arXiv subjects

Jie Ji

Publications and source records attributed to Jie Ji.

32 records · Page 2Linked to original sources

arXiv2024

On the Boltzmann equation with soft potentials: Existence, uniqueness and smoothing effect of mild solutions

We consider the spatially inhomogeneous Boltzmann equation without angular cutoff for soft potentials. For any given initial datum such that the mass, energy and entropy densities are bounded and the mass is away from vacuum, we establish the local-in-time existence and uniqueness of mild solutions, and further provide the first result on sharp smoothing effect in analytic space or Gevrey space for soft potentials.

math.AP↗

arXiv2024

On Landau equation with harmonic potential: nonlinear stability of time-periodic Maxwell-Boltzmann distributions

We provide the first and rigorous confirmations of the hypotheses by Ludwig Boltzmann in his seminal paper \cite{Boltzmann} within the context of the Landau equation in the presence of a harmonic potential. We prove that (i) Each {\it entropy-invariant solution} can be identified as a {\it time-periodic Maxwell-Boltzmann distribution}. Moreover, these distributions can be characterized by thirteen conservation laws, which sheds light on the global dynamics. (ii) Each {\it time-periodic Maxwell-Boltzmann distribution} is nonlinearly stable, including neutral asymptotic stability and Lyapunov stability. Furthermore, the convergence rate is entirely reliant on the thirteen conservation laws and is optimal when compared to the linear scenario.

math.AP↗

arXiv2024

Data Overfitting for On-Device Super-Resolution with Dynamic Algorithm and Compiler Co-Design

Deep neural networks (DNNs) are frequently employed in a variety of computer vision applications. Nowadays, an emerging trend in the current video distribution system is to take advantage of DNN's overfitting properties to perform video resolution upscaling. By splitting videos into chunks and applying a super-resolution (SR) model to overfit each chunk, this scheme of SR models plus video chunks is able to replace traditional video transmission to enhance video quality and transmission efficiency. However, many models and chunks are needed to guarantee high performance, which leads to tremendous overhead on model switching and memory footprints at the user end. To resolve such problems, we propose a Dynamic Deep neural network assisted by a Content-Aware data processing pipeline to reduce the model number down to one (Dy-DCA), which helps promote performance while conserving computational resources. Additionally, to achieve real acceleration on the user end, we designed a framework that optimizes dynamic features (e.g., dynamic shapes, sizes, and control flow) in Dy-DCA to enable a series of compilation optimizations, including fused code generation, static execution planning, etc. By employing such techniques, our method achieves better PSNR and real-time performance (33 FPS) on an off-the-shelf mobile phone. Meanwhile, assisted by our compilation optimization, we achieve a 1.7$\times$ speedup while saving up to 1.61$\times$ memory consumption. Code available in https://github.com/coulsonlee/Dy-DCA-ECCV2024.

cs.CV↗

arXiv2024

Source Localization for Cross Network Information Diffusion

Source localization aims to locate information diffusion sources only given the diffusion observation, which has attracted extensive attention in the past few years. Existing methods are mostly tailored for single networks and may not be generalized to handle more complex networks like cross-networks. Cross-network is defined as two interconnected networks, where one network's functionality depends on the other. Source localization on cross-networks entails locating diffusion sources on the source network by only giving the diffused observation in the target network. The task is challenging due to challenges including: 1) diffusion sources distribution modeling; 2) jointly considering both static and dynamic node features; and 3) heterogeneous diffusion patterns learning. In this work, we propose a novel method, namely CNSL, to handle the three primary challenges. Specifically, we propose to learn the distribution of diffusion sources through Bayesian inference and leverage disentangled encoders to separately learn static and dynamic node features. The learning objective is coupled with the cross-network information propagation estimation model to make the inference of diffusion sources considering the overall diffusion process. Additionally, we also provide two novel cross-network datasets collected by ourselves. Extensive experiments are conducted on both datasets to demonstrate the effectiveness of \textit{CNSL} in handling the source localization on cross-networks.

cs.SI↗

arXiv2024

Uncertainty Quantification for In-Context Learning of Large Language Models

In-context learning has emerged as a groundbreaking ability of Large Language Models (LLMs) and revolutionized various fields by providing a few task-relevant demonstrations in the prompt. However, trustworthy issues with LLM's response, such as hallucination, have also been actively discussed. Existing works have been devoted to quantifying the uncertainty in LLM's response, but they often overlook the complex nature of LLMs and the uniqueness of in-context learning. In this work, we delve into the predictive uncertainty of LLMs associated with in-context learning, highlighting that such uncertainties may stem from both the provided demonstrations (aleatoric uncertainty) and ambiguities tied to the model's configurations (epistemic uncertainty). We propose a novel formulation and corresponding estimation method to quantify both types of uncertainties. The proposed method offers an unsupervised way to understand the prediction of in-context learning in a plug-and-play fashion. Extensive experiments are conducted to demonstrate the effectiveness of the decomposition. The code and data are available at: https://github.com/lingchen0331/UQ_ICL.

