Data analyses

The analysis procedure (Machi et al. 1997) used to convert the measured yield to hydrogen concentration takes into account the energy loss of the incident projectile ion beam in the target, the scattering of hydrogen at a depth X by the projectile ion, and the energy loss of the ejected hydrogen in the foils in front of the detector. 

The yield of the detected recoils Y x) in a detector solid angle df (originating from depth x) during an irradiation of a sample of thickness Ax by N incident ions, is given by 

The analysis of the experimental results is typically performed by fitting a model function S(t) to the time traces recorded at various probe wavelengths [3, 31]. 

I 4 Femtosecond Pump-Probe Spectroscopy of Photoinduced Tautomerism 

The function consists of a transmission decrease Sgg (t) at time zero due to ESA and a transmission increase Sgj(t) which rises in a step-like manner with a small delay and reflects the onset of the product emission. The total transient signal is convoluted with a Gaussian cross correlation CC(t). 

The ESA sets in with a step at time zero modeled by the Heavyside function 

2 Data Analysis - Simple protocols have been reported for correcting commercial spectrofluorimeters and for biasing against the inner filter effect. Various ways, such as log-normal, three-dimensional, or reciprocal-space, have been outlined that allow presentation of luminescence spectra so as to better illustrate particular features of interest. An analysis of the transient 

A treatment for analysing the excitation and fluorescence multiwavelength polarized decay surfaces has been given for the case of a mixture of noninteracting species. An improved model for analysis of fluorescence anisotropy measurements has been presented. Limitations to the use of intense excitation pulses in fluorescence and thermal lens spectrophotometers are discussed in terms of optical saturation. Such artefacts can be eliminated by reference to the fluorescence quantum yield of Rhodamine 6G. A model has been given to describe spectral diffusion in time-resolved hole-burning spectroscopy.  

Chemistry in Microtime Selected Writings on Flash Photolysis, Free Radicals, and the Excited State ed. G. Porter, Imperial College Press, London, 1996. 

Pandey, M. K. Ghorai, and S, Hajra, Pure Appl Chem., 1996,68, 652. 

Smirnov, C. Braun, S. Ankner-Mylon, K. Grzeskowiak, S. Greenfield, and M. R. Wasielewski, Mol Cryst. Liq. Cryst. Technol, Sect. A, 1996,283,243. 

5 Data Analysis. - The vocabulary and principles used in stable isotope tracer studies have been reviewed.  

A network model of ATP free energy metabolism in muscle consisting of actomyosin ATPase, sarcoplasmic reticulum Ca -ATPase and mitochondria has been developed. The model was used to analyse ATP metabolic flux and cytosolic ATP/ADP steady state at six contraction frequencies between 0 and 2 Hz measured in the forearm flexor muscle using P NMR.  

Several studies have presented analyses of resonance 

XAi and XBi data of group A and B, respectively niA and ms mean of the respective values ua and nn number of data of the respective groups F degree of freedom 

Prerequisite for the t-test is a normal distribution of data, i.e., the frequencies of data with the same deviation from mean forms a bell-shaped curve. In case of a large number of experimentally obtained data, mostly a Gaussian distribution is given. 

In practice, P is given as a threshold for statistical significance and a low P is read as more significant than a higher value. In a strong sense, this definition is not correct, but this interpretation is common usage. Table 9.2 gives P values and their explanation as found very often in scientific literature. 

Armitage P, Berry G, Matthews JNS (2002) Statistical methods in medical 

Dawson BD, Trapp RG (2000) Basic and clinical biostatistics. Appleton and 

In processing LIBS data, one must ensure that the effects described in Section 9.3.7 are minimized or avoided. 

Currently available software enables the accumulation of spectra from an arbitrary number of laser shots with an arbitrary number of successive repetitions. This mode of operation is specially suitable for depth profile analysis. By way of example, in order to determine two components in a depth profiling study, a series of pulses are accumulated by maintaining a constant laser fluence. The experimentally measured intensities of the lines selected for the two elements are normalized to their maximum values to account for the difference in oscillator strength of the lines. Such values are then normalized to the sum of the intensities of both elements. Normalization to the combined intensities is equivalent to normalization to the ablated mass. This procedure is unsuitable for the lower layers of a sandwich close to the substrate, for which normalization should also include the line intensity for the substrate element. 

The analysis of the data obtained aims at extracting information on the local neighbours of the stimulated atom, namely the number, distance and type of neighbours. 

