Prediction vector

This b (also known as p = the prediction vector) is often referred to as the regression vector or set of regression coefficients. Note that (A A)-1 A is referred to as the pseudoinverse of A designated as A+. Note that there is one regression coefficient for each frequency (or data channel). 

While trying to resolve which sources are present in the data, one starts with an initial guess of the elemental composition of the source material. This concentration profile is then used as the test vector, b, in equation 21. From the rotation vector and b, a predicted vector, b, can be calculated. The error observed between the original test vector b and the predicted test vector b gives an indication as to whether the test vector is a reasonable representation of a factor. 

The fit of the target vectors in matrix L and the predicted vectors in matrix L based on the transformation matrix according to Eq. (5.77) is usually estimated by the average relative deviation as follows ... 

Based on a measured spectmm of an unknown (vector a comprising p absorbance values) and on the calibration matrix, the concentrations of the m components can now be predicted (vector comprising m concentration values) ... 

Unfolded hypercube Prediction vector Prediction image... 

Calculations using the semiempirical PM3 method with standard convergence criteria of 0.0003 aii on the maximum component of the gradient vector and either an energy change from the previous cycle of < 10 hartree or a maximum predicted displacement for the next step of < 0.0003 au. 

The ordinary BO approximate equations failed to predict the proper symmetry allowed transitions in the quasi-JT model whereas the extended BO equation either by including a vector potential in the system Hamiltonian or by multiplying a phase factor onto the basis set can reproduce the so-called exact results obtained by the two-surface diabatic calculation. Thus, the calculated hansition probabilities in the quasi-JT model using the extended BO equations clearly demonshate the GP effect. The multiplication of a phase factor with the adiabatic nuclear wave function is an approximate treatment when the position of the conical intersection does not coincide with the origin of the coordinate axis, as shown by the results of [60]. Moreover, even if the total energy of the system is far below the conical intersection point, transition probabilities in the JT model clearly indicate the importance of the extended BO equation and its necessity. 

The idea behind this approach is simple. First, we compose the characteristic vector from all the descriptors we can compute. Then, we define the maximum length of the optimal subset, i.e., the input vector we shall actually use during modeling. As is mentioned in Section 9.7, there is always some threshold beyond which an inaease in the dimensionality of the input vector decreases the predictive power of the model. Note that the correlation coefficient will always be improved with an increase in the input vector dimensionality. 

Prediction implies the generation of unknown properties. On the basis of example data, a model is established which is able to relate an object to its property. This model can then be used for predicting values for new data vectors. 

These are the flux relations associated with the dusty gas model. As explained above, they would be expected to predict only the diffusive contributions to the flux vectors, so they should be compared with equations (2.25) obtained from simple momentum transfer arguments. Equations (3,16) are then seen to be just the obvious vector generalization of the scalar equations (2.25), so the dusty gas model provides justification for the simple procedure of adding momentum transfer rates. 

Normally, one does not have hue values of the elements of the slope mah ix M for comparison. It is always possible, however, to obtain y, the vector of predicted y values at each of the known Xi from any of the slope vectors m obtained by the multivariate procedure... 

Many of the tools are aimed at classification and prediction problems, such as the handwriting example, where a training set of data vectors for which the property is known is used to develop a classification rule. Then the rule can be appHed to a test set of data vectors for which the property is... 

It cannot be stated generally how accurate the predicted results are. Due to the limitations of geometric, physical, and mathematical modeling, not all of the produced numbers (e.g., air velocity vectors) are at a high level of accuracy, and the results are therefore subjected to experienced weighting. In some cases, the values can be as accurate as within 5% of the real values in other cases, they are not as accurate as could be wished. But results can be still very strong and helpful in a comparative judgment, i.e., if a number of similar case.s are compared with observed tendencies. 

Although the experimental and simulation time scales differ, the CFD simulation (Figure 8.29(a),(c),(e)) for the zeroth moment (Mq) indicates that once the particles reach the observable size, they will appear approximately in the experimentally observed regions (Figure 8.29 (b),(d),(f)). Predicted velocity vectors are superimposed on supersaturation profiles in Figure 8.30. 

Studies on the electronic structure of carbon nanotube (CNT) is of much importance toward its efficient utilisation in electronic devices. It is well known that the early prediction of its peculiar electronic structure [1-3] right after the lijima s observation of multi-walled CNT (MWCNT) [4] seems to have actually triggered the subsequent and explosive series of experimental researches of CNT. In that prediction, alternative appearance of metallic and semiconductive nature in CNT depending on the combination of diameter and pitch or, more specifically, chiral vector of CNT expressed by two kinds of non-negative integers (a, b) as described later (see Fig. 1). 

Gaussian also predicts dipole moments and higher multipole moments (through hexadecapole). The dipole moment is the first derivative of the energy with respect to an applied electric field. It is a measure of the asymmetry in the molecular charge distribution, and is given as a vector in three dimensions. For Hartree-Fock calculations, this is equivalent to the expectation value of X, Y, and Z, which are the quantities reported in the output. 

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