cs.CL↗

arXiv2023

Regularity estimates for the non-cutoff soft potential Boltzmann equation with typical rough and slowly decaying data

In the present work, we investigate estimates of regularity for weak solutions to the non-cutoff Boltzmann equation with soft potentials. We restrict our focus to the so-called "typically rough and slowly decaying data", which is constructed to satisfy typical properties: low regularity and having exact polynomial decay in high velocity regimes. By exploring the degenerate and non-local properties of the collision operator, we demonstrate that (i) such data induce only finite smoothing effects for weak solutions in Sobolev spaces; (ii) this finite smoothing property implies that the Leibniz rule does not hold for high derivatives of the collision operator (even in the weak sense). Moreover, we can also prove that the average of the solution or the average of the collision operator on a special domain in $\mathbb{R}^3_v$ will induce discontinuity in the $x$ variable. These facts present major obstacles to proving the conjecture that solutions to the equation will instantly become infinitely smooth for both spatial and velocity variables at any positive time if the initial data has only polynomial decay in high velocity regimes.

math.AP↗

arXiv2023

Towards High-Quality and Efficient Video Super-Resolution via Spatial-Temporal Data Overfitting

As deep convolutional neural networks (DNNs) are widely used in various fields of computer vision, leveraging the overfitting ability of the DNN to achieve video resolution upscaling has become a new trend in the modern video delivery system. By dividing videos into chunks and overfitting each chunk with a super-resolution model, the server encodes videos before transmitting them to the clients, thus achieving better video quality and transmission efficiency. However, a large number of chunks are expected to ensure good overfitting quality, which substantially increases the storage and consumes more bandwidth resources for data transmission. On the other hand, decreasing the number of chunks through training optimization techniques usually requires high model capacity, which significantly slows down execution speed. To reconcile such, we propose a novel method for high-quality and efficient video resolution upscaling tasks, which leverages the spatial-temporal information to accurately divide video into chunks, thus keeping the number of chunks as well as the model size to minimum. Additionally, we advance our method into a single overfitting model by a data-aware joint training technique, which further reduces the storage requirement with negligible quality drop. We deploy our models on an off-the-shelf mobile phone, and experimental results show that our method achieves real-time video super-resolution with high video quality. Compared with the state-of-the-art, our method achieves 28 fps streaming speed with 41.6 PSNR, which is 14$\times$ faster and 2.29 dB better in the live video resolution upscaling tasks. Code available in https://github.com/coulsonlee/STDO-CVPR2023.git

cs.CV↗

arXiv2023

Multi-Loss Convolutional Network with Time-Frequency Attention for Speech Enhancement

The Dual-Path Convolution Recurrent Network (DPCRN) was proposed to effectively exploit time-frequency domain information. By combining the DPRNN module with Convolution Recurrent Network (CRN), the DPCRN obtained a promising performance in speech separation with a limited model size. In this paper, we explore self-attention in the DPCRN module and design a model called Multi-Loss Convolutional Network with Time-Frequency Attention(MNTFA) for speech enhancement. We use self-attention modules to exploit the long-time information, where the intra-chunk self-attentions are used to model the spectrum pattern and the inter-chunk self-attention are used to model the dependence between consecutive frames. Compared to DPRNN, axial self-attention greatly reduces the need for memory and computation, which is more suitable for long sequences of speech signals. In addition, we propose a joint training method of a multi-resolution STFT loss and a WavLM loss using a pre-trained WavLM network. Experiments show that with only 0.23M parameters, the proposed model achieves a better performance than DPCRN.

cs.SD↗

arXiv2022

Uniqueness and global dynamics of spatially homogeneous non cutoff Boltzmann equation with moderate soft potentials

Departing from the weak solution, we prove the uniqueness, smoothing estimates and the global dynamics for the non cutoff spatially homogeneous Boltzmann equation with moderate soft potentials. Our results show that the behavior of the solution(including the production of regularity and the longtime behavior) can be {\it characterized quantitatively} by the initial data at the large velocities, i.e.(i). initially polynomial decay at the large velocities in $L^1$ space will induce the finite smoothing estimates in weighted Sobolev spaces and the polynomial convergence rate (including the lower and upper bounds) to the equilibrium; (ii). initially the exponential decay at the large velocities in $L^1$ space will induce $C^\infty$ regularization effect and the stretched exponential convergence rate. The new ingredients of the proof lie in the development of the localized techniques in phase and frequency spaces and the propagation of the exponential momentum.

math.AP↗

arXiv2022

Propagation of moments and sharp convergence rate for inhomogeneous non-cutoff Boltzmann equation with soft potentials