The EXAFS interference expressed in terms of the fractional modula- 

This is known as the plane wave approximation, i.e. the electron wave is approximated by a plane wave. The latter is only applicable when the radius of the emitting atom is small in comparison to the curvature of the outgoing wave which is the case when the photoelectron energy is high. A more accurate description, often known as exact curved wave theory has been given by Lee and Pendiy (1975). For a review of the theories and procedures see Gurman (1990). 

The Nj are the number of scattering atoms at distance Rj in the th shell of atoms and are the parameters of main investigative interest. 

The steps involved in obtaining the Nj, Rj and phase shift data are follows  

For each measurement, the data consist of a series of FITS files. Each FITS file consist of a series of CCD camera frames corresponding to the sampled optical path lengths for a given baseline separation and rotation of the scene and the metrology data for each delay line position. The delay line moves approximate increments of 

The best way to understand how the data is structured is looking at actual data. One of the first data sets obtained by WIIT with CHIP as the scene projector on June 2012 measured a 5 x 5 point sources array. The baseline separations range from 30 to 220 mm with 10 mm steps. For each baseline separation the CHIP scene is rotated to simulate the rotation of the sky and span the Mv-coverage. For example, for a baseline separation of 30 mm the rotations of the scene are 0,45,90 —45 and —90°. As the centre of the baseline is aligned with the centre of the source scene, a rotation of 90° is equivalent to a rotation of -90°. For longer baselines, smaller rotation steps need to be recorded for a better coverage of the scene, i.e. for a 220 mm baseline 35 different rotations are recorded. 

To correct the background illumination Mathematical Morphology (Serra 1983) techniques are applied. Mathematical Morphology was bom in 1964 from the collaborative work of Georges Matheron and Jean Serra, at the Ecole des Mines de Paris, France. It provides an approach to the processing of digital images which is based on shape. 

Once the data has been cleaned a study of the interferogram can be performed. However, the first step consist in the reduction of the noise of the interferograms. To do this, a 3 X 3 binning is performed so the signal-to-noise ratio is increased. In this situation the loss of resolution is not an issue as we are not trying to resolve point source next to each other. 

Currently the possible factors for this disagreement are being studied, but it seems there might be a malposition of the re-focusing lens system previous to the CCD camera. In any case, this disagreement on the WIIT plate scale is not relevant to the visibility analysis. 

We are now ready to analyze the data. This is done in several distinct stages, the first of which is data reduction. This is the process of extracting the intensities from the raw measured data, i.e. integrating the reflection intensity over a certain angle region on the detector. A reflection is, of course, not an exact point but has some width, due to experimental imprecision such as beam divergence as well as atom alignment in the 

In principle, it should now be possible to construct a map of electron density within the cell from a set of X-ray structure factors - but there is a major stumbling block. The structure factors are not just numbers but are complex quantities corresponding to sums of wave motions, and therefore have both amplitudes and phases (Eqs 10.8-10.10). All detectors measure intensities integrated over a period of time, so aU we can obtain are the moduli of the structure factors, Ffj i. The so-called crystallographic phase problem is therefore to deduce the phases of the structure factors, as well as the amplitudes. If we manage to do this, we have solved the structure. Note that the term structure solution is used specifically to describe the initial approximate identification of the atom positions within the unit cell, and is distinct from the subsequent refinement of those positions. 

The Patterson method has now been largely replaced with a more powerful technique known as direct methods [32]. This is based on two fundamental physical principles. First, the electron density in the unit cell cannot be negative at any point, and so the large majority of possible sets of values for the phases of the various structure factors are not allowed. Secondly, the electron density in the cell is not randomly distributed, but is mainly concentrated in small volumes, which we identify as atoms. A consequence of these two principles is that certain theoretical probability relationships will exist between the phases of some sets of reflections (usually groups of three) that have particular combinations of Miller indices. It is therefore possible to assign probable phases to some reflections (usually the most intense ones), and then the positions of some or all of the heaviest atoms can be located. 

Once the positions of some atoms have been determined, by whatever method, the phase of every reflection can be calculated. Of course, all this hard work is usually done by powerful software packages, some of them automated to the extent that space-group determination, structure solution by direct methods and atom assignment is all done in one go. The user is provided with a three-dimensional picture, which often is close to the final structure. 

Once we know the phases, we can also calculate the electron density at each point (x, y, z) of a grid in the asymmetrie unit using Eq. 10.12. We return to this in Section 10.9. 

