Describing Patterns

One of the main advantages of RDF descriptors is that they are interpretable. A simple approach to the recognition of structural features is to search for patterns, which provide valuable information in RDF descriptors for similarity searches. The importance of recognizing patterns in chemical data has already been emphasized. 

Some simple adaptations of radial functions lead to useful descriptors for pattern recognition. Althongh the components of the previously introduced RDF descriptors are calculated for a continuous range of distance intervals, RDF pattern functions rely on the 6-fnnction 

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Richardson, J.S. Describing patterns of protein tertiary structure. Methods Enzymol. 115 349-358, 1985. 

This Chapter has two main parts. Section 14.1, Patterns for Specifying Components, on page 613, describes patterns often useful when building a component specification. Section 14.2 onwards illustrates the construction of a specification for the case study. 

Imposed Field Effects. In this section we have set forth a set of equations to describe pattern formation in a multicellular electrophysiological system. A central goal of the theory is to study the effects of applied electric fields. This is done by imposing appropriate boundary conditions on the equations developed here. For example, assume we subject a one dimensional tissue to fixed ionic currents 1. Then if the tissue is in the interval 0 x along the x axis, the boundary conditions for the electro-diffusion model of the small gradient theory, i.e. (6k), are replaced by J = I at x = 0, L. One expects the richness of effects to include hyperpolarizability, induction of new phenomena and imperfect bifurcations to be found in these systems... 

The properties characteristic for electrochemical nonlinear phenomena are determined by the electrical properties of electrochemical systems, most importantly the potential drop across the electrochemical double layer at the working electrode (WE). Compared to the characteristic length scales of the patterns that develop, the extension of the double layer perpendicular to the electrode can be ignored.2 The potential drop across the double layer can therefore be lumped into one variable, DL, and the temporal evolution law of DL at every position r along the (in general two-dimensional) electrode electrolyte interface is the central equation of any electrochemical model describing pattern formation.3 It results from a local charge bal-... 

The writer complains that the brake sleeves [ Manchette ] of the combined Oil and Westing-house brakes was broken in several places. According to an information provided by the company Steyr-Daimler-Puch, successor of Saurer Company, the mentioned brake sleeves were rubber-made cup packings of the vacuum power-steering device which broke frequently. The described pattern was not used to cast the sleeves but to vulcanize them.44 Consequently, Becker would not have been able to produce his own sleeves, since casting air tight, vacuum proof mbber sleeves in patterns behind the Russian front is nearly impossible, but had to order them in an unvulcanized form from the manufacturer in order to vulcanize them in his self-made patterns (if this was possible at all, has not... 

Fig. 2. Illustration of the concept of the active-area density used to describe patterned electrode surfaces (A) bare, flat electrode, (B and C) flat electrodes covered by resist patterns of different density, (D) electrode with topographic pattern. (Reprinted by permission of the publisher. The Electrochemical Society, Inc. [25]).

Ttie conclusion was [33] that only mixed explosives, for example ammonium nitrate — TNT give the described pattern. 

Cyclical Modification of Inverse Bateman Function A cosine function can be used to describe patterns similar to the exponential and inverse Bateman models and can therefore be used as the function for disease progress. However, this same cosine function can also be used to impose a cyclical modulation on another function. 

To describe patterns of combustion processes, ideal models are often introduced such as piston flow or a perfectly stirred reactor as well as an ideal stirred boiler. For describing the flameless oxidation the model of the loop reactor is appropriate. Figure 23.6 shows different combinations of loop reactors. Here the piston flow (k, = 0) and the well-stirred reactor (k, = °°) can be considered as limiting cases of loop reactors. 

The origin of this phenomenon can he traced to the drying step of the liquid development process. During the development step, after the resist-patterned wafer has been contacted with the developer solution for a given length of time and subsequently rinsed with deionized water, the level of the rinse liquid at some point attains a condition similar to that shown in Fig. 11.45, where the space between adjacent resist lines is partially filled with fluid. The fluid meniscus exhibits a curvamre due to the differences in pressure across the fluid interface that result from surface tension in the confined space between the resist lines. Tanaka et al. developed a cantilever beam mechanical model for describing pattern collapse. The Laplace equation relates the pressure differential across the meniscus... 

Movement of a soluble chemical throughout a water body such as a lake or river is governed by thermal, gravitational, or wind-induced convection currents that set up laminar, or nearly frictionless, flows, and also by turbulent effects caused by inhomogeneities at the boundaries of the aqueous phase. In a river, for example, convective flows transport solutes in a nearly uniform, constant-velocity manner near the center of the stream due to the mass motion of the current, but the friction between the water and the bottom also sets up eddies that move parcels of water about in more randomized and less precisely describable patterns where the instantaneous velocity of the fluid fluctuates rapidly over a relatively short spatial distance. The dissolved constituents of the water parcel move with them in a process called eddy diffusion, or eddy dispersion. Horizontal eddy diffusion is often many times faster than vertical diffusion, so that chemicals spread sideways from a point of discharge much faster than perpendicular to it (Thomas, 1990). In a temperature- and density-stratified water body such as a lake or the ocean, movement of water parcels and their associated solutes will be restricted by currents confined to the stratified layers, and rates of exchange of materials between the layers will be slow. 

Pheromones are often described by function, by the effect they have. For example, sex pheromones describe those involved in mate-finding or attraction. Others include aggregation, alarm, and trail pheromones. Some responses are context-specific - for example in some ant species alarm pheromones cause ants to disperse if released far from the nest but to attack if released close to the nest. In a way, these descriptors allow us simply to describe the range of behaviors mediated by pheromones and then generalize from these to describe patterns in use, say, of sex pheromones across taxa. 

Micelles containing heavy chains could be separated from those containing light chains by centrifugation, and experiments conducted on the individual chains confirmed the above-described pattern of catalytic efficiency [39]. 

There are many various predefined trees in the incident investigation field. Some of them, e.g. the tree predefined in (WANO, 1998) seem to be close to the above described pattern. 

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