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[CT048]

CT048 (1/1) : Miscellaneous topics in partial differential equations (35R) / Multivariate analysis (62H)

Session Time & Room : 4E (Aug.24, 17:40-19:20) @G701
Type : Contributed Talk
Abstract : We proposed a definition of Radon measure solutions to the compressible Euler equations with general constitutive relations. With this definition, we proved the Newton-Busemann law for stationary hypersonic flow passing bodies, constructed delta shock solutions to the Riemann problems of the rectilinear barotropic Euler equations, justified the interpretation of delta shocks as free pistons. This shows the possibility of treating solid-fluid interaction problems by simpler Cauchy problems with solutions in the class of Radon measures.
Classification : 35R06, 35Q31, 35D99
Format : Talk at Waseda University
Author(s) :
- Hairong Yuan (East China Normal University )
- Aifang Qu (Shanghai Normal University )

Session Time & Room : 4E (Aug.24, 17:40-19:20) @G701
Type : Contributed Talk
Abstract : Fractional partial differential equations model nonlocal processes such as wave absorption in the brain, long-range geophysical effects, and Lévy flights. We introduce a spectral method for the fractional Laplacian in one dimension that induces sparse linear systems. We only deal with the coefficients of the expansion and thus time-stepping is fast. We consider a number of examples including the fractional heat and fractional wave propagation equations.
Classification : 35R11, 65N35, 65M70, 65R10, Numerical Analysis, Nonlocal PDEs
Format : Talk at Waseda University
Author(s) :
- Ioannis P. A. Papadopoulos (Imperial College London)

Session Time & Room : 4E (Aug.24, 17:40-19:20) @G701
Type : Contributed Talk
Abstract : We propose some estimation techniques to estimate the elementary chirp model parameters. We derive asymptotic properties of least squares estimators (LSEs) and approximate least squares estimators (ALSEs) for the one-component elementary chirp model. We propose sequential LSEs and sequential ALSEs to estimate the multiple-component elementary chirp model parameters and prove that they have the same theoretical properties as the LSEs. We illustrate the performance of the proposed sequential algorithm on a bat data.
Classification : 62H12, 62F12
Format : Talk at Waseda University
Author(s) :
- Anjali Mittal (Indian Institute of Technology Kanpur)
- Rhythm Grover (Indian Institute of Technology Guwahati)
- Debasis Kundu (Indian Institute of Technology Kanpur)
- Amit Mitra (Indian Institute of Technology Kanpur)

Session Time & Room : 4E (Aug.24, 17:40-19:20) @G701
Type : Contributed Talk
Abstract : In this work, we propose a new nonparametric model to estimate distribution functions and densities with bounded support. In addition, we study the asymptotic properties of our estimator such as asymptotic bias, variance and asymptotic normality. The method is illustrated by simulation study and an application to a real data set.
Classification : 62H10, 62H12, 62H05, 65C20, 60E05
Format : Online Talk on Zoom
Author(s) :
- Nezha Mohaoui (Moulay Ismail University )

Session Time & Room : 4E (Aug.24, 17:40-19:20) @G701
Type : Contributed Talk
Abstract : The brain has a complex structure where different neurons are connected. To study brain activity and disorders, it is important to analyze the functional connectivity of the brain through network analysis. Because of high temporal and spatial resolution, MEG$\text{(magnetoencephalography)}$ can provide useful information for brain network analysis. We analyzed functional connectivity using static/temporal network statistics, MCCA$\text{(multiset canonical correlation analysis)}$, and TERGM$\text{(temporal exponential random graph model)}$ with epilepsy MEG data.
Classification : 62H22, 62P10
Format : Talk at Waseda University
Author(s) :
- Haeji Lee (Duksung women's university)
- Jaehee Kim (Duksung women's university)