In most cases, the statistical error is not a good estimate of the real precision of the data and a much better estimate is obtained by calculating the variance over the 

For weak reflections, the variance is dominated by the statistical error, but for strong reflections, the systematic errors become the most important For such strong reflections, different sets of equivalent reflections should have a similar relative variance. The average, relative variance of strong reflections describes the overall systematic error of the data. A criterion for strong is to require Fj) to be at least twice the statistical error. Then 

Since e can be assumed to be a property of the entire data set, it will also apply to reflections that have been measured only once. A good estimate of the error of each nonequivalent reflection is now obtained by taking the square sum of the statistical error and the systematic error as represented by e 

Using this averaging procedure, the full list of structure factors derived from all scans in an experiment is reduced to a list of nonequivalent reflections with appropriate error bars. In bulk crystallography, one often uses a so-called J -factor (reliability factor) to describe the average discrepancy of symmetry-equivalent reflections 

This factor ignores the error bars of the data. 

In this section we focus on the three main types of ideal reactors BR, CSTR, and PFR. Laboratory data are usually in the form of concentrations or partial pressures versus batch time (batch reactors), concentrations or partial pressures versus distance from reactor inlet or residence time (PFR), or rates versus residence time (CSTR). Rates can also be calculated from batch and PFR data by differentiating the concentration versus time or distance data, usually by numerical curve fitting first. It follows that a general classification of experimental methods is based on whether the data measure rates directly (differential or direct method) or indirectly (integral of indirect method). Table 7-13 shows the pros and cons of these methods. 

Some simple reaction kinetics are amenable to analytical solutions and graphical linearized analysis to calculate the kinetic parameters from rate data. More complex systems require numerical solution of nonlinear systems of differential and algebraic equations coupled with nonlinear parameter estimation or regression methods. 

Differential Data Analysis As indicated above, the rates can be obtained either directly from differential CSTR data or by differentiation of integral data. A common way of evaluating the kinetic parameters is by rearrangement of the rate equation, to make it linear in parameters (or some transformation of parameters) where possible. For instance, using the simple nth-order reaction in Eq. (7-165) as an example, taking the natural logarithm of both sides of the equation results in a linear relationship Between the variables In r, 1/T, and In C  

Multilinear regression can be used to find the constants k0, E, and n. For constant-temperature (isothermal) data, Eq. (7-167) can be simplified by using the Arrhenius form as 

The preexponential k0 and activation energy E can be obtained from multiple isothermal data sets at different temperatures by using the linearized form of the Arrhenius equation 

This section first considers the general features of data analysis software and future trends in this area. Then we focus on analysis of transient strain or stress tests, particularly sinusoidal oscillations. We will apply this analysis to data from rotational rheometers, but some of the strategies are also applicable to pressure-driven shear rheometers and extensional rheometers described in the following sections. 

The rest of the test will be automatic. Every 30 seconds the control computer will translate each desired shear rate to an angular velocity set point for the circuit that controls the motor speed. The tachometer sends back the true velocity, which the software uses with eq.5.3.11 to calculate the shear rate. In some instruments the software may make corrections for wide gap using data from the preceding low shear rates (eq.S.3.24). The voltage from the torque transducer is typically averaged over several seconds, then converted to shear stress with eq 5.3.8. scosity is calculated and plotted versus shear rate as the test is running. 

Such types of analysis and control will probably be the greatest area for innovation in future rheometer design. Fitting of con- 

Methods for measuring G (a) wave speed, (b) resonance, and (c) forced oscillations. AT is a geometry constant free. 

The most commonly measured viscoelastic material function is G (a), T). It is so popular because sinusoidal oscillations can be used to follow viscoelastic changes with time, such as during curing and ciystallization. As discussed below, cross-correlation analysis of the signal can provide accurate G and G values over a wide range of frequency and signal levels. 

Spectroscopic data obtained from spectroelectrochemical experiments require careful and case-specific analysis. The Fe /Fe redox couple has a unique role in diflferent iron-containing proteins. It is hypothesised that the mammalian iron-transport protein transferrin uses the Fe /Fe redox couple as a switch that controls the time and site-specific release of iron, while other iron-containing proteins, such as myoglobin, are able to hold on to iron in both oxidation states. Therefore, it is very important to evaluate the protein and its interaction with both the oxidised and reduced states of iron and accordingly develop a data-analysis model. The spectroelectrochemical response of an iron binding protein can be ideal Nernstian, non-Nernstian resulting from coupled 

After a successful conversion of the raw data in (he filial x(k) function, the last step of daia analysis consists of the determination of the struc dual parameters rJ% N - and a,. To do (his, one dies by variation of these parameters according to equation (10.4), to describe (he experimental y(A) function optimally with a minimal basis set. i.e. preferably few baekscatierers. Frequently, the experimental EXaFS function is. however, first dismantled by means of the Fourier filtering  

