Guest lectures and seminars - Page 49

In this talk I will discuss the variational form of Bayes theorem by Zellner (1988). This result is the rationale behind the variational (approximate) inference scheme, although it is not always that clear in modern presentations. I will discuss two applications of this results. First, I will show how to do a low-rank mean correction within the INLA framework (with amazing results), which is essential for the next generation of the R-INLA software currently in development. In the second one, I will introduce the Bayesian   learning rule, which unify many machine-learning algorithms from fields such as optimization, deep learning, and graphical models. This includes classical algorithms such as ridge regression, Newton's method, and Kalman filter, as well as modern deep-learning algorithms such as stochastic-gradient descent, RMSprop, and Dropout.

The first part of the talk is based on our recent research at KAUST, while the second part is based upon \texttt{arxiv.org/abs/2107.04562} with Dr. Mohammad Emtiyaz Khan, RIKEN Center for AI Project, Tokyo.

Abstract: The concept of symmetry breaking is well-known in physics, for instance in condensed matter, where it results from interactions in a many-body system — e.g., phase transition in a spin system. Yet, as physicists, we tend not to think of the patterned structures seen in living, many-body systems in terms of broken symmetries. Whether it is the spacing of knuckles on our hand, the collective alignment of hairs on an insect wing, or more globally the transformation of a homogeneous, isotropic embryo into a developed organism, symmetry breaking abounds in biology. What new insights can a physicist bring to understand the origin of these complex phenomena? (Click title to read full abstract below...)

Abstract: Elimination of substances from the brain is believed to occur by a combination of convection and diffusion. In previous work, transport along perivascular spaces around blood vessels have been explicitly meshed and modeled, and also 1D-3D models have been used to model the interaction between blood and brain tissue. A problem with both these approaches is that it requires spatial information of all blood vessels within the brain and in addition may result in a computationally expensive system to solve. In this talk, I will introduce a homogenized model of transport in the brain, also taking into account transfer between different compartments (like blood and brain tissue) within the brain. Fluid flow in and between compartments are modeled with the mulitple-porosity elasticity theory (MPET), while transport within and between compartments are modeled with convection-diffusion equations. I will further show preliminary results from our model and compare with experimental data obtained in a glioma (brain tumor) patient, where transport between blood and brain is typically altered.

This talk is part of the Mechanics Lunch Seminar series. Bring-your-own-lunch and lots of questions.