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This is a half-day online workshop on PDEs in physical systems. Abstracts and Zoom link can be found here!

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

This talk will focus on recent work about the sequential detection of anomalies within partially observed functional data, motivated by a problem encountered by an industrial collaborator. Classical sequential changepoint detection approaches look for changes in the parameters, or structure, of a data sequence and are not equipped to handle the complex non-stationarity and dependency structure of functional data. Conversely, existing functional data approaches require the full observation of the curve before anomaly detection can take place. We propose a new method, FAST, that performs sequential detection of anomalies in partially observed functional data. This talk will introduce the approach, and some associated theoretical results, and highlight its application on telecommunications data.

This is joint work with Idris Eckley and Lawrence Bardwell.

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

The human brain has no lymphatic vessels, so how does the brain clear metabolic waste? In 2012, Iliff et al. proposed a theory about waste clearance of the brain, called the "glymphatic" theory. The theory suggest that the waste clearances is bio-mechanical, and that impaired clearance may be the cause of some neurodegenerative diseases and disorders. The inaccessibility of the human brain have been a hurdle in the research, as experiments on rat brains do not translate to the human brain. Researchers at Oslo university hospital Rikshospitalet have shown clearance using tracers visible in magnetic resonance images (MRI). However, the MRI only provide snapshots of different states in time, therefore computational modeling is needed to fill in the gaps. In this presentation, we will look at computational modeling with the MRI to infer material parameters in the brain.

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

Stalagmites grow on the floor of caves by precipitation of calcium ions found in the residual water film covering the top of the stalagmite, which is progressively drained away. Drops dripping from stalactites ensure the renewal of these ions.
Previous models of stalagmite growth assumed that drops fall on a straight vertical line from stalactites. Through high-speed imaging during field experiments in caves, we however observe that the impact point position of the drops is scattered. Using a Langevin-like equation to describe the fall of drops in response to gravity and aerodynamic forces, we then propose a prediction of the impact point dispersal. We show that measured stalagmite widths are correlated to the impact point dispersal of the drops.
In a second time, we focus on the mixing of calcium ions between the drop and the film during impact. The drop produces a crown when impacting the film, accompanied by a large amount of secondary droplet ejections. This is at the very heart of the film thickness variability post-impact. We record high-speed imaging of drop impacts on films of controlled thickness in a lab environment and assess the mixing between the drop and the film. We deduce how much liquid coming from the initial drop remains in the film.

Time and place: , Abels Utsikt (NHA 1259)
Time and place: , Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor

A flexible predictive density combination is introduced for large financial data sets which allows for model set incompleteness. Dimension reduction procedures that include learning allocate the large sets of predictive densities and combination weights to relatively small subsets.  Given the representation of the probability model in extended nonlinear state-space form, efficient simulation-based Bayesian inference is proposed using parallel dynamic clustering as well as nonlinear filtering, implemented on graphics processing units. The approach is applied to combine predictive densities based on a large number of individual US stock returns of daily observations over a period that includes the Covid-19 crisis period.  Evidence on dynamic cluster composition, weight patterns and model set incompleteness gives valuable signals for improved modelling. This enables higher predictive accuracy and better assessment of uncertainty and risk for investment fund management.

Time and place: , NHA B1120
Hilbert schemes of points on a smooth projective curve are simply symmetric powers of the curve itself; they are smooth and we know essentially everything about them. We propose a variation by studying double nested Hilbert schemes of points, which parametrize flags of 0-dimensional subschemes satisfying certain nesting conditions dictated by Young diagrams. These moduli spaces are almost never smooth but admit a virtual structure à la Behrend-Fantechi. We explain how this virtual structure plays a key role in (re)proving the correspondence between Gromov-Witten invariants and stable pair invariants for local curves, and say something on their K-theoretic refinement.
Time and place: , Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor

Online changepoint detection algorithms based on likelihood-ratio tests have excellent statistical properties. However, a simple exact online implementation is computationally infeasible as, at time T, it involves considering O(T) possible locations for the change. To improve on this, we use functional pruning ideas to reduce the set of changepoint locations that need to be stored at time T to approximately log T. Furthermore, we show how we need only maximise the likelihood-ratio test statistic over a small subset of these possible locations. Empirical results show that the resulting exact online algorithm, which can detect changes under a wide range of models, has a constant-per-iteration cost on average. We consider applications of this algorithm in the context of detecting increases in radiation count that represent astronomical or nuclear events of interest.

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

The Kolmogorov N-width describes the best possible error one can achieve by elements of an N-dimensional linear space. Its decay has extensively been studied in Approximation Theory and for the solution of Partial Differential Equations (PDEs). Particular interest has occurred within Model Order Reduction (MOR) of parameterized PDEs e.g. by the Reduced Basis Method (RBM). While it is known that the N-width decays exponentially fast (and thus admits efficient MOR) for certain problems, there are examples of the linear transport and the wave equation, where the decay rate deteriorates to N-1/2. On the other hand, it is widely accepted that a smooth parameter dependence admits a fast decay of the N-width. However, a detailed analysis of the influence of properties of the data (such as regularity or slope) on the rate of the N-width seems to lack. In this work, we use techniques from Fourier Analysis to derive exact representations of the N-width in terms of initial and boundary conditions of the linear transport equation modeled by some function g for half-wave symmetric data. For arbitrary functions g, we derive bounds and prove that these bounds are sharp. In particular, we prove that the N-width decays as cr N(-r-1/2) for functions in the Sobolev space, g ∈ Hr. Our theoretical investigations are complemented by numerical experiments which confirm the sharpness of our bounds and give additional quantitative insigh.