At this point it must be noted that the backseat-tering amplitudes of neighbouring elements in the 

In both pulse and phase fluorometries, the most widely used method of data analysis is based on a nonlinear least-squares method. The basic principle of this method is to minimize a quantity which expresses the mismatch between data and fitted function. This quantity is the reduced chisquare defined as the weighted sum of the squares of the deviations of the experimental response R(t ) from the calculated ones 

In the single-photon timing technique, the statistics obeys the Poisson distribution and the expected deviation o-(i) is approximated to so that Eq. (7.9) be- 

In phase fluorometry, no deconvolution is required curve fitting is indeed performed in the frequency domain, i.e. directly using the variations of the phase shift C and the modulation ratio M as functions of the modulation frequency. Phase data and modulation data can be analyzed separately, or simultaneously. In the latter case the reduced chi-squared is given by 

In addition to the value of/, it is useful to display graphical tests. The most important of them is the plot of the weighted residuals defined as 

In some cases, a distribution of decay times best describes the observed phenomena. The recovery of such distributions is very difficult. The data can be analyzed either by methods that do not require an a priori assumption of the distribution shape [17, 18], or by using a mathematical function describing the distribution [19]. 

Peak heights of calibration standards, measured fi om the LOCC baseline, are used for calibration the best fit line is found by linear regression analysis. Peak measurement using an integrator and/or suitable computer software is an alternative method for calibrating the instrument. 

Usually, we measure a set of ac impedance data in a wide frequency range. But only two constant values, and Q, are used in the analysis. This means that a large part of ac impedance data, which may include a considerable amount of information about the interfacial kinetics, is unused. 

These problems are resolved by a refined method proposed by Gaigalas [73-75]. The same proposal was described later by Yamada and Finklea and coworkers [21, 71, 72]. 

The refinements described here are all incorporated into the analysis described in the next section. 

While this is not the place for a complete description of the theory, uses, and ramihcations of all possible processing treatments that can be applied to chemical imaging data, the majority of NIR chemical images recorded to date have been obtained from solid or powder samples, measured predominantly by diffuse reflectance. As such, the following discussions may serve as a general outline of the more common procedures and their applications to these types of imaging data. 

These sketches serve to illustrate that there is structure in the photopeak which can yield information, albeit with relatively low resolution, on the details of electronic structure. Analysis routines have been developed which take account of the detailed shape of the peak, with a view to maximising the amount of information obtained in Doppler broadening experiments (see, e.g., [31]). We shall later that by decreasing background significantly, detailed analysis of the peak shape can yield considerable fruit. 

For the moment we shall consider the standard method for describing the Doppler-broadened linewidth—i.e. by using a simple lineshape parameter. By far the most common parameters used—called S and W—are defined 

Neither S nor IF have absolute values (they are arbitrarily chosen to be 0.5 and 0.25, although these figures are not necessarily optimum). However, it is becoming more common to endeavour to express the parameters in reduced form, e.g. S/Sbuiki where is the parameter associated with the defect-free bulk material being studied, measured with the same apparatus— especially in the case of Si. 

The choice of which parameter to use, and the limits of regions A to E, should be investigated first for each system studied. The figure of merit here is the difference between S (W) and Sbuik ( buik), expressed as a number of statistical standard deviations. 

If Sf and Wt are the S and W parameter characteristic of free positrons, then we can define a new parameter R, = 1(5—Sf)/(W—Wt), which depends only on the nature of the defect, and not on its concentration. If R is found to be constant then this points to the existence of only one kind of defect [32], 

2D chromatograms were prepared by loading total ion current (TIC) data from each reversed-phase chromatogram from MassLynx onto the data analysis software 

It is sometimes difficult to totally remove (by the emission monochromator and appropriate filters) the light scattered by turbid solutions or solid samples. A subtraction algorithm can then be used in the data analysis to remove the light scattering contribution. 

While this is not the place for a complete description of the theory, uses, and ramifications of all possible processing treatments that can be applied to chemical 

For two-channel microarrays, conventional wisdom suggests that comparisons of greatest interest should be paired on the same microarray. Table 9 shows examples of the different microarray designs, and when these scenarios may be appropriate. 

