh ne can explit the fact that C ff =ff is mntne decreasing in ff. One culd determine the ptimal sequential allcatin prcedure under the cst mdel by using the same apprach as fr the cnstraint mdel, with nly minr changes t add the switching csts. Hwever, this wuld be impractical, because ne wuld need t set S = N 1 t insure that all pssibilities are analyzed, which wuld greatly reduce the size f experiment that culd be analyzed. Instead, at each state v, we determine nly P quantities. Let R i (v) dente the expected value f the bjective functin plus all csts frm v t the end f the experiment, given that the next bservatin is n ppulatin i and that ne then prceeds ptimally t minimize this quantity. Nte that R i (v) des nt include any csts incurred in reaching v, merely thse in prceeding nward frm v. It is straightfrward t see that minfr i (0) :i 2f1;:::;Pgg is the value f the ptimal sequential allcatin prcedure satisfying the cst mdel, and that R i (v) is crrectly determined by the recursive equatins in Figure 3. Therem 4.1 The value f the ptimal experiment f N bservatins with P Bernulli ppulatins, minimizing the bjective functin plus csts, can be determined in (P 2 N 2P =(2P )!) time and (PN 2P 1 =(2P 1)!) space by the algrithm in Figure Examples T shw that the algrithms f the previus sectins are practical, they are applied t tw illustrative prblems. Fr bth f these, P = 2 and beta distributins are used as the prirs n bth ppulatins. Our primary example is the 2-armed bandit prblem with finite hrizn, n discunting, and unifrm weights. We chse this example because it is wellknwn and has been widely studied, althugh we culd find n wrk n the expected number f switches. Our gal is t fr all terminal states v (i.e., states where jvj = N) fr all ppulatins i 2f1;:::;Pg initialize R i (v) =R Λ (v) initialize C i (v) =0 fr all m = n 1 dwnt 0 fr all states v with jvj = m fr all ppulatins i 2f1;:::;Pg js = argminfc(i; j)+r j (v + si) :j 2f1;:::;Pgg jf = argminfc(i; j)+r j (v + fi) :j 2f1;:::;Pgg R i (v) =p i (v) [c(i; js) +R js (v + si)] + (1 p i (v)) [c(i; jf )+R jf (v + fi)] C i (v) =p i (v) [c(i; js) +C js (v + si)] + (1 p i (v)) [c(i; jf )+C jf (v + fi)] Expected value = minfr i (0) C i (0) :i 2f1;:::;Pgg Figure 3: Optimal Experiment fr Cst Mdel shw that the general algrithms can be applied t prblems f interesting sizes. (We have slved prblems as large as N = 600 using standard wrkstatins.) N special prperties f the bandit prblem were explited t reduce the run-time r space required. T emphasize this, we applied the same prgrams t ur secnd example. By changing nly the bjective functin, we addressed the prblem f minimizing the mean squared errr f the estimate f the prduct P 1 P 2,whereP i is the success prbability f ppulatin i. Nte that fr the bandit prblem the gal is t stay n the better ppulatin, while fr the estimatin prblem ne shuld have extensive bservatins frm bth ppulatins Armed Bandit Fr the 2-armed bandit with binary respnse, hrizn N,and n discunting, the bjective is t minimize the ttal number f failures. In Figure 4, the expected number f switches when using the ptimal sequential slutin, with n switching cnsideratins, is pltted as a functin f the sample size N. Nte that the number f switches grws rughly as the square rt f N, fr the range f N and values f the prirs cnsidered, but that the grwth rate seems t be slwing. The maximum number f switches is nearly N in all cases, and is nt shwn. In Figure 5 a), the ptimal tradeffs between the expected value f the bjective functin and the expected number f switches are pltted. In Figure 5 b) the ptimal tradeffs invlve the maximum number f switches. These tradeffs are expressed in terms f the efficiency f the bjective functin. Fr a), the tradeffs are btained using the algrithm in Figure 3 with cst structures f the frm c(i; i) = 0 and c(i; j) = ff, i 6= j, while fr b) the tradeffs are btained using the algrithm in Figure 2. Nte that, in bth cases, ne

5 Lg(Expected Number Switches) Efficiency Ppulatin prirs: Lg(Sample Size) + Be(1,9), Be(1,9) 4 Be(1,1), Be(1,1) Λ Be(1,1), Be(2,2) Figure 4: 2-Armed Bandit, N Switching Cnsideratins btains very high efficiency with relatively few switches. 5.2 Prduct Estimatin The prblem f estimating the prduct f tw success prbabilities arises in reliability settings, and has been studied several times (see [3, 5] and the references therein). The bjective functin is the mean squared errr f the terminal estimate f P 1 P 2,whereP i is the success prbability f ppulatin i. In Figure 6 the ptimal tradeffs f bjective functin vs. expected number f switches are shwn. Due t space cnstraints, ther behavirs f this estimatin prblem cannt be shwn here, but the basic prperties bserved fr the bandit prblem have als been seen t ccur fr this prblem. In particular, sequential allcatin prcedures which d nt incrprate switching cnsideratins exhibit high numbers f switches, and the switches are dramatically reduced, with nly miniscule lss f efficiency, by the ptimal prcedures that d incrprate switching cnsideratins. 6 Final Remarks Practical cnsideratins are imprtant in the cnduct f experiments, s it is useful t give investigatrs ways t directly address such cnsideratins in the design f their experiments. One such cnsideratin is the extensive switching that cmmnly ccurs with sequential designs. This paper Efficiency Expected Number f Switches a) Expected Number f Switches Maximum Number f Switches b) Maximum Number f Switches Figure 5: N = 200, Unifrm prirs n bth ppulatins has addressed this cncern by giving algrithms that ptimize bjective functin vs. switching cnsideratin tradeffs. Given an arbitrary bjective functin, and given either switching csts r switching cnstraints, the algrithms herein determine the ptimal sequential experiment fr the resulting mdel. In sme cases an investigatr may nt utilize the sequential allcatin prcedure that ptimizes a tradeff, but may want t use it as a benchmark against which subptimal designs are evaluated. The cst mdel can easily be extended t depend n the number f bservatins s far, and n the utcme f the bservatin. This wuld allw ne t ptimize interesting cases such as bandit prblems with nn-unifrm weights. Fr such

