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Guest lectures and seminars - Page 11

Adam Lee: Locally robust and efficient tests for non-regular semiparametric models

Time and place: Nov. 21, 2023 9:15 AM – 10:15 AM, Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor

This paper considers hypothesis testing in semiparametric models which may be non – regular for certain values of a (potentially infinite dimensional) nuisance parameter. In such models no (locally) regular estimator of the parameter of interest exists. The situation for testing is somewhat different: I establish that C(α) – style test statistics achieve their limiting distributions in a (locally) regular manner under mild conditions, leading to tests with correct size in situations where standard tests fail to control size. Additionally, I characterise the appropriate limit experiment in which to study local (asymptotic) optimality of tests in the case where the efficient information matrix is singular. This permits the generalisation of classical power bounds to the non – regular case. I provide appropriate statements of these bounds and give conditions under which they are attained by the proposed C(α) – style tests. Three examples are worked out in detail.

Rami Masri - Pressure correction discontinuous Galerkin methods for Navier-Stokes and Cahn-Hilliard-Navier-Stokes systems

Time and place: Nov. 17, 2023 12:15 PM – 1:00 PM, Niels Henrik Abels hus, 9th floor

We combine a pressure correction scheme with interior penalty discontinuous Galerkin (dG) discretisation to solve the time-dependent Navier–Stokes equations. We prove unconditional energy stability and a priori error estimates for the velocity. With duality arguments, optimal L2 error rates are obtained. Convergence of the discrete pressure is also established. Further, we propose a splitting scheme, integrating the pressure correction approach, for the Cahn–Hilliard–Navier–Stokes system The numerical analysis of dG combined with this scheme is discussed. Namely, we show well--posedness, stability, and error estimates. Numerical results with manufactured solutions display our theoretical findings, and a spinodal decomposition example portrays the robustness of our approach.

Time and place: Nov. 14, 2023 2:15 PM – 3:15 PM, Erling Svedrups plass and Zoom https://uio.zoom.us/j/64912028556?pwd=QmJpa1ZPS0hBNTFZUDhzWDlaMmJKQT09

Traditional quantile estimators are not well-suited for data streams because the memory and computational time increase with the volume of data received from the stream. Incremental quantile estimators refer to a class of methods designed to maintain quantile estimates for data streams. These methods operate by making small updates to the estimate every time a new observation is received from the stream. In this presentation, I will introduce some of the incremental quantile estimators we have developed.

Marie Rognes - Brains in motion: Computational modelling of the brain's waterscape

Time and place: Nov. 10, 2023 1:00 PM – 2:00 PM, Niels Henrik Abels hus, 9th floor

Your brain has its own waterscape: whether you are reading, thinking or sleeping, fluid flows through or around the brain tissue, clearing waste in the process. These biophysical processes are crucial for the well-being and function of the brain. In spite of their importance we understand them but little, and mathematical and computational modelling could play a crucial role in gaining new insight. In this talk, I will give an overview of mathematical, mechanical and numerical approaches to understand mechanisms underlying pulsatility, fluid flow and solute transport in the human brain. Topics include fluid-structure interactions, generalized poroelasticity, mixed finite element discretizations and preconditioning, uncertainty quantification, and optimal control.