Binary representation

Rather than being defined by lengthy explicit listings of their local action, rules are instead conventionally identified by a compact code. If the bottom eight binary digits of the r = 1 mod 2 rule in the example cited above are interpreted as the binary representation of a decimal number, then the code, i [ 2], is given by that base-10 equivalent ... 

J f = 2 entries of the rule table be filled in. Each configuration can be interpreted as being the binary representation of some whole number between 0 and A/" — 1. This suggests that the behavior of N, k = N)-neis is equivalent to the behavior of a random mapping of a finite set of A/" integers to itself. 

In early work, GA strings were binary coded. Computer scientists are comfortable with binary representations and the problems tackled at that time could be easily expressed using this type of coding. Binary coding is sometimes appropriate in scientific applications, but it is less easy to interpret than alternative forms, as most scientific problems are naturally expressed using real numbers. 

Phase diagrams are often constructed to provide a visual picture of the existence and extent of the presence of solid and liquid phases in binary, ternary and other mixtures of substances. Phase diagrams are normally two-component (binary) representations but multicomponent phase diagrams can also be constructed. Interactions between active substances and excipients can often be evaluated using phase diagrams. 

The binary representation is applicable to various other oxide materials. However, an important distinction can be made between borates and other main group element oxide systems, such as aluminates and silicates. In the latter systems cations predominantly reside at sites created by the demands of rigid anionic oxide frameworks. Although some degree of structural control may be obtained by varying cations or by use of template synthesis, the oxide frameworks of these systems tend to be relatively inflexible in comparison with... 

In 1996, Sheridan et al. [16] were the first to use pharmacophoric atom types for an autocorrelation approach. This technique is suited to characterize ligand-receptor interactions in a general way, allowing for more different but equally interacting molecules to be identified as similar. Sheridan et al. also extended the topological Carhart approach to the 3D case, and this was soon followed up by a binary representation of such a descriptor [17]. In 2003, Stiefl and Baumann [18] reported an autocorrelation approach using surface points representing pharmacophoric features. 

A structural interaction fingerprint is a ID binary representation of the interaction patterns from a 3D protein-inhibitor complex. The fingerprint representation of the interaction patterns is compact and allows for rapid clustering and analysis of massive numbers of complexes. 

In another popular definition of mutate and crossover, a binary representation of the unknown variables is required whereby the simulated DNA is converted into a concatenated sequence of binary numbers (0 s and l s). To obtain a binary representation of the ionic coordinates, the ions are constrained in that they can only sit on one of 2m discrete grid points across the unit cell (Fig. 1). For each grid point there is a unique binary number of length m. Note that the grid points can either be numbered 0 to 2m-l (000 to 111 for m=3) or, as shown in Fig. 1, have... 

Of course there is no reason for swapping just one section. Using the binary representation of the simulated DNA, we can vary the number and length of the random sections of 0 s and l s. Whether swapping one or many sections is more beneficial will depend on the environment, or indeed the stage (earlier or later populations) of the GA [29]. Some experimenting with the GA parameters/move class operators is always advisable. 

Binary representation Presence or absence of particular structural features in a molecule can be represented by bitstrings. Binary representation can also be used to characterize values of physico-chemical properties over or below a certain limit. 

If we interpret a as 0 and b as 1 , and if additionally we put 0. in firont of every sequence, the set S is equivalent with the binary representation of all the real numbers in the unit interval. Therefore, as a corollary, we have established the fact that the real numbers in [0,1] are uncountable. Thus, a set is uncountable (or overcountable ) if its cardinality is at least Mi, a higher order of infinity. 

Apb is the scattering length density difference, Q is Porod s invariant, and Y the mean chord length. For the calculation of Yo(r) we approximated I(q) hy a cubic spline. The equations used for the calculation of " pore and " soUd are to be found in [8,30,39-41,47]. Analytical expressions for the descriptors of RES were published in [10,11,13,42,43]. In its most simple variant, the stochastic optimization procedure evolves the two-point probability S2 (r) of a binary representation of the sample towards S2(r) by randomly excWiging binary ceUs of different phases, starting from a random configuration which meets the preset volume fractions. After each exchange the objective function... 

Structure and data storage is shown on the right. A structure table contains the structures, their internal identifiers, and their external identifiers, if any. The structures are stored in a compact binary representation that includes the connection table, the coordinates, the ring information, and any stereochemical, valence, isomer, isotope, or bond information. Certain types of structure-specific information such as polymer or component designations are stored here, whereas other types of structure-specific information (atom- or bond-specific data, and more verbose text data) are stored in their own tables, referenced by the internal identifier, and the atom or bond numbers to which the data correspond. A formula table contains the molecular formula and various atom and atom-type indexes to enhance formula searching and sorting. 

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