6 Efficiency Expected Number f Switches N = 200, Bth ppulatins have prir Be(9,1) Figure 6: Optimal Tradeffs, Estimating P 1 P 2 bandits the bjective functin cannt be evaluated with just a knwledge f the standard state space, but can be evaluated by the path-based apprach used t evaluate switching csts. Fr arbitrary bjective functins, with trivial changes either algrithm culd be adapted t ptimize the wrst-case values f the bjective functin, rather than the expected case. One can als merge the tw algrithms t ptimize the expected bjective functin plus switching csts, under a cnstraint n the maximal number f switches allwed. The algrithms were applied t tw examples t shw their utility, and t shw sme f the behavir that ccurs. It was bserved that sequential designs ptimized withut regard fr switching cnsideratins tend t have extensive switches, but that the number f switches can be dramatically reduced with nly minr lss f efficiency in the bjective functin. It was als bserved that, fr the prblems cnsidered, the expected number f switches fr standard ptimal sequential designs grws fairly rapidly, rughly n the rder f the square rt f the sample size, fr sample sizes f a few hundred. This grwth seems t slw dwn as the sample size increases, hwever, and this leads us t believe that the asympttic rate is far slwer. Thus it is expected that purely asympttic results wuld prly predict the bserved behavir. Because asympttics ften give weak guidance fr the design f specific experiments, we believe that cmputatinal insight and ptimizatin fills an imprtant rle. Hwever, t better fill that rle, it helps t have cmputatinal appraches that mdel all f the factrs that are relevant t the experimenter. This wrk is just a small piece in a larger prject t develp such mdels and prgrams. References [1] Assawa, M. and Teneketzis, D. (1996), Multi-armed bandits with switching penalties, IEEE Trans. Aut. Cntrl 41: [2] Benzing, H., Kalin, D., Thedrescu, R. (1987), Optimal plicies fr sequential Bernulli experiments with switching csts, J. Infrm. Prcess. Cybernet. 23: [3] Hardwick, J. and Stut, Q.F. (1993), Optimal allcatin fr estimating the prduct f tw means, Cmputing Science and Stat. 24: [4] Hardwick, J. and Stut, Q.F. (1995), Determining ptimal few-stage allcatin prcedures, Cmputing Science and Stat. 27. [5] Page, C. (1987), Sequential designs fr estimating prducts f parameters, Seq. Anal. 6: [6] Schmitz, N. (1993), Optimal Sequentially Planned Decisin Prcedures, Springer-Verlag Lecture Ntes.

Bootstrap Method > # Purpose: understand how bootstrap method works > obs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(obs) >

Bootstrap Method > # Purpose: understand how bootstrap method works > obs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(obs) > Btstrap Methd > # Purpse: understand hw btstrap methd wrks > bs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(bs) > mean(bs) [1] 21.64625 > # estimate f lambda > lambda = 1/mean(bs);

More information

Admin. MDP Search Trees. Optimal Quantities. Reinforcement Learning

Admin. MDP Search Trees. Optimal Quantities. Reinforcement Learning Admin Reinfrcement Learning Cntent adapted frm Berkeley CS188 MDP Search Trees Each MDP state prjects an expectimax-like search tree Optimal Quantities The value (utility) f a state s: V*(s) = expected

More information

Pattern Recognition 2014 Support Vector Machines

Pattern Recognition 2014 Support Vector Machines Pattern Recgnitin 2014 Supprt Vectr Machines Ad Feelders Universiteit Utrecht Ad Feelders ( Universiteit Utrecht ) Pattern Recgnitin 1 / 55 Overview 1 Separable Case 2 Kernel Functins 3 Allwing Errrs (Sft

More information

CHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India

CHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India CHAPTER 3 INEQUALITIES Cpyright -The Institute f Chartered Accuntants f India INEQUALITIES LEARNING OBJECTIVES One f the widely used decisin making prblems, nwadays, is t decide n the ptimal mix f scarce

More information

A New Evaluation Measure. J. Joiner and L. Werner. The problems of evaluation and the needed criteria of evaluation

A New Evaluation Measure. J. Joiner and L. Werner. The problems of evaluation and the needed criteria of evaluation III-l III. A New Evaluatin Measure J. Jiner and L. Werner Abstract The prblems f evaluatin and the needed criteria f evaluatin measures in the SMART system f infrmatin retrieval are reviewed and discussed.