Normalization attempts to remove technical variation in the data that is not attributed to biological or treatment related variation. Examples of technical variation include differences in dye incorporation, physical differences in fluorescence efficiency of incorporated dyes, print-surface irregularities, and print- 

Microarray data may require transformation to stabilize the variance by applying a global logarithmic transformation prior to normalization and further analysis. This may unpredictably skew the measurement, making further analysis difficult and unreliable (39). As many of the techniques used for the analysis of microarray data are not robust to the equal variance assumption, a family of variance stabilizing transformation (VST) methods for microarray data have been proposed (4CM14). 

For dose-response studies the Reference can be either pooled vehicle samples or a pool of all samples. In the latter case, one of the Dn samples would represent a vehicle sample For a population comparisons the Reference should be a pool of all samples 

The depicted time-course experiment would be appropriate if identifying differentially expressed genes at any time-point compared to vehicle and temporal expression changes within treatment (including vehicle) compared to an adjacent time-point Population comparisons can be carried out between parent tumor samples (Tn) and metastases (Vn), as well as between all parent and metastases 

Univariate statistical techniques are not appropriate for multivariate structures. Repeated ANOVAs are not warranted and can even be misleading. 

Multivariate methods are more suitable for the data analysis of multispecies toxicity tests. No one multivariate technique is always best. Given that many responses of multispecies toxicity tests are nonlinear, techniques that do not assume linear relationships may allow a more accurate interpretation of the test system. 

Multivariate techniques that account for variability may be misled by the noisy variables and may miss the important relationships. 

Techniques such as PCA may prevent the discovery of novel patterns. Clustering and other exploratory techniques can lead to the discovery of novel patterns and relationships. 

Do not assume that the combination of variables that are best for determining clusters or treatments on one sampling day will be the most appropriate for every sampling day. As the structure and function of the multispecies toxicity test change over time, so will the important variables. 

The basal dialysate concentrations in the striatum for the experiments were 11.9 0.7 (n = 79) fmol/min. 

When the courses of the curves after s.c. administration of compounds 11, 80, and 12, respectively, are compared it can be seen that the duration of action of the N- -propyl analogues is longer than that of R-(-)-apomorphine. 

General procedures for avoiding tins are discussed later in the chapter. 

Data Analysis Methods for Very Large Numbers OF Variables 

Newer data analysis methods overcome the difficulties that small sample-to-variabies ratios create for traditional statistical methods. These new methods fall into two major categories (1) support-vector classification and regression methods, and (2) feature selection and construction techniques, The former are effectively determined by only a small portion of the training data (sample), while the latter select only a small subset of variables such that the available sample is enough for traditional and newer classification techniques. 

This example and discussion demonstrate that within the framework of SVMs it is possible to build classifiers even when the number of predictors is orders of magnitude larger than the available sample size (something not possible in classical regression-based classifiers) and such classifiers can exhibit very good classification performmce. 

These appfications are only a small sample of a large number of molecular-profiling clinical bioinformatics models that apply advanced computational techniques on mass-throughput data to address questions of prevention. 

Arnaut and S. J. Formosinho, Wiley Ser. Photosci. Photoeng., 1997, 2 (Homogeneous Photocatalysis), 55. 

EverdijandD.A.Wiersma, Femtochem. Femtobiol Ultrafast React. Dynamics. Nobel Symp., 1997, lOl, 488, V. Sundstroem, Imperial College Press, London. 

Malaga, and T. Okada, Pure Appl. Chem., 1997, 69, 797. 

Hammarstroem, T. Norrby, H. Berglund, R. Davydov, M. Andersson, A. Boerje, P. Korall, C. Philouze, M. Almgren, S. Styring, and B. Aakermark, Chem. Commun., 1997,607. 

Rosenbluth, B. Weiss-Lopez, and A. F. Olea, Photochem. Photobiol., 1997, 66, 802. 

1 Sensitivity of an OFET Sensor Gate Voltage Dependence and Contributions of Mobility and Threshold Voltage Changes 

2 Self-Consistent Equation Based on Simple Saturation Current 

When analyte (DMMP for this case) molecules are diffused into the semiconductor active layer, dipoles of the molecules induce changes in /. and Vth, noted as A/, and A Vth, so that the saturation drain current /D,sat(anaiyte) °f the OFET in analyte vapor becomes (7.3)  

FIGURE 15.11 Schematic showing a plan to develop indicators for a given site. 

To reduce the dimensionality of multivariate datasets, PCA or similar ordination methods are commonly used to reduce the number of variables in a dataset with minimal information loss (Wackernagel, 2003). Canonical correlation analysis (CCA) (Goovaerts, 1994 Wackemagel, 2003) is another method suited for multivariate indicator analysis with the aim to analyze relationships between sets of variables. 

