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Instead of being derivatives, the bisectrices of the factor pairs have become the central concepts This play of musical chairs comes about because of the closer association of the central vectors with p, which entitles them to their position In passing, the model resolves the uneasiness of inserting orthogonal axes into an essentially oblique structure; it rigorously de nes oblique axes without giving up the convenience of an orthogonal base The only price is that the number of musical chairs has to be increased, from four dimensions onward: There are n(n 1)/2 central vectors, with n the number of dimensions or factors However, that extension will be welcomed by those who have always wondered whether ve is all there is The model has shaken off the last remnants of simple-structure thinking Parenthetically, I note that the model is equally appropriate in other domains, notably, intelligence.

With four dimensions, the rotated factors are at an angle of 60 deg with respect to the p factor; the central model vectors are at 45 deg from that pivot With ve dimensions, the factors are at 634 deg, and the central vectors are at 507 deg Still, the model rotation maximizes the sum of the correlations of the central axes with p, and in that sense minimizes their average neutralness Conversely, any other orthogonal.

When the program was run, it would output an image like Figure 5-9.

Note that when p is close to 1 and when the noise variance is relatively small, D1 u DZ M 0. Likewise, when p is relatively small, we get D1 % I. :

Sardinas Patterson test for unique decodability. A code is not uniquely decodable if and only if there exists a nite sequence of code symbols which can be resolved into sequences of codewords in two different ways. That is, a situation such as

interpolation is itself a fascinating and important topic, most of which is unfortunately beyond the scope of this text. Interpolation in the presence of noise and balanced analysis of computational complexity and image delity are particularly important considerations. See Refs. 234 and 230 for relatively recent overviews. While the primary focus of this text is on image capture system design, over the next several chapters we regularly return to joint design of optical coding, sampling, and signal interpolation. For the present purposes, it is most important to understand that postmeasurement interpolation is necessary, natural, and powerful. While optical imaging systems are always bandlimited, undersampling relative to the optical Nyquist limit is common in digital imaging systems. One may well ask whether our analysis of Shannon interpolation applies in undersampled systems. The short answer is Yes. Undersampling aliases signals into the reconstructed bandwidth but does not reduce the MTF. This is illustrated in Fig. 7.8, which shows sample data and the reconstructed signal for various phase shifts for a signal at uo 1.5 Nyquist. As expected, the signal reconstructs faithfully the aliased signal corresponding to the frequency 20.5 Nyquist. While mindful of the fact that the ideal display image is interpolated from measurement data, we nd direct visualization of the measured data suf cient in

example, Zautra et al (1999) found that FM patients used more avoidant strategies than their OA counterparts Despite the evidence for an association between active coping and favorable outcomes in individuals with RA and OA, studies focusing on individuals with FM have yielded con icting results In individuals with FM, increases in both passive and active coping have been associated with depression (Nicassio, Schoenfeld-Smith, Radojevic, & Schuman, 1995), and more coping effort was associated with increased physical disability, although less psychological disability (Martin et al, 1996) These results suggest that coping responses which may be adaptive in some conditions (RA and OA) may actually be maladaptive in another (FM) For instance, in conditions such as OA, where pain is somewhat predictable and controllable, active coping processes may reduce pain symptoms As a result, an individual may experience increased feelings of self-esteem and self-ef cacy, and subsequently less depression.

In contrast, when pain is experienced in spite of active coping responses, as in FM, these coping responses may be interpreted as failures to affect pain, resulting in decreased self-ef cacy and increased feelings of helplessness and depression Thus, the adaptiveness of speci c coping responses may be in uenced by symptom characteristics unique to each disorder Social Stress Factors In addition to the data highlighting the psychological aspects of stress, there is mounting evidence that social stressors are particularly stressful for patients coping with chronic illnesses Family con ict has been associated with poor psychological adjustment to RA (Manne & Zautra, 1989) Indeed, patients with chronic illness may be more sensitive than their healthy counterparts to interpersonal con ict with individuals who are major sources of support, such as family and close friends (Revenson, Schiaf no, Majerovitz, & Gibofsky, 1991).