RESUMO
Written language is complex. A written text can be considered an attempt to convey a meaningful message which ends up being constrained by language rules, context dependence and highly redundant in its use of resources. Despite all these constraints, unpredictability is an essential element of natural language. Here we present the use of entropic measures to assert the balance between predictability and surprise in written text. In short, it is possible to measure innovation and context preservation in a document. It is shown that this can also be done at the different levels of organization of a text. The type of analysis presented is reasonably general, and can also be used to analyze the same balance in other complex messages such as DNA, where a hierarchy of organizational levels are known to exist.
Assuntos
Entropia , Redação , Humanos , Idioma , Modelos Teóricos , Análise de SistemasRESUMO
It is shown how to reconstruct the stacking sequence from the pairwise correlation functions between layers in close-packed structures. First, of theoretical interest, the analytical formulation and solution of the problem are presented when the exact pairwise correlation counts are known. In the second part, the practical problem is approached. A simulated annealing procedure is developed to solve the problem using as initial guess approximate solutions from previous treatments. The robustness of the procedure is tested with synthetic data, followed by an experimental example. The developed approach performs robustly over different synthetic and experimental data, comparing favorably with the reported methods.
RESUMO
Extrinsic faulting has been discussed previously within the so-called difference method and random walk calculation. In this contribution it is revisited under the framework of computational mechanics, which allows expressions to be derived for the statistical complexity, entropy density and excess entropy as a function of faulting probability. The approach allows one to compare the disordering process of an extrinsic fault with other faulting types. The â-machine description of the faulting mechanics is presented. Several useful analytical expressions such as probability of consecutive symbols in the Hägg coding are presented, as well as hexagonality. The analytical expression for the pairwise correlation function of the layers is derived and compared with results previously reported. The effect of faulting on the interference function is discussed in relation to the diffraction pattern.
RESUMO
This is the second contribution in a series of papers dealing with dynamical models in equilibrium theories of polytypism. A Hamiltonian introduced by Ahmad & Khan [Phys. Status Solidi B (2000), 218, 425-430] avoids the unphysical assignment of interaction terms to fictitious entities given by spins in the Hägg coding of the stacking arrangement. In this paper an analysis of polytype generation and disorder in close-packed structures is made for such a Hamiltonian. Results are compared with a previous analysis using the Ising model. Computational mechanics is the framework under which the analysis is performed. The competing effects of disorder and structure, as given by entropy density and excess entropy, respectively, are discussed. It is argued that the Ahmad & Khan model is simpler and predicts a larger set of polytypes than previous treatments.
RESUMO
The stacking problem is approached by computational mechanics, using an Ising next-nearest-neighbour model. Computational mechanics allows one to treat the stacking arrangement as an information processing system in the light of a symbol-generating process. A general method for solving the stochastic matrix of the random Gibbs field is presented and then applied to the problem at hand. The corresponding phase diagram is then discussed in terms of the underlying â-machine, or optimal finite-state machine. The occurrence of higher-order polytypes at the borders of the phase diagram is also analysed. The applicability of the model to real systems such as ZnS and cobalt is discussed. The method derived is directly generalizable to any one-dimensional model with finite-range interaction.
RESUMO
The HK representation of close-packed polytypes is studied as a binary code. It is shown that the HK code can be seen as operators forming a group. The neutrality condition is then translated to HK sequences that result in the identity operator. The symmetry of an HK word can be related to the space-group symmetry of the corresponding polytype. All HK code types corresponding to all possible close-packed space groups are reported. From a coding perspective, equivalent HK codes correspond to bracelet equivalent classes. An efficient algorithm with execution time constant per generated object is modified to generate all non-equivalent polytypes of a given length.
RESUMO
A systematic use of binary codes derived from the Hagg symbol are used to study close-packed polytypes. Seitz operators acting over the corresponding binary codes are defined and used. The number of non-equivalent polytypes of a given length are calculated through the use of the Seitz operators. The same procedure is applied to the problem of counting the number of polytypes complying with a given symmetry group. All counting problems are reduced to an eigenvector problem in the binary code space. The symmetry of the binary codes leads to the different space groups to which polytypes can belong.