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[CT058]

Session Date & Time : 1C (Aug.21, 13:20-15:00)
Type : Contributed Talk
Abstract : This talk deals with Hermite's osculatory interpolating splines. For a partition of a real interval endowed with a refinement consisting in dividing each subinterval into two small subintervals, we consider a space of smooth splines with super-smoothness at the vertices of the initial partition, and of the lowest possible degree. A normalized B-spline-like representation for the considered spline space is provided. In addition, several quasi-interpolation operators based on blossoming and control polynomials have also been developed. Some numerical tests are presented and compared with some recent works to illustrate the performance of the proposed approach.
Classification : 41A15
Author(s) :
- Mohamed BOUSHABI (Abdelmalek Essaadi University, LaSAD, ENS, 93030 Tetouan, Morocco)
- Salah Eddargani ( University of Rome Tor Vergata Rome)
- María José Ibáñez (University of Granada)
- Abdellah Lamnii (Abdelmalek Essaadi University, LaSAD, ENS, 93030 Tetouan, Morocco)

Session Date & Time : 1C (Aug.21, 13:20-15:00)
Type : Contributed Talk
Abstract : Neural networks show strong performance for function approximation, but provable guarantees typically rely on hand-picked weights and are therefore not fully practical. The aim for a small number of weights in approximation is opposed to over-parametrization by very wide or even infinitely wide networks in contemporary optimization results. The talk reconciles approximation and optimization results and provides approximation bounds that are guaranteed for gradient descent trained neural networks.
Classification : 41A46, 65K10, 68T07
Author(s) :
- Gerrit Welper (University of Central Florida)
- Russell Gentile (n/a)

Session Date & Time : 1C (Aug.21, 13:20-15:00)
Type : Contributed Talk
Abstract : Brain tumour is the uncontrolled growth of normal brain cells and most malignant form is known as glioma. In this work, the formulation and implementation of the Arithmetic Mean iterative methods for solving glioma growth models are presented. Numerical results and convergence analysis are included to verify the performance of the proposed methods.
Classification : 41A55, 45A05, 45B05, 65D32, 65F10
Author(s) :
- Mohana Sundaram Muthuvalu (Universiti Teknologi PETRONAS)
- Jumat Sulaiman (Universiti Malaysia Sabah)
- Elayaraja Aruchunan (Universiti Malaya)
- Majid Ali (Universiti Sains Malaysia)
- Ramoshweu Solomon Lebelo (Vaal University of Technology)

Session Date & Time : 1C (Aug.21, 13:20-15:00)
Type : Contributed Talk
Abstract : We propose novel graph convolution models for analyzing graph-structured time series data. Graph convolutional networks (GCNs) is a generalization of convolutional neural networks from regular grid data to irregular graph data. The major building block of a GCN is the filter. Graph filters are designed for graph convolution in spatial and spectral domains. We also propose novel graph wavelet transform methods to be jointly used with graph convolution filters, which can further improve the results.
Classification : 42BXX, Machine learning, graph signal processing
Author(s) :
- Jia He (Illinois Institute of Technology)
- Maggie Cheng (Illinois Institute of Technology)

Session Date & Time : 1C (Aug.21, 13:20-15:00)
Type : Contributed Talk
Abstract : We present, in our talk, an alternative version of the convolution and duality formula, and we give some results on functions and distribution spaces for the general double-sided orthogonal planes split quaternion Fourier transform. We provide the discrete representation of Z2−periodic function for continuous quaternion Wavelet transform. Finally, we prove the Plancherel and inversion formulas for the continuous General double-sided orthogonal 2D−planes split quaternionic Wavelet transform.
Classification : 42C40, 42B10, 14D21
Author(s) :
- Hakim Monaim (Moulay Ismail University)