Notes on Calculating Computer Performance
|
|
- Gerald Kelley
- 7 years ago
- Views:
Transcription
1 otes on Calculatng Computer Performance Bruce Jacob and Trevor Mudge Advanced Computer Archtecture Lab EECS Department, Unversty of Mchgan Abstract Ths report explans what t means to characterze the performance of a computer, and whch methods are approprate and napproprate for the task. The most wdely used metrc s the performance on the SPEC benchmark sute of programs; currently, the results of runnng the SPEC benchmark sute are compled nto a sngle number usng the geometrc mean. The prmary reason for usng the geometrc mean s that t preserves values across normalzaton, but unfortunately, t does not preserve total run tme, whch s probably the fgure of greatest nterest when performances are beng compared. Cycles per Instructon (CPI) s another wdely used metrc, but ths method s nvald, even f comparng machnes wth dentcal clock speeds. Comparng CPI values to judge performance falls prey to the same problems as averagng normalzed values. In general, normalzed values must not be averaged and nstead of the geometrc mean, ether the harmonc or the arthmetc mean s the approprate method for averagng a set runnng tmes. The arthmetc mean should be used to average tmes, and the harmonc mean should be used to average rates (1/tme). A number of publshed SPECmarks are recomputed usng these means to demonstrate the effect of choosng a favorable algorthm. 1.0 Performance and the Use of Means We want to summarze the performance of a computer; the easest way uses a sngle number that can be compared aganst the numbers of other machnes. Ths typcally nvolves runnng tests on the machne and takng some sort of mean; the mean of a set of numbers s the central value when the set represents fluctuatons about that value. There are a number of dfferent ways to defne a mean value; among them the arthmetc mean, the geometrc mean, and the harmonc mean. The arthmetc mean s defned as follows: The geometrc mean s defned as follows: ArthmetcMean ( a 1, a 2, a 3,, a ) = a The harmonc mean s defned as follows GeometrcMean ( a 1, a 2, a 3,, a ) = a HarmoncMean ( a 1, a 2, a 3,, a ) = 1 a
2 In the mathematcal sense, the geometrc mean of a set of n values s the length of one sde of an n-dmensonal cube havng the same volume as an n-dmensonal rectangle whose sdes are gven by the n values. As ths s nether ntutve nor nformatve, the wsdom of usng the geometrc mean for anythng s questonable 1. Its only apparent advantage s that t s unaffected by normalzaton: whether you normalze by a set of weghts frst or by the geometrc mean of the weghts afterward, the result s the same. Ths property has been used to suggest that the geometrc mean s superor, snce t produces the same results when comparng several computers rrespectve of whch computer s tmes are used as the normalzaton factor [Flemng86]. However, the argument was rebutted n [Smth88], where the meannglessness of the geometrc mean was frst llustrated. In ths report, we wll consder only the arthmetc and harmonc means. Snce the two are nverses of each other, and snce the arthmetc mean the average s more easly vsualzed than the harmonc mean, we wll stck to the average from now on, relatng t back to the harmonc mean when approprate. UITS AD MEAS: An Example ArthmetcMean ( a 1, a 2, a 3, ) We begn wth a smple llustratve example of what can go wrong when we try to summarze performance. Rather than demonstrate ncorrectness, the ntent s to confuse the ssue by hntng at the subtle nteractons of unts and means. A machne s tmed runnng two benchmark tests and receves the followng scores: test1: 3 sec (most machnes run t n 12 seconds) test2: 300 sec (most machnes run t n 600 seconds) How fast s the machne? Let us look at dfferent ways of calculatng performance: Method 1 one way of lookng at ths s by the ratos of the runnng tmes: test1: The machne s performance on test 1 s four tmes faster than an average machne, ts performance on test 2 s twce as fast as average, therefore our machne s (on average) three tmes as fast as most machnes. Method 2 another way of lookng at ths s by the ratos of the runnng tmes: test1: The machne s runnng tme on test 1 s 1/4 the tme t takes most machnes, ts runnng tme on test 2 s 1/2 the tme t takes most machnes, so our machne (on average) takes 3/8 the tme a typcal machne does to run a program, or, put another way, our machne s 8/3 (2.67) tmes as fast as the average machne. Method 3 yet another way of lookng at ths s by the ratos of the runnng tmes: test1: = HarmoncMean (,,, ) a 1 a 2 a 3 The machne ran the benchmarks n a total of 303 seconds, the average machne runs the benchmarks n 612 seconds, therefore our machne takes the amount of tme to run the benchmarks as most machnes do, and so s roughly twce as fast as the typcal machne (on average). test2: test2: test2: Compare ths to just one physcal nterpretaton of the arthmetc mean; fndng the center of gravty n a set of objects (possbly havng dfferent weghts) placed along a see-saw. There are countless other nterpretatons whch are just as ntutve and meanngful. 2
3 Method 4 and then you can always look at the ratos of the runnng tmes... How can these calculatons seem reasonable and yet produce completely dfferent results? The answer s that they seem reasonable because they are reasonable; they all gve perfectly accurate answers, just not to the same queston. Lke n many other areas, the answers are not hard to come by the dffcult part s n askng the rght questons. 