Piotr Minakowski

Pierre Degond, Piotr Minakowski, Laurent Navoret et al.

We are interested in the numerical simulations of the Euler system with variable congestion encoded by a singular pressure. This model describes for instance the macroscopic motion of a crowd with individual congestion preferences. We propose an asymptotic preserving (AP) scheme based on a conservative formulation of the system in terms of density, momentum and density fraction. A second order accuracy version of the scheme is also presented. We validate the scheme on one-dimensional test-cases and extended here to higher order accuracy. We finally carry out two dimensional numerical simulations and show that the model exhibit typical crowd dynamics.

Piotr Minakowski, Jan Peszek

We present a data segmentation method based on a first-order density-induced consensus protocol. We provide a mathematically rigorous analysis of the consensus model leading to the stopping criteria of the data segmentation algorithm. To illustrate our method, the algorithm is applied to two-dimensional shape datasets and selected images from Berkeley Segmentation Dataset. The method can be seen as an augmentation of classical clustering techniques for multimodal feature space, such as DBSCAN. It showcases a curious connection between data clustering and collective behavior.

Timon Klein, Piotr Minakowski, Sebastian Sager

Subject-specific distribution shifts represent an important obstacle to the development of foundation models for EEG decoding. To address this, we propose Subject-Conditioned Layer,, an adaptive layer designed as a drop-in replacement for standard linear or convolutional layers in any neural network architecture. Our layer captures subject-specific variability by decomposing its weights into a shared, subject-invariant component and a lightweight, low-rank correction unique to each subject. This explicit separation of general knowledge from personalized adaptation allows existing models to become robust to subject shifts. Empirically, models equipped with our layer outperform both a shared-weight-only model (subject-agnostic model) and the average of individually trained subject-specific models. Consequently, the Subject-Conditioned Layer, offers a practical and scalable path towards building effective cross-subject foundation models for EEG.