Scenario II assumes that indicator variables are collocated, meaning they are sampled at the same sites X , that is, sample sites are shared (isotopic data) (Wackernagel, 2003). A special case arises if an indicator variable of interest (e.g., level III indicator that is difficult to measure, labor-intensive or costly to measure—phosphate sorption index) is known at a few sites and an auxiliary variable known at many sites (e.g., level I indicator that is easy and cheap to measure—total phosphorus). 

Such heterotrophic data are suited to derive predictive models using simple covariance function models (Wackernagel, 2003). Assuming that successful and robust functional relationships are derived, models can be used to predict a target variable (e.g., level 111 indicator variable) at unsampled locations across a wetland(s). The prediction range should match the model range to avoid extrapolations with high uncertainties. 

Demonstration studies of a multivariate approach were presented by Grunwald et al. (2007a), Mitsch et al. (2005), and Kennedy et al. (2006). 

For an ideal photoelectrode, the equivalent circuit can be simplified to a resistor (R) and a capacitor (C) in series. The R represents the resistance of the semiconductor bulk (plus any series resistance from the electrode wires and the electrolyte), and the C represents the capacitance of the space charge region (Csc)- For an ideal system, a plot of 1/C versus electrode potential ( ) yields a straight line. The line is extrapolated to 1/C = 0. The x-intercept equals Eft, + kT/e and the slope is proportional to the charge carrier concentration or doping density (iVoopant), as shown by Eq. (6.2). This equation is obtained by substimting the relevant terms from Eq. (6.1). 

The relative permittivity of the semiconductor (Sj) is often assumed to be 10 because it is usually slightly above or below this value [21, 22]. However, this is dependent on each material. Researchers should consult the literature for values appropriate for their materials. Typical A oopam values for semiconductors are in 

If the M-S plot is not linear over the entire measured potential range, then one can attempt to fit only the linear portion (200 mV range minimum) of the plot to a line. However, accuracy will likely be poor due to the subjectivity in this approach. Some plots may never exhibit a linear portion, as shown in Fig. 6.6. 

The M-S measurement is performed at several different frequencies to verify that the slope and x-intercept do not change. If they do change and/or the M-S plot is not linear, as is the case in Fig. 6.6, then a more detailed analysis using frequencies over multiple decades (e.g. 1 x 10 -1 x 10 Hz) should be used in conjunction with a more sophisticated equivalent circuit model [14, 23]. 

Once the Ffb for each pH is determined, plot the Ffb as a function of pH in order to determine the dependence of the band stmcture on pH as explained previously in section Open-Circuit Potential and pH . 

The ability to measure residual structure and dynamics in weakly structured regions of proteins is one advantage of millisecond HX however, there are additional benefits that arise from making measurements on the same timescale as the rate of chemical exchange. 

Experimental decay curves measured after a pulsed excitation are affected by the limited frequency response of the detection system and the width of the exciting light pulse. Assuming a linear response for all contributions, the measured decay curve / t) is given by the convolution integral 

For lifetime measurements, the typical shape of the true fluorescence decay can be approximated by one or more exponential decay curves. 

Us denotes the relative contribution of the individual terms and their time constants. The additional parameter b accounts for experimental time delays between the excitation pulse and the beginning of the exponential part of the decay curve. The goal of the analysis is the determination of the free parameters a, and b in Eq. (5). This problem was solved [12] by transforming the expansion (5) into Fourier space. The free parameters are then obtained by a nonlinear least-squares fit to H o)) in Fourier space. 

In a SIFT or SIFT-MS flow tube for an analyte A, even though the analyte A is at trace levels, its concentration [A] [H30T and therefore pseudo first order kinetics can be applied. The reaction time t can be defined as the reaction length /, divided by the ion velocity v. In addition to reactive ion loss, there is loss of H3O+ by diffusion. If 3 + is the diffusion coefficient and A the diffusion length (which depends on the flow mbe diameter and length) then the kinetic equation expressing the loss of the reagent ion H3O is [97] 

In the SIFT mode of operation, Eq. (8.47) indicates that the semilogarithmic decay of [H30 (which is proportional to the ion count of / jjjq ) against the reac- 

Provided both the flow rate of analyte gas and concentration of analyte in the gas sample is small, the reduction in the reagent count is also small (a fractional reduction of 10% is required for good quantitation) then the ratio of product ion counts to reagent ion counts gives the analyte concentration in the mixture. Smith and Spanel have shown the analytical solution to the set of differential equations for [AH+] in the limit as [A]=0, to be [98] 

k is the rate coefficient for reaction, the quantities in square brackets are the number densities of the ions and analyte A, t is the reaction time and De is a differential diffusion enhancement coefBcient that accommodates the difference in diffusion rate to the walls between reagent ions and product ions. Ions with larger m/z generally have slower rates of diffusion than smaller ions. Another important factor when using quadrupole mass filters is to account for the reduced transmission of heavier ions. The two opposing effects of diffusion and transmission oppose each other. A proper analysis will account for both effects. 

