Biomedical subjects
Publications and source records attributed to Luis A Aguirre.
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It is known that the observability of a system depends crucially on the choice of the observable. Locally, such a feature results directly from the couplings between the dynamical variables (globally, it will also depend on symmetry). Using a feedback circuit description, it is shown how the location of the nonlinearity can affect the observability of a system. A graphical interpretation is introduced to determine--without any computation--whether a variable provides full observability of the system or not. Up to a certain degree of accuracy, this graphical interpretation allows us to rank the variables from the best to the worst. In addition to that, it is shown that provided that the system is observable, it can be rewritten under the form of a jerk system. The Rössler system and nine simple Sprott systems, having two fixed points, are investigated here.
Molecular testing for mutations in the gene encoding connexin-26 (GJB2) at the DFNB1 locus has become the standard of care for genetic diagnosis and counseling of autosomal recessive non-syndromic hearing impairment (ARNSHI). The spectrum of mutations in GJB2 varies considerably among the populations, different alleles predominating in different ethnic groups. A cohort of 34 families of Spanish Romani (gypsies) with ARNSHI was screened for mutations in GJB2. We found that DFNB1 deafness accounts for 50% of all ARNSHI in Spanish gypsies. The predominating allele is W24X (79% of the DFNB1 alleles), and 35delG is the second most common allele (17%). An allele-specific PCR test was developed for the detection of the W24X mutation. By using this test, carrier frequencies were determined in two sample groups of gypsies from different Spanish regions (Andalusia and Catalonia), being 4% and 0%, respectively. Haplotype analysis for microsatellite markers closely flanking the GJB2 gene revealed five different haplotypes associated with the W24X mutation, all sharing the same allele from marker D13S141, suggesting that a founder effect for this mutation is responsible for its high prevalence among Spanish gypsies.
In the analysis of a scalar time series, which lies on an m-dimensional object, a great number of techniques will start by embedding such a time series in a d-dimensional space, with d>m. Therefore there is a coordinate transformation phi(s) from the original phase space to the embedded one. The embedding space depends on the observable s(t). In theory, the main results reached are valid regardless of s(t). In a number of practical situations, however, the choice of the observable does influence our ability to extract dynamical information from the embedded attractor. This may arise in problems in nonlinear dynamics such as model building, control and synchronization. To some degree, ease of success will depend on the choice of the observable simply because it is related to the observability of the dynamics. In this paper the observability matrix for nonlinear systems, which uses Lie derivatives, is revisited. It is shown that such a matrix can be interpreted as the Jacobian matrix of phi(s)--the map between the original phase space and the differential embedding induced by the observable--thus establishing a link between observability and embedding theory.
For many systems it is advantageous if analysis and modeling can be accomplished from a scalar time series because this greatly facilitates the experimental setup. Moreover, in real-life systems it is hardly true that all the state variables are available for analysis and modeling. Since the late 1980s, techniques have been put forward for building mathematical models from a scalar time series. One of the objectives of this paper is to verify if it is possible to obtain global non-linear models (non-linear differential equations) from scalar time series. Such data are obtained using a model of biochemical reaction with aperiodic (chaotic) oscillations as recently observed in the case of a glycolytic reaction (Nielsen, K., Sorensen, P.G., Hynne, F., 1997. Chaos in glycolysis. J Theor. Biol. 186, 303-306.). The main objective, however, is to investigate which state variable is more convenient for the task in practice. It is shown that observability indices seem to quantify quite well which variable should be preferred as the observable. The validity of the results are established performing rigorous topological analysis on the original system and the obtained models. The influence of noise, always present in experimental time series, on the dynamics underlying such a system is also investigated.
This work investigated if methods used to produce a uniformly sampled heart rate variability (HRV) time series significantly change the deterministic signature underlying the dynamics of such signals and some nonlinear measures of HRV. Two methods of preprocessing were used: the convolution of inverse interval function values with a rectangular window and the cubic polynomial interpolation. The HRV time series were obtained from 33 Wistar rats submitted to autonomic blockade protocols and from 17 healthy adults. The analysis of determinism was carried out by the method of surrogate data sets and nonlinear autoregressive moving average modelling and prediction. The scaling exponents alpha, alpha(1) and alpha(2) derived from the detrended fluctuation analysis were calculated from raw HRV time series and respective preprocessed signals. It was shown that the technique of cubic interpolation of HRV time series did not significantly change any nonlinear characteristic studied in this work, while the method of convolution only affected the alpha(1) index. The results suggested that preprocessed time series may be used to study HRV in the field of nonlinear dynamics.