32 citations · 82 across the 17 of their papers we have counts for
5 papers · 1 filter
Inevitable monokineticity of strongly singular alignment
Michał Fabisiak, Jan Peszek
We prove that certain types of measure-valued mappings are monokinetic i.e. the distribution of velocity is concentrated in a Dirac mass. These include weak measure-valued solution…
A fuzzy -closest alignment model
Piotr B. Mucha, Jan Peszek
The paper examines the problems related to the well-posedness of the Cucker-Smale model with communication restricted to the -closest neighbors, known also as the Cucker-Dong mo…
Measure solutions to a kinetic Cucker-Smale model with singular and matrix-valued communication
Jan Peszek, David Poyato
We introduce a multi-dimensional variant of the kinetic Cucker-Smale model with singular and matrix-valued communication weight, which reduces to the singular kinetic Cucker-Smale…
Data Clustering as an Emergent Consensus of Autonomous Agents
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…
Heterogeneous gradient flows in the topology of fibered optimal transport
Jan Peszek, David Poyato
We introduce an optimal transport topology on the space of probability measures over a fiber bundle, which penalizes the transport cost from one fiber to another. For simplicity, w…