scholarly journals Relaxation Limit and Initial-Layers for a Class of Hyperbolic-Parabolic Systems

2018 ◽  
Vol 50 (4) ◽  
pp. 4655-4697
Author(s):  
Vincent Giovangigli ◽  
Zai-Bao Yang ◽  
Wen-An Yong
Keyword(s):  
Parabolic Systems ◽  
Initial Layers

scholarly journals Bottom-up and Layerwise Domain Adaptation for Pedestrian Detection in Thermal Images

2021 ◽  
Vol 17 (1) ◽  
pp. 1-19
Author(s):  
My Kieu ◽  
Andrew D. Bagdanov ◽  
Marco Bertini
Keyword(s):  
Domain Adaptation ◽  
State Of The Art ◽  
Pedestrian Detection ◽  
Challenging Problem ◽  
Top Down ◽  
Bottom Up ◽  
Security Applications ◽  
Lighting Conditions ◽  
Initial Layers ◽  
Single Modality

Pedestrian detection is a canonical problem for safety and security applications, and it remains a challenging problem due to the highly variable lighting conditions in which pedestrians must be detected. This article investigates several domain adaptation approaches to adapt RGB-trained detectors to the thermal domain. Building on our earlier work on domain adaptation for privacy-preserving pedestrian detection, we conducted an extensive experimental evaluation comparing top-down and bottom-up domain adaptation and also propose two new bottom-up domain adaptation strategies. For top-down domain adaptation, we leverage a detector pre-trained on RGB imagery and efficiently adapt it to perform pedestrian detection in the thermal domain. Our bottom-up domain adaptation approaches include two steps: first, training an adapter segment corresponding to initial layers of the RGB-trained detector adapts to the new input distribution; then, we reconnect the adapter segment to the original RGB-trained detector for final adaptation with a top-down loss. To the best of our knowledge, our bottom-up domain adaptation approaches outperform the best-performing single-modality pedestrian detection results on KAIST and outperform the state of the art on FLIR.

Stability in 𝐿𝑞-norm for inverse source parabolic problems

2020 ◽  
Vol 28 (6) ◽  
pp. 797-814
Author(s):  
Elena-Alexandra Melnig
Keyword(s):  
Parabolic Equations ◽  
Main Tool ◽  
Parabolic Systems ◽  
Carleman Estimates ◽  
Parabolic Problems ◽  
Lebesgue Spaces ◽  
First Order ◽  
Lipschitz Estimates ◽  
Systems Of Parabolic Equations

AbstractWe consider systems of parabolic equations coupled in zero and first order terms. We establish Lipschitz estimates in {L^{q}}-norms, {2\leq q\leq\infty}, for the source in terms of the solution in a subdomain. The main tool is a family of appropriate Carleman estimates with general weights, in Lebesgue spaces, for nonhomogeneous parabolic systems.

scholarly journals Lorentz spaces in action on pressureless systems arising from models of collective behavior

2021 ◽  
Author(s):  
Raphaël Danchin ◽  
Piotr Bogusław Mucha ◽  
Patrick Tolksdorf
Keyword(s):  
Initial Data ◽  
Collective Behavior ◽  
Existence And Uniqueness ◽  
Maximal Regularity ◽  
Parabolic Systems ◽  
Lorentz Spaces ◽  
Regularity Estimate ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Time Existence

AbstractWe are concerned with global-in-time existence and uniqueness results for models of pressureless gases that come up in the description of phenomena in astrophysics or collective behavior. The initial data are rough: in particular, the density is only bounded. Our results are based on interpolation and parabolic maximal regularity, where Lorentz spaces play a key role. We establish a novel maximal regularity estimate for parabolic systems in $$L_{q,r}(0,T;L_p(\Omega ))$$ L q , r ( 0 , T ; L p ( Ω ) ) spaces.

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