More information

SUPPLEMENTARY MATERIAL GaGa: a simple and flexible hierarchical model for microarray data analysis

SUPPLEMENTARY MATERIAL GaGa: a simple and flexible hierarchical model for microarray data analysis SUPPLEMENTARY MATERIAL GaGa: a simple and flexible hierarchical mdel fr micrarray data analysis David Rssell Department f Bistatistics M.D. Andersn Cancer Center, Hustn, TX 77030, USA rsselldavid@gmail.cm

More information

Department of Electrical Engineering, University of Waterloo. Introduction

Department of Electrical Engineering, University of Waterloo. Introduction Sectin 4: Sequential Circuits Majr Tpics Types f sequential circuits Flip-flps Analysis f clcked sequential circuits Mre and Mealy machines Design f clcked sequential circuits State transitin design methd

More information

The blessing of dimensionality for kernel methods

The blessing of dimensionality for kernel methods fr kernel methds Building classifiers in high dimensinal space Pierre Dupnt Pierre.Dupnt@ucluvain.be Classifiers define decisin surfaces in sme feature space where the data is either initially represented

More information

Hypothesis Tests for One Population Mean

Hypothesis Tests for One Population Mean Hypthesis Tests fr One Ppulatin Mean Chapter 9 Ala Abdelbaki Objective Objective: T estimate the value f ne ppulatin mean Inferential statistics using statistics in rder t estimate parameters We will be

More information

Five Whys How To Do It Better

Five Whys How To Do It Better Five Whys Definitin. As explained in the previus article, we define rt cause as simply the uncvering f hw the current prblem came int being. Fr a simple causal chain, it is the entire chain. Fr a cmplex

More information

NUMBERS, MATHEMATICS AND EQUATIONS

NUMBERS, MATHEMATICS AND EQUATIONS AUSTRALIAN CURRICULUM PHYSICS GETTING STARTED WITH PHYSICS NUMBERS, MATHEMATICS AND EQUATIONS An integral part t the understanding f ur physical wrld is the use f mathematical mdels which can be used t

More information

Lead/Lag Compensator Frequency Domain Properties and Design Methods

Lead/Lag Compensator Frequency Domain Properties and Design Methods Lectures 6 and 7 Lead/Lag Cmpensatr Frequency Dmain Prperties and Design Methds Definitin Cnsider the cmpensatr (ie cntrller Fr, it is called a lag cmpensatr s K Fr s, it is called a lead cmpensatr Ntatin

More information

CAUSAL INFERENCE. Technical Track Session I. Phillippe Leite. The World Bank

CAUSAL INFERENCE. Technical Track Session I. Phillippe Leite. The World Bank CAUSAL INFERENCE Technical Track Sessin I Phillippe Leite The Wrld Bank These slides were develped by Christel Vermeersch and mdified by Phillippe Leite fr the purpse f this wrkshp Plicy questins are causal

More information

Floating Point Method for Solving Transportation. Problems with Additional Constraints

Floating Point Method for Solving Transportation. Problems with Additional Constraints Internatinal Mathematical Frum, Vl. 6, 20, n. 40, 983-992 Flating Pint Methd fr Slving Transprtatin Prblems with Additinal Cnstraints P. Pandian and D. Anuradha Department f Mathematics, Schl f Advanced

More information

COMP 551 Applied Machine Learning Lecture 9: Support Vector Machines (cont d)

COMP 551 Applied Machine Learning Lecture 9: Support Vector Machines (cont d) COMP 551 Applied Machine Learning Lecture 9: Supprt Vectr Machines (cnt d) Instructr: Herke van Hf (herke.vanhf@mail.mcgill.ca) Slides mstly by: Class web page: www.cs.mcgill.ca/~hvanh2/cmp551 Unless therwise

More information

What is Statistical Learning?

What is Statistical Learning? What is Statistical Learning? Sales 5 10 15 20 25 Sales 5 10 15 20 25 Sales 5 10 15 20 25 0 50 100 200 300 TV 0 10 20 30 40 50 Radi 0 20 40 60 80 100 Newspaper Shwn are Sales vs TV, Radi and Newspaper,

More information

Revision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax

Revision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax .7.4: Direct frequency dmain circuit analysis Revisin: August 9, 00 5 E Main Suite D Pullman, WA 9963 (509) 334 6306 ice and Fax Overview n chapter.7., we determined the steadystate respnse f electrical

More information

Computational modeling techniques

Computational modeling techniques Cmputatinal mdeling techniques Lecture 4: Mdel checing fr ODE mdels In Petre Department f IT, Åb Aademi http://www.users.ab.fi/ipetre/cmpmd/ Cntent Stichimetric matrix Calculating the mass cnservatin relatins

More information

Support-Vector Machines

Support-Vector Machines Supprt-Vectr Machines Intrductin Supprt vectr machine is a linear machine with sme very nice prperties. Haykin chapter 6. See Alpaydin chapter 13 fr similar cntent. Nte: Part f this lecture drew material

More information

Reinforcement Learning" CMPSCI 383 Nov 29, 2011!

Reinforcement Learning CMPSCI 383 Nov 29, 2011! Reinfrcement Learning" CMPSCI 383 Nv 29, 2011! 1 Tdayʼs lecture" Review f Chapter 17: Making Cmple Decisins! Sequential decisin prblems! The mtivatin and advantages f reinfrcement learning.! Passive learning!

More information

NUROP CONGRESS PAPER CHINESE PINYIN TO CHINESE CHARACTER CONVERSION

NUROP CONGRESS PAPER CHINESE PINYIN TO CHINESE CHARACTER CONVERSION NUROP Chinese Pinyin T Chinese Character Cnversin NUROP CONGRESS PAPER CHINESE PINYIN TO CHINESE CHARACTER CONVERSION CHIA LI SHI 1 AND LUA KIM TENG 2 Schl f Cmputing, Natinal University f Singapre 3 Science

More information

Admissibility Conditions and Asymptotic Behavior of Strongly Regular Graphs

Admissibility Conditions and Asymptotic Behavior of Strongly Regular Graphs Admissibility Cnditins and Asympttic Behavir f Strngly Regular Graphs VASCO MOÇO MANO Department f Mathematics University f Prt Oprt PORTUGAL vascmcman@gmailcm LUÍS ANTÓNIO DE ALMEIDA VIEIRA Department

