... The advent of modern computers has had a profound effect in all branches of engineering especially in hydraulics. The recent development of numerical methods and the capabilities of modern machines ... plot of water surface in 2D simulation of Exp-1 …………….95 Figure 6.35 Carpet plot of water surface in 2D simulation of Exp-2…………… 95 Figure 6.36 Carpet plot of water surface in 2D simulation of ... plot of water surface in 2D simulation of Exp-4…………… 96 Figure 6.38 Carpet plot of water surface in 2D simulation of Exp-5…………… 97 Figure 6.39 Carpet plot of water surface in 2D simulation of...
... measure of goodness -of- fit. When the third item suggests that the modelis an unlikely match to the data, then items (i) and (ii) are probably worthless.Unfortunately, many practitioners of parameter ... RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Permission ... based on? The answerto these questions takes us into the subject of maximum likelihood estimators.Given a particular data set of xi’s and yi’s, we have the intuitive feeling thatsome parameter...
... distribution is often rather poorly realized, if it isrealized at all. We are often taught, rather casually, that, on average, measurementswill fall within ±σ of the true value 68 percent of the time, ... time, within ±2σ 95 percent of the time, and within ±3σ 99.7 percent of the time. Extending this, one wouldexpect a measurement to be off by ±20σ only one time out of 2 × 1088.Weallknow that ... that thestandard deviations σ of these normal distributionsare the same for all points. Thenthe probability of the data set is the product of the probabilities of each point,P ∝Ni=1exp−12yi−...
... problem of fitting a set of N data points (xi,yi)toa straight-line modely(x)=y(x;a, b)=a+bx (15.2.1)666Chapter 15. Modelingof DataSample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... variance of the linear combination yi− a − bxi of two randomvariables xiand yi,Var( yi− a − bxi)=Var( yi)+b2Var( xi)=σ2yi+b2σ2xi≡1/wi(15.3.3)The sum of the square of N ... 662Chapter 15. Modelingof DataSample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992...
... float *xx,*yy,*sx,*sy,*ww,aa,offs;float chixy(float bang)Captive function of fitexy, returns the value of (χ2−offs) for the slopeb=tan(bang).Scaled data andoffsare communicated via the ... variance of the linear combination yi− a − bxi of two randomvariables xiand yi,Var(yi− a − bxi)=Var(yi)+b2Var(xi)=σ2yi+b2σ2xi≡1/wi(15.3.3)The sum of the square of N ... of varying b, successful numerical root-findingleads to a value of ∆a that minimizes χ2for the value of ∆b that gives ∆χ2=1.This(seeFigure 15.3.1) directly gives the tangent projection of...
... combinations of the columns of V, with coefficients obtained by forming dot products of the columns672Chapter 15. Modelingof DataSample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... thestandard deviationsof themeasureddependentvariable.The measured values of the dependent variable do not enter the design matrix.Solution by Use of the Normal EquationsThe minimum of (15.4.3) occurs ... twox;pl[j]=(f2*pl[j-1]-f1*pl[j-2])/d;}}}Multidimensional FitsIf you are measuring a single variable y as a functionof more than one variable—say,avector of variables x, then your basis functionswill be functionsof a vector,X1(x), ,XM(x).Theχ2merit...
... andalamdade-creases by a factor of 10. If a step failsalamdagrows by a factor of 10. You must call this684Chapter 15. Modelingof DataSample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... even when they must be offered without proof.Figure 15.6.1 shows the conceptual scheme of an experiment that “measures”a set of parameters. There is some underlying true set of parameters atruethat ... name of the game is to find some way of estimating or approximatingthe probability distributionof a(i)−atruewithout knowing atrueand withouthavingavailable to us an infinite universe of hypothetical...
... even when they must be offered without proof.Figure 15.6.1 shows the conceptual scheme of an experiment that “measures”a set of parameters. There is some underlying true set of parameters atruethat ... name of the game is to find some way of estimating or approximatingthe probability distributionof a(i)−atruewithout knowing atrueand withouthavingavailable to us an infinite universe of hypothetical ... techniques, and seek to minimize the uncertainty of the result accordingto any desired criteria. Offered the choice between mastery of a five-foot shelf of analytical statistics books and middling...
... presence of noise. If the signal is known to be characterized by some number of parameters that vary only slowly, then the formalism of Kalman filtering tellshow the incoming, raw measurements of the ... formaldefinition.Someotherkindsof robusttechniques, coming from the fields ofoptimalcontroland filtering rather than fromthe field of mathematical statistics, are mentioned at theend of this section. Some ... example, the equality orinequality of two distributions can be estimated by the Wilcoxon test of computingthe mean rank of one distribution in a combined sample of both distributions.The Kolmogorov-Smirnov...
... tRNAArgICG.Distances between C1¢ of C72 of the 1Æ72 pair in theacceptor stem, C1¢ of G18 forming a hydrogen bondto U55 of the T-loop and C1¢ of C31 or G39 of 31Æ39 of the anticodon stem of tRNA were compared ... the 2¢-OH group of the ribose of A76 and O2H of thea-carboxyl group of Arg. Arrows indicate the sequential transfer of the bond in the intermediate.M. Konno et al. Modelingof tRNA-assisted ... guanidium moiety of Arg-AMP can donate a proton from NeH of the cyclicform instead of the 2¢-OH group of tRNA to C@Oofthe Ca–(C@O)–O–Pa moiety of Arg-AMP, the 2¢-OHgroup of tRNA becomes free....
... sides of the ring, whereas this is not the case for GS12.We can ask whether or not the observed order of biophysical or biological potencies of GS itself and of thethree ring- size analogs of GS ... behavior of Myr2Gro-PChoMLVstoagreaterextentthandoesGSitself [9].DSC heating scans of MLVs composed of Myr2Gro-PEtn alone, or of Myr2Gro-PEtn containing 4 mole percent of one of the three ring- size ... Myr2Gro-PGro and other members of the homologous series of linear saturated PGs, see Zhanget al. [24].The addition of 4 mol percent of one of the three GS ring- size analogs of GS studied has a relatively...
... Molecular modelingof the dimeric structure of LPL. Two dimeric model structures of LPL were constructed usingINSIGHT IIversion 2000 ona Silicon Graphics workstation. The model structure of the ... the active site from the solvent.After the homology modeling, addition of hydrogen,modification of bonds, potentials of forcefield, and fixation of heavy atom, backbone, and Ca, were performed formolecular ... theDISCOVER_3module of INSIGHT IIwas used at a constant temperature of 298.0 K for 5000 steps of 1.0 fs time-step.RESULTSModel structure of human LPLAll model structures of dimeric human LPL...
... accurate modelingof R-D curves of real encoders is always challengingdue to the diversity of source images and the complexity of transmission channels[82]. Therefore, a third type of R-D models, ... TRAFFIC MODELING OF SCALABLE VIDEO CODERSA DissertationbyMIN DAISubmitted to the Office of Graduate Studies of Texas A&M Universityin partial fulfillment of the requirements for the degree of DOCTOR ... the characteristics of existing video traffic. Rate-distortion(R-D) based schemes are often applied to improve and stabilize video quality; how-ever, the lack of R-D modelingof scalable coders...