Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

Strange Nonchaotic Attractors

Aperiodic dynamics which is nonchaotic is realized on Strange Nonchaotic attractors (SNAs). Such attractors are generic in quasiperiodically driven nonlinear systems, and like strange attractors, are geometrically fractal. The largest Lyapunov exponent is zero or negative: trajectories do not show exponential sensitivity to initial conditions. In recent years, SNAs have been seen in a number of diverse experimental situations ranging from quasiperiodically driven mechanical or electronic systems to plasma discharges. An important connection is the equivalence between a quasiperiodically driven system and the Schr\"odinger equation for a particle in a related quasiperiodic potential, giving a correspondence between the localized states of the quantum problem with SNAs in the related dynamical system. In this review we discuss the main conceptual issues in the study of SNAs, including the different bifurcations or routes for the creation of such attractors, the methods of characterization, and the nature of dynamical transitions in quasiperiodically forced systems. The variation of the Lyapunov exponent, and the qualitative and quantitative aspects of its local fluctuation properties, has emerged as an important means of studying fractal attractors, and this analysis finds useful application here. The ubiquity of such attractors, in conjunction with their several unusual properties, suggest novel applications.Comment: 34 pages, 9 figures(5 figures are in ps format and four figures are in gif format

Imaging time series for the classification of EMI discharge sources

In this work, we aim to classify a wider range of Electromagnetic Interference (EMI) discharge sources collected from new power plant sites across multiple assets. This engenders a more complex and challenging classification task. The study involves an investigation and development of new and improved feature extraction and data dimension reduction algorithms based on image processing techniques. The approach is to exploit the Gramian Angular Field technique to map the measured EMI time signals to an image, from which the significant information is extracted while removing redundancy. The image of each discharge type contains a unique fingerprint. Two feature reduction methods called the Local Binary Pattern (LBP) and the Local Phase Quantisation (LPQ) are then used within the mapped images. This provides feature vectors that can be implemented into a Random Forest (RF) classifier. The performance of a previous and the two new proposed methods, on the new database set, is compared in terms of classification accuracy, precision, recall, and F-measure. Results show that the new methods have a higher performance than the previous one, where LBP features achieve the best outcome