Unipolar axis

Fig. 31.3. (a,b) Reproduction of distances D and angular distances 0 in a score plot (a = 1) or loading plot (p = 1) in the common factor-space (c,d) Unipolar axis through the representation of a row or column and through the origin 0 of space. Reproduction of the data X is obtained by perpendicular projection of the column- or row-pattern upon the unipolar axis (a + P = 1). (e,0 Bipolar axis through the representation of two rows or two columns. Reproduction of differences (contrasts) in the data X is obtained by perpendicular projection of the column- or row-pattern upon the bipolar axis (a + P = 1). 

Figure 31.4 shows the biplot of the trace elements and wind directions for the case when a = p = 0.5. Since here we have that a + P equals 1, we can reconstruct the values in the columns of the data table X by means of perpendicular projections upon unipolar axes. In Fig. 31.4a we have drawn a unipolar axis through Cl. Perpendicular projection of the four wind directions upon this axis reconstructs the order of the concentrations of Cl at the four wind directions as listed in Table 31.1. Now we have established a way which leads back from the graphic display to the tabulated data. This interpretation of the biplot emphasizes the one-to-one relationship between the data and the plot. Such a relationship is also inherent in the ordinary bivariate (or Cartesian) diagram. 

Fig. 31.4. (a) Biplot in which the concentrations of an atmospheric trace element (Cl) are reconstructed by perpendicular projection upon a unipolar axis, (b) Biplot in which the differences (contrasts) between two atmospheric trace elements (Cl, Si) are reproduced by perpendicular projection upon a bipolar axis. 

There are two outstanding poles on this biplot. DMSO and dimethylchloride are at a large distance from the origin and from one another. These poles are the most likely candidates for the construction of unipolar axes. As has been explained in the previous section, perpendicular projections of points (representing compounds) upon a unipolar axis (representing a method) leads to a reproduction of the data in Table 31.3. In this case we have to substitute the untransformed value in eq. (31.35) by Zy of eq. (31.42) ... 

Since m, is a constant for the given unipolar axis through the Jth method, we obtain that the projections on this axis are equal to Xy minus a constant. 

The unipolar axis through the origin and DMSO reproduces rather well the data in the corresponding column of Table 31.2. By perpendicular projection of the... 

Fig. 31.17. (a) In a classical PCA biplot, data values xy can be estimated by means of perpendicular projection of the ith row-point upon a unipolar axis which represents theyth column-item of the data table X. In this case the axis is a straight line through the origin (represented by a small cross), (b) In a non-linear PCA biplot, the jth column-item traces out a curvilinear trajectory. The data value is now estimated by defining the shortest distance between the ith row point and theyth trajectory. 

Unipolar and bipolar axes have been discussed in Section 31.2. Briefly, a unipolar axis is defined by the origin and the representation of a row or column. A bipolar axis is drawn through the representations of two rows or through the representations of two columns. Projections upon unipolar axes reproduce the values in the transformed data table. Projections upon bipolar axes reproduce the contrasts (i.e. differences) between values in the data table. 

Fig. 31.6. Biplot of chromatographic retention times in Table 31.2, after column-centering of the data. Two unipolar axes and one bipolar axis have been drawn through the representations of the methods DMSO and methylenedichloride (CH2CI2). The projections of three selected compounds are indicated by dashed lines. TTie values read off from the unipolar axes reproduce the retention times in the corresponding columns. The values on the bipolar axis reproduce the differences between retention times.

Finally, we have constmcted a bipolar axis through DMSO and methylenedichloride. By perpendicular projection of the centers of the circles upon this bipolar axis we obtain the differences in retention times obtained respectively with DMSO and with methylenedichloride. Using a similar reasoning as developed above for unipolar axes we can perform a substitution of eq. (31.42) in eq. (31.38) which leads to ... 

Chen, Y. W. and Dilsaver, S. C. Lifetime rates of suicide attempts among subjects with bipolar and unipolar disorders relative to subjects with other Axis I disorders. Biol. Psych. 39 896-899,1996. 

Dysregulation of the hypothalamic-pituitary-thyroid axis causes a reduction in thyroid function. There may be a relationship between an abnormal TSH response to TRH and depressive symptoms. Thus, unipolar patients undergoing the TRH-TSH test (which measures the difference between baseline TSH and peak postinfusion TSH after they are given synthetic TRH) reportedly have a blunted response, whereas bipolar, depressed patients have an elevated response (see also Chapter 1,... 

