Boolean density

The state of the automaton at time t can be completely determined by the boolean variable n, r,t), which is equal to 1(0) if a particle is present (absent) on site r with velocity c,. From this it follows that the local microscopic density p and flow velocity u at site r are given by... 

A simple spreadsheet, such as Microsoft Excel, can serve as the foundation of a database that has forward and reverse search capabilities. For instance, a table of normal alkanes, together with their densities, boiling points, and melting points, can serve as the starting point. If we want to know all the normal paraffins that boil between 0 and 40 C, all we have to do is to do a sort operation on the boiling-point column and obtain the result that the only paraffin that is in the range is normal heptane with a boiling point of 36.1 °C. For the more advanced Boolean search of normal alkanes that boil between 0 and 40 °C AND melt between —40 and 0 °C, it would be a far more laborious task in a spreadsheet. 

A database such as Microsoft Access would be able to do this Boolean search with ease. The Filter by Form, the Filter by Selection, and the Advanced filter/sort function allow the user to specify density >0.6 AND <0.7 or bp >-40 AND <0. This search yields three results ... 

In order to bridge the gap between the discretized micro- and macro-worlds, averaging of the variables is necessary. Macroscopic variables in the N-S equation, are the density p and the momentum I, which are functions of the lattice space vector r and time t. The local density p is the summation of the average number of particles travelling along each of six (hexagonal) directions, with velocity c. Multiplication of the density p by the velocity vector u equals linear momentum (I = pu). Boolean algebra is applied for the expressions of the discretized variables density and momentum, respectively, as follows ... 

Databases can be searched by simple Boolean operations using both structural keys and fingerprints. The latter have a higher information density than structural keys without losing specificity. Hence, database searches using fingerprints instead of structural keys are more efficient. 

Mezey, Eds., JAI Press, London, 1998, pp. 43-72. Fuzzy Sets and Boolean Tagged Sets Vector Semispaces and Convex Sets Quantum Similarity Measures and ASA Density Functions Diagonal Vector Spaces and Quantum Chemistry. 

The most serious setback for a modern theory of matter was the deliberate suppression of Erwin Schrodinger s demonstration that the behavior of electrons in an atom cannot be described correctly by a particle model and quantum jumps [5,6]. A beautiful theory, based on a wave model of matter, was buried through professional rivalry to be replaced by incomprehensible concepts such as particles with wavelike properties—even Zitterbewegung, infinite self-energy, probability density, non-Boolean algebra of observables and other weird properties. Remember how Newton described particles as... 

Abstract. In this paper we show that a well-known model of genetic regulatory networks, namely that of Random Boolean Networks (RBNs), allows one to study in depth the relationship between two important properties of complex systems, i.e. dynamical criticality and power-law distributions. The study is based upon an analysis of the response of a RBN to permanent perturbations, that may lead to avalanches of changes in activation levels, whose statistical properties are determined by the same parameter that characterizes the dynamical state of the network (ordered, critical or disordered). Under suitable approximations, in the case of large sparse random networks an analytical expression for the probability density of avalanches of different sizes is proposed, and it is shown that for not-too-smaU avalanches of critical systems it may be approximated by a power law. In the case of small networks the above-mentioned formula does not maintain its validity, because of the phenomenon of self-interference of avalanches, which is also explored by numerical simulations. 

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