Concept
Commutative property
Related publications (32)
Probabilistic and Deterministic Wellposedness for Low Regularity Dispersive Equations
Katie Sabrina Catherine Rosie Marsden
In this thesis we will present two results on global existence for nonlinear dispersive equations with data at or below the scaling regularity. In chapter 1 we take a probabilistic perspective to study the energy-critical nonlinear Schrödinger equation in ...
EPFL2024On the commutativity of flows of rough vector fields
In the class of Sobolev vector fields in R-n of bounded divergence, for which the theory of DiPerna and Lions provides a well defined notion of flow, we characterize the vector fields whose flow commutes in terms of the Lie bracket and of a regularity cond ...
ELSEVIER2022Finding symmetry breaking order parameters with Euclidean neural networks
Curie's principle states that "when effects show certain asymmetry, this asymmetry must be found in the causes that gave rise to them." We demonstrate that symmetry equivariant neural networks uphold Curie's principle and can be used to articulate many sym ...
AMER PHYSICAL SOC2021Algebraic Homotopy Interleaving Distance
The theory of persistence, which arises from topological data analysis, has been intensively studied in the one-parameter case both theoretically and in its applications. However, its extension to the multi-parameter case raises numerous difficulties, wher ...
SPRINGER INTERNATIONAL PUBLISHING AG2021Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention
François Fleuret, Nikolaos Pappas, Angelos Katharopoulos, Apoorv Vyas
Transformers achieve remarkable performance in several tasks but due to their quadratic complexity, with respect to the input’s length, they are prohibitively slow for very long sequences. To address this limitation, we express the self-attention as a line ...
Idiap2020Survey on the Figà–Talamanca Herz algebra
This paper presents a self contained approach to the theory of convolution operators on locally compact groups (both commutative and non commutative) based on the use of the Figà–Talamanca Herz algebras. The case of finite groups is also considered. ...
2019Generalized Optical Signal Processing Based on Multioperator Metasurfaces Synthesized by Susceptibility Tensors
This paper theoretically proposes a multichannel nonlocal metasurface computer characterized by generalized sheet transition conditions (GSTCs) and surface susceptibility tensors. The study explores polarization- and angle-multiplexed metasurfaces enabling ...
AMER PHYSICAL SOC2019Parallel integro-differential equation solving via multi-channel reciprocal bianisotropic metasurface augmented by normal susceptibilities
Analog optical signal processing has dramatically transcended the speed and energy limitations accompanied with its digital microelectronic counterparts. Motivated by recent metasurface?s evolution, the angular scattering diversity of a reciprocal passive ...
IOP PUBLISHING LTD2019Tensor product of correspondence functors
As part of the study of correspondence functors, the present paper investigates their tensor product and proves some of its main properties. In particular, the correspondence functor associated to a finite lattice has the structure of a commutative algebra ...
2018An Indicator-Based Approach for Analyzing the Resilience of Transitions for Energy Regions – Concept, empirics and reflection
Claudia Rebeca Binder Signer, Romano Tobias Wyss, Susan Marie Mühlemeier
The transition of our current energy system from a fossil-based system to a system based on renewables is likely to be one of the most complex and long-term societal transitions in history. The need for a fundamental system transformation raises the questi ...
2018