Algorithms estimation

Figure 1. Comparison between true values and algorithm estimates of p and B...

Figure 2. Comparison between true values and algorithm estimates of p, B, and S during the transient following a sudden increase of dilution rate of a chemostat. Key -------------, true values x, estimates and O, smoothed estimates.

INVESTIGATION PROBLEM TYPE m, or VALUES MODEL EQS.2 DESCENT NO. of 6 s ALGORITHM ESTIMATED ... 

Dong s algorithm estimates from an initial error estimate 5o (Eq. 2.19) the final error estimate SE)e (Eq. 2.20), based on the m effects, E, that are not considered important, that is, those that fulfill the requirement Ek < 2.5 Sa. The estimated critical effect (Eq. 2.16) from the algorithm of Dong is also called the margin of error ... 

As stated in Chap. 2, in a PET scanner, block detectors are cut into small detectors and coupled with four PM tubes, which are arranged in arrays of rings. Each detector is connected in coincidence to as many as N/2 detectors, where N is the number of small detectors in the ring. So which two detectors detected a coincidence event within the time window must be determined. Pulses produced in PM tubes are used to determine the locations of the two detectors (Fig. 3.2). As in scintillation cameras, the position of each detector is estimated by a weighted centroid algorithm. This algorithm estimates... 

At this step of the work we evaluated the fitting performances of six further rate equations, derived from assumed reaction mechanisms and congruent with previous findings obtained with power law rate equations. Among them, it has been reported the model named Centi modified, which represents our proposal to take into account the effect of O2 partial pressure on the overall kinetics under the same hypotheses of the model of Centi [24]. The results of parameters identification, carried out for each temperature investigated, are reported in Tab.3b and show different performances of the models. The model Centi modified does not produce effective results, since the relevant values are still very low and the minimisation algorithm estimated some unacceptable parameters value (for example, a negative value for K no at 450°C). 

Since the system activates an emergency brake when the values estimated by the odometry system exceed the authorized limits, the odometry algorithm has to provide accurate and reliable measurements. Thus, the algorithm is usually based on a fault-tolerant sensor-fusion approach. In this case, we design the algorithm following one of the approaches described by Malvezzi et al. in [16]. The algorithm estimates the speed of the train and the traveled distance with the information provided by an accelerometer that measures the acceleration of the train and two encoders that measure the speed of a different wheel each. 

The algorithm employed in the estimation process linearizes the constraint equations at each iterative step at current estimates of the true values for the variables and parameters. 

Various partitions, resulted from the different combinations of clustering parameters. The estimation of the number of classes and the selection of optimum clustering is based on separability criteria such as the one defined by the ratio of the minimum between clusters distance to the maximum of the average within-class distances. In that case the higher the criterion value the more separable the clustering. By plotting the criterion value vs. the number of classes and/or the algorithm parameters, the partitions which maximise the criterion value is identified and the number of classes is estimated. 

To search for the forms of potentials we are considering here simple mechanical models. Two of them, namely cluster support algorithm (CSA) and plane support algorithm (PSA), were described in details in [6]. Providing the experiments with simulated and experimental data, it was shown that the iteration procedure yields the sweeping of the structures which are not volumetric-like or surface-like, correspondingly. While the number of required projections for the reconstruction is reduced by 10 -100 times, the quality of reconstruction estimated quantitatively remained quite comparative (sometimes even with less artefacts) with that result obtained by classic Computer Tomography (CT). 

The adaptive estimation of the pseudo-inverse parameters a n) consists of the blocks C and E (Fig. 1) if the transformed noise ( ) has unknown properties. Bloek C performes the restoration of the posterior PDD function w a,n) from the data a (n) + (n). It includes methods and algorithms for the PDD function restoration from empirical data [8] which are based on empirical averaging. Beeause the noise is assumed to be a stationary process with zero mean value and the image parameters are constant, the PDD function w(a,n) converges, at least, to the real distribution. The posterior PDD funetion is used to built a back loop to block B and as a direct input for the estimator E. For the given estimation criteria f(a,d) an optimal estimation a (n) can be found from the expression... 

For the iteration algorithm (5) the optimal estimations (6) are directly used by a second back loop to block B (long dashed line in Fig. 1). 

Note The segmentation operation yields a near-optimal estimate x that may be used as initialization point for an optimization algoritlim that has to find out the global minimum of the criterion /(.). Because of its nonlinear nature, we prefer to minimize it by using a stochastic optimization algorithm (a version of the Simulated Annealing algorithm [3]). 

The algorithm contains five minimisation procedures which are performed the same way as in the method " i.e. by minimisation of the RMS between the measured unidirectional distribution and the corresponding theoretical distribution of die z-component of the intensity of the leakage field. The aim of the first minimisation is to find initial approximations of the depth d, of the crack in the left half of its cross-section, die depth d in its right half, its half-width a, and the parameter c. The second minimisation gives approximations of d, and d and better approximations of a and c based on estimation of d,= d, and d,= d,j. Improved approximations of d] and d4 are determined by the third minimisation while fixing new estimations of d dj, dj, and dj. Computed final values dj , d/, a and c , whieh are designated by a subscript c , are provided by the fourth minimisation, based on improved estimations of d, dj, dj, and d . The fifth minimisation computes final values d, , d, dj, d while the already computed dj , d/, a and c are fixed. 

Deserno M and C Holm 1998b. How to Mesh Up Ewald Sums. II. An Accurate Error Estimate for the Particle-Particle-Particle-Mesh Algorithm. Journal of Chemical Physics 109 7694-7701. 

One limitation of clique detection is that it needs to be run repeatedly with differei reference conformations and the run-time scales with the number of conformations pt molecule. The maximum likelihood method [Bamum et al. 1996] eliminates the need for reference conformation, effectively enabling every conformation of every molecule to a< as the reference. Despite this, the algorithm scales linearly with the number of conformatior per molecule, so enabling a larger number of conformations (up to a few hundred) to b handled. In addition, the method scores each of the possible pharmacophores based upo the extent to which it fits the set of input molecules and an estimate of its rarity. It is nc required that every molecule has to be able to match every feature for the pharmacophor to be considered. 

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