More information

Administrativia. Assignment 1 due thursday 9/23/2004 BEFORE midnight. Midterm exam 10/07/2003 in class. CS 460, Sessions 8-9 1

Administrativia. Assignment 1 due thursday 9/23/2004 BEFORE midnight. Midterm exam 10/07/2003 in class. CS 460, Sessions 8-9 1 Administrativia Assignment 1 due thursday 9/23/2004 BEFORE midnight Midterm eam 10/07/2003 in class CS 460, Sessins 8-9 1 Last time: search strategies Uninfrmed: Use nly infrmatin available in the prblem

More information

Math Foundations 20 Work Plan

Math Foundations 20 Work Plan Math Fundatins 20 Wrk Plan Units / Tpics 20.8 Demnstrate understanding f systems f linear inequalities in tw variables. Time Frame December 1-3 weeks 6-10 Majr Learning Indicatrs Identify situatins relevant

More information

ENSC Discrete Time Systems. Project Outline. Semester

ENSC Discrete Time Systems. Project Outline. Semester ENSC 49 - iscrete Time Systems Prject Outline Semester 006-1. Objectives The gal f the prject is t design a channel fading simulatr. Upn successful cmpletin f the prject, yu will reinfrce yur understanding

More information

Dead-beat controller design

Dead-beat controller design J. Hetthéssy, A. Barta, R. Bars: Dead beat cntrller design Nvember, 4 Dead-beat cntrller design In sampled data cntrl systems the cntrller is realised by an intelligent device, typically by a PLC (Prgrammable

More information

3.4 Shrinkage Methods Prostate Cancer Data Example (Continued) Ridge Regression

3.4 Shrinkage Methods Prostate Cancer Data Example (Continued) Ridge Regression 3.3.4 Prstate Cancer Data Example (Cntinued) 3.4 Shrinkage Methds 61 Table 3.3 shws the cefficients frm a number f different selectin and shrinkage methds. They are best-subset selectin using an all-subsets

More information

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents WRITING THE REPORT Organizing the reprt Mst reprts shuld be rganized in the fllwing manner. Smetime there is a valid reasn t include extra chapters in within the bdy f the reprt. 1. Title page 2. Executive

More information

Least Squares Optimal Filtering with Multirate Observations

Least Squares Optimal Filtering with Multirate Observations Prc. 36th Asilmar Cnf. n Signals, Systems, and Cmputers, Pacific Grve, CA, Nvember 2002 Least Squares Optimal Filtering with Multirate Observatins Charles W. herrien and Anthny H. Hawes Department f Electrical

More information

Distributions, spatial statistics and a Bayesian perspective

Distributions, spatial statistics and a Bayesian perspective Distributins, spatial statistics and a Bayesian perspective Dug Nychka Natinal Center fr Atmspheric Research Distributins and densities Cnditinal distributins and Bayes Thm Bivariate nrmal Spatial statistics

More information

Chapter 3: Cluster Analysis

Chapter 3: Cluster Analysis Chapter 3: Cluster Analysis } 3.1 Basic Cncepts f Clustering 3.1.1 Cluster Analysis 3.1. Clustering Categries } 3. Partitining Methds 3..1 The principle 3.. K-Means Methd 3..3 K-Medids Methd 3..4 CLARA

More information

Tree Structured Classifier

Tree Structured Classifier Tree Structured Classifier Reference: Classificatin and Regressin Trees by L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stne, Chapman & Hall, 98. A Medical Eample (CART): Predict high risk patients

More information

COMP 551 Applied Machine Learning Lecture 11: Support Vector Machines

COMP 551 Applied Machine Learning Lecture 11: Support Vector Machines COMP 551 Applied Machine Learning Lecture 11: Supprt Vectr Machines Instructr: (jpineau@cs.mcgill.ca) Class web page: www.cs.mcgill.ca/~jpineau/cmp551 Unless therwise nted, all material psted fr this curse

More information

Broadcast Program Generation for Unordered Queries with Data Replication

Broadcast Program Generation for Unordered Queries with Data Replication Bradcast Prgram Generatin fr Unrdered Queries with Data Replicatin Jiun-Lng Huang and Ming-Syan Chen Department f Electrical Engineering Natinal Taiwan University Taipei, Taiwan, ROC E-mail: jlhuang@arbr.ee.ntu.edu.tw,

More information

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007 CS 477/677 Analysis f Algrithms Fall 2007 Dr. Gerge Bebis Curse Prject Due Date: 11/29/2007 Part1: Cmparisn f Srting Algrithms (70% f the prject grade) The bjective f the first part f the assignment is

More information

BOUNDED UNCERTAINTY AND CLIMATE CHANGE ECONOMICS. Christopher Costello, Andrew Solow, Michael Neubert, and Stephen Polasky

BOUNDED UNCERTAINTY AND CLIMATE CHANGE ECONOMICS. Christopher Costello, Andrew Solow, Michael Neubert, and Stephen Polasky BOUNDED UNCERTAINTY AND CLIMATE CHANGE ECONOMICS Christpher Cstell, Andrew Slw, Michael Neubert, and Stephen Plasky Intrductin The central questin in the ecnmic analysis f climate change plicy cncerns

More information

Determining Optimum Path in Synthesis of Organic Compounds using Branch and Bound Algorithm

Determining Optimum Path in Synthesis of Organic Compounds using Branch and Bound Algorithm Determining Optimum Path in Synthesis f Organic Cmpunds using Branch and Bund Algrithm Diastuti Utami 13514071 Prgram Studi Teknik Infrmatika Seklah Teknik Elektr dan Infrmatika Institut Teknlgi Bandung,

More information

Name: Block: Date: Science 10: The Great Geyser Experiment A controlled experiment

Name: Block: Date: Science 10: The Great Geyser Experiment A controlled experiment Science 10: The Great Geyser Experiment A cntrlled experiment Yu will prduce a GEYSER by drpping Ments int a bttle f diet pp Sme questins t think abut are: What are yu ging t test? What are yu ging t measure?

