ENHANCING MULTISCALE FRACTAL DESCRIPTORS USING FUNCTIONAL DATA ANALYSIS

This work presents a novel approach in order to increase the recognition power of Multiscale Fractal Dimension (MFD) techniques, when applied to image classification. The proposal uses Functional Data Analysis (FDA) with the aim of enhancing the MFD technique precision achieving a more representative descriptors vector, capable of recognizing and characterizing more precisely objects in an image. FDA is applied to signatures extracted by using the Bouligand-Minkowsky MFD technique in the generation of a descriptors vector from them. For the evaluation of the obtained improvement, an experiment using two datasets of objects was carried out. A dataset was used of characters shapes (26 characters of the Latin alphabet) carrying different levels of controlled noise and a dataset of fish images contours. A comparison with the use of the well-known methods of Fourier and wavelets descriptors was performed with the aim of verifying the performance of FDA method. The descriptor vectors were submitted to Linear Discriminant Analysis (LDA) classification method and we compared the correctness rate in the classification process among the descriptors methods. The results demonstrate that FDA overcomes the literature methods (Fourier and wavelets) in the processing of information extracted from the MFD signature. In this way, the proposed method can be considered as an interesting choice for pattern recognition and image classification using fractal analysis.

Solvatochromism in Binary Mixtures: First Report on a Solvation Free Energy Relationship between Solvent Exchange Equilibrium Constants and the Properties of the Medium

We have employed UV-vis spectroscopy in order to investigate details of the solvation of six solvatochromic indicators, hereafter designated as ""probes"", namely, 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (RB); 4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePM; 1-methylquinolinium-8-olate, QB; 2-bromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr, 2,6-dichloro-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (WB); and 2,6-dibromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr,, respectively. These can be divided into three pairs, each includes two probes of similar pK(a) in water and different lipophilicity. Solvation has been studied in binary mixtures, BMs, of water, W, with 12 protic organic solvents, S, including mono- and bifunctional alcohols (2-alkoxyethanoles, unsaturated and chlorinated alcohols). Each medium was treated as a mixture of S, W, and a complex solvent, S-W, formed by hydrogen bonding. Values of lambda(max) (of the probe intramolecular charge transfer) were converted into empirical polarity scales, E(T)(probe) in kcal/mol, whose values were correlated with the effective mole fraction of water in the medium, chi w(effective). This correlation furnished three equilibrium constants for the exchange of solvents in the probe solvation shell; phi(W/S) (W substitutes S): phi(S-W/W) (S-W substitutes W), and phi(S-W/S) (S-W substitutes S), respectively. The values of these constants depend on the physicochemical properties of the probe and the medium. We tested, for the first time, the applicability of a new solvation free energy relationship: phi = constant + a alpha(BM) + b beta(BM) + s(pi*(BM) + d delta) + p log P(BM), where a, b, s, and p are regression coefficients alpha(BM), beta(BM), and pi*(BM) are solvatochromic parameters of the BM, delta is a correction term for pi*, and log P is an empirical scale of lipophilicity. Correlations were carried out with two-, three-, and four-medium descriptors. In all cases, three descriptors gave satisfactory correlations; use of four parameters gave only a marginal increase of the goodness of fit. For phi(W/S), the most important descriptor was found to be the lipophilicity of the medium; for phi(S-W/W) and phi(S-W/S), solvent basicity is either statistically relevant or is the most important descriptor. These responses are different from those of E(T)(probe) of many solvatochromic indicators in pure solvents, where the importance of solvent basicity is usually marginal, and can be neglected.

Cellulose swelling by protic solvents: which properties of the biopolymer and the solvent matter?

The question posed in the title has been addressed by studying the swelling of celluloses at 20 C by twenty protic solvents, including water; linear- and branched-chain aliphatic alcohols; unsaturated aliphatic alcohols, and alkoxyalcohols. The biopolymers investigated included microcrystalline cellulose, MC, native and never-dried mercerized cotton cellulose, cotton and M-cotton, and native and never-dried mercerized eucalyptus cellulose, eucalyptus and M-eucalyptus, respectively. In most cases, better correlations with the physico-chemical properties of the solvents were obtained when the swelling was expressed as number of moles of solvent/anhydroglucose unit, nSw, rather than as % increase in sample weight. The descriptors employed in these correlations included, where available, Hildebrand`s solubility parameters, Gutmann`s acceptor and donor numbers, solvent molar volume, V(S), as well as solvatochromic parameters. The latter, employed for the first time for correlating the swelling of biopolymers, included empirical solvent polarity, E(T)(30), solvent ""acidity"", alpha(S), ""basicity"", beta(S), and dipolarity/polarizability, pi(S)*, respectively. Small regression coefficients and large sums of the squares of the residues were obtained when values of nSw were correlated with two solvent parameters. Much better correlations were obtained with three solvent parameters. The most statistically significant descriptor in the correlation equation depends on the cellulose, being pi(S)* for MC, cotton, and eucalyptus, and V(S) for M-cotton and M-eucalyptus. The best correlations were obtained with the same set of four parameters for all celluloses, namely, solvent pKa (or alpha(S)) beta(S), pi(S)*, and V(S), respectively. These results indicate that the supra-molecular structure of the biopolymer, in particular the average sizes of crystallites and micro-pores, and the presence of its chains in parallel (cellulose I) or anti-parallel (cellulose II) arrangements control its swelling. At least for the present biopolymer/solvent systems, use of solvatochromic parameters is a superior alternative to Hildebrand`s solubility parameters and/or Gutmann`s acceptor and donor numbers. The relevance of these results to the accessibility of the hydroxyl groups of cellulose, hence to its reactivity, is briefly discussed.