Matematikkens Aften

Susanne Ditlevsen: Hvad er et tipping point – og kan vi forudsige det?

I de senere år er der kommet en stigende opmærksomhed på eventuelle risici for sammenbrud eller tipping points i en lang række komplekse systemer, fra individuelle sygdomme, pandemier og økosystemer til klima, finans og samfund. Selv i systemer, hvor de styrende ligninger er kendte, såsom atmosfærens strømninger, er forudsigelighed begrænset af systemets kaotiske natur.

Jeg vil fortælle om min forskning i tipping points i klimaet, og om sandsynligheden for et muligt kollaps af en vigtig havstrøm.

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Sira Gratz: Friezes and friends

We see how the “pentagramma mirificum’’—-a beautiful shape known for its symmetries already by Napier more than 400 years ago and studied extensively by Gauss—-inspires the introduction of friezes, which remain objects of interest in state-of-the-art mathematical research. We show an astonishing connection between friezes and triangulations of polygons, which can both be counted by the somewhat magical Catalan number.

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Matthias Christandl: How to use quantum computers for biomolecular free energies

Free energy calculations are at the heart of physics-based analyses of biochemical processes. They allow us to quantify molecular recognition mechanisms, which determine a wide range of biological phenomena from how cells send and receive signals to how pharmaceutical compounds can be used to treat diseases. Quantitative and predictive free energy calculations require computational models that accurately capture both the varied and intricate electronic interactions between molecules as well as the entropic contributions from motions of these molecules and their aqueous environment. However, accurate quantum-mechanical energies and forces can only be obtained for small atomistic models, not for large biomacromolecules. Here, we demonstrate how to consistently link accurate quantum-mechanical data obtained for substructures to the overall potential energy of biomolecular complexes by machine learning in an integrated algorithm. We do so using a two-fold quantum embedding strategy where the innermost quantum cores are treated at a very high level of accuracy. We demonstrate the viability of this approach for the molecular recognition of a ruthenium-based anticancer drug by its protein target, applying traditional quantum chemical methods. As such methods scale unfavorable with system size, we analyze requirements for quantum computers to provide highly accurate energies that impact the resulting free energies. Once the requirements are met, our computational pipeline FreeQuantum is able to make efficient use of the quantum computed energies, thereby enabling quantum computing enhanced modeling of biochemical processes. This approach combines the exponential speedups of quantum computers for simulating interacting electrons with modern classical simulation techniques that incorporate machine learning to model large molecules.