2.0 The Semantcs of Means In general, there are a number of possbltes for fndng the performance, gven a set of expermental tmes and a set of reference tmes. One can take the average of the raw tmes, the raw rates (nverse of tme) 1, the ratos of the tmes (expermental tme over reference), or the ratos of the rates (reference tme over expermental). Each opton represents a dfferent queston and as such gves a dfferent answer; each has a dfferent meanng as well as a dfferent set of mplcatons. An average need not be meanngless, but t may be f the mplcatons are not true. If one understands the mplcatons of averagng rates, tmes, and ther ratos, then one s less apt to wnd up wth meanngless nformaton. THE SEMATICS OF TIME, RATE, AD RATIO Remember the correspondence between the arthmetc and harmonc means: ArthmetcMean ( tmes) HarmoncMean ( rates) ArthmetcMean ( rates) HarmoncMean ( tmes) The Semantcs of Tme A set of tmes s a collecton of numbers representng Tme Taken per Unt Somethngs Accomplshed. The nformaton contaned n ther arthmetc mean s therefore On Average, How Much Tme s Taken per Unt Somethngs Accomplshed; the average amount of tme t takes to accomplsh a prototypcal task. On Average n ths case s defned across Somethngs and not Tme. For example, a book s read n two hours, another n four; the average s 3 hours per book. If books smlar to these are read contnuously one after another and the reader s progress s sampled n tme (say once every mnute) then the value of 4 hrs/book wll come up twce as often as the value of 2 hrs/book, gvng an ncorrect average of 10/3 hours per book. However, f the readng tme s sampled per book (say once every book), the average wll come out correctly. Tme s what we are concerned wth n omparng the performance of computers. Though t s just as mportant a measure of performance, we are not concerned wth throughput snce jugglng both would confuse the pont. In ths paper we want to know how long t takes to perform a task, rather than how many tasks the machne can perform per unt tme. If the set of tmes s taken from representatve programs, then the average wll be an accurate predctor of how long a typcal program would take, and thus ndcate the machne s performance. The Semantcs of Rate A set of rates s n unts of Somethngs Accomplshed per Unt Tme, and the nformaton contaned n ther arthmetc mean s then On Average, How Many Somethngs You Can Expect to Accomplsh per Unt Tme. Here, the average s 1. We wll use the word rate to descrbe a unt where tme s n the denomnator despte what may be n the numerator (unless t s also tme, n whch case the unt s a pure number). Tme and rate are related n that the arthmetc mean of one s the nverse of the harmonc mean of the other. 3
4 defned across Tme and not Somethngs; f you ntend to take the arthmetc mean of a set of rates, the rates should represent nstantaneous measures taken n Tme and should OT represent measurements taken for every Somethng Accomplshed. Take the above book example; f we try to average 1/2 book per hour and 1/4 book per hour (the values obtaned f we sample over books), we obtan a measurement of 3/8 books per hour; what good s ths nformaton? It cannot be combned wth the number of books we read to produce how long t should have taken (t took 6 hours, not 16/3 hours). Ths confuson arses because of an ncorrect use of the arthmetc mean. If, however, we sample the readng rate at perodc ponts n tme, we fnd that there wll be twce as many values of 1/4 book per hour as 1/2 book per hour, whch wll gve us (1/4 + 1/4 + 1/2, dvded by 3); an average rate of 1/3 book per hour, correspondng ncely wth realty. When measurng computers, we are generally presented wth a set of values taken per task completed a set of benchmark results, each the tme taken to perform one of several tests not a set of nstantaneous measurements of progress, sampled every unt of tme. Therefore, n general, fndng the arthmetc mean of a set of rates s not a good dea, as t wll lead to erroneous and msleadng results. Use the harmonc mean nstead. The Semantcs of Ratos Computer performance s often represented by a rato of rates or tmes. It s a untless number, and when the reference tme s n the numerator (as n a rato of rates) the measurement means how much faster one thng s than another. When the reference tme s n the denomnator (as n a rato of tmes) the measurement means what fracton of tme the machne n queston takes to perform a task, relatve to the reference machne. What does t mean to average a set of untless ratos? The arthmetc mean of a set of ratos s a weghted average where the weghts happen to be the runnng tmes of the reference machne. What nformaton s contaned n ths value? If the reference tmes are thought of as the expected amount of tme for each benchmark, the weghtng mght ensure that no benchmark result counts more than any other, and the arthmetc mean would then represent what proporton of the expected tme the average benchmark takes. 3.0 Problems wth ormalzaton Problems arse f we take the average of a set of normalzed numbers. The followng examples demonstrate the errors that occur. The frst example compares the performance of two machnes, usng a thrd as a benchmark. The second example extends the frst to show the error n usng CPI values to compare performance. EXAMPLE I: Average ormalzed by Reference Tmes There are two machnes, A and B, and a reference machne. There are two tests, T1 and T2, and we obtan the followng scores for the machnes: Scenaro I Test T1 Test T2 Machne A: 10 sec 100 sec Machne B: 1 sec 1000 sec Reference: 1 sec 100 sec In scenaro I, the performance of machne A relatve to the reference machne s 0.1 on test T1 and 1 on test T2. The performance of machne B relatve to the reference machne s 1 on test T1 and 0.1 on test T2. Snce tme s n the denomnator (the reference s n the numerator), we are averagng rates, therefore we use the harmonc mean. The fact that the reference value s also n unts of tme s rrelevant; the tme measurement we are concerned wth s n the denomnator, thus we are averagng rates. 4