More information

Department of Economics, University of California, Davis Ecn 200C Micro Theory Professor Giacomo Bonanno. Insurance Markets

Department of Economics, University of California, Davis Ecn 200C Micro Theory Professor Giacomo Bonanno. Insurance Markets Department f Ecnmics, University f alifrnia, Davis Ecn 200 Micr Thery Prfessr Giacm Bnann Insurance Markets nsider an individual wh has an initial wealth f. ith sme prbability p he faces a lss f x (0

More information

On Huntsberger Type Shrinkage Estimator for the Mean of Normal Distribution ABSTRACT INTRODUCTION

On Huntsberger Type Shrinkage Estimator for the Mean of Normal Distribution ABSTRACT INTRODUCTION Malaysian Jurnal f Mathematical Sciences 4(): 7-4 () On Huntsberger Type Shrinkage Estimatr fr the Mean f Nrmal Distributin Department f Mathematical and Physical Sciences, University f Nizwa, Sultanate

More information

READING STATECHART DIAGRAMS

READING STATECHART DIAGRAMS READING STATECHART DIAGRAMS Figure 4.48 A Statechart diagram with events The diagram in Figure 4.48 shws all states that the bject plane can be in during the curse f its life. Furthermre, it shws the pssible

More information

1996 Engineering Systems Design and Analysis Conference, Montpellier, France, July 1-4, 1996, Vol. 7, pp

1996 Engineering Systems Design and Analysis Conference, Montpellier, France, July 1-4, 1996, Vol. 7, pp THE POWER AND LIMIT OF NEURAL NETWORKS T. Y. Lin Department f Mathematics and Cmputer Science San Jse State University San Jse, Califrnia 959-003 tylin@cs.ssu.edu and Bereley Initiative in Sft Cmputing*

More information

You need to be able to define the following terms and answer basic questions about them:

You need to be able to define the following terms and answer basic questions about them: CS440/ECE448 Sectin Q Fall 2017 Midterm Review Yu need t be able t define the fllwing terms and answer basic questins abut them: Intr t AI, agents and envirnments Pssible definitins f AI, prs and cns f

More information

BASD HIGH SCHOOL FORMAL LAB REPORT

BASD HIGH SCHOOL FORMAL LAB REPORT BASD HIGH SCHOOL FORMAL LAB REPORT *WARNING: After an explanatin f what t include in each sectin, there is an example f hw the sectin might lk using a sample experiment Keep in mind, the sample lab used

More information

MATCHING TECHNIQUES. Technical Track Session VI. Emanuela Galasso. The World Bank

MATCHING TECHNIQUES. Technical Track Session VI. Emanuela Galasso. The World Bank MATCHING TECHNIQUES Technical Track Sessin VI Emanuela Galass The Wrld Bank These slides were develped by Christel Vermeersch and mdified by Emanuela Galass fr the purpse f this wrkshp When can we use

More information

Section 6-2: Simplex Method: Maximization with Problem Constraints of the Form ~

Section 6-2: Simplex Method: Maximization with Problem Constraints of the Form ~ Sectin 6-2: Simplex Methd: Maximizatin with Prblem Cnstraints f the Frm ~ Nte: This methd was develped by Gerge B. Dantzig in 1947 while n assignment t the U.S. Department f the Air Frce. Definitin: Standard

More information

Resampling Methods. Chapter 5. Chapter 5 1 / 52

Resampling Methods. Chapter 5. Chapter 5 1 / 52 Resampling Methds Chapter 5 Chapter 5 1 / 52 1 51 Validatin set apprach 2 52 Crss validatin 3 53 Btstrap Chapter 5 2 / 52 Abut Resampling An imprtant statistical tl Pretending the data as ppulatin and

More information

k-nearest Neighbor How to choose k Average of k points more reliable when: Large k: noise in attributes +o o noise in class labels

k-nearest Neighbor How to choose k Average of k points more reliable when: Large k: noise in attributes +o o noise in class labels Mtivating Example Memry-Based Learning Instance-Based Learning K-earest eighbr Inductive Assumptin Similar inputs map t similar utputs If nt true => learning is impssible If true => learning reduces t

More information

Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018

Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018 Michael Faraday lived in the Lndn area frm 1791 t 1867. He was 29 years ld when Hand Oersted, in 1820, accidentally discvered that electric current creates magnetic field. Thrugh empirical bservatin and

More information

, which yields. where z1. and z2

, which yields. where z1. and z2 The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin

More information

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y=

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y= Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents

More information

ChE 471: LECTURE 4 Fall 2003

ChE 471: LECTURE 4 Fall 2003 ChE 47: LECTURE 4 Fall 003 IDEL RECTORS One f the key gals f chemical reactin engineering is t quantify the relatinship between prductin rate, reactr size, reactin kinetics and selected perating cnditins.

More information

Computational modeling techniques

Computational modeling techniques Cmputatinal mdeling techniques Lecture 2: Mdeling change. In Petre Department f IT, Åb Akademi http://users.ab.fi/ipetre/cmpmd/ Cntent f the lecture Basic paradigm f mdeling change Examples Linear dynamical

More information

B. Definition of an exponential

B. Definition of an exponential Expnents and Lgarithms Chapter IV - Expnents and Lgarithms A. Intrductin Starting with additin and defining the ntatins fr subtractin, multiplicatin and divisin, we discvered negative numbers and fractins.

