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f2 2.0

the Newton method when used for maximizing log-likelihood functions and is, therefore, a specialized method In Section 66, an expression is derived for the Newton iteration step for maximizing the log-likelihoodfunction for normally distributed observations As a consequenceof the particular form of the log-likelihoodfunction concerned,this step is also the Newton step for minimizingthe nonlinear least squares criterion for observationsof any distribution From the Newton step for normal observations, a much simpler approximate step is derived The method using this step is called the Gauss-Newton method and is the subject of Section 67 The Newton steps for maximizing the Poisson and the multinomial log-likelihood functions are discussed in Section 68 and Section 69, respectively In Section 610, an expressionis derived for the Newton step for maximizingthe log-likelihood function if the distribution of the observations is a linear exponential family.

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The endothelium is crucial to several important functions of arteries, including the regulation of coagulation, the prevention of thrombus formation and the control of vasomotor tone. The latter is particularly dependent on the production of powerful vasodilators, prostacyclin and nitric oxide (NO) by the endothelium; these diffuse to the underlying vascular smooth muscle and cause relaxation. NO is particularly important. It is produced from arginine under the action of the speci c endothelial isoform of the enzyme NO synthase, eNOS; expression of eNOS is upregulated, and NO production therefore enhanced, by various factors such as insulin, bradykinin and acetylcholine, acting through their respective receptors on the endothelium (Mombouli and Vanhoutte, 1999). Leptin has also been shown to induce

The positive square root of the variance is called the standard deviation in the literature in English. In other languages the variance is sometimes mentioned as s.

From this Newton step, a much simpler approximate step is derived that is used by the generalized Gauss-Newton method This method is the subject of Section 61 1 In Section 612, the iteratively reweighted least squares method is described It is shown that it is identical to the generalized Gauss-Newton method and with the Fisher scoring method if the assumed distribution of the observations is a linear exponential family Like the Newton method, the Gauss-Newton method solves a system of linear equations in each step The LevenbergMarquardt method, discussed in Section 613, is a version of the Gauss-Newton method that can handle (near-)singularity of these equations that could occur during the iteration process Section 614 summarizes the numerical optimization methods discussed in this chapter Finally, Section 615 is devoted to the methodology of estimating parameters of expectation models.

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When a qubit is measured, the result will always be either 0 or 1, even if it was both 0 and 1 before the measurement. Thus, after 2N parallel computations, only one of the corresponding output values will be measured; while QuCs cannot give us the output value for all possible input values at the same time, special quantum algorithms are able to exploit quantum parallelism to solve relevant problems in exponentially fewer steps than is possible classically. The best-known quantum algorithm is Peter Shor s 1994 algorithm for e ciently nding the prime factors of large integer numbers; another algorithm, invented by Lov Grover in 1996, o ers a quadratic speedup for unstructured search problems [421].

In it, consecutive steps are proposed to be made in the process starting with the choice of model of the observations and ending with actually estimating the parameters..

Object Solids Bodies Polyface meshes Polygon meshes Polylines with thickness Result Flat surfaces become regions; curved surfaces become bodies. Curved surfaces become single-surface bodies; flat bodies become regions or curves. 3D faces. 3D faces. Lines.

For the derivation of the stability condition, we can remark that the re ection coef cient is related to admittance and impedance parameters by conformal transformations; therefore, angles are preserved, and so the requirement that (Figure 5.15) 0 < < 180 and = 90 for maximum stability. This can be obtained by analytical calculations also [8]. We rst write the re ection coef cients as j j (5.78) s (A) = e d ( ) = e The stability condition eq. (5.70) reads as d d d d >0 dA d dA d (5.79)

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