Time series approach

W.Y. Goh, C.P. Lim, and K.K. Peh, Predicting drug dissolution profiles with an ensemble of boosted neural networks A time series approach, IEEE T. Neural Networ., 14 (2), 459-463,... 

As discussed in Chapter 4, there are three ways of looking at forecasts the qualitative approach, the mathematical or time series approach, and the causal approach. In reality, all three are interlinked and should be taken into account when determining a forecasted demand figure. 

Table 7.1 presents us with something of a dilemma. We would obviously desire to explore i much of the phase space as possible but this may be compromised by the need for a sma time step. One possible approach is to use a multiple time step method. The underlyir rationale is that certain interactions evolve more rapidly with rime than other interaction The twin-range method (Section 6.7.1) is a crude type of multiple time step approach, i that interactions involving atoms between the lower and upper cutoff distance remai constant and change only when the neighbour list is updated. However, this approac can lead to an accumulation of numerical errors in calculated properties. A more soph sticated approach is to approximate the forces due to these atoms using a Taylor seri< expansion [Streett et al. 1978] ... 

The positive results obtained at production scale give us confidence in the validity of our approach. Derivation of a simple scaling factor enabled us to conduct a series of experiments in a small pilot plant which would have been expensive and time-consuming on a production scale. Time series analysis not only provided us with estimates of the process gain, dead time and the process time constants, but also yielded an empirical transfer function which is process-specific, not one based on... 

Numeric-symbolic approaches are particularly important in process applications because the time series of data is by far the dominant form of input data, and they are the methods of choice if annotated data exist to develop the interpretation system. With complete dependence on the annotated data to develop the feature mapping step, numeric-symbolic mappers can be used to assign labels directly. However, as the amount and coverage of available annotated data diminishes for the given label of interest, there is a need to integrate numeric-symbolic approaches with... 

In a series of more advanced studies, this problem was partially addressed by systematically adjusting a limited number of internal coordinates (bond lengths, valence angles, and torsion angles) to find the geometry of metal chelates with the lowest energy t5-81. However, due to the computational limitations of the time, the approach was limited in that only a small number of internal coordinates could be adjusted simulta-... 

In order to calculate the absorption spectrum in the time-independent approach one solves the time-independent Schrodinger equation for a series of total energies and evaluates the overlap of the total continuum wavefunction, defined in (2.70), with the bound wavefunction of the parent molecule, ( tot(E) Pio I o(Ei)). Any structures in the spectrum are thus related to the energy dependence of the stationary wavefunction "Jftot(E). As illustrated schematically in Figure 7.4 for the one-... 

Stochastic modeling is used when a measurable output is available but the inputs or causes are unknown or cannot be described in a simple fashion. The black-box approach is used. The model is determined from past input and output data. An example is the description of incomplete mixing in a stirred tank reactor, which is done in terms of contributions of dead zones and short circuiting. In these cases, a sequence of output called a time series is known, but the inputs or causes are numerous and not known in addition, they may be unobservable. Though the causes for the response of the system are unknown, the development of a model is important to gain understanding of the process, which may be used for future planning. 

To analyze the spectral composition of the pressure variations in more detail we have made use of a wavelet approach [9]. This approach, which allows us to determine instantaneous values of the frequencies and amplitudes of the various oscillatory components, is particularly useful for biological time series that often are neither homogeneous nor stationary. 

It may appear that Table 1 contains an essentially complete summary of patterns that may form in electrochemical systems. This impression is misleading, since Table 1 only roughly summarizes results observed so far or predicted with models. These are investigations concentrating on phenomena that can be described with two essential variables (two-component systems). This survey is certainly not yet completed. Furthermore, numerous examples of current or potential oscillations involve complex time series. Only in a few cases does the complex time series result from the spatial patterns. In most cases, the additional degree of freedom will be from a third dependent variable, such as from a concentration that adds an additional feedback loop into the system, as discussed in Section 3.1.3. Spatial pattern formation in three-variable systems is an area that currently develops strongly in nonlinear dynamics. In the electrochemical context, the problem of pattern formation in three-variable systems has not yet been approached. 

Sensitivity of choices NA If a different assumption or approach is selected (e.g. time series versus steady state), the results will change... 

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