More information

Multiple Source Multiple. using Network Coding

Multiple Source Multiple. using Network Coding Multiple Surce Multiple Destinatin Tplgy Inference using Netwrk Cding Pegah Sattari EECS, UC Irvine Jint wrk with Athina Markpulu, at UCI, Christina Fraguli, at EPFL, Lausanne Outline Netwrk Tmgraphy Gal,

More information

In the OLG model, agents live for two periods. they work and divide their labour income between consumption and

In the OLG model, agents live for two periods. they work and divide their labour income between consumption and 1 The Overlapping Generatins Mdel (OLG) In the OLG mdel, agents live fr tw perids. When ung the wrk and divide their labur incme between cnsumptin and savings. When ld the cnsume their savings. As the

More information

Technical Bulletin. Generation Interconnection Procedures. Revisions to Cluster 4, Phase 1 Study Methodology

Technical Bulletin. Generation Interconnection Procedures. Revisions to Cluster 4, Phase 1 Study Methodology Technical Bulletin Generatin Intercnnectin Prcedures Revisins t Cluster 4, Phase 1 Study Methdlgy Release Date: Octber 20, 2011 (Finalizatin f the Draft Technical Bulletin released n September 19, 2011)

More information

Optimization Programming Problems For Control And Management Of Bacterial Disease With Two Stage Growth/Spread Among Plants

Optimization Programming Problems For Control And Management Of Bacterial Disease With Two Stage Growth/Spread Among Plants Internatinal Jurnal f Engineering Science Inventin ISSN (Online): 9 67, ISSN (Print): 9 676 www.ijesi.rg Vlume 5 Issue 8 ugust 06 PP.0-07 Optimizatin Prgramming Prblems Fr Cntrl nd Management Of Bacterial

More information

Physics 2010 Motion with Constant Acceleration Experiment 1

Physics 2010 Motion with Constant Acceleration Experiment 1 . Physics 00 Mtin with Cnstant Acceleratin Experiment In this lab, we will study the mtin f a glider as it accelerates dwnhill n a tilted air track. The glider is supprted ver the air track by a cushin

More information

AN INTERMITTENTLY USED SYSTEM WITH PREVENTIVE MAINTENANCE

AN INTERMITTENTLY USED SYSTEM WITH PREVENTIVE MAINTENANCE J. Operatins Research Sc. f Japan V!. 15, N. 2, June 1972. 1972 The Operatins Research Sciety f Japan AN INTERMITTENTLY USED SYSTEM WITH PREVENTIVE MAINTENANCE SHUNJI OSAKI University f Suthern Califrnia

More information

MATCHING TECHNIQUES Technical Track Session VI Céline Ferré The World Bank

MATCHING TECHNIQUES Technical Track Session VI Céline Ferré The World Bank MATCHING TECHNIQUES Technical Track Sessin VI Céline Ferré The Wrld Bank When can we use matching? What if the assignment t the treatment is nt dne randmly r based n an eligibility index, but n the basis

More information

COMP 551 Applied Machine Learning Lecture 5: Generative models for linear classification

COMP 551 Applied Machine Learning Lecture 5: Generative models for linear classification COMP 551 Applied Machine Learning Lecture 5: Generative mdels fr linear classificatin Instructr: Herke van Hf (herke.vanhf@mail.mcgill.ca) Slides mstly by: Jelle Pineau Class web page: www.cs.mcgill.ca/~hvanh2/cmp551

More information

Compressibility Effects

Compressibility Effects Definitin f Cmpressibility All real substances are cmpressible t sme greater r lesser extent; that is, when yu squeeze r press n them, their density will change The amunt by which a substance can be cmpressed

More information

Lecture 17: Free Energy of Multi-phase Solutions at Equilibrium

Lecture 17: Free Energy of Multi-phase Solutions at Equilibrium Lecture 17: 11.07.05 Free Energy f Multi-phase Slutins at Equilibrium Tday: LAST TIME...2 FREE ENERGY DIAGRAMS OF MULTI-PHASE SOLUTIONS 1...3 The cmmn tangent cnstructin and the lever rule...3 Practical

More information

x 1 Outline IAML: Logistic Regression Decision Boundaries Example Data

x 1 Outline IAML: Logistic Regression Decision Boundaries Example Data Outline IAML: Lgistic Regressin Charles Suttn and Victr Lavrenk Schl f Infrmatics Semester Lgistic functin Lgistic regressin Learning lgistic regressin Optimizatin The pwer f nn-linear basis functins Least-squares

More information

Computational modeling techniques

Computational modeling techniques Cmputatinal mdeling techniques Lecture 11: Mdeling with systems f ODEs In Petre Department f IT, Ab Akademi http://www.users.ab.fi/ipetre/cmpmd/ Mdeling with differential equatins Mdeling strategy Fcus

More information

initially lcated away frm the data set never win the cmpetitin, resulting in a nnptimal nal cdebk, [2] [3] [4] and [5]. Khnen's Self Organizing Featur

initially lcated away frm the data set never win the cmpetitin, resulting in a nnptimal nal cdebk, [2] [3] [4] and [5]. Khnen's Self Organizing Featur Cdewrd Distributin fr Frequency Sensitive Cmpetitive Learning with One Dimensinal Input Data Aristides S. Galanpuls and Stanley C. Ahalt Department f Electrical Engineering The Ohi State University Abstract

More information

Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeoff

Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeoff Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeff Reading: Chapter 2 STATS 202: Data mining and analysis September 27, 2017 1 / 20 Supervised vs. unsupervised learning In unsupervised

More information

Assessment Primer: Writing Instructional Objectives

Assessment Primer: Writing Instructional Objectives Assessment Primer: Writing Instructinal Objectives (Based n Preparing Instructinal Objectives by Mager 1962 and Preparing Instructinal Objectives: A critical tl in the develpment f effective instructin

