Binary values

The calculation of a distance measure for two objects s and t represented by binary desaiptors and jq with m binary values is based on the frequencies of common and different components. For this purpose we define the frequencies a, h, c, and d as follows ... 

For the selection of descriptors, GA simulated evolution of a population. Each individual of the population represents a subset of descriptors and is defined by a chromosome of binary values. The chromosome has as many genes as there are possible descriptors (92 for the aromatic group, 119 for non-rigid aliphatic,... 

While none of the 256 possible radius r = 1 binary valued CA are believed to be capable of universal computation, the rule whose long time behavior has proven to be the most difficult to understand fully is rule R22 ... 

The simplest binary valued CA proven to be computation universal is John Conway s two-dimensional Life rule, about which we will have much to say later in this chapter. Many of the key ingredients necessary to prove universality, however, such as sets of propagating structures out of which analogs of conventional hardware components (i.e., wires, gates and memory) may be explicitly constructed, appear, at least in principle, to be supported by certain one-dimensional rules as well. The most basic component required is a mechanism for transporting localized packets of information from one part of the lattice to another i.e., particle-like persistent propagating patterns, whose presence is usually indicative of class c4 behavior. 

Perhaps the single most studied (and joyfully played with) rule - certainly the most famous is the two-dimensional Moore neighborhood binary-valued CA invented by John H. Conway, and popularized extensively by Martin Gardner in his Mathematical Gaines column in Scientific. American in the early 1970 s ([gardnerTO], [gardnerTl], [gardner78]). 

We now consider two special cases of the symmetric matrix A] namely, (1) the entries of A are allowed to take on only integer values, and (2) the entries of A are all binary valued. 

Multithreshold rules are natural extensions of the (binary-valued) generalized threshold rule defined in equation 5.121. Using fc-state variables a G 0,1,..., A - 1 and using the j entry of the A threshold vector to define the j threshold at that site (= bij), the generalized multithreshold rule is defined as follows ... 

Fig. 2. Distance between two binary-valued feature vectors vA and vB is not given by the Euclidean distance but the Hamming distance between the two.

Most similarity measures for binary-valued feature vectors in use today are symmetric Tversky (6), however, has defined an infinite family of asymmetric measures... 

Feature vectors with integer- or categorical-valued components are identical in form to binary-valued vectors (see Eq. 2.16). In contrast, however, each component takes on a finite number of values... 

Subheading 2.2. describes the properties of discrete-valued feature vectors, with components given by finite, ordered sets of values. The most prevalent class is that of vectors with binary-valued components, which are mathemati-... 

Table 3.3. Spectral moments of the neon-argon liquid mixture along the coexistence curve measurement [107] compared with binary values calculated from first principles. (Calculated ternary moments are given in Table 3.2 above.)...

Let us consider the following components of the Okhotsk Sea ecosystem mentioned in Table 6.21. The trophic pyramid X = vy, where xtj is a binary value equal to 1 or 0 under the existence or absence of a nutritive correlation between the z th and y th components, respectively. Let us define the biocomplexity as a function ... 

A nice feature of this method is that it is easily applied to other aldose systems and to the L-family of sugars. The aldopentoses are given by the mnemonic Ribs Are eXtra Lean. While not factually correct, this phrase corresponds to the sugars ribose, arabinose, xylose, and lyxose, and the binary values of zero, one, two, and three, respectively. To access the structures of the L-family of sugars, just use your left hand. 

One of the most commonly used structural descriptors in similarity and diversity studies is that of the 2D fragment bitstring where a molecule is represented by a vector of binary values that indicate the presence or absence of structural features, or fragments, within the molecule. Many different similarity measures or coefficients have been developed to quantify the degree of similarity between such vector based descriptors [5-7]. Usually, the values that can be taken by a coefficient lie in the range 0..1, or they can be normalised to be within this range. A similarity coefficient of 1 indicates that the two molecules are identical with respect to the structural descriptors and a value of 0 indicates that the two molecules are maximally different... 

Molecular similarity and diversity methods typically represent molecules by a vector of real-valued properties (molecular weight, logP etc.) or binary values (0 for absence, 1 for presence of a substructure feature for example) in a bit-string or... 

In the binary system, each place from right to left is valued at 2 times the place to its right. Thus the first place can be zero or one, the second place to the left is valued at two, the third place to the left is valued at four, the fourth place to the left is valued at eight, and so on. The following list indicates the binary values of the first ten numbers of a decimal system ... 

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