...
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 model
is 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 answer
to these questions takes us into the subject of maximum likelihood estimators.
Given a particular data set of x
i
’s and y
i
’s, we have the intuitive feeling that
some parameter...
... distribution is often rather poorly realized, if it is
realized at all. We are often taught, rather casually, that, on average, measurements
will 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 would
expect a measurement to be off by ±20σ only one time out of 2 × 10
88
.Weall
know that ... that the
standard deviations σ of these normal distributionsare the same for all points. Then
the probability of the data set is the product of the probabilities of each point,
P ∝
N
i=1
exp
−
1
2
y
i
−...
... problem of fitting a set of N data points (x
i
,y
i
)to
a straight-line model
y(x)=y(x;a, b)=a+bx (15.2.1)
666
Chapter 15. Modelingof Data
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... variance of the linear combination y
i
− a − bx
i
of two random
variables x
i
and y
i
,
Var( y
i
− a − bx
i
)=Var( y
i
)+b
2
Var( x
i
)=σ
2
yi
+b
2
σ
2
xi
≡1/w
i
(15.3.3)
The sum of the square of N ... 662
Chapter 15. Modelingof Data
Sample 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 (χ
2
−
offs
) for the slope
b=tan(bang)
.
Scaled data and
offs
are communicated via the ... variance of the linear combination y
i
− a − bx
i
of two random
variables x
i
and y
i
,
Var(y
i
− a − bx
i
)=Var(y
i
)+b
2
Var(x
i
)=σ
2
yi
+b
2
σ
2
xi
≡1/w
i
(15.3.3)
The sum of the square of N ... of varying b, successful numerical root-finding
leads to a value of ∆a that minimizes χ
2
for the value of ∆b that gives ∆χ
2
=1.This(see
Figure 15.3.1) directly gives the tangent projection of...
... combinations of
the columns of V, with coefficients obtained by forming dot products of the columns
672
Chapter 15. Modelingof Data
Sample 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 Equations
The minimum of (15.4.3) occurs ... twox;
pl[j]=(f2*pl[j-1]-f1*pl[j-2])/d;
}
}
}
Multidimensional Fits
If 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,
X
1
(x), ,X
M
(x).Theχ
2
merit...
... and
alamda
de-
creases by a factor of 10. If a step fails
alamda
grows by a factor of 10. You must call this
684
Chapter 15. Modelingof Data
Sample 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 a
true
that ... name of the game is to find some way of estimating or approximating
the probability distributionof a
(i)
−a
true
without knowing a
true
and withouthaving
available 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 a
true
that ... name of the game is to find some way of estimating or approximating
the probability distributionof a
(i)
−a
true
without knowing a
true
and withouthaving
available to us an infinite universe of hypothetical ... techniques, and seek to minimize the uncertainty of the result according
to 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 tells
how the incoming, raw measurements of the ... formal
definition.
Someotherkindsof robusttechniques, coming from the fields ofoptimalcontrol
and filtering rather than fromthe field of mathematical statistics, are mentioned at the
end of this section. Some ... example, the equality or
inequality of two distributions can be estimated by the Wilcoxon test of computing
the mean rank of one distribution in a combined sample of both distributions.
The Kolmogorov-Smirnov...
... tRNA
Arg
ICG
.
Distances between C1¢ of C72 of the 1Æ72 pair in the
acceptor stem, C1¢ of G18 forming a hydrogen bond
to 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 the
a-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 N
e
H of the cyclic
form instead of the 2¢-OH group of tRNA to C@Oof
the Ca–(C@O)–O–Pa moiety of Arg-AMP, the 2¢-OH
group 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 the
three ring- size analogs of GS ... behavior of
Myr
2
Gro-PChoMLVstoagreaterextentthandoesGS
itself [9].
DSC heating scans of MLVs composed of Myr
2
Gro-
PEtn alone, or of Myr
2
Gro-PEtn containing 4 mole percent
of one of the three ring- size ... Myr
2
Gro-PGro and other members of
the homologous series of linear saturated PGs, see Zhang
et 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 using
INSIGHT II
version 2000 on
a 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 for
molecular ... the
DISCOVER
_3
module of
INSIGHT II
was used at a constant temperature of
298.0 K for 5000 steps of 1.0 fs time-step.
RESULTS
Model structure of human LPL
All model structures of dimeric human LPL...
... accurate modelingof R-D curves of real encoders is always challenging
due 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 CODERS
A Dissertation
by
MIN DAI
Submitted to the Office of Graduate Studies of
Texas A&M University
in 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...