No abstract

We present a cylindrically symmetric model for a sunspot atmosphere using the similarity principle of Schliiter and Temesvary for the magnetic field configu~'ation. The equations of magnetostatic equilibrium are used, augmented by a radial Evershed flow. The LTE radiative transfer equations for the Stokes vector were solved under a variety of conditions for a ray emerging from a typical penumbral point. The contribution from isolated lines to the broadband circular polarization in sunspot penumbrae is evaluated, using a more realistic model sunspot atmosphere than has hitherto been considered. Results indicate that the inclusion of a velocity field along B is unable to give a net circular polarization of sufficient magnitude, although the variation with the angle between the line-of-sight and B is in qualitative agreement with observations. The corresponding results for the net linear polarization are satisfactory.

No abstract

Despite the fact that artificial neural networks (ANNs) are universal function approximators, their black box nature (that is, their lack of direct interpretability or expressive power) limits their utility. In contrast, univariate decision trees (UDTs) have expressive power, although usually they are not as accurate as ANNs. We propose an improvement, C-Net, for both the expressiveness of ANNs and the accuracy of UDTs by consolidating both technologies for generating multivariate decision trees (MDTs). In addition, we introduce a new concept, recurrent decision trees, where C-Net uses recurrent neural networks to generate an MDT with a recurrent feature. That is, a memory is associated with each node in the tree with a recursive condition which replaces the conventional linear one. Furthermore, we show empirically that, in our test cases, our proposed method achieves a balance of comprehensibility and accuracy intermediate between ANNs and UDTs. MDTs are found to be intermediate since they are more expressive than ANNs and more accurate than UDTs. Moreover, in all cases MDTs are more compact (i.e., smaller tree size) than UDTs.

We present an algorithm, FUZZEX, for learning fuzzy rules from a corpus of data mapping input antecedents to output consequents. The input and output spaces are first divided into a grid of cells and primitive if % then rules formulated from each occupied input cell in the role of an antecedent. The distribution of output cells into which data in the input cell maps, plays the role of the consequent interpreted as a fuzzy set. Those input cells associated with sufficiently similar fuzzy output sets are then combined to form a composite rule. A concise set of rules in Disjunctive Normal Form (DNF) is formed by combining adjacent input cells belongingto the same rule, thereby simplifying the logical expression of the antecedents. Optionally, more succinctness of expression may be obtained by recruiting into a rule, adjacent input cells with (little or) no data, but which happen to simplify rule expression. Preliminary testing on testbed datasets is presented. FUZZEX can be applied effectively to problems of large dimensionality.