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determining the distance from all observations to these new group centers. If an observation is closer to the center of another group, it is moved to the group it is closest to. The centers of its old and new groups are now recalculated. The process of comparing and moving observations where appropriate is repeated until there is no further need to move any observations. To illustrate the process of clustering using k-means, a set of 11 hypothetical observations are used: a, b, c, d, e, f, g, h, i, j. These observations are shown as colored circles in Figure 6.21. It had been determined from the start that three groups should be generated. Initially, an observation is randomly assigned to each of the

Figure 7.2 We can predict our own movements better than those of other people This gure shows the number 2 and semi-circle in the author s appalling handwriting. If you watched the movements of the pen, would you be able to predict whether the stroke was going to finish as a 2 or a semi-circle You can predict very well, but only if what you are watching is a recording of your own handwriting movements. Source: Redrawn after: Knoblich, G., Seigerschmidt, E., Flach, R., & Prinz, W. (2002). Authorship effects in the prediction of handwriting strokes: Evidence for action simulation during action perception. Quarterly Journal of Experimental Psychology, Section A, 55(3), 1027 1046.

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Various aspects of the instrumentation used in infrared spectroscopy were dealt with in this chapter. Traditional dispersive spectrometers were described. The operation and capabilities of Fourier-transform infrared spectrometers were also discussed. Transmission methods for obtaining infrared spectra were also examined. The sampling methods which can be used for solids, solutions, liquids and gases were presented. The different re ectance methods that are now widely available, such as ATR spectroscopy, specular re ectance and diffuse re ectance, along with photoacoustic spectroscopy, were also introduced. The various microsampling techniques, which have emerged as effective methods for investigating small quantities of complex samples, were also described. Infrared spectrometers can also be used in conjunction with other analytical methods such as chromatography and thermal techniques and these were introduced in this chapter.

In recent years, infrared spectroscopy has emerged as a powerful tool for characterizing tissue and disease diagnosis [9, 14, 31 38]. The pressure-dependence on parameters such as wavenumber, intensity and bandshape may provide further information about the structural changes associated with malignancy. For example, it is possible to detect cervical cancer arising from a pre-malignant state termed dysplasia by using infrared band differences among normal, dysplastic and malignant cervical cells [39]. A study of the pressure-dependence of the wavenumbers of bands indicates that there are extensive changes in the degree of hydrogen bonding of phosphodiester groups of nucleic acids and the C OH groups of proteins. Pressure studies also indicate changes in the degree of disorder of methylene chains of lipids in the malignant tissue. The infrared spectra of tissue samples with dysplasia demonstrate the same changes to a lesser degree than those observed for the cancer samples. Figure 7.11 shows the pressuredependence of the CH2 bending mode wavenumber of the methylene chain of lipids for both normal and malignant tissue. Pressure increases this wavenumber because it induces ordering of the methylene chains in the lipid bilayers, thus increasing inter-chain interactions. In malignant cervical tissue, pressure induces a smaller shift in the wavenumber of this mode when compared with normal tissue. The difference indicates that in cervical cancer the methylene chains of lipids are more disordered than in normal cervical tissue.

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Let A0 fx ; fy ; f d be the angular spectrum of U 0 x2 ; y2 ; f d . Provided that the Fresnel approximation is valid for the distance d, the angular spectrum of the wave eld at the focal plane is given by A xf ; yf ; f A0 fx ; fy ; f d e j 2d xf yf

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