When multiple product ion channels from an analyte are present in a gas mixture with the product ions represented by Pj, P2, etc., and analyte reactions occur with both the primary HjO reagent ion and its water clusters H3O+.H2O, then [A] is given by [97] 

The amino acid sequence differs for each individual protein. Therefore, protein digestion using a specific protease results in a specific, distinct peptide pattern -the peptide mass fingerprint (PMF) - which is individual for every single protein. 

The PMF data thus obtained are evaluated automatically using search algorithms that compare measured data with theoretically estimated data from protein and DNA databases. The data evaluation is performed using different search programs, which are freely accessible on the Internet, such as Profound (prowl.rockefeUer.edu/profoimd bin/WebProFoimd.exe) [21], 

Mascot (http //www.rnatrixsdence.com/search form select.html) [22], or MSFit (http //prospector.ucsf.edu/) [23]. 

Since the EXAFS region of the XAS spectrum is dominated by single scattering processes, it is much easier for the theoretical understanding of the observed structures and this has been achieved by Sayers et alP They showed that the Fourier transform of an EXAFS spectrum should peak at the distances corresponding to the radial distance of the excited atom to the neighboring coordination shells. 

Interpretation of EXAFS data is normally based on the EXAFS equation  

The XANES signals are much larger than the EXAFS, but the interpretation of XANES is complicated by the fact that there is no simple analytic (or even physical) description of XANES. The main difficulty is that the EXAFS equation breaks down at low k, due to the 1/k term and the increase in the mean-free-path at very low k. Still, there is much chemical information from the XANES region, notably formal valence (very difficult to experimentally determine in a nondestructive way) and coordination environment. For 

As mentioned above, it is possible to extract information about the electronic and geometric environment of absorber atom based on the comparison 

In the study of mercury and selenium interaction, an examination of the energies and shapes of Se K-edge XANES and Hg Em XANES of plasma from 

Marine accidents that have occurred could have been prevented with greater attention to safety. This is particularly true for fishing vessels. Recent inquiries into the losses of fishing 

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Type C requires the most complex data analysis. To illustrate, we have reduced the data of Henty (1964) for the system furfural-benzene-cyclohexane-2,2,4-trimethylpentane. VLB data were used in conjunction with one ternary tie line for each ternary to determine optimum binary parameters for each of the two type-I ternaries cyclohexane-furfural-benzene and 2,2,4-... 

W. Von der Linden Maximum-entropy data analysis. J. Appl. Physics. A. NA60, 1995, pp. 155-165. 

And the end, various results have been compared detected defects (1), non detected defects (2) and errors (3). The following figures illustrate some factors which have been extracted from final data analysis. 

F. CARTIER, L. PARADIS, O. VAILHEN, S. MASTORCHIO NDE data analysis station the CIVA-PACE coupling - Proceedings, COFREND Congress on NDT, Nantes, Sept. 97,pp.887-891. 

The search for Turing patterns led to the introduction of several new types of chemical reactor for studying reaction-diffusion events in feedback systems. Coupled with huge advances in imaging and data analysis capabilities, it is now possible to make detailed quantitative measurements on complex spatiotemporal behaviour. A few of the reactor configurations of interest will be mentioned here. 

Powder diffraction studies with neutrons are perfonned both at nuclear reactors and at spallation sources. In both cases a cylindrical sample is observed by multiple detectors or, in some cases, by a curved, position-sensitive detector. In a powder diffractometer at a reactor, collimators and detectors at many different 20 angles are scaimed over small angular ranges to fill in the pattern. At a spallation source, pulses of neutrons of different wavelengdis strike the sample at different times and detectors at different angles see the entire powder pattern, also at different times. These slightly displaced patterns are then time focused , either by electronic hardware or by software in the subsequent data analysis. 

The above approximation, however, is valid only for dilute solutions and with assemblies of molecules of similar structure. In the event that concentration is high where intemiolecular interactions are very strong, or the system contains a less defined morphology, a different data analysis approach must be taken. One such approach was derived by Debye et al [21]. They have shown tliat for a random two-phase system with sharp boundaries, the correlation fiinction may carry an exponential fomi. 

