Theory of wavelets, a small oscillation limited in duration, is a mathematical model for non-stationary signals through a set of components in the form of small waves termed as wavelets. The theory is reliant on two notions which are scaling and translation as well as multiresolution analysis. As mathematical functions decomposing data into different frequency components and analyzing each of the components with a resolution which matches its scale, wavelets serving as a building block to reconstruct a signal or dataset are scaled to capture differing levels of detail and translated for analyzing specific regions of a signal. Multiresolution enables wavelets to analyze data at different levels of detail, which can in a way provide a zoom-in and zoom-out benefit to achieve higher resolution prospects and broader views, respectively.

Wavelets owing to their efficient and versatile qualities have a broad range of applications over diverse domains including but are not limited to signal processing, time-frequency analysis, medical imaging, signal and / or image processing, fluid dynamics, machine learning and artificial intelligence (AI). The employment of wavelets in these areas provide significant benefits related to efficiency, practicality, localization and multiscale aspects.

Multifractal analysis, employed to investigate various datasets frequently along with other fractal methods and lacunarity analysis, which as a technique involves the distorting of datasets that are extracted from patterns for generating multifractal spectra, depicting how scaling varies across the dataset. Multifractal analysis and wavelets are closely linked for the purposes of signal processing and data analysis, concerning multifractal formalism, where wavelets provide a framework with respect to describing the geometric and statistical distribution of singularities in a function, which in turn facilitates the understanding of the scaling behavior regarding functions and signals. Moreover, characterizing local regularity and addressing wavelet series with multifractal behavior are other aspects to be noted as wavelet series exhibiting   multifractal behavior can be employed for constructing series toward analyzing and  synthesizing of multifractal signals. These features make multifractal analysis and wavelets versatile, numerically robust and beneficial for analyzing complex signals and data in different areas like mathematics, engineering, applied sciences, medicine, genetics, neuroscience, biology, psychics, geophysics, computer and information sciences, finance, to name some.

Mathematical modeling, in these regards, can establish the foundation for wavelet-based analysis owing to the representation of the inherent dynamics of complex systems. At this juncture, wavelets are employed for facilitating multiscale decomposition of data, which allows multifractal analysis to reveal the elaborate critical scaling patterns and elements.

Based on these multilayered and integrative theories, methods, numerical analyses, techniques and applications, our special session aims at showcasing novel applications surrounding wavelets, multifractal analysis, machine learning, deep learning and AI while integrating them with other applicable mathematical models.

The topics include but are not limited to: