Tue, 03 Nov 2026

12:30 - 13:00
C3

Modelling the loss of cell cycle synchrony in embryo development

Ben Stephens
(Mathematical Institute, University of Oxford)
Abstract

Cell proliferation has been widely studied across experimental systems and mathematical modelling frameworks, from early embryonic development to regenerating tissues. A characteristic feature of early embryonic development is that initially synchronous cell populations progressively lose synchrony after a species-specific number of divisions. Here, we use an age-dependent branching process to determine how variability in cell-cycle duration controls the persistence of synchrony. We derive analytical expressions for the mean and variance of cell number and show how they identify the underlying generation-time distribution. For gamma-distributed generation times, this establishes a direct relationship between cell-cycle variability and the number of synchronous divisions. We use these results to infer generation-time statistics from population-level cell counts and investigate how systematic changes in cell-cycle duration can bias inference under a stationary model. Our results provide a quantitative framework linking the precision of individual cell-cycle clocks to observable population-level dynamics.

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Tue, 20 Oct 2026

12:30 - 13:00
L5

Solving a sequence of eigenvalue problems using snapshot and row subsampling

Francesco Hrobat
(Mathematical Institute, University of Oxford)
Abstract
We consider a sequence of eigenvalue problems
$$A_i\vec{x}_i=\lambda_i\vec{x}_i,\qquad i=1,\ldots,N,$$
where \(N\) is large and the eigenvalue of interest is usually the largest or smallest one. Often, the matrices are generated by a smooth parameter-dependent matrix function, so that \(A_i=A(p_i)\), with \(A(p)\in\mathbb{C}^{n\times n}\).
 
Our method uses a small number \(r\ll N\) of parameter values, called \textit{snapshot points}. The eigenvectors computed at these points are used to construct an orthonormal basis \(Q\in\mathbb{C}^{n\times r}\). For each remaining parameter value \(p_i\), we approximate the eigenvector \(\vec{x}_i\) in the subspace spanned by the columns of \(Q\).
 
To reduce the computational cost, we select a subset of rows of \(A(p_i)\) and use them to form the projection onto this subspace. This is especially useful when the matrices are accessed entry by entry and evaluating an entry is expensive. Once the snapshot points and a suitable set of row indices have been chosen, the same rows can be used for all parameter values in the sequence. 


 

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An interpretable deep learning framework for classifying neuronal morphologies using topology and graph neural networks
 Kanari, L Schmidt, S Casalegno, F Delattre, E Lukic, J Negrello, T Shi, Y Meystre, J Defferrard, M Schürmann, F Markram, H Scientific Reports (22 Sep 2026) doi:10.1038/s41598-026-71217-7
Algorithms in 4-manifold topology
 Bastl, S Burke, R Chatterjee, R Dey, S Durst, A Friedl, S Galvin, D Rivas, A Hirsch, T Hobohm, C Hsueh, C Kegel, M Kern, F Lee, S Löh, C Manikandan, N Mousseau, L Munser, L Pencovitch, M Perras, P Powell, M Quintanilha, J Schambeck, L Suchodoll, D Tancer, M Thiele, A Truöl, P Uschold, M Veselá, S Weiß, M Wunsch-Rolshoven, M (13 Nov 2024) https://arxiv.org/abs/2411.08775v2
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