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Database Tomography (DT) is a textual database analysis system consisting of two major components: (1) algorithms for extracting multi-word phrase frequencies and phrase proximities (physical closeness of the multi-word technical phrases) from any type of large textual database, to augment (2) interpretative capabilities of the expert human analyst. DT was used to obtain technical intelligence from a Fractals database derived from the Science Citation Index/Social Science Citation Index (SCI). Phrase frequency analysis by the technical domain experts provided the pervasive technical themes of the Fractals database, and the phrase proximity analysis provided the relationships among the pervasive technical themes. Bibliometric analysis of the Fractals literature supplemented the DT results with author/journal/institution publication and citation data.

In this paper, the human fingerprint, which is independent of rotation and scaling, is recognized. The multiple classification technique, based on wavelet and fractal analysis, is used. It is shown that systematic incorporation of decision from various classifiers leads to a better decision rather than simply fusing them. Multiple classifiers can serve as a means of enhancing the performance of pattern recognition problems. Multiple classifier system design involves the problem of classifier fusion. This paper deals with multi-classifier systems in which each classifier uses its own representation of the input pattern, based on features collected from multiple sources. The multiple feature sources considered here are multi-fractals, wavelets and fast Fourier transforms coefficients. A clustering algorithm is used to observe the efficacy of the feature sources. The multiple sources were graded according to their effectiveness of providing more non-overlapping clusters for different groups into which the samples are to be separated. This approach first considers the best source for the feature parameters. If this feature classifies the test sample into more than one cluster, then the feature next to the best is summoned to finish up the remaining part of the classification process. The continuation of this process along with the judicious selection of classifiers succeeds in identifying a single cluster for the test sample. The results obtained after the experiments on a set of fingerprint images shows that this novel technique can go a long way in avoiding ambiguity and thus limiting the need for use of soft-computing tools for making decisions. Our method provides a hard, concrete and accurate solution to pattern recognition problems employing multiple classifiers.

In order to research mechanics of rock fracture instant, it is one of methods that rock fracture mechanics are researched by rock fracture surfaces’ morphology. Some researched results which come from international and domestic researches in decades are described and summarized from mathematics in this paper. For example, fractal dimension method, “Small Island Method”, fractal interpolation method, Multi-fractal method, the accumulation power spectral density method. In addition, advantages and insufficiencies of every method are reviewed and commented. In the end, the future researched expectations are put forward from three aspects of rock fracture surfaces’ morphology.

For the purpose of transmitting data in smart grids, broadband communication over power lines (PLC) is considered to be one of the feasible technologies. Due to the multi-path effect of the signal propagation in complicate electrical networks, PLC signals present some dynamic features in time and space domains. The mono-fractal and multi-fractal theories are introduced to understand such dynamic features in PLC signals. Four common methods, namely, re-scaled range analysis, variance–time plot method, periodic diagram analysis and wavelet-based method are used to study the nonlinear properties and self-similarity. Fractal analysis at different frequencies and times is also performed to verify further. The paper also tests multi-fractal properties of PLC signals by the means of multi-fractal detrended fluctuation analysis (MFDFA). The multi-fractal spectrum of power low exponents is estimated from the measured PLC signals. We also proposed a new algorithm to improve the performance of the traditional MFDFA, where wavelet theory is integrated. By simulations, the better performance of the proposed method is verified.

It is found that the pore microstructures of Juncus effusus (JE), a yearly renewable and high-yield cellulose fiber with unique three-dimensional network structure and interconnected channels, exhibit the fractal characters. The cross-sectional images are measured by SEM and the fractal dimensions are calculated by the box-counting method. In order to reveal more details of JE, the multi-fractal spectrum method is employed to analyze its local features, which further shows the fractal structures. The results indicate that the fractal characteristics are obvious although JE is complex and disordered in structure. The present fractal study may have the potential and significance on fractal analysis of mechanical properties and transport properties of these natural fibers.