# Forskningsarrangementer

## Kommende 5 dager

**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...)

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.

The PDE seminars for the Autumn of 2021 will be held every Tuesday from 10:15–12:00

The talk is elementary and discusses empirical modelling of single variables with insurance losses as example. There are in such cases little or no theory to go on, and the amount of data is many situation quite scarce. Why do we so often limit ourselves to fit two-parameter families? It will be suggested that it may be a good idea to work with more flexible models with three or four parameters and that this may provide a nice framework for automating the entire procedure for the computer to work alone. Sure, with little data the parameters may be unstably estimated, but that may not apply equally to the distributions they define. Many-parameter families suitable for insurance losses will be reviewed with some simple asymptotics in an example allowing this and with Monte Carlo to throw light on the issue in other cases.

Senior Engineer Sigrid Rønneberg, Justervesenet (The Norwegian Metrology Service)

**Abstract:** *Mixed-dimensional partial differential equations (PDEs) are equations coupling unknown fields defined over domains of differing topological dimensions. Such mixed-dimensional PDEs naturally arise in a wide range of fields including geology, biomedicine, and fracture mechanics. We introduce an automated framework dedicated to mixed-dimensional problems as part of the FEniCS library. This talk gives an overview of the abstractions and algorithms involved. The introduced tools will be illustrated by concrete examples of applications in biomedicine (see below for more detailed context).*

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

## Flere kommende arrangementer

Professor Dan Crisan, Imperial College London, author of several books on filtering is now holding an intensive course.

PhD candidate William B. Reinar at the Department of Biosciences will be defending the thesis "Genomic short tandem repeats as modulators of gene expression and protein function" for the degree of PhD.

Ph.d.-kandidat Thea Sveva Faleide ved Institutt for geofag, Det matematisk-naturvitenskapelige fakultet, vil forsvare avhandlingen **Seismic imaging of faults and sedimentary systems of the Hoop region, Barents Sea – seismic facies, fault geometries and detection thresholds **for graden Philosophiae Doctor.

Sondre Vik Furuseth, Rosseland Centre for Solar Physics, UiO.