Special Issue "Wavelets, Fractals and Information Theory III"
A special issue of Entropy (ISSN 1099-4300).
Deadline for manuscript submissions: closed (31 October 2017)
Prof. Dr. Carlo Cattani
Engineering School (DEIM) University of Tuscia, 01100 Largo dell'Università, Viterbo, Italy
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Interests: wavelets; fractals; fractional calculus; dynamical systems; data analysis; time series analysis; image analysis; computer science; computational methods; composite materials; elasticity; nonlinear waves
Wavelet Analysis and Fractals are playing fundamental roles in Science, Engineering applications, and Information Theory. Wavelet and fractals are the most suitable methods to analyze complex systems, localized phenomena, singular solutions, non-differentiable functions, and, in general, nonlinear problems. Nonlinearity and non-regularity usually characterize the complexity of a problem; thus being the most studied features in order to approach a solution to complex problems. Wavelets, fractals, and fractional calculus might also help to improve the analysis of the entropy of a system.
In information theory, entropy encoding might be considered a sort of compression in a quantization process, and this can be further investigated by using wavelet compression. There are many types of entropy definitions that are very useful in the Engineering and Applied Sciences, such as the Shannon-Fano entropy, the Kolmogorov entropy, etc. However, only entropy encoding is optimal for the complexity of large data analyses, such as in data storage. In fact, the principal advantage of modeling a complex system via wavelet analysis is the minimization of the memory space for storage or transmission. Moreover, this kind of approach reveals some new aspects and promising perspectives in many other kinds of applied and theoretical problems. For instance, in engineering applications, the best way to model traffic in wireless communications is based on fractal geometry, whereas the data are efficiently studied through wavelet basis.
This Special Issue will also be an opportunity for extending the research fields of image processing, differential/integral equations, number theory and special functions, image segmentation, the sparse component analysis approach, generalized multiresolution analysis, and entropy as a measure in all aspects of the theoretical and practical studies of Mathematics, Physics, and Engineering.
The main topics of this Special Issue include (but are not limited to):
- Entropy encoding, wavelet compression, and information theory.
- Fractals, Non-differentiable functions. Theoretical and applied analytical problems of fractal type, fractional equations.
- Fractal and wavelet solutions of fractional differential equations
- Wavelet Analysis, integral transforms and applications.
- Wavelet-fractal entropy encoding and computational mathematics in data analysis and time series, including in image analysis.
- Wavelet-fractal approach.
- Artifical Neural Networks.
Prof. Dr. Carlo Cattani
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1500 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
- Data analysis
- Image Analysis
- Dynamical System
- Differential Operators
The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.
Tentative title: Jumps and structural breaks in financial markets
Author: Ramazan Gencay and Ege Yazgan
Abstract: We evaluate the performance of jump detection tests by using simulated and real time high-frequency data in which frequent jumps and structural breaks are present. We define jumps as more than 3 standard deviation departures in the data with rapid mean reversion property; and structural breaks as without mean reversion (permanent breaks) or returning mean very sluggishly after initial departure (temporary breaks). We pay special attention to the performance of wavelet based jump test and find that the wavelet based test, especially when augmented by wavestrrapping, provide better performance.
Tentative title: Information Entropy in Metal Fractal Electrodeposits
Author: Rabih Sultan
Affiliation: Department of Chemistry, American University of Beirut