Multifractal analysis of complex networks

Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal dimensions. Multifractal analysis is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. In this paper, we introduce a new box covering algorithm for multifractal analysis of complex networks. This algorithm is used to calculate the generalized fractal dimensions $D_{q}$ of some theoretical networks, namely scale-free networks, small world networks and random networks, and one kind of real networks, namely protein-protein interaction networks of different species. Our numerical results indicate the existence of multifractality in scale-free networks and protein-protein interaction networks, while the multifractal behavior is not clear-cut for small world networks and random networks. The possible variation of $D_{q}$ due to changes in the parameters of the theoretical network models is also discussed.Comment: 18 pages, 7 figures, 4 table

Emotions Detection based on a Single-electrode EEG Device

The study of emotions using multiple channels of EEG represents a widespread practice in the field of research related to brain computer interfaces (Brain Computer Interfaces). To date, few studies have been reported in the literature with a reduced number of channels, which when used in the detection of emotions present results that are less accurate than the rest. To detect emotions using an EEG channel and the data obtained is useful for classifying emotions with an accuracy comparable to studies in which there is a high number of channels, is of particular interest in this research framework. This article uses the Neurosky Maindwave device; which has a single electrode to acquire the EEG signal, Matlab software and IBM SPSS Modeler; which process and classify the signals respectively. The accuracy obtained in the detection of emotions in relation to the economic resources of the hardware dedicated to the acquisition of EEG signal is remarkable

The Fractal Dimension of SAT Formulas

Modern SAT solvers have experienced a remarkable progress on solving industrial instances. Most of the techniques have been developed after an intensive experimental testing process. Recently, there have been some attempts to analyze the structure of these formulas in terms of complex networks, with the long-term aim of explaining the success of these SAT solving techniques, and possibly improving them. We study the fractal dimension of SAT formulas, and show that most industrial families of formulas are self-similar, with a small fractal dimension. We also show that this dimension is not affected by the addition of learnt clauses. We explore how the dimension of a formula, together with other graph properties can be used to characterize SAT instances. Finally, we give empirical evidence that these graph properties can be used in state-of-the-art portfolios.Comment: 20 pages, 11 Postscript figure

Application of Fractal and Wavelets in Microcalcification Detection

Breast cancer has been recognized as one or the most frequent, malignant tumors in women, clustered microcalcifications in mammogram images has been widely recognized as an early sign of breast cancer. This work is devote to review the application of Fractal and Wavelets in microcalcifications detection

Classification and Verification of Online Handwritten Signatures with Time Causal Information Theory Quantifiers

We present a new approach for online handwritten signature classification and verification based on descriptors stemming from Information Theory. The proposal uses the Shannon Entropy, the Statistical Complexity, and the Fisher Information evaluated over the Bandt and Pompe symbolization of the horizontal and vertical coordinates of signatures. These six features are easy and fast to compute, and they are the input to an One-Class Support Vector Machine classifier. The results produced surpass state-of-the-art techniques that employ higher-dimensional feature spaces which often require specialized software and hardware. We assess the consistency of our proposal with respect to the size of the training sample, and we also use it to classify the signatures into meaningful groups.Comment: Submitted to PLOS On