5 The performance results of Scenaro I: Scenaro I Harmonc Mean Machne A: HMean(0.1, 1) = 2/11 Machne B: HMean(1, 0.1) = 2/11 The two machnes perform equally well. Ths makes ntutve sense; on one test machne A was ten tmes faster, on the other test machne B was ten tmes faster. Therefore they should be of equal performance. As t turns out, ths lne of reasonng s erroneous. Let us consder scenaro II, where the only thng that has changed s the reference machne s tmes (from 100 seconds on test T2 to 10 seconds): Here, the performance numbers for A relatve to the reference machne are 1/10 and 1/10, the performance numbers for B are 1 and 1/100, and these are the results: Accordng to ths, machne A performs about 5 tmes better than machne B. And f we try yet another scenaro changng only the reference machne s performance on test T2, we obtan the result that machne A performs worse than machne B. The lesson: do not average test results whch have been normalzed. EXAMPLE II: Average ormalzed by umber of Operatons Scenaro II Test T1 Test T2 Machne A: 10 sec 100 sec Machne B: 1 sec 1000 sec Reference: 1 sec 10 sec Scenaro II Harmonc Mean Machne A: HMean(0.1, 0.1) = 1/10 Machne B: HMean(1, 0.01) = 2/101 Scenaro III Test T1 Test T2 Harmonc Mean Machne A: 10 sec 100 sec HMean(0.1, 10) = 20/101 Machne B: 1 sec 1000 sec HMean(1, 1) = 1 Reference: 1 sec 1000 sec The example extends even further; what f the numbers were not a set of normalzed runnng tmes but CPI measurements? Takng the average of a set of CPI values should not be susceptble to ths knd of error, because the numbers are not untless; they are not the rato of the runnng tmes of two arbtrary machnes. Let us test ths theory. Let us take the average of a set of CPI values, n three scenaros. The unts are cycles per nstructon, and snce the tme-related porton (cycles) s n the numerator, we wll be able to use the arthmetc mean. The followng are the three scenaros, where the only dfference between each scenaro s the number of nstructons performed n Test2. The runnng tmes for each machne on each test do not change, therefore we should expect the performance of each machne relatve to the other to reman the same. Scenaro I Test1 Test2 Arthmetc Mean Machne A: 10 cycles 100 cycles AMean(10, 10) = 10 CPI Machne B: 1 cycle 1000 cycles AMean(1, 100) = 50.5 CPI Instructons: 1 nstr 10 nstr Result: Machne A faster Scenaro II Test1 Test2 Arthmetc Mean Machne A: 10 cycles 100 cycles AMean(10, 1) = 5.5 CPI 5
6 However, we obtan the anomalous result that the machnes have dfferent relatve performances whch depend upon the number of nstructons that were executed. The theory s flawed. Average CPI values are not vald measures of computer performance. Takng the average of a set of CPI values s not nherently wrong, but the result cannot be used to compare performance. The erroneous behavor s due to normalzng the values before averagng them. If we average the runnng tmes before normalzaton, we get a value of 55 cycles for Machne A, and a value of cycles for Machne B. Ths alone s the vald comparson. Agan, ths example s not meant to mply that average CPI values are meanngless, they are smply meanngless when used to compare the performance of machnes. O SPECMARKS Machne B: 1 cycle 1000 cycles AMean(1, 10) = 5.5 CPI Instructons: 1 nstr 100 nstr Result: Equal performance Scenaro III Test1 Test2 Arthmetc Mean Machne A: 10 cycles 100 cycles AMean(10, 0.1) = 5.05 CPI Machne B: 1 cycle 1000 cycles AMean(1, 1) = 1 CPI Instructons: 1 nstr 1000 nstr Result: Machne B faster We have demonstrated that the followng s an erroneous method to fnd a performance number for a machne, based upon a set of test results. The mplcaton s that ratos such as SPECmarks should never be averaged; they should frst be converted back nto the orgnal tme values or rate values, and then averaged. The followng demonstrates the relaton between ths and SPEC. AVG has been calculated usng erroneous methods, and so t s a meanngless number. However, ths meanngless number can be easly transformed nto the harmonc mean of SPECmarks, as the followng demonstrates: 1 AVG To repeat, performance ratos should not be averaged. ormalzed values should not be averaged. Indvdual SPECmarks, whch are the rato of the reference machne s runnng tme to the test machne s runnng tme, are normalzed values. Ther average s therefore meanngless. The only meanngful performance number s the rato of the arthmetc means of the reference and test machnes runnng tmes. 4.0 The Meanng of Performance AVG = OurTme RefTme = = = OurTme 1 RefTme SPECmark We have determned that the arthmetc mean s approprate for averagng tmes (whch mples that the harmonc mean s approprate for averagng rates), and that ormalzaton, f performed, should be carred out after the averagng. The queston arses: what does ths mean? When we say that the followng descrbes the performance of a machne based upon the runnng of a number of standardzed tests (whch s the rato of the arthmetc means, wth the constant terms cancellng out), HarmoncMean ( SPECmarks) 6
7 then we mplctly beleve that every test counts equally, n that on average t s used the same number of tmes as all other tests. Ths means that tests whch are much longer than others wll count more n the results. POIT OF VIEW: Performance s Tme Saved OurTme RefTme j We wsh to be able to say, ths machne s X tmes faster than that machne. Ambguty arses because we are often unclear on the concept of performance. What do we mean when we talk about the performance of a machne? Why do we wsh to be able to say ths machne s X tmes faster than that machne? The reason s that we have been usng that machne (machne A) for some tme and wsh to know how much tme we would save by usng ths machne (machne B) nstead. How can we measure ths? Frst, we fnd out what programs we tend to run on machne A. These programs (or ones smlar to them) wll be used as the benchmark sute to run on machne B. ext, we measure how often we tend to use the programs. These values wll be used as weghts n computng the average (programs used more should count more), but the problem s that t s not clear whether we should use values n unts of tme or number of occurrences; do we count each program the number of tmes per day t s used or the number of hours per day t s used? We have an dea about how often we use programs; for nstance, every tme we edt a source fle we mght recomple. So we would assgn equal weghts to the word processng benchmark and the compler benchmark. We mght