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