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    Automatic construction of rules fuzzy for modelling and prediction of the central nervous system

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    The main goal of this work is to study the performance of CARFIR (Automatic Construction of Rules in Fuzzy Inductive Reasoning) methodology for the modelling and prediction of the human central nervous system (CNS). The CNS controls the hemodynamical system by generating the regulating signals for the blood vessels and the heart. The main idea behind CARFIR is to expand the capacity of the FIR methodology allowing it to work with classical fuzzy rules. CARFIR is able to automatically construct fuzzy rules starting from a set of pattern rules obtained by FIR. The new methodology preserves as much as possible the knowledge of the pattern rules in a compact fuzzy rule base. The prediction results obtained by the fuzzy prediction process of CARFIR methodology are compared with those of other inductive methodologies, i.e. FIR, NARMAX and neural networksPostprint (published version

    Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources

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    We deal with zero-delay source coding of a vector-valued Gauss-Markov source subject to a mean-squared error (MSE) fidelity criterion characterized by the operational zero-delay vector-valued Gaussian rate distortion function (RDF). We address this problem by considering the nonanticipative RDF (NRDF) which is a lower bound to the causal optimal performance theoretically attainable (OPTA) function and operational zero-delay RDF. We recall the realization that corresponds to the optimal "test-channel" of the Gaussian NRDF, when considering a vector Gauss-Markov source subject to a MSE distortion in the finite time horizon. Then, we introduce sufficient conditions to show existence of solution for this problem in the infinite time horizon. For the asymptotic regime, we use the asymptotic characterization of the Gaussian NRDF to provide a new equivalent realization scheme with feedback which is characterized by a resource allocation (reverse-waterfilling) problem across the dimension of the vector source. We leverage the new realization to derive a predictive coding scheme via lattice quantization with subtractive dither and joint memoryless entropy coding. This coding scheme offers an upper bound to the operational zero-delay vector-valued Gaussian RDF. When we use scalar quantization, then for "r" active dimensions of the vector Gauss-Markov source the gap between the obtained lower and theoretical upper bounds is less than or equal to 0.254r + 1 bits/vector. We further show that it is possible when we use vector quantization, and assume infinite dimensional Gauss-Markov sources to make the previous gap to be negligible, i.e., Gaussian NRDF approximates the operational zero-delay Gaussian RDF. We also extend our results to vector-valued Gaussian sources of any finite memory under mild conditions. Our theoretical framework is demonstrated with illustrative numerical experiments.Comment: 32 pages, 9 figures, published in IEEE Journal of Selected Topics in Signal Processin
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