run a dfferent set of 3 or 4 n-body smulatons every tme we recompled the smulator; we would then weght the smulator benchmark 3 or 4 tmes as heavly as the compler and text edtor. Of course, t s not qute as smple as ths, but you get the pont; we tend to know how often we use a program, ndependent of how slowly or quckly the machne we use performs t. What does ths buy us? Say for the moment that we consder all benchmarks n the sute equally mportant (we use each as often as the other); all we need to do s total up the tmes t took the new machne to perform the tests, total up the tmes t took the reference machne to perform the tests, and compare the two results. It does not matter f one test takes three mnutes and another takes three days f the reference machne performs the short test n less than a second (ndcatng that your new machne s extremely slow) and t performs the long test n three days and sx hours (ndcatng that your new machne s margnally faster than the old one), the tme saved s about sx hours. Even f you use the short program a hundred tmes as often as the long program, the tme saved s stll an hour over the old machne. The error s that we consdered performance to be a value whch can be averaged; the problem s our percepton that performance s a smple number. The reason for the problem s that we often forget the dfference between the followng statements: on average, the amount of tme saved by usng machne A over machne B s... on average, the relatve performance of machne A to machne B s... HOW WROG IS WROG: Performance Comparsons of 7 Hgh-Profle Computers j What effect does ths have upon performance calculatons, besdes beng wrong? How wrong s t? Presented n the followng fgures are comparsons of machne performances, wth the performance numbers calculated accordng to the geometrc mean, the harmonc mean, and the arthmetc mean. The number produced by the geometrc mean s the number publshed as the computer s SPEC ratng. It s found by takng the geometrc mean of the SPEC ratos. It s a meanngless number. The number produced by the harmonc mean s smply the harmonc mean of the SPEC ratos; t, too, s a meanngless number. The fnal number s produced the correct way, by dervng the orgnal tme measurements from the SPECmark and the publshed runnngs tmes for the 7
8 150.0 SPECnt92 (GMean) Harmonc Mean of Ratos Rato of Arthmetc Means SPECmarks MHz MHz PowerPC 66MHz Pentum 150MHz R MHz HP MHz POWER2 200MHz Alpha Comparatve SPECmarks, Integer A number of publshed SPECmarks are shown, compared to the values recomputed usng the harmonc mean on the ndvdual SPECmarks and the arthmetc mean on the ndvdual runnng tmes. As nether of the means were computed wth any weght nformaton, all tests are weghted equally. Only the Rato of Arthmetc Means s correct. VAX 11/780. These numbers are averaged wth the arthmetc mean and compared to the arthmetc mean of the VAX. The numbers are shown n Fg. 1 and Fg. 2, showng the dfference between usng varous approprate and napproprate methods. The publshed SPECnt92 and SPECfp92 numbers are to the left, the value recomputed usng the harmonc mean s n the mddle, and the value recomputed wth the raw runnng tmes s on the rght. The dfferences are on the order of ten percent; not enormous, but certanly enough to reorder the lst f the examples chosen had been clustered together. As t s, the 72MHz POWER2 chp turns out to be faster than the 200MHz Alpha n both nteger and floatng pont when the averages are recomputed. The numbers are taken from [Corp93a] and [Corp93b]. 5.0 Rethnkng Performance We usually know what we need to do; we are nterested n how much of t we can get done wth ths computer versus that one. In ths context, the only thng that matters s how much tme s saved by usng one machne over another. The fallacy s n consderng performance a measure unto tself. Performance s n realty a specfc nstance of the followng: two machnes, a set of programs to be run on them, and an ndcaton of how mportant each of the programs s to us. Performance s therefore not a sngle number, but really a collecton of mplcatons. It s nothng more or less than the measure of how much tme we save runnng our tests on the machnes n queston. If someone else has smlar needs to ours, our performance numbers wll be useful to them. However, two people wth dfferent sets of crtera wll lkely walk away wth two completely dfferent performance numbers for the same machne. 8
9 300.0 SPECfp92 (GMean) Harmonc Mean of Ratos Rato of Arthmetc Means SPECmarks MHz MHz Pentum 66MHz PowerPC 150MHz R MHz HP MHz Alpha 72MHz POWER2 Comparatve SPECmarks, Floatng Pont A number of publshed SPECmarks are shown, compared to the values recomputed usng the harmonc mean on the ndvdual SPECmarks and the arthmetc mean on the ndvdual runnng tmes. As nether of the means were computed wth any weght nformaton, all tests are weghted equally. Only the Rato of Arthmetc Means s correct. 6.0 Summary Interpretatons of the arthmetc, geometrc, and harmonc means have been gven, wth the geometrc mean wrtten off as a curosty. umerous examples have llustrated the reasons for usng dfferent means n dfferent crcumstances, wth an attempt to gve nsght nto the semantcs of the varous choces. The prmary results nclude the followng: RULES TO LIVE BY 1. When presented wth a number of tmes for a set of benchmarks, the approprate average s the arthmetc mean. 2. When presented wth a number of rate ratos for a set of benchmarks (reference tme over expermental tme, such as n SPECmarks), sum the ndvdual runnng tmes and use the rato of the sums (equvalent to the rato of the arthmetc means). 3. When presented wth a number of tme ratos for a set of benchmarks (expermental tme over reference tme), sum the ndvdual runnng tmes and use the rato of the sums (equvalent to the rato of the arthmetc means). 4. When presented wth a set of rates, frst determne f they are per benchmark or sampled perodcally n tme. If per benchmark (whch s more lkely), the harmonc mean s approprate; f sampled n tme, the arthmetc mean s approprate. References [Corp93a] Standard Performance Evaluaton Corp. SPEC ewsletter, September [Corp93b] Standard Performance Evaluaton Corp. SPEC ewsletter, December [Flemng86] Phlp J. Flemng and John J. Wallace. How not to le wth statstcs: the correct way to summarze benchmark results. CACM, 29(3): , March [Smth88] James E. Smth. Characterzng Computer Performance wth a Sngle umber. CACM, 31(10): , October