More information

Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeoff

Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeoff Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeff Reading: Chapter 2 STATS 202: Data mining and analysis September 27, 2017 1 / 20 Supervised vs. unsupervised learning In unsupervised

More information

Chapter Summary. Mathematical Induction Strong Induction Recursive Definitions Structural Induction Recursive Algorithms

Chapter Summary. Mathematical Induction Strong Induction Recursive Definitions Structural Induction Recursive Algorithms Chapter 5 1 Chapter Summary Mathematical Inductin Strng Inductin Recursive Definitins Structural Inductin Recursive Algrithms Sectin 5.1 3 Sectin Summary Mathematical Inductin Examples f Prf by Mathematical

More information

THE LIFE OF AN OBJECT IT SYSTEMS

THE LIFE OF AN OBJECT IT SYSTEMS THE LIFE OF AN OBJECT IT SYSTEMS Persns, bjects, r cncepts frm the real wrld, which we mdel as bjects in the IT system, have "lives". Actually, they have tw lives; the riginal in the real wrld has a life,

More information

Public Key Cryptography. Tim van der Horst & Kent Seamons

Public Key Cryptography. Tim van der Horst & Kent Seamons Public Key Cryptgraphy Tim van der Hrst & Kent Seamns Last Updated: Oct 5, 2017 Asymmetric Encryptin Why Public Key Crypt is Cl Has a linear slutin t the key distributin prblem Symmetric crypt has an expnential

More information

How do scientists measure trees? What is DBH?

How do scientists measure trees? What is DBH? Hw d scientists measure trees? What is DBH? Purpse Students develp an understanding f tree size and hw scientists measure trees. Students bserve and measure tree ckies and explre the relatinship between

More information

Methods for Determination of Mean Speckle Size in Simulated Speckle Pattern

Methods for Determination of Mean Speckle Size in Simulated Speckle Pattern 0.478/msr-04-004 MEASUREMENT SCENCE REVEW, Vlume 4, N. 3, 04 Methds fr Determinatin f Mean Speckle Size in Simulated Speckle Pattern. Hamarvá, P. Šmíd, P. Hrváth, M. Hrabvský nstitute f Physics f the Academy

More information

Particle Size Distributions from SANS Data Using the Maximum Entropy Method. By J. A. POTTON, G. J. DANIELL AND B. D. RAINFORD

Particle Size Distributions from SANS Data Using the Maximum Entropy Method. By J. A. POTTON, G. J. DANIELL AND B. D. RAINFORD 3 J. Appl. Cryst. (1988). 21,3-8 Particle Size Distributins frm SANS Data Using the Maximum Entrpy Methd By J. A. PTTN, G. J. DANIELL AND B. D. RAINFRD Physics Department, The University, Suthamptn S9

More information

IAML: Support Vector Machines

IAML: Support Vector Machines 1 / 22 IAML: Supprt Vectr Machines Charles Suttn and Victr Lavrenk Schl f Infrmatics Semester 1 2 / 22 Outline Separating hyperplane with maimum margin Nn-separable training data Epanding the input int

More information

Kinetic Model Completeness

Kinetic Model Completeness 5.68J/10.652J Spring 2003 Lecture Ntes Tuesday April 15, 2003 Kinetic Mdel Cmpleteness We say a chemical kinetic mdel is cmplete fr a particular reactin cnditin when it cntains all the species and reactins

More information

Determining the Accuracy of Modal Parameter Estimation Methods

Determining the Accuracy of Modal Parameter Estimation Methods Determining the Accuracy f Mdal Parameter Estimatin Methds by Michael Lee Ph.D., P.E. & Mar Richardsn Ph.D. Structural Measurement Systems Milpitas, CA Abstract The mst cmmn type f mdal testing system

More information

Eric Klein and Ning Sa

Eric Klein and Ning Sa Week 12. Statistical Appraches t Netwrks: p1 and p* Wasserman and Faust Chapter 15: Statistical Analysis f Single Relatinal Netwrks There are fur tasks in psitinal analysis: 1) Define Equivalence 2) Measure

More information

Inflow Control on Expressway Considering Traffic Equilibria

Inflow Control on Expressway Considering Traffic Equilibria Memirs f the Schl f Engineering, Okayama University Vl. 20, N.2, February 1986 Inflw Cntrl n Expressway Cnsidering Traffic Equilibria Hirshi INOUYE* (Received February 14, 1986) SYNOPSIS When expressway

More information

Emphases in Common Core Standards for Mathematical Content Kindergarten High School

Emphases in Common Core Standards for Mathematical Content Kindergarten High School Emphases in Cmmn Cre Standards fr Mathematical Cntent Kindergarten High Schl Cntent Emphases by Cluster March 12, 2012 Describes cntent emphases in the standards at the cluster level fr each grade. These

More information

Lab #3: Pendulum Period and Proportionalities

Lab #3: Pendulum Period and Proportionalities Physics 144 Chwdary Hw Things Wrk Spring 2006 Name: Partners Name(s): Intrductin Lab #3: Pendulum Perid and Prprtinalities Smetimes, it is useful t knw the dependence f ne quantity n anther, like hw the

More information

Lecture 13: Markov Chain Monte Carlo. Gibbs sampling

Lecture 13: Markov Chain Monte Carlo. Gibbs sampling Lecture 13: Markv hain Mnte arl Gibbs sampling Gibbs sampling Markv chains 1 Recall: Apprximate inference using samples Main idea: we generate samples frm ur Bayes net, then cmpute prbabilities using (weighted)

More information

2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS

2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 6. An electrchemical cell is cnstructed with an pen switch, as shwn in the diagram abve. A strip f Sn and a strip f an unknwn metal, X, are used as electrdes.

