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Time and place: , Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor

Deep learning (DL) has had unprecedented success and is now entering scientific computing with full force. However, current DL methods typically suffer from instability, even when universal approximation properties guarantee the existence of stable neural networks (NNs). In this talk we will show that there are basic well-conditioned problems in scientific computing where NNs with great approximation qualities are proven to exist, however, there does not exist any algorithm, even randomised, that can train (or compute) such a NN to even 1-digit of accuracy with a probability greater than 1/2. These results provide basic foundations for Smale’s 18th problem ("What are the limits of AI?") and imply a potentially vast classification theory describing conditions under which (stable) NNs with a given accuracy can be computed by an algorithm. We begin this theory by initiating a unified theory for compressed sensing and DL, leading to sufficient conditions for the existence of algorithms that compute stable NNs in inverse problems. We introduce Fast Iterative REstarted NETworks (FIRENETs), which we prove and numerically check (via suitable stability tests) are stable. The reference for this talk is: https://arxiv.org/abs/2101.08286 (to appear in Proc. Natl. Acad. Sci. USA).

Time and place: , Niels Henrik Abels hus, 9th floor, seminar room 919

Abstract: The fungal kingdom is one of the most species-rich organismal groups, containing up to 6 million species worldwide with a large diversity of ecosystem functions. Multicellularity has evolved independently in fungi, and over time many different growth forms and structures have originated. I will present some basics on fungal growth and the formation of complex multicellular structures.

Online participation is possible too. Please contact "timokoch at uio.no" for the Zoom link. This talk is part of the Mechanics Lunch Seminar series. Bring-your-own-lunch and lots of questions.

Time and place: , Online
Time and place: , NHA B1120
Hilbert schemes of points for a surface are a well studied subject with many famous results like Göttsche’s formula for its Betti numbers. A natural generalization comes from studying Grothendieck’s Quot-schemes and the associated enumerative invariants. Unlike the former, punctual Quot-schemes are smooth only virtually admitting perfect obstruction theories and virtual fundamental classes. This has recently been used to study invariants counting zero-dimensional quotients of trivial vector bundles by multiple authors who used virtual localization and therefore could not treat the case of a general vector bundle. We rely on other techniques which use a general wall-crossing framework of D. Joyce to study these. Our methods rely on existence of a Lie algebra coming from vertex algebras constructed out of topological data. I will explain how these arise naturally in the Quot-scheme setting and how one can obtain explicit invariants and study their symmetries.
Time and place: , Erling Svedrups plass (Niels Henrik Abel Hus, 8th floor) & ZOOM

Super-resolution is a hot topic in current day Machine Learning.  The origin of the methodology dates back to applications in seismic imaging. I discuss the evolution from the early days and highlight some papers which have given new theoretical insights along the way. I illustrate the bridge between traditional convex optimization and current day convolutional neural nets. Along the way I show some examples where we have used this for current day applications in seismic imaging.

Time and place: , Zoom

Doctoral candidate Christopher Lawrence at the Department of Mathematics, Faculty of Mathematics and Natural Sciences, is  defending the thesis Extreme Wave Statistics of Surface Gravity Waves over Bathymetry for the degree of Philosophiae Doctor.

Time:

Winter school at University of Oslo

Time and place: , Niels Henrik Abels hus, 9th floor, seminar room 919

Abstract: Transport and mixing in multiphase flow through porous media plays a key role in a range of biological, geological, and engineered systems. Here, we use numerical simulations to investigate the effect of intermittent multiphase flow on fluid stretching and folding, a fundamental mechanism driving solute mixing and reaction in porous media. We show that, in contrast to steady single-phase flows, the concurrent flow of two immiscible phases induces chaotic mixing, characterized by exponential stretching in the pore space. The stretching rate is found to decay with increasing capillary number, implying that the increasing flow intermittency observed at lower capillary numbers enhances the mixing efficiency. We propose a mechanistic model to link the basic multiphase flow properties to the chaotic mixing rate, opening new perspectives to understand mixing and reaction in multiphase porous media flows. The results presented here form part of the background for the recently started RCN-funded project M4: Mixing in Multiphase flow through Microporous Media, which will also be introduced.

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

Time and place: , Niels Henrik Abels hus, 9th floor, seminar room 919

Abstract:  The cerebral circulation must ensure continuous blood perfusion of the brain which is the biggest oxygen consumer in the human body. It must also provide mechanisms for adaptability to changing oxygen demand as well as resilience to local blockages. We will look at such mechanisms at the level of the microcirculation where the mechanics of blood flow is dominated by red blood cells. We will find that red blood cells do not only play the role of oxygen carriers, but that they are an important element of blood flow regulation itself. To this end, we will compare results from in vitro studies in microfluidic chips to theoretical and computational models and to in vivo data from mice. We will derive local auto-regulation mechanisms for blood flow and will study how local modifications in the vascular network can modify the global hematocrit distribution. These results will emphasize the relevance of red blood cell mechanics and microvascular network geometry in cerebral blood perfusion.

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

Time and place: , University of Oslo

For the third year in a row, STORM and TMS organize a workshop on rough path theory and related topics. It is held on 25-26 November 2021. 

Time and place: , Niels Henrik Abels hus, 9th floor, seminar room 919

Abstract:  Swimming bacteria, growing cell tissues, molecular motors, and microtubule systems confined to a substrate are examples of active matter films that exhibit long-range nematic (orientational) order. Intrinsic activity in these systems builds mechanical stresses that tend to destroy local nematic order through topological defects, which act as sources of persistent active flows.  The overall evolution and functionality of biological matter is greatly influenced by these orientational defects. Yet, their formation and dynamics are driven by a complex interplay between topological singularities in the nematic order and active flow instabilities, and this is not completely understood. 