10 otes on Calculatng Computer Performance Bruce Jacob and Trevor Mudge Advanced Computer Archtecture Lab EECS Department, Unversty of Mchgan Abstract Ths report explans what t means to characterze the performance of a computer, and whch methods are approprate and napproprate for the task. The most wdely used metrc s the performance on the SPEC benchmark sute of programs; currently, the results of runnng the SPEC benchmark sute are compled nto a sngle number usng the geometrc mean. The prmary reason for usng the geometrc mean s that t preserves values across normalzaton, but unfortunately, t does not preserve total run tme, whch s probably the fgure of greatest nterest when performances are beng compared. Cycles per Instructon (CPI) s another wdely used metrc, but ths method s nvald, even f comparng machnes wth dentcal clock speeds. Comparng CPI values to judge performance falls prey to the same problems as averagng normalzed values. In general, normalzed values must not be averaged and nstead of the geometrc mean, ether the harmonc or the arthmetc mean s the approprate method for averagng a set runnng tmes. The arthmetc mean should be used to average tmes, and the harmonc mean should be used to average rates (1/tme). A number of publshed SPECmarks are recomputed usng these means to demonstrate the effect of choosng a favorable algorthm. Unversty of Mchgan Tech Report CSE-TR March,
An Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationCalculation of Sampling Weights
Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a two-stage stratfed cluster desgn. 1 The frst stage conssted of a sample
More information8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by
6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng
More information1. Measuring association using correlation and regression
How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a
More informationSection 5.4 Annuities, Present Value, and Amortization
Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 Multple-Choce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multple-choce questons. For each queston, only one of the answers s correct.
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationCHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES
CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationThe Mathematical Derivation of Least Squares
Pscholog 885 Prof. Federco The Mathematcal Dervaton of Least Squares Back when the powers that e forced ou to learn matr algera and calculus, I et ou all asked ourself the age-old queston: When the hell
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMI-SP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationThe Development of Web Log Mining Based on Improve-K-Means Clustering Analysis
The Development of Web Log Mnng Based on Improve-K-Means Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
More informationWhat is Candidate Sampling
What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble
More information21 Vectors: The Cross Product & Torque
21 Vectors: The Cross Product & Torque Do not use our left hand when applng ether the rght-hand rule for the cross product of two vectors dscussed n ths chapter or the rght-hand rule for somethng curl
More informationTexas Instruments 30X IIS Calculator
Texas Instruments 30X IIS Calculator Keystrokes for the TI-30X IIS are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the
More informationIDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS
IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,
More informationLecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.
Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook
More informationImplementation of Deutsch's Algorithm Using Mathcad
Implementaton of Deutsch's Algorthm Usng Mathcad Frank Roux The followng s a Mathcad mplementaton of Davd Deutsch's quantum computer prototype as presented on pages - n "Machnes, Logc and Quantum Physcs"
More informationThe Greedy Method. Introduction. 0/1 Knapsack Problem
The Greedy Method Introducton We have completed data structures. We now are gong to look at algorthm desgn methods. Often we are lookng at optmzaton problems whose performance s exponental. For an optmzaton
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationFINANCIAL MATHEMATICS
3 LESSON FINANCIAL MATHEMATICS Annutes What s an annuty? The term annuty s used n fnancal mathematcs to refer to any termnatng sequence of regular fxed payments over a specfed perod of tme. Loans are usually
More informationTypes of Injuries. (20 minutes) LEARNING OBJECTIVES MATERIALS NEEDED
U N I T 3 Types of Injures (20 mnutes) PURPOSE: To help coaches learn how to recognze the man types of acute and chronc njures. LEARNING OBJECTIVES In ths unt, coaches wll learn how most njures occur,
More informationLinear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits
Lnear Crcuts Analyss. Superposton, Theenn /Norton Equalent crcuts So far we hae explored tmendependent (resste) elements that are also lnear. A tmendependent elements s one for whch we can plot an / cure.
More informationSupport Vector Machines
Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More information) of the Cell class is created containing information about events associated with the cell. Events are added to the Cell instance
Calbraton Method Instances of the Cell class (one nstance for each FMS cell) contan ADC raw data and methods assocated wth each partcular FMS cell. The calbraton method ncludes event selecton (Class Cell
More informationwhere the coordinates are related to those in the old frame as follows.
