32 citations · 82 across the 17 of their papers we have counts for
19 papers
On the Diverse Dynamical Behaviors Arising in Deep Linear Transformers
Sixu Li, Thomas Jacob Maranzatto, Jan Peszek +5
We study the inference-time behavior of deep linear encoder-only transformers through the lens of interacting particle systems. In this perspective, tokens are modeled as particles…
Alignment with nonlinear velocity couplings: collision-avoidance and micro-to-macro mean-field limits
Young-Pil Choi, Michał Fabisiak, Jan Peszek
We investigate the pressureless fractional Euler-alignment system with nonlinear velocity couplings, referred to as the -Euler-alignment system. This model features a nonlinear…
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…
Density-induced Consensus Protocol
Piotr Minakowski, Piotr B. Mucha, Jan Peszek
The paper introduces a model of collective behavior where agents receive information only from sufficiently dense crowds in their immediate vicinity. The system is an asymmetric, d…
Flocking with short-range interactions
Javier Morales, Jan Peszek, Eitan Tadmor
We study the large-time behavior of continuum alignment dynamics based on Cucker-Smale (CS)-type interactions which involve short-range kernels, that is, communication kernels with…
Singular Cucker-Smale Dynamics
Piotr Minakowski, Piotr B. Mucha, Jan Peszek +1
The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mes…
A collisionless singular Cucker-Smale model with decentralized formation control
Young-Pil Choi, Dante Kalise, Jan Peszek +1
We address the design of decentralized feedback control laws inducing consensus and prescribed spatial patterns over a singular interacting particle system of Cucker-Smale type. Th…
Regular solutions to the fractional Euler alignment system in the Besov spaces framework
Raphaël Danchin, Piotr B. Mucha, Jan Peszek +1
We here construct (large) local and small global-in-time regular unique solutions to the fractional Euler alignment system in the whole space , in the case where the…
Cucker-Smale model with a bonding force and a singular interaction kernel
Jeongho Kim, Jan Peszek
We prove the lack of asymptotic collisions between particles following the Cucker-Smale flocking model with a bonding force and its simplification. Moreover, we prove that in the c…
Flocking particles in a non-Newtonian shear thickening fluid
Piotr B. Mucha, Jan Peszek, Milan Pokorny
We prove existence and uniqueness of strong solutions to the Cucker--Smale flocking model coupled with an incompressible viscous non-Newtonian fluid, with the stress tensor of a po…
Sharp conditions to avoid collisions in singular Cucker-Smale interactions
Jose A. Carrillo, Young-Pil Choi, Piotr B. Mucha +1
We consider the Cucker-Smale flocking model with a singular communication weight with . We provide a critical value of the exponent in the communication w…
The Cucker-Smale equation: singular communication weight, measure-valued solutions and weak-atomic uniqueness
Piotr B. Mucha, Jan Peszek
The Cucker-Smale flocking model belongs to a wide class of kinetic models that describe a collective motion of interacting particles that exhibit some specific tendency e.g. to agg…
Discrete Cucker-Smale's flocking model with a weakly singular weight
Jan Peszek
For the discrete Cucker-Smale's flocking model with a singular communication weight , with , we prove that the velocity component of certain type of weak s…
Existence of piecewise weak solutions of a discrete Cucker-Smale's flocking model with a singular communication weight
Jan Peszek
We prove existence of global piecewise weak solutions for the discrete Cucker-Smale's flocking model with the communication weight We also discuss the p…
On some nonlinear extensions of the Gagliardo-Nirenberg inequality with applications to nonlinear eigenvalue problems
Agnieszka Kałamajska, Jan Peszek
We derive inequality [\int_{\r} |f^{'}(x)|^ph(f(x))dx \le (\sqrt{p-1})^p\int_{\r}(\sqrt{|f^{"}(x){\cal T}_h(f(x))|})^ph(f(x))dx,] where belongs locally to Sobolev space $W^{2,1…