There are many different data analysis schemes to estimate the structure and molecular parameters of polymers from the neutron scattering data. Herein, we will present several connnon methods for characterizing the scattering profiles, depending only on the applicable q range. These methods, which were derived based on different assumptions, have... 

Saarilahti J and Rauhala E 1992 Interactive personal-computer data analysis of ion backscattering spectra A/uc/. Instrum. Methods B 64 734... 

Bain A D and Duns G J 1994 Simultaneous determination of spin-lattioe (T1) and spin-spin (T2) relaxation times in NMR a robust and faoile method for measuring T2. Optimization and data analysis of the offset-saturation experiment J. Magn. Reson. A 109 56-64... 

Ferrenberg A M and Swendsen R H 1989 Optimized Monte Carlo data analysis Phys. Rev.L 63 1195-8... 

ELECTRAS - web-based data analysis system. The software supports 2x2 different modes of action the modes for expert and novice engineers and the modes for expert and novice computational chemists. htip //www2.chemie.uni-erlangen.de/projects/eDAS/index.himl... 

L. Eriksson, E. Johansson, N. Kettaneh-Wold, S. Wold. Introduction to Multi-and Megavariate Data Analysis using Projection Methods (PCA ai PLS). Umetrics AB, Umea, 1999. 

Chemical data contain information about various characteristics of chemical compounds and a wide spectrum of methods are applied to extract the relevant information from the data sets. Data analysis, however, not only deals with the extraction of primary information from data but also with the generation of secondary... 

This chapter gives a general introduction into the data analysis methodology. 

To enable the application of electronic data analysis methods, the chemical structures have to be coded as vectors see Chapter 8). Thus, a chemical data set consists of data vectors, where each vector, i.e., each data object, represents one chemical structure. 

For example, the objects may be chemical compounds. The individual components of a data vector are called features and may, for example, be molecular descriptors (see Chapter 8) specifying the chemical structure of an object. For statistical data analysis, these objects and features are represented by a matrix X which has a row for each object and a column for each feature. In addition, each object win have one or more properties that are to be investigated, e.g., a biological activity of the structure or a class membership. This property or properties are merged into a matrix Y Thus, the data matrix X contains the independent variables whereas the matrix Ycontains the dependent ones. Figure 9-3 shows a typical multivariate data matrix. 

Sections 9A.2-9A.6 introduce different multivariate data analysis methods, including Multiple Linear Regression (MLR), Principal Component Analysis (PCA), Principal Component Regression (PCR) and Partial Least Squares regression (PLS). 

A detailed description of multivariate data analysis in chemistry is given in Chapter IX, Section 1.2 of the Handbook. 

A first step in a data analysis process is the detection of relationships between variables. This can be achieved through correlation analysis. 

One task of data analysis is to establish a model which quantitatively describes the relationships between data variables and can then be used for prediction. 

For most data analysis applications the first three to five principal components give the predominant part of the variance. 

Tools Electronic Data Analysis Service (ELECTRAS)... 

The electronic data analysis service (ELECTRAS), which was developed at the Com-puter-Chemie-Centrum of the University of Erlangen-Ntlmberg through a project supported by the DFN-Verein and the BMBF, is a web-based application which presents an interface to various kinds of data analysis methods. It offers the methods... 

The data analysis module of ELECTRAS is twofold. One part was designed for general statistical data analysis of numerical data. The second part offers a module For analyzing chemical data. The difference between the two modules is that the module for mere statistics applies the stati.stical methods or rieural networks directly to the input data while the module for chemical data analysis also contains methods for the calculation ol descriptors for chemical structures (cl. Chapter 8) Descriptors, and thus structure codes, are calculated for the input structures and then the statistical methods and neural networks can be applied to the codes. 

Data input for both modules can be done via file upload, whereby the module for mere statistics reads in plain ASCI I files and the module For chemical data analysis takes the chemical structures in the Form of SD-files (cf. Chapter 2) as an input. In... 

Figure )-11 gives an ovemew of the building hloc ks of the ELECTRAS system ELECTRAS was designed for two levels of user experience. The novice part offers a guided data analysis for inexperienced users. Experienced users can analyze their data fast and directly using the expert mode. 

An additional feature of ELECTRAS is a module which provides an introduction to various data analysis techniques One part of this module provides a typical work flow for data analysis. It explains the important steps when conducting a data analysis and describes the output of the data analysis methods. The second part gives a description of the methods offered. This modvJe can be used both as a guideline for novice users and as a reference for experts. 

SONNIA is a self-organizing neural network for data analysis and visualization. 

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