When randomising the timestep sizes in Euler‘s method, we need to linearly interpolate between subsequent timepoints to approximate the ODE solution at times of interest. The resulting piecewise linear path can sometimes be written as a Markov process.
I have analysed this Markov process:
Andrea Bertozzi, Nadia Drenska, Matt Thorpe, and I have guest edited a theme issue on “Partial differential equations in data science” in the Philosophical Transactions of the Royal Society A.
Take a look: royalsocietypublishing.org/toc/rsta/202...
@royalsociety.org @royalsocietypublishing.org
#Oberwolfach: every mathematician’s happy place
Exciting news! 😊
Best of luck for the election, Master!
A few years ago, Björn Sprungk and I had written a contribution towards the “Snapshots of Modern Mathematics from #Oberwolfach” (publications.mfo.de/handle/mfo/3...).
Once in a while a collection of snapshots is published in a volume. I have received my copy today. 😊
Why do people call it _adaptive MCMC_ instead of
- CMC
- “M”CMC
- \hat{M}CMC
- M😉CMC
#sciencememe
Please find below the announcement for the
2nd RSS/Turing Workshop on Gradient Flows for Sampling, Inference, and Learning
(I am a speaker ☺️)
Earlier today I gave my first talk for 2025 — in the Applied Mathematics Seminar at the University of Glasgow! Great audience and nice discussions afterwards. 😊
Luxair plane at an airport
Did you know that Schengen is a small village in Luxembourg? It is right at the French-German-Luxembourgish trijunction. I grew up nearby and I can assure you that it is my favourite border to cross.
See you in 2025! ☺️
Stationary Gaussian processes are often inappropriate as priors in Bayesian image reconstruction. When using non-stationary priors, the non-stationarity needs to be carefully estimated.
New preprint (with Aretha L. Teckentrup and Simon Urbainczyk)
arxiv.org/abs/2412.10248
Overleaf is down. What was the last thing you were writing about on there?
I‘ll start: the K-Means method
Thank you for the nice feedback! 😊
At last year‘s Edinburgh Science Festival, we organised a ‚Mathematics Showdown‘: five PhD students give engaging research talks for a general audience, the audience votes for a winner.
Here are the talks:
Markovian #Meme.
Open PhD position
Anna Scaife and I are looking for a PhD student interested in analysing astronomical images using modern physics-on-graphs-based machine learning methods. The position is within the UKRI-CDT AI in Decision Making for Complex Systems.
Please share with potential candidates! 😊
Me talking to my algorithm… #meme
Discretisation memes! 😊
Would love to join! :)
I need to slowly move all my #mathematics #memes to the #mathsky. Let’s start with _Tolkien and convergence to stationarity_.
A few weeks ago, my student Alix Leroy and I were visiting Siemens Energy in Berlin for #knowledgeexchange and a guided tour around their production facilities. 😊
Say, you discretise an ODE with forward Euler choosing iid exponentially distributed stepsizes and linearly interpolate between discretisation points. Then, your interpolated path can be written as a continuous-time Markov process.
An analysis of this Markov process: arxiv.org/abs/2408.01409
Finding the Lyapunov function you are looking for = finding happiness. 😊
The really scary stuff to me are those with heavy tails…
Ever felt insecure about your own work? You are not alone.
Gauss in a letter to Bessel:
“When I am new to a subject, I distrust my own notions - especially if they contradict Laplace.”
(from W. Ahrens: “Scherz und Ernst in der Mathematik”, Teubner, Leipzig 1904.)
Hi #mathsky and everyone!
My name is Jonas, I do applied maths for living — usually solving problems that concern data, uncertainties, or both. I am based at the University of Manchester, UK.