We prove the well-posedness for the non-cutoff Boltzmann equation with soft potentials when the initial datum is close to the {\it global Maxwellian} and has only polynomial decay at the large velocities in $L^2$ space. As a result, we get the {\it propagation of the exponential moments} and the {\it sharp rates} of the convergence to the {\it global Maxwellian} which seems the first results for the original equation with soft potentials. The new ingredients of the proof lie in localized techniques, the semigroup method as well as the propagation of the polynomial and exponential moments in $L^2$ space.

math.AP↗

arXiv2022

Realization of a photonic topological insulator in Kagome crystals at terahertz wavelengths

Topological systems are inherently robust to disorder and continuous perturbations, resulting in dissipation-free edge transport of electrons in quantum solids, or reflectionless guiding of photons and phonons in classical wave systems characterized by topological invariants. Despite considerable efforts, direct experimental demonstration of theoretically predicted robust, lossless energy transport in topological insulators operating at terahertz frequencies is needed further investigations to shed affirmative light on the unique properties enabled by topological protection. Here, we introduce Kagome lattice that exhibits a new class of symmetry-protected topological phases with very low Berry curvature but nontrivial bulk polarization, and fabricate an optical topological insulator that provide the valley hall effect. Theoretical analysis show that four type edge states can be obtained. Measurements of THz-TDs with high time-resolution demonstrate that terahertz wave propagating along the straight topological edge and Z-shape edge with sharp turns have almost same high transmission in 0.440 THz to 0.457 THz domain range. Those results quantitatively illustrate the suppression of backscattering due to the non-trivial topology of the structure. The THz-TDs measurement yields amplitude and phase information, showing significant advantage compared to general broadband infrared, single wavelength continuous-wave THz measurements and visible spectroscopy. It allows further exploration of the effective refractive index, group velocity and dispersion relations of edge states. Our work offers possibilities for advanced control of the propagation and manipulation of THz waves, and facilitates the applications including sixth-generation (6G) wireless communication, terahertz integrated circuits, and interconnects for intrachip and interchip communication.

physics.optics↗

arXiv2020

Fermi velocity renormalization in graphene probed by terahertz time-domain spectroscopy

We demonstrate terahertz time-domain spectroscopy (THz-TDS) to be an accurate, rapid and scalable method to probe the interaction-induced Fermi velocity renormalization νF^* of charge carriers in graphene. This allows the quantitative extraction of all electrical parameters (DC conductivity σDC, carrier density n, and carrier mobility μ) of large-scale graphene films placed on arbitrary substrates via THz-TDS. Particularly relevant are substrates with low relative permittivity (< 5) such as polymeric films, where notable renormalization effects are observed even at relatively large carrier densities (> 10^12 cm-2, Fermi level > 0.1 eV). From an application point of view, the ability to rapidly and non-destructively quantify and map the electrical (σDC, n, μ) and electronic (νF^* ) properties of large-scale graphene on generic substrates is key to utilize this material in applications such as metrology, flexible electronics as well as to monitor graphene transfers using polymers as handling layers.

cond-mat.mes-hall↗

arXiv2020

Detecting Problem Statements in Peer Assessments

Effective peer assessment requires students to be attentive to the deficiencies in the work they rate. Thus, their reviews should identify problems. But what ways are there to check that they do? We attempt to automate the process of deciding whether a review comment detects a problem. We use over 18,000 review comments that were labeled by the reviewees as either detecting or not detecting a problem with the work. We deploy several traditional machine-learning models, as well as neural-network models using GloVe and BERT embeddings. We find that the best performer is the Hierarchical Attention Network classifier, followed by the Bidirectional Gated Recurrent Units (GRU) Attention and Capsule model with scores of 93.1% and 90.5% respectively. The best non-neural network model was the support vector machine with a score of 89.71%. This is followed by the Stochastic Gradient Descent model and the Logistic Regression model with 89.70% and 88.98%.

cs.IR↗

arXiv2014

Elastic Properties of Chemical-Vapor-Deposited Monolayer MoS2, WS2, and Their Bilayer Heterostructures

Elastic properties of materials are an important factor in their integration in applications. Chemical vapor deposited (CVD) monolayer semiconductors are proposed as key components in industrial-scale flexible devices and building blocks of 2D van der Waals heterostructures. However, their mechanical and elastic properties have not been fully characterized. Here we report high 2D elastic moduli of CVD monolayer MoS2 and WS2 (~ 170 N/m), which is very close to the value of exfoliated MoS2 monolayers and almost half the value of the strongest material, graphene. The 2D moduli of their bilayer heterostructures are lower than the sum of 2D modulus of each layer, but comparable to the corresponding bilayer homostructure, implying similar interactions between the hetero monolayers as between homo monolayers. These results not only provide deep insight to understanding interlayer interactions in 2D van der Waals structures, but also potentially allow engineering of their elastic properties as desired.

cond-mat.mtrl-sci↗