Click title to continue reading abstract...

Time and place: , NHA B1120
When does the Zariski topology determine a variety? This certainly does not hold for curves, and examples of Wiegand and Krauter show it is neither true for countable surfaces. The cardinality assumption is important: The reconstruction theorem says that two homeomorphic (normal, projective) varieties of dimension at least two over non-countable fields of characteristic zero  K and L (a priori different) are in fact isomorphic (as schemes).
I shall present my version (a slight simplification of the original proof) of the cluster of ideas leading up to the reconstruction theorem (and maybe a miniscule extension to positive characteristic)
Time and place: , Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor

For many real-life phenomena one may assume that the units of observation, typically patients, transition through a set of discrete states on their way towards an absorbing state. The states often constitute various stages of a disease, from perfect health through various stages of dementia for example. Multi-state models are a class of statistical models which allow us to study the time spent in different states, the probability of transitioning between states, and the relationship between these quantities and covariates of interest. In many applications the transition times between states are not observed exactly; instead, the current state of the patients is queried at arbitrary times. The transition times are therefore interval censored, and this makes inference and modelling challenging. Most current approaches are based on the Markov assumption, for example the simplest parametric model available - the time-homogeneous Markov model. Here, we propose a new, general framework for parametric inference with interval censored multi-state data. Our models allow non-Markovian behaviour. I will present the framework and an algorithm for the automatic construction of the likelihood function, along with real-data examples. This talk is based on joint work with Marthe Aastveit and Nils Lid Hjort.

Time and place: , Niels Henrik Abels hus, 9th floor, seminar room 919

Abstract:  Exchange processes across a porous-medium free-flow interface occur in a wide range of environmental, technical, and bio-mechanical systems.  In the course of these processes, flow dynamics in the porous domain and in the free-flow domain exhibit strong coupling, often controlled by mechanisms at the common interfaces.  Such processes need to be analyzed on small scales and new scale-bridging modeling concepts need to be developed for an accurate description also on larger scales (REV scale). Recent developments within the Collaborative Research Center "Interface-Driven Multi-Field Processes in Porous Media – Flow, Transport and Deformation" and the Cluster of Excellence SimTech at the University Stuttgart regarding such aspects for coupled free-flow and porous-medium flow systems will be presented in this talk.

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

Time and place: , Niels Henrik Abels hus, 9th floor, seminar room 919

Abstract:  We present a second-order numerical scheme to compute capillary bridges between arbitrary solids by minimizing the total energy of all interfaces. From a theoretical point of view, this approach can be interpreted as the computation of generalized minimal surfaces using a Newton-scheme utilizing the shape Hessian. In particular, we give an explicit representation of the shape Hessian for functionals on shells involving the normal vector without reverting back to a volume formulation. From an algorithmic perspective, we combine a resolved interface via a triangulated surface for the liquid with a level-set description for the constraints stemming from the arbitrary geometry. The actual shape of the capillary bridge is then computed via finite elements provided by the FEniCS environment, minimizing the shape derivative of the total interface energy.

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

Time and place: , Zoom

To keep up the attention high in stochastics and its applications, we organise 1 day workshop on line. Welcome!

Time and place: , NHA 720

C*-algebra seminar talk by Ole Brevig (University of Oslo)

Time and place: , NHA B1119

Second of two lectures on constructing non-Fourier-Mukai functors

Time and place: , Niels Henrik Abels hus, 9th floor, seminar room 919

Abstract:  After a broad overview of the activities of MecaWet group at PMMH, the presentation will focus on the “dry side” of MecaWet.

Drawing a flat map of the Earth is fundamentally challenging as continents unavoidably end up distorted. Reciprocally, complex natural shapes such as the delicate shape of Orchidea petals emanate from differential growth. From an engineering point of view, similar shape changes can be obtained when flat patches embedded with a network of channels are inflated. We will discuss two opposite strategies involving stretchable elastomers or, conversely, stiff fabrics. Can we program the resulting 3D shapes? How robust are such inflated structures?

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

Time and place: , NHA B1120

First of two lectures on constructing non-Fourier-Mukai functors

Time and place: , NHA B1120
Time and place: , Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor

Cards are drawn, one at a time, with replacement, from a deck of n cards. I study the total time W_n needed until we have seen all n cards, via different perspectives, along with a Gumbel limiting distribution. Various non-trivial identities, involving different perspectives for moments and Laplace transformations, are found as corollaries. These findings are also used to estimate the number of different cards,if uknown. If I needed to sample 133 words from a document, before I had 50 different words, what is the vocabulary size for the document? How many words did Shakespeare know (including those he never used in his writing)? 

An Abels Tårn podcast about some of these themes, which attracted a fair amount of inspired comments and guesses from the public (specifically, finding the mean of W_n above, for the case of n = 52 cards), can be found on the Abels Tårn website, July 2021, as a conversation with Torkild Jemterud, Jo Røislien, and myself. 

Time and place: , Room 720, Niels Henrik Abels hus, Zoom

Doctoral candidate Qinghua Liu at the Department of Mathematics, Faculty of Mathematics and Natural Sciences, is  defending the thesis Bayesian Preference Learning with the Mallows Model for the degree of Philosophiae Doctor.

Time and place: , Seminar room 1020, Niels Henrik Abel's house

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