Smooth Selection for Infinite Sets

Whitneys extension problem asks the following: Given a compact set $Esubsetmathbb{R}^n$ and a function $f:Eto mathbb{R}$, how can we tell whether there exists $Fin C^m(mathbb{R}^n)$ such that $F|_E=f$? A 2006 theorem of Charles Fefferman answers this question in its full generality. In this paper, we establish a version of this theorem adapted for variants of the Whitney extension problem, including nonnegative extensions and the smooth selection problems. Among other things, we generalize the results of Fefferman-Israel-Luli (2016) to the setting of infinite sets.

Unsupervised clothing change adaptive person ReID

Clothing changes and lack of data labels are both crucial challenges in person ReID. For the former challenge, people may occur multiple times at different locations wearing different clothing. However, most of the current person ReID research works focus on the benchmarks in which a persons clothing is kept the same all the time. For the last challenge, some researchers try to make model learn information from a labeled dataset as a source to an unlabeled dataset. Whereas purely unsupervised training is less used. In this paper, we aim to solve both problems at the same time. We design a novel unsupervised model, Sync-Person-Cloud ReID, to solve the unsupervised clothing change person ReID problem. We developer a purely unsupervised clothing change person ReID pipeline with person sync augmentation operation and same person feature restriction. The person sync augmentation is to supply additional same person resources. These same persons resources can be used as part supervised input by same person feature restriction. The extensive experiments on clothing change ReID datasets show the out-performance of our methods.

$C^2$ Interpolation with Range Restriction

Given $ -infty< lambda < Lambda < infty $, $ E subset mathbb{R}^n $ finite, and $ f : E to [lambda,Lambda] $, how can we extend $ f $ to a $ C^m(mathbb{R}^n) $ function $ F $ such that $ lambdaleq F leq Lambda $ and $ ||F||_{C^m(mathbb{R}^n)} $ is within a constant multiple of the least possible, with the constant depending only on $ m $ and $ n $? In this paper, we provide the solution to the problem for the case $ m = 2 $. Specifically, we construct a (parameter-dependent, nonlinear) $ C^2(mathbb{R}^n) $ extension operator that preserves the range $[lambda,Lambda]$, and we provide an efficient algorithm to compute such an extension using $ O(Nlog N) $ operations, where $ N = #(E) $.

Towards fully ab initio simulation of atmospheric aerosol nucleation

Atmospheric aerosol nucleation contributes to around half of cloud condensation nuclei (CCN) globally and the nucleated particles can grow larger to impact air quality and consequently human health. Despite the decades efforts, the detailed nucleation mechanism is still poorly understood. The ultimate goal of theoretical understanding aerosol nucleation is to simulate nucleation in ambient condition. However, there is lack of accurate reactive force field. Here for the first time, we propose the reactive force field with good size scalability for nucleation systems based on deep neural network and further bridge the simulation in the limited box with cluster kinetics towards boosting the aerosol simulation to be fully ab initio. We found that the formation rates based on hard sphere collision rate constants tend to be underestimated. Besides, the framework here is transferable to other nucleation systems, potentially revolutionizing the atmospheric aerosol nucleation field.

Algorithms for Nonnegative $C^2(mathbb{R}^2)$ Interpolation

Let $ E subset mathbb{R}^2 $ be a finite set, and let $ f : E to [0,infty) $. In this paper, we address the algorithmic aspects of nonnegative $C^2$ interpolation in the plane. Specifically, we provide an efficient algorithm to compute a nonnegative $C^2(mathbb{R}^2)$ extension of $ f $ with norm within a universal constant factor of the least possible. We also provide an efficient algorithm to approximate the trace norm.

Resolution-invariant Person ReID Based on Feature Transformation and Self-weighted Attention

Person Re-identification (ReID) is a critical computer vision task which aims to match the same person in images or video sequences. Most current works focus on settings where the resolution of images is kept the same. However, the resolution is a crucial factor in person ReID, especially when the cameras are at different distances from the person or the cameras models are different from each other. In this paper, we propose a novel two-stream network with a lightweight resolution association ReID feature transformation (RAFT) module and a self-weighted attention (SWA) ReID module to evaluate features under different resolutions. RAFT transforms the low resolution features to corresponding high resolution features. SWA evaluates both features to get weight factors for the person ReID. Both modules are jointly trained to get a resolution-invariant representation. Extensive experiments on five benchmark datasets show the effectiveness of our method. For instance, we achieve Rank-1 accuracy of 43.3% and 83.2% on CAVIAR and MLR-CUHK03, outperforming the state-of-the-art.

Extended Self-similar Solution for Circumstellar Material-Supernova Ejecta Interaction

In this note, we present a detailed self-similar solution to the interaction of a uniformly expanding gas and a stationary ambient medium, with an application to supernovae interacting with preexisting circumstellar media (Type IIn SNe). We implement the generalized solution into the Modular Open Source Fitter for Transients (MOSFiT), an open-source Python package for fitting extragalactic transient light curves.

RGB-IR Cross-modality Person ReID based on Teacher-Student GAN Model

RGB-Infrared (RGB-IR) person re-identification (ReID) is a technology where the system can automatically identify the same person appearing at different parts of a video when light is unavailable. The critical challenge of this task is the cross-modality gap of features under different modalities. To solve this challenge, we proposed a Teacher-Student GAN model (TS-GAN) to adopt different domains and guide the ReID backbone to learn better ReID information. (1) In order to get corresponding RGB-IR image pairs, the RGB-IR Generative Adversarial Network (GAN) was used to generate IR images. (2) To kick-start the training of identities, a ReID Teacher module was trained under IR modality person images, which is then used to guide its Student counterpart in training. (3) Likewise, to better adapt different domain features and enhance model ReID performance, three Teacher-Student loss functions were used. Unlike other GAN based models, the proposed model only needs the backbone module at the test stage, making it more efficient and resource-saving. To showcase our models capability, we did extensive experiments on the newly-released SYSU-MM01 RGB-IR Re-ID benchmark and achieved superior performance to the state-of-the-art with 49.8% Rank-1 and 47.4% mAP.

Illumination adaptive person reid based on teacher-student model and adversarial training

Most existing works in Person Re-identification (ReID) focus on settings where illumination either is kept the same or has very little fluctuation. However, the changes in the illumination degree may affect the robustness of a ReID algorithm significantly. To address this problem, we proposed a Two-Stream Network that can separate ReID features from lighting features to enhance ReID performance. Its innovations are threefold: (1) A discriminative entropy loss to ensure the ReID features contain no lighting information. (2) A ReID Teacher model trained by images under neutral lighting conditions to guide ReID classification. (3) An illumination Teacher model trained by the differences between the illumination-adjusted and original images to guide illumination classification. We construct two augmented datasets by synthetically changing a set of predefined lighting conditions in two of the most popular ReID benchmarks: Market1501 and DukeMTMC-ReID. Experiments demonstrate that our algorithm outperforms other state-of-the-art works and particularly potent in handling images under extremely low light.

Nonnegative Whitney Extension Problem for $C^1(mathbb{R}^n)$

Let $ f $ be a real-valued function on a compact subset in $ mathbb{R}^n $. We show how to decide if $ f $ extends to a nonnegative and $ C^1 $ function on $ mathbb{R}^n $. There has been no known result for nonnegative $ C^m $ extension from a general compact set $ E $ when $ m > 0 $. The nonnegative extension problem for $ m geq 2 $ remains open.