Chapter 2 - Cartesan Vectors and Tensors: Ther Algebra Defnton of a vector Examples of vectors Scalar multplcaton Addton of vectors coplanar vectors Unt vectors A bass of non-coplanar vectors Scalar product
More informationExtending Probabilistic Dynamic Epistemic Logic
Extendng Probablstc Dynamc Epstemc Logc Joshua Sack May 29, 2008 Probablty Space Defnton A probablty space s a tuple (S, A, µ), where 1 S s a set called the sample space. 2 A P(S) s a σ-algebra: a set
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationAn Interest-Oriented Network Evolution Mechanism for Online Communities
An Interest-Orented Network Evoluton Mechansm for Onlne Communtes Cahong Sun and Xaopng Yang School of Informaton, Renmn Unversty of Chna, Bejng 100872, P.R. Chna {chsun,yang}@ruc.edu.cn Abstract. Onlne
More informationVision Mouse. Saurabh Sarkar a* University of Cincinnati, Cincinnati, USA ABSTRACT 1. INTRODUCTION
Vson Mouse Saurabh Sarkar a* a Unversty of Cncnnat, Cncnnat, USA ABSTRACT The report dscusses a vson based approach towards trackng of eyes and fngers. The report descrbes the process of locatng the possble
More informationLuby s Alg. for Maximal Independent Sets using Pairwise Independence
Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent
More informationA Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy S-curve Regression
Novel Methodology of Workng Captal Management for Large Publc Constructons by Usng Fuzzy S-curve Regresson Cheng-Wu Chen, Morrs H. L. Wang and Tng-Ya Hseh Department of Cvl Engneerng, Natonal Central Unversty,
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More information"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *
Iranan Journal of Scence & Technology, Transacton B, Engneerng, ol. 30, No. B6, 789-794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC
More informationQUESTIONS, How can quantum computers do the amazing things that they are able to do, such. cryptography quantum computers
2O cryptography quantum computers cryptography quantum computers QUESTIONS, Quantum Computers, and Cryptography A mathematcal metaphor for the power of quantum algorthms Mark Ettnger How can quantum computers
More informationFeature selection for intrusion detection. Slobodan Petrović NISlab, Gjøvik University College
Feature selecton for ntruson detecton Slobodan Petrovć NISlab, Gjøvk Unversty College Contents The feature selecton problem Intruson detecton Traffc features relevant for IDS The CFS measure The mrmr measure
More information14.74 Lecture 5: Health (2)
14.74 Lecture 5: Health (2) Esther Duflo February 17, 2004 1 Possble Interventons Last tme we dscussed possble nterventons. Let s take one: provdng ron supplements to people, for example. From the data,
More informationSPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:
SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationA Performance Analysis of View Maintenance Techniques for Data Warehouses
A Performance Analyss of Vew Mantenance Technques for Data Warehouses Xng Wang Dell Computer Corporaton Round Roc, Texas Le Gruenwald The nversty of Olahoma School of Computer Scence orman, OK 739 Guangtao
More informationBrigid Mullany, Ph.D University of North Carolina, Charlotte
Evaluaton And Comparson Of The Dfferent Standards Used To Defne The Postonal Accuracy And Repeatablty Of Numercally Controlled Machnng Center Axes Brgd Mullany, Ph.D Unversty of North Carolna, Charlotte
More informationStudy on Model of Risks Assessment of Standard Operation in Rural Power Network
Study on Model of Rsks Assessment of Standard Operaton n Rural Power Network Qngj L 1, Tao Yang 2 1 Qngj L, College of Informaton and Electrcal Engneerng, Shenyang Agrculture Unversty, Shenyang 110866,
More informationSimple Interest Loans (Section 5.1) :
Chapter 5 Fnance The frst part of ths revew wll explan the dfferent nterest and nvestment equatons you learned n secton 5.1 through 5.4 of your textbook and go through several examples. The second part
More informationImplied (risk neutral) probabilities, betting odds and prediction markets
Impled (rsk neutral) probabltes, bettng odds and predcton markets Fabrzo Caccafesta (Unversty of Rome "Tor Vergata") ABSTRACT - We show that the well known euvalence between the "fundamental theorem of
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More informationAdaptive Clinical Trials Incorporating Treatment Selection and Evaluation: Methodology and Applications in Multiple Sclerosis
Adaptve Clncal Trals Incorporatng Treatment electon and Evaluaton: Methodology and Applcatons n Multple cleross usan Todd, Tm Frede, Ngel tallard, Ncholas Parsons, Elsa Valdés-Márquez, Jeremy Chataway
More information1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)
6.3 / -- Communcaton Networks II (Görg) SS20 -- www.comnets.un-bremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes
More informationJoe Pimbley, unpublished, 2005. Yield Curve Calculations
Joe Pmbley, unpublshed, 005. Yeld Curve Calculatons Background: Everythng s dscount factors Yeld curve calculatons nclude valuaton of forward rate agreements (FRAs), swaps, nterest rate optons, and forward
More informationFast degree elevation and knot insertion for B-spline curves
Computer Aded Geometrc Desgn 22 (2005) 183 197 www.elsever.com/locate/cagd Fast degree elevaton and knot nserton for B-splne curves Q-Xng Huang a,sh-mnhu a,, Ralph R. Martn b a Department of Computer Scence
More informationHÜCKEL MOLECULAR ORBITAL THEORY
1 HÜCKEL MOLECULAR ORBITAL THEORY In general, the vast maorty polyatomc molecules can be thought of as consstng of a collecton of two electron bonds between pars of atoms. So the qualtatve pcture of σ
More informationtotal A A reag total A A r eag
hapter 5 Standardzng nalytcal Methods hapter Overvew 5 nalytcal Standards 5B albratng the Sgnal (S total ) 5 Determnng the Senstvty (k ) 5D Lnear Regresson and albraton urves 5E ompensatng for the Reagent
More informationConversion between the vector and raster data structures using Fuzzy Geographical Entities
Converson between the vector and raster data structures usng Fuzzy Geographcal Enttes Cdála Fonte Department of Mathematcs Faculty of Scences and Technology Unversty of Combra, Apartado 38, 3 454 Combra,
More informationWe are now ready to answer the question: What are the possible cardinalities for finite fields?
Chapter 3 Fnte felds We have seen, n the prevous chapters, some examples of fnte felds. For example, the resdue class rng Z/pZ (when p s a prme) forms a feld wth p elements whch may be dentfed wth the
More informationv a 1 b 1 i, a 2 b 2 i,..., a n b n i.
