International Conference on Applications of Fractals and Wavelets
The department of Mathematics, Amrita School of Engineering, Coimbatore campus organized a two-day international conference on Applications of Fractals and Wavelets (ICAFW) – 2015 from January 10-11, 2015. The two-day conference was inaugurated by Padma Shri. V. P. Dimri, Former Director, Distinguished Professor, CSIR – National Geophysical Research Institute, Hyderabad, India.
A total of 61 abstracts were received from the research community of both Mathematics and Engineering domain across the world. Among those submitted abstracts, only 49 full length articles were received. After the preliminary review, a total of 32 articles were accepted for the oral presentation in the conference. Meanwhile, a peer review committee was formed to identify the highly contributory articles among the articles accepted for presentation to bring out a special issue in Scopus indexed Journal.
The plenary talks held during the conference are as follows:-
Professor Ashish Ghosh, Head, Machine Intelligence Unit, Indian Statistical Institute Kolkata, India addressed the gathering on the topic, Image Analysis. The pre-processing, data reduction and feature analysis of an image to extract information in solving a problem of interest was the focus of his talk. Most specifically noise reduction and edge detection involving Wavelets were insisted in his talk and threw some light on the recent developments in this domain.
Padma Shri. V. P. Dimri, NGRI - CSIR, Hyderabad, India delivered talk on FractalApproach to Geophysical Studies. He introduced the concept of fractal geology to the participants and established the relation between fractal geology and its geophysical response. He concluded that the fractal based approach for geophysical data performs better than the conventional methods.
A talk on Transformations on Attractors of Iterated Function System was handled by Professor P. B. Vinodkumar, Rajagiri School of Engineering and Technology, Kerala, India. He discussed about the iterated function system on topological spaces and various conditions for such systems to have unique attractor.
Professor Govindan Rangarajan, Head, Department of Mathematics, Indian Institute of Science, Bangalore, India dealt with the topic of Quantifying Functional Connectivity in Brain Networks using Granger Causality. He stressed the increasing importance of detecting functional connectivity between different regions of a neuronal network. He further extended the Granger formulation to the non-parametric case and Granger Causality point processes using spectral factorization.
Professor M. A. Navascues, Department of Mathematics, University of Zaragoza, Spain spoke on Construction of Fractal Bases for Spaces of Functions. She expressed the significance of families of fractal functions that generalize the classical Schauder system of Banach spaces and the orthonormal bases of Hilbert spaces. She insisted the appropriate selection of the coefficients of Iterated function system that span the most important spaces of functions.
Professor AKB Chand, Department of Mathematics, IIT Madras, Chennai, India elucidated on the Restricted Range Approximation with Fractal Trigonometric Polynomials. “An appropriate element of Fractal Interpolation function was identified so that the corresponding fractal function lies always either above or below certain function. This basic result was applied to deduce the one sided approximation in the context of traditional trigonometric polynomials,” he explained. Prof Chand could establish that this effort is the humble attempt to take a step forward in the theory of fractal approximation.
Professor CS Sastry, Department of Mathematics, IIT Hyderabad, India shed light on the topic Next Generation Bases for Sparse Representation: Theory and Applications. His presentation aim at identifying two types of more general bases that provides sparse representation to data of several types. In particular he discussed the theory and applications of data driven as well data independent dictionaries as a result of thinking ahead of Wavelets.
The conference came to a close with a valedictory note stressing the significance of Fractals and Wavelets and their applications to the real time problems and the participants expressed their satisfaction over the theme and the quality of the plenary talks and the way the conference was organized.