Hypothalamic-pituitary-adrenal axis function in bipolar disorder has been reviewed, but lithium was mentioned only in passing (617). Two studies (n = 25, n = 24), possibly reporting many of the same patients, showed that lithium augmentation of antidepressant-resistant unipolar depression increased hypothalamic-pituitary-adrenal axis activity, measured by the dexamethasone suppression test, either alone or combined with the corticotropin releasing hormone test (618,619). However, the tests did not distinguish between lithium responders and nonresponders. 

We can say that such a static device is a U( ) unipolar, set rotational axis, sampling device and the fast polarization (and rotation) modulated beam is a multipolar, multirotation axis, SU(2) beam. The reader may ask how many situations are there in which a sampling device, at set unvarying polarization, samples at a slower rate than the modulation rate of a radiated beam The answer is that there is an infinite number, because from the point of the view of the writer, nature is set up to be that way [26], For example, the period of modulation can be faster than the electronic or vibrational or dipole relaxation times of any atom or molecule. In other words, pulses or wavepackets (which, in temporal length, constitute the sampling of a continuous wave, continuously polarization and rotation modulated, but sampled only over a temporal length between arrival and departure time at the instantaneous polarization of the sampler of set polarization and rotation—in this case an electronic or vibrational state or dipole) have an internal modulation at a rate greater than that of the relaxation or absorption time of the electronic or vibrational state. 

The representation of the sampling by a unipolar, single-rotation-axis, U(l) sampler of a SU(2) continuous wave that is polarization/rotation-modulated is shown in Fig. 2, which shows the correspondence between the output space sphere and an Argand plane [28]. The Argand plane, S, is drawn in two dimensions, x and v, with z = 0, and for a set snapshot in time. A point on the Poincare sphere is represented as P(t,x,y,z), and as in this representation t = 1 (or one step in the future), specifically as P(l,x,y,z). The Poincare sphere is also identified as a 3-sphere, S 1, which is defined in Euclidean space as follows ... 

In addition, it exerts beneficial effects in many disorders as an adjuvant to other treatment modalities. Such effects are apparent only if it is administered to an already pharmacologically treated patient. For example, in unresponsive major depressive disorder, the co-administration of lithium to an ongoing antidepressant treatment increases the response rate by up to 50%. In most cases, the response to lithium augmentation is either considerable or not at all ( all-or-none phenomenon). Some (currently not convincing) results have also been reported in unipolar depression, bulimia nervosa, and attention deficit hyperactivity disorder (ADHD). Lithium also exerts antiaggressive effects in conduct disorder, independent of any mood disorder, and can reduce behavioral dyscontrol and self-mutilation in mentally retarded patients. One of the most striking effects of lithium is its antisuicidal effect in patients who suffer from bipolar and unipolar depressive disorder irrespective of comorbid axis I disorder. ... 

Figure 6.11 Unipolar potentials from a current dipole moving along the horizontal x-axis. Dipole length is L c) the unit of the x-axis is L c- The recording electrode is at distance SL c and lOLcc (a) horizontal dipole orientation, biphasic waveforms, and high spatial resolution (b) vertical dipole orientation, monophasic waveforms, and largest signal amplitude of...

Fig. 16. Electron micrograph of a blood lily Haemanthus katherinae) chromosome in early mitotic prometaphase. Unipolar malorientation to a pole toward the left is suggested by the chromosomal microtubule arrangement at the two sister kinetochores ("ki/ The overall spindle axis is indicated by the arrow at the lower left side. The circle is a stain mark. XI 2,000. (From Bajer and Mole -Bajer. 1969. Chromosoma, 27 448-484.)...

In a perfect QMF there is no acceleration along the z axis, so the ion is transmitted with a constant axial velocity. This velocity is determined essentially by the difference between the ion s energy (that is, the kinetic energy that it would have were it to enter a grounded environment) and the (constant) potential along the axis of the QMF. In equation (2.1.9) the axial potential is zero, but often a constant unipolar potential is superimposed. This is known as the pole bias or sometimes the field axis potential. It causes the ions to speed up or slow down within the QMF, so that they can be transmitted with optimal axial velocity. 

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