Valley narrow

A geographical analogy can be a helpful way to illustrate many of the concepts we shall encounter in this chapter. In this analogy minimum points correspond to the bottom of valleys. A minimum may be described as being in a long and narrow valley or a flat and featureless plain. Saddle points correspond to mountain passes. We refer to algorithms taking steps uphill or downhill. ... 

These sigma values are for unrestricted flow over relatively flat, uniform terrain. They may require modification for application to rough terrain or restricted flow conditions (e.g., within the confines of a narrow valley, coastal or desert areas - see IAEA, 1980). 

Figure 15.7 is intended to show conceptually some important mathematical aspects of a scale-disparate, nonlinear problem. The lines are contours of a norm of the residual vector F in a two-dimensional space. The position on the figure (i.e., cartesian coordinates) represents the y vector. As illustrated, the residual norm is characterized by a long, narrow, valley. The solution, which is a global minimum in the residual norm, lies near one end of the valley. In a highly scale-disparate problem, the valleys are greatly elongated and the valley walls are very steep. Nonlinearity is represented by curvature of the valleys. 

The radiation may be due to emissions from a hot source, or to the luminescence, fluorescence or phosphorescence of the sample. An emission spectrum consists of a number of generally very narrow peaks (called spectral lines) occurring at certain wavelengths which are characteristic of the materials contained within the source. The amplitudes of the peaks are related to the abundance or concentration of the materials present. Alternatively, radiation from a source is passed through a sample. In this case the quantity absorbed by the sample at a particular wavelength is again characteristic of the materials present in the sample. This is termed absorption spectrometry and produces spectral transmission lines in the form of equally narrow valleys—or peaks (Fig. 6.42) where the information is expressed in terms of absorbance (si) rather than transmittance (20<57>, and ... 

Fig. 4. The role of neutral networks in evolutionary optimization through adaptive walks and random drift. Adaptive walks allow to choose the next step arbitrarily from all directions where fitness is (locally) nondecreasing. Populations can bridge over narrow valleys with widths of a few point mutations. In the absence of selective neutrality (upper part) they are, however, unable to span larger Hamming distances and thus will approach only the next major fitness peak. Populations on rugged landscapes with extended neutral networks evolve along the network by a combination of adaptive walks and random drift at constant fitness (lower part). In this manner, populations bridge over large valleys and may eventually reach the global maximum ofthe fitness landscape.

Temperature Effects at Hli t- During the dn3 Time the temperatun limited area, say a square mile, is about the same unless there arc marked changes in topography or soil. On days wit h much sunshine and a low wind velocity, the low cr points, particularly those in narrow valleys, may be a few tenths of a degree warmer than the upper parts of the area. At night, the layer of air next to the ground grows colder and denser and drains like water into the valleys and places of low elevation. If the wind is unable to remove these pockets of cold air, a... 

Convergence can be slow, especially if the minimum exists in a long narrow valley in parameter space. Press et al. describe several more efficient multidimension optimization strategies. 

N. The hills in KMTR are characterized by numerous folds and extension engulfing small, narrow valleys and the elevation varies from 50 to 1869m (Manickam et al., 2004). It is the 17th Tiger Reserve in the country and it is a priority area for conservation of its rich floral and faunal diversity, both in terms of species richness and endemism (Melkani, 2001). 

Fig. 5. Steepest descents down a long narrow valley Press et al., 1989). Copyright Cambridge University Press 1986, 1992 and reprinted with permission of Cambridge University Press.

The conjugate gradients method produces a set of directions which does not show the oscillatory behaviour of the steepest descents method in narrow valleys. In the steepest descents method both the gradients and the direction of successive steps are orthogonal. 

For a large mass asymmetry (r] 0.8,0.9) there exist very narrow valleys. They are not as clearly visible in Figure 8.3, but they have interesting consequences. Through these narrow valleys nuclei can emit spontaneously not only a-particles (Helium nuclei) but also Ne, Mg, and other nuclei. Thus, we are lead... 

Communication was also impeded by physical line-of-sight restrictions. The Black Hawks were flying in narrow valleys among very high mountains that disrupted communication depending on line-of-sight transmissions. 

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