More information

A New Approach to Increase Parallelism for Dependent Loops

A New Approach to Increase Parallelism for Dependent Loops A New Apprach t Increase Parallelism fr Dependent Lps Yeng-Sheng Chen, Department f Electrical Engineering, Natinal Taiwan University, Taipei 06, Taiwan, Tsang-Ming Jiang, Arctic Regin Supercmputing Center,

More information

4th Indian Institute of Astrophysics - PennState Astrostatistics School July, 2013 Vainu Bappu Observatory, Kavalur. Correlation and Regression

4th Indian Institute of Astrophysics - PennState Astrostatistics School July, 2013 Vainu Bappu Observatory, Kavalur. Correlation and Regression 4th Indian Institute f Astrphysics - PennState Astrstatistics Schl July, 2013 Vainu Bappu Observatry, Kavalur Crrelatin and Regressin Rahul Ry Indian Statistical Institute, Delhi. Crrelatin Cnsider a tw

More information

Elements of Machine Intelligence - I

Elements of Machine Intelligence - I ECE-175A Elements f Machine Intelligence - I Ken Kreutz-Delgad Nun Vascncels ECE Department, UCSD Winter 2011 The curse The curse will cver basic, but imprtant, aspects f machine learning and pattern recgnitin

More information

OF SIMPLY SUPPORTED PLYWOOD PLATES UNDER COMBINED EDGEWISE BENDING AND COMPRESSION

OF SIMPLY SUPPORTED PLYWOOD PLATES UNDER COMBINED EDGEWISE BENDING AND COMPRESSION U. S. FOREST SERVICE RESEARCH PAPER FPL 50 DECEMBER U. S. DEPARTMENT OF AGRICULTURE FOREST SERVICE FOREST PRODUCTS LABORATORY OF SIMPLY SUPPORTED PLYWOOD PLATES UNDER COMBINED EDGEWISE BENDING AND COMPRESSION

More information

CHAPTER 4 DIAGNOSTICS FOR INFLUENTIAL OBSERVATIONS

CHAPTER 4 DIAGNOSTICS FOR INFLUENTIAL OBSERVATIONS CHAPTER 4 DIAGNOSTICS FOR INFLUENTIAL OBSERVATIONS 1 Influential bservatins are bservatins whse presence in the data can have a distrting effect n the parameter estimates and pssibly the entire analysis,

More information

February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA

February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA Mental Experiment regarding 1D randm walk Cnsider a cntainer f gas in thermal

More information

We can see from the graph above that the intersection is, i.e., [ ).

We can see from the graph above that the intersection is, i.e., [ ). MTH 111 Cllege Algebra Lecture Ntes July 2, 2014 Functin Arithmetic: With nt t much difficulty, we ntice that inputs f functins are numbers, and utputs f functins are numbers. S whatever we can d with

More information

Biplots in Practice MICHAEL GREENACRE. Professor of Statistics at the Pompeu Fabra University. Chapter 13 Offprint

Biplots in Practice MICHAEL GREENACRE. Professor of Statistics at the Pompeu Fabra University. Chapter 13 Offprint Biplts in Practice MICHAEL GREENACRE Prfessr f Statistics at the Pmpeu Fabra University Chapter 13 Offprint CASE STUDY BIOMEDICINE Cmparing Cancer Types Accrding t Gene Epressin Arrays First published:

More information

Sections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.

Sections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic. Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage

More information

This section is primarily focused on tools to aid us in finding roots/zeros/ -intercepts of polynomials. Essentially, our focus turns to solving.

This section is primarily focused on tools to aid us in finding roots/zeros/ -intercepts of polynomials. Essentially, our focus turns to solving. Sectin 3.2: Many f yu WILL need t watch the crrespnding vides fr this sectin n MyOpenMath! This sectin is primarily fcused n tls t aid us in finding rts/zers/ -intercepts f plynmials. Essentially, ur fcus

More information

5 th grade Common Core Standards

5 th grade Common Core Standards 5 th grade Cmmn Cre Standards In Grade 5, instructinal time shuld fcus n three critical areas: (1) develping fluency with additin and subtractin f fractins, and develping understanding f the multiplicatin

More information

Internal vs. external validity. External validity. This section is based on Stock and Watson s Chapter 9.

Internal vs. external validity. External validity. This section is based on Stock and Watson s Chapter 9. Sectin 7 Mdel Assessment This sectin is based n Stck and Watsn s Chapter 9. Internal vs. external validity Internal validity refers t whether the analysis is valid fr the ppulatin and sample being studied.

More information

MODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards:

MODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards: MODULE FOUR This mdule addresses functins SC Academic Standards: EA-3.1 Classify a relatinship as being either a functin r nt a functin when given data as a table, set f rdered pairs, r graph. EA-3.2 Use

More information

Comprehensive Exam Guidelines Department of Chemical and Biomolecular Engineering, Ohio University

Comprehensive Exam Guidelines Department of Chemical and Biomolecular Engineering, Ohio University Cmprehensive Exam Guidelines Department f Chemical and Bimlecular Engineering, Ohi University Purpse In the Cmprehensive Exam, the student prepares an ral and a written research prpsal. The Cmprehensive

More information

o o IMPORTANT REMINDERS Reports will be graded largely on their ability to clearly communicate results and important conclusions.

o o IMPORTANT REMINDERS Reports will be graded largely on their ability to clearly communicate results and important conclusions. BASD High Schl Frmal Lab Reprt GENERAL INFORMATION 12 pt Times New Rman fnt Duble-spaced, if required by yur teacher 1 inch margins n all sides (tp, bttm, left, and right) Always write in third persn (avid

More information