SECTION 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS 455 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS All the vector spaces we have studed thus far n the text are real vector spaces snce the scalars are
More information1 Example 1: Axis-aligned rectangles
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture # 6 Scrbe: Aaron Schld February 21, 2013 Last class, we dscussed an analogue for Occam s Razor for nfnte hypothess spaces that, n conjuncton
More informationHow To Calculate The Accountng Perod Of Nequalty
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
More informationWe assume your students are learning about self-regulation (how to change how alert they feel) through the Alert Program with its three stages:
Welcome to ALERT BINGO, a fun-flled and educatonal way to learn the fve ways to change engnes levels (Put somethng n your Mouth, Move, Touch, Look, and Lsten) as descrbed n the How Does Your Engne Run?
More informationAn Overview of Financial Mathematics
An Overvew of Fnancal Mathematcs Wllam Benedct McCartney July 2012 Abstract Ths document s meant to be a quck ntroducton to nterest theory. It s wrtten specfcally for actuaral students preparng to take
More informationHollinger Canadian Publishing Holdings Co. ( HCPH ) proceeding under the Companies Creditors Arrangement Act ( CCAA )
February 17, 2011 Andrew J. Hatnay ahatnay@kmlaw.ca Dear Sr/Madam: Re: Re: Hollnger Canadan Publshng Holdngs Co. ( HCPH ) proceedng under the Companes Credtors Arrangement Act ( CCAA ) Update on CCAA Proceedngs
More informationRapid Estimation Method for Data Capacity and Spectrum Efficiency in Cellular Networks
Rapd Estmaton ethod for Data Capacty and Spectrum Effcency n Cellular Networs C.F. Ball, E. Humburg, K. Ivanov, R. üllner Semens AG, Communcatons oble Networs unch, Germany carsten.ball@semens.com Abstract
More informationQuestion 2: What is the variance and standard deviation of a dataset?
Queston 2: What s the varance and standard devaton of a dataset? The varance of the data uses all of the data to compute a measure of the spread n the data. The varance may be computed for a sample of
More informationLecture 2: Single Layer Perceptrons Kevin Swingler
Lecture 2: Sngle Layer Perceptrons Kevn Sngler kms@cs.str.ac.uk Recap: McCulloch-Ptts Neuron Ths vastly smplfed model of real neurons s also knon as a Threshold Logc Unt: W 2 A Y 3 n W n. A set of synapses
More informationLatent Class Regression. Statistics for Psychosocial Research II: Structural Models December 4 and 6, 2006
Latent Class Regresson Statstcs for Psychosocal Research II: Structural Models December 4 and 6, 2006 Latent Class Regresson (LCR) What s t and when do we use t? Recall the standard latent class model
More informationPerformance attribution for multi-layered investment decisions
Performance attrbuton for mult-layered nvestment decsons 880 Thrd Avenue 7th Floor Ne Yor, NY 10022 212.866.9200 t 212.866.9201 f qsnvestors.com Inna Oounova Head of Strategc Asset Allocaton Portfolo Management
More informationCan Auto Liability Insurance Purchases Signal Risk Attitude?
Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159-164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? Chu-Shu L Department of Internatonal Busness, Asa Unversty, Tawan Sheng-Chang
More informationLaws of Electromagnetism
There are four laws of electromagnetsm: Laws of Electromagnetsm The law of Bot-Savart Ampere's law Force law Faraday's law magnetc feld generated by currents n wres the effect of a current on a loop of
More informationFaraday's Law of Induction
Introducton Faraday's Law o Inducton In ths lab, you wll study Faraday's Law o nducton usng a wand wth col whch swngs through a magnetc eld. You wll also examne converson o mechanc energy nto electrc energy
More informationTime Value of Money Module
Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the
More informationPerformance Analysis of Energy Consumption of Smartphone Running Mobile Hotspot Application
Internatonal Journal of mart Grd and lean Energy Performance Analyss of Energy onsumpton of martphone Runnng Moble Hotspot Applcaton Yun on hung a chool of Electronc Engneerng, oongsl Unversty, 511 angdo-dong,
More information1.1 The University may award Higher Doctorate degrees as specified from time-to-time in UPR AS11 1.
HIGHER DOCTORATE DEGREES SUMMARY OF PRINCIPAL CHANGES General changes None Secton 3.2 Refer to text (Amendments to verson 03.0, UPR AS02 are shown n talcs.) 1 INTRODUCTION 1.1 The Unversty may award Hgher
More informationInstructions for Analyzing Data from CAHPS Surveys:
Instructons for Analyzng Data from CAHPS Surveys: Usng the CAHPS Analyss Program Verson 4.1 Purpose of ths Document...1 The CAHPS Analyss Program...1 Computng Requrements...1 Pre-Analyss Decsons...2 What
More informationSection C2: BJT Structure and Operational Modes
Secton 2: JT Structure and Operatonal Modes Recall that the semconductor dode s smply a pn juncton. Dependng on how the juncton s based, current may easly flow between the dode termnals (forward bas, v
More informationNordea G10 Alpha Carry Index
Nordea G10 Alpha Carry Index Index Rules v1.1 Verson as of 10/10/2013 1 (6) Page 1 Index Descrpton The G10 Alpha Carry Index, the Index, follows the development of a rule based strategy whch nvests and
More informationAssessing the Fairness of a Firm s Allocation of Shares in Initial Public Offerings: Adapting a Measure from Biostatistics
Assessng the Farness of a Frm s Allocaton of Shares n Intal Publc Offerngs: Adaptng a Measure from Bostatstcs by Efstatha Bura and Joseph L. Gastwrth Department of Statstcs The George Washngton Unversty
