arXiv subjects

Li Chen

Publications and source records attributed to Li Chen.

At least 289 records · Page 16Linked to original sources

arXiv2024

Connection between a degenerate particle flow model and a free boundary problem

In this paper a strongly degenerate parabolic equation derived from a density dependent particle flow model is studied. Furthermore, a free boundary problem and its connection to the strongly degenerate parabolic equation is investigated. First, it is shown that the strongly degenerate parabolic equation has a unique global bounded weak solution that converges towards a steady state for large time horizons. Two scenarios might occur: When the average density $ρ_{\infty}$ is larger than a certain critical density $ρ_{cr}$, the steady state coincides with $ρ_{\infty}$ and the convergence rate is exponential in the $L^2$ norm; while in the opposite case $ρ_{\infty}<ρ_{cr}$, the steady state is unknown and the convergence is algebraic in a negative Sobolev seminorm. Further investigations show that for radially symmetric and decreasing initial data, the solution of the strongly degenerate parabolic equation can be constructed by using the solution of a corresponding free boundary problem. Moreover, the global existence of weak solutions to the latter problem is proved. Finally, numerical experiments in two space dimensions are presented, which show that segregation phenomena can appear when the initial average density is smaller than the critical density.

math.AP↗

arXiv2024

Fluctuations around the mean-field limit for attractive Riesz potentials in the moderate regime

A central limit theorem is shown for moderately interacting particles in the whole space. The interaction potential approximates singular attractive or repulsive potentials of sub-Coulomb type. It is proved that the fluctuations become asymptotically Gaussians in the limit of infinitely many particles. The methodology is inspired by the classical work of Oelschläger on fluctuations for the porous-medium equation. The novelty in this work is that we can allow for attractive potentials in the moderate regime and still obtain asymptotic Gaussian fluctuations. The key element of the proof is the mean-square convergence in expectation for smoothed empirical measures associated to moderately interacting $N$-particle systems with rate $N^{-1/2-\varepsilon}$ for some $\varepsilon>0$. To allow for attractive potentials, the proof uses a quantitative mean-field convergence in probability with any algebraic rate and a law-of-large-numbers estimate as well as a systematic separation of the terms to be estimated in a mean-field part and a law-of-large-numbers part.

math.PR↗

arXiv2024

Multi-fidelity topology optimization of flow boiling heat transfer in microchannels

Topology optimization (TO) is a powerful method to design innovative structures with improved heat transfer performance. In the present study, a multi-fidelity TO method with a delicately defined objective function is developed for flow boiling heat transfer in microchannels. Low-fidelity TO is conducted for the reduced-order process of single-phase laminar convective heat transfer, which generates a set of structure candidates for subsequent high-fidelity evaluation of flow boiling heat transfer. To avoid the possible iteration between the low-fidelity TO and high-fidelity evaluation which leads to inefficient solution of the multi-fidelity TO, distributions of velocity, temperature and two-phase in microchannels with single-phase and/or flow boiling heat transfer are investigated and compared in detail, based on which a new objective function is delicately defined, which can be employed in the low-fidelity TO yet can stand for the performance of the high-fidelity problem. With the help of the new objective function, the efficiency of the multi-fidelity TO is significantly improved and TO structures are designed with hot spots eliminated, thermal resistance reduced and temperature uniformity improved. The present work provides a new method for TO of complicated heat and mass transfer problems. Keywords: topology optimization, flow boiling, multi-fidelity optimization, microchannels, convective heat transfer

physics.flu-dyn↗

arXiv2024

Navigating User Experience of ChatGPT-based Conversational Recommender Systems: The Effects of Prompt Guidance and Recommendation Domain

Conversational recommender systems (CRS) enable users to articulate their preferences and provide feedback through natural language. With the advent of large language models (LLMs), the potential to enhance user engagement with CRS and augment the recommendation process with LLM-generated content has received increasing attention. However, the efficacy of LLM-powered CRS is contingent upon the use of prompts, and the subjective perception of recommendation quality can differ across various recommendation domains. Therefore, we have developed a ChatGPT-based CRS to investigate the impact of these two factors, prompt guidance (PG) and recommendation domain (RD), on the