MATLAB correlation

In all cases we have used mean spectrum as reference spectrum (other references were tested no reference, first spectrum, last spectrum but the mean spectrum is the one giving the better results). All calculations were made under Matlab 6.5 with home made functions based on Noda s theories. The negative correlations are shaded in all the two-dimensional plots. 

Throughout this book, we have seen that when more than one species is involved in a process or when energy balances are required, several balance equations must be derived and solved simultaneously. For steady-state systems the equations are algebraic, but when the systems are transient, simultaneous differential equations must be solved. For the simplest systems, analytical solutions may be obtained by hand, but more commonly numerical solutions are required. Software packages that solve general systems of ordinary differential equations— such as Mathematica , Maple , Matlab , TK-Solver , Polymath , and EZ-Solve —are readily obtained for most computers. Other software packages have been designed specifically to simulate transient chemical processes. Some of these dynamic process simulators run in conjunction with the steady-state flowsheet simulators mentioned in Chapter 10 (e.g.. SPEEDUP, which runs with Aspen Plus, and a dynamic component of HYSYS ) and so have access to physical property databases and thermodynamic correlations. 

If the parameters enter the equation linearly, then the minimization problem reduces to a set of linear equations which are solved easily by Excel and MATLAB. The effectiveness of the curve fit is often reported as values of the linear correlation coefficient squared, r. The linear correlation coefficient is defined as (Press et al., 1986, p. 484) ... 

Hydrolysis and fermentation models were developed using two hydrolysis datasets and two SSF datasets and by using modified Michaelis-Menten and Monod-type kinetics. Validation experiments made to represent typical kitchen waste correlated well with both models. The models were generated in Matlab Simulink and represent a simple method for implementing ODE system solvers and parameter estimation tools. These types of visual dynamic models may be useful for applying kinetic or linear-based metabolic engineering of bioconversion processes in the future. 

PLS (Partial Least Squares) regression was used for quantification and classification of aristeromycin and neplanocin A (Figure 4). Matlab was used for PCA (Principal Components Analysis) (according to the NIPALS algorithm) to identify correlations amongst the variables from the 882 wavenumbers and reduce the number of inputs for Discriminant Function Analysis (DFA) (first 15 PCA scores used) (Figure 5). 

Cross-correlation and spectral analysis have proven invaluable tools for quantifying the frequency dependent characteristics of the human subject. The cross-spectral density function, or cross-spectrum Sxyif), can be obtained from the random target x t) and random response y t) by taking the Fourier transform of the cross-correlation function Vxyir), that is, Sxyif) = Ffr yfr), or in the frequency domain via Sxy if) = X(/) y(/), or by a nonparametric system identification approach (e.g., spa.m in Matlab ). The cross-spectrum provides estimates of the relative amphtude (i.e., gain) and phase-lag at each frequency. Gain, phase, and remnant frequency response curves provide objective measures of pursuit... 

It was interesting to see that both ER and ACE techniques show good correlations with the measured results of the vertical load over the samples. Noises in the frequencies out of 2-20kHz were cut by means of a butterfly filter. ACE and ER data had the noise amplimde of 0.21 0.3dB and l 0.5m 3 respectively. At last, a threshold of IdB and 3mQ were defined as minimum ACE and ER variations. The hits(events) were then saved into MATLAB objects whenever a change higher than noise levels was observed in each of load, ACE amplitudes or ER values. Figure 9 and 10 show an example of data captured by acquisition systems. 

The artificial crack was allowed to propagate for 150,000 cycles. During the test, a Matlab function, based on the correlation between crack tip position and the minimum of the BPS distribution obtained by FE analyses, evaluated the position of the crack tip. The propagation of the crack was also monitored by means of an optical microscope. 

A time series plot of the mean summer temperature is shown in Fig. 5.1. In this example, the autocorrelation of the mean summer temperature will be determined. Also, the cross-correlation between the mean summer temperature and the mean spring temperature will be examined. The methods used to compute these plots can be found in either Chap. 7 for MATLAB or Chap. 8 for Excel . 

There are many factors that can affect the reduced value of fluence rate from (1278.1 mW.mm ) at (0.02 mm) to (890.84 mW.mm ) at (0.08 mm). The amounts of light in the diffusion region are decreased and converted to scattered photons and absorbed photons because the transition photons from the stratum corneum to the epidermis were chromophore dependence and skin depth dependence. The part of fig 2b represents a fitting curve that was not linearly but an exponential relation. The correlation coefficients were 0.97 to 0.98 for all curves. Curve fitting by MATLAB software was used to estimate the transmission through epidermis and to calculate the photodynamic dose per penetration depth of skin. 

Methods 1 and 2 are based on simple transfer function models and will be considered in Section 12.2. The controller tuning relations of Method 3 are analytical expressions and correlations for the PID controller settings. They are considered in Section 12.3. Design techniques based on frequency response analysis (Method 4) are the subject of Chapter 14. Computer simulation of the controlled process (Method 5) can provide considerable insight into dynamic behavior and control system performance. In particular, software such as MATLAB and Lab VIEW facilitates the comparison of alternative control strategies and different controller settings. (See Appendices C and E of Doyle (2000).) Method 6, on-line tuning, is considered in Section 12.5. 

A related technique is to cross-correlate waveforms from all events in a catalog against each other, to discover all event families. The MATLAB toolbox GISMO includes tools to automate this process. During unrest at Redoubt Volcano in 2009, this was used in near real time to monitor the evolution of swarms (Buurman et al. 2012) (Fig. 9). 

In MATLAB, the built-in function corrcoef x,y) calculates the matrix of the correlation coefficients of the vectors of the same length x andj fEq. (7.34)]. If a is a matrix where each row is an observation and each column a variable, corrcoef(x) also returns the correlation coefficients matrix. 

Numerical Methods for Chemical Engineers Using Excel , VBA, and MATLAB 7.3.2 Correlation Coefficient... 

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