More information: ;,i! i.i.i; " '^! THE LOGIC THEORY MACHINE; EMPIRICAL EXPLORATIONS WITH A CASE STUDY IN HEURISTICS
! EMPRCAL EXPLORATONS WTH THE LOGC THEORY MACHNE; A CASE STUDY N HEURSTCS. :, by Allen Newell, J. C. Shaw, & H. A. Smon Ths s a case study n problem-solvng, representng part of a program of research on
More informationMONITORING METHODOLOGY TO ASSESS THE PERFORMANCE OF GSM NETWORKS
Electronc Communcatons Commttee (ECC) wthn the European Conference of Postal and Telecommuncatons Admnstratons (CEPT) MONITORING METHODOLOGY TO ASSESS THE PERFORMANCE OF GSM NETWORKS Athens, February 2008
More informationTHE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES
The goal: to measure (determne) an unknown quantty x (the value of a RV X) Realsaton: n results: y 1, y 2,..., y j,..., y n, (the measured values of Y 1, Y 2,..., Y j,..., Y n ) every result s encumbered
More informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes cause-and-effect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More informationTraffic-light a stress test for life insurance provisions
MEMORANDUM Date 006-09-7 Authors Bengt von Bahr, Göran Ronge Traffc-lght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE-113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax
More informationAnalysis of Premium Liabilities for Australian Lines of Business
Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton
More informationStaff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall
SP 2005-02 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 14853-7801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent
More informationAn Analysis of Central Processor Scheduling in Multiprogrammed Computer Systems
STAN-CS-73-355 I SU-SE-73-013 An Analyss of Central Processor Schedulng n Multprogrammed Computer Systems (Dgest Edton) by Thomas G. Prce October 1972 Techncal Report No. 57 Reproducton n whole or n part
More informationA hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm
Avalable onlne www.ocpr.com Journal of Chemcal and Pharmaceutcal Research, 2014, 6(7):1884-1889 Research Artcle ISSN : 0975-7384 CODEN(USA) : JCPRC5 A hybrd global optmzaton algorthm based on parallel
More informationFREQUENCY OF OCCURRENCE OF CERTAIN CHEMICAL CLASSES OF GSR FROM VARIOUS AMMUNITION TYPES
FREQUENCY OF OCCURRENCE OF CERTAIN CHEMICAL CLASSES OF GSR FROM VARIOUS AMMUNITION TYPES Zuzanna BRO EK-MUCHA, Grzegorz ZADORA, 2 Insttute of Forensc Research, Cracow, Poland 2 Faculty of Chemstry, Jagellonan
More informationAn Evaluation of the Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products and Services
An Evaluaton of the Extended Logstc, Smple Logstc, and Gompertz Models for Forecastng Short Lfecycle Products and Servces Charles V. Trappey a,1, Hsn-yng Wu b a Professor (Management Scence), Natonal Chao
More informationTrivial lump sum R5.0
Optons form Once you have flled n ths form, please return t wth your orgnal brth certfcate to: Premer PO Box 2067 Croydon CR90 9ND. Fll n ths form usng BLOCK CAPITALS and black nk. Mark all answers wth
More informationSYSTEM-LEVEL PERFORMANCE METRICS FOR MULTIPROGRAM WORKLOADS
... SYSTEM-LEVEL PERFORMANCE METRICS FOR MULTIPROGRAM WORKLOADS... ASSESSING THE PERFORMANCE OF MULTIPROGRAM WORKLOADS RUNNING ON MULTITHREADED HARDWARE IS DIFFICULT BECAUSE IT INVOLVES A BALANCE BETWEEN
More information10.2 Future Value and Present Value of an Ordinary Simple Annuity
348 Chapter 10 Annutes 10.2 Future Value and Present Value of an Ordnary Smple Annuty In compound nterest, 'n' s the number of compoundng perods durng the term. In an ordnary smple annuty, payments are
More informationPRACTICE 1: MUTUAL FUNDS EVALUATION USING MATLAB.
PRACTICE 1: MUTUAL FUNDS EVALUATION USING MATLAB. INDEX 1. Load data usng the Edtor wndow and m-fle 2. Learnng to save results from the Edtor wndow. 3. Computng the Sharpe Rato 4. Obtanng the Treynor Rato
More informationPSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12
14 The Ch-squared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annuty-mmedate, and ts present value Study annuty-due, and
More informationSIMPLE LINEAR CORRELATION
SIMPLE LINEAR CORRELATION Smple lnear correlaton s a measure of the degree to whch two varables vary together, or a measure of the ntensty of the assocaton between two varables. Correlaton often s abused.
More informationSoftware project management with GAs
Informaton Scences 177 (27) 238 241 www.elsever.com/locate/ns Software project management wth GAs Enrque Alba *, J. Francsco Chcano Unversty of Málaga, Grupo GISUM, Departamento de Lenguajes y Cencas de
More informationOn the Optimal Control of a Cascade of Hydro-Electric Power Stations
On the Optmal Control of a Cascade of Hydro-Electrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;
More informationHALL EFFECT SENSORS AND COMMUTATION
OEM770 5 Hall Effect ensors H P T E R 5 Hall Effect ensors The OEM770 works wth three-phase brushless motors equpped wth Hall effect sensors or equvalent feedback sgnals. In ths chapter we wll explan how
More informationMathematics of Finance
CHAPTER 5 Mathematcs of Fnance 5.1 Smple and Compound Interest 5.2 Future Value of an Annuty 5.3 Present Value of an Annuty; Amortzaton Revew Exercses Extended Applcaton: Tme, Money, and Polynomals Buyng
More informationLecture 2 Sequence Alignment. Burr Settles IBS Summer Research Program 2008 bsettles@cs.wisc.edu www.cs.wisc.edu/~bsettles/ibs08/
Lecture 2 Sequence lgnment Burr Settles IBS Summer Research Program 2008 bsettles@cs.wsc.edu www.cs.wsc.edu/~bsettles/bs08/ Sequence lgnment: Task Defnton gven: a par of sequences DN or proten) a method
More information