Time and place: , room 1259 (Abels Utsikt) - Niels Henrik Abels hus

Doctoral candidate Alise Danielle Midtfjord at the Department of Mathematics will be defending the thesis Machine learning methods for safety-critical systems with time dependency for the degree of Philosophiae Doctor.

Time and place: , NHA B1120
Donaldson-Thomas theory is a well-celebrated modern tool for studying Calabi-Yau threefolds. In this theory, one studies weighted Euler characteristics of moduli spaces of sheaves on threefolds. Elliptic genus on the other hand is a refinement of Euler characteristic motivated by a hypothesis of Witten. In this talk I will discuss and present evidence of a surprising relationship between the two. That is, a relationship between the Elliptic genus of sheaves surfaces and the Donaldson-Thomas theory of elliptically fibred threefolds.
Time and place: , Abels Utsikt (NHA 1259)
Time and place: , Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor

This talk will introduce a recent suite of research focussed on the statistical detection of anomalous structure in online data settings. The challenge of efficiently identifying anomalies in data sequences is an important statistical problem that now arises in many applications. Whilst there has been substantial work aimed at making statistical analyses robust to outliers, or point anomalies, there has been much less work on detecting anomalous segments, or collective anomalies, particularly in those settings where point anomalies might also occur. This is the challenge we seek to address, demonstrating theoretical results in both the offline and online settings as well as introducing some applied case studies.

Time and place: , NHA107

C*-algebra seminar talk by Makoto Yamashita (University of Oslo)

Time and place: , University of Oslo

You are cordially welcome to participate in this three-day workshop on energy, climate, and ESG. As last year, the workshop will gather academics and practitioners from the industry, discussing the latest advances on the stochastics of risk measuring, modelling and managing, with a focus on energy systems, climate, and finance (ESG).

Key topics involve modelling uncertainty in weather and climate, optimisation problems related to energy systems to control emissions, as well as measuring risk factors related to climate change. 

There will be several invited talks by leading researchers as well as selected contributed talks by participants.

Time and place: , NHA 723 and Online
Time and place: , Abels Utsikt (NHA 1259)
Time and place: , Niels Henrik Abels hus, 9th floor

We discuss discretizations and solvers for a class of numerical methods for convection diffusion equations in arbitrary spatial dimensions. Targeted applications include the Nernst-Plank equations for transport of species in a charged media. We illustrate how such exponentially fitted methods are derived. A main step in proving error estimates is showing unisolvence for the quasi-polynomial spaces of differential forms defined as weighted spaces of differential forms with polynomial coefficients. We show that the unisolvent set of functionals for such spaces on a simplex in any spatial dimension is the same as the set of such functionals used for the polynomial spaces. We are able to prove our results without the use of Stokes' Theorem, which is the standard tool in showing the unisolvence of functionals in polynomial spaces of differential forms.
This is joint work with Shuonan Wu (Beijing University)

Time and place: , NHA 723 and Online
Time and place: , NHA B1120

I will talk about some new examples of varieties where the coniveau and strong coniveau filtrations are different. This is joint work with Jørgen Vold Rennemo.

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

Douglas Wiens (Department of Mathematics and Statistical Sciences, University of Alberta, CAN) will give a talk on Wednesday April 19th at 14:15 in the Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor.

Time and place: , NHA107

Operator algebra seminar by Alexander Müller-Hermes (University of Oslo)

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

Variable selection methods based on L0 penalties have excellent theoretical properties to select sparse models in a high-dimensional setting. There exist modifications of BIC which either control the family wise error rate (mBIC) or the false discovery rate (mBIC2) in terms of which regressors are selected to enter a model. However, the minimization of L0 penalties comprises a mixed integer problem which is known to be NP hard and therefore becomes computationally challenging with increasing numbers of regressor variables. This is one reason why alternatives like the LASSO have become so popular, which involve convex optimization problems which are easier to solve. The last few years have seen some real progress in developing new algorithms to minimize  L0 penalties. We will compare the performance of these algorithms in terms of minimizing L0 based selection criteria.
Simulation studies covering a wide range of scenarios which are inspired by genetic association studies are used to compare the values of selection criteria obtained with different algorithms. Additionally some statistical characteristics of the selected models and the runtime of algorithms are compared.

Time and place: , Abels Utsikt (Niels Henrik Abels hus) and Online

Lecturer: Christa Cuchiero (University of Vienna)

Time and place: , NHA107

QOMBINE seminar talk by Vebjørn Hallberg Bakkestuen (UiO)