RESUMO
Correlation dimension (CD), singularity exponents, also called scaling exponents, are widely used in multifractal chaotic series analysis. CD and other measures of effective dimensionality are used for characterization of data in applications. A direct use of CD to multidimensional data classification has not been hitherto presented. There are observations that the correlation integral is a distribution function of distances between all pairs of data points, and that by using polynomial expansion of distance with exponent equal to the CD this distribution is transformed into locally uniform. The classifier is based on consideration that the influence of neighbor points of some class on the probability that the query point belongs to this class is inversely proportional to its distance to the CD, power. New classification approach is based on summing up all these influences for each class. We prove that a resulting formula gives an estimate of probability of the class, not a measure of membership to a class only, to which the query point belongs. For this assertion to be valid, it is necessary that exponent of the polynomial transformation must be the CD. We also propose an averaging approach that speeds up computation of the CD especially for large data sets. It is demonstrated that the CD-based classifier can outperform more sophisticated classifiers.
RESUMO
The molecular basis of cellular auxin transport is still not fully understood. Although a number of carriers have been identified and proved to be involved in auxin transport, their regulation and possible activity of as yet unknown transporters remain unclear. Nevertheless, using single-cell-based systems it is possible to track the course of auxin accumulation inside cells and to specify and quantify some auxin transport parameters. The synthetic auxins 2,4-dichlorophenoxyacetic acid (2,4-D) and naphthalene-1-acetic acid (NAA) are generally considered to be suitable tools for auxin transport studies because they are transported specifically via either auxin influx or efflux carriers, respectively. Our results indicate that NAA can be metabolized rapidly in tobacco BY-2 cells. The predominant metabolite has been identified as NAA glucosyl ester and it is shown that all NAA metabolites were retained inside the cells. This implies that the transport efficiency of auxin efflux transporters is higher than previously assumed. By contrast, the metabolism of 2,4-D remained fairly weak. Moreover, using data on the accumulation of 2,4-D measured in the presence of auxin transport inhibitors, it is shown that 2,4-D is also transported by efflux carriers. These results suggest that 2,4-D is a promising tool for determining both auxin influx and efflux activities. Based on the accumulation data, a mathematical model of 2,4-D transport at a single-cell level is proposed. Optimization of the model provides estimates of crucial transport parameters and, together with its validation by successfully predicting the course of 2,4-D accumulation, it confirms the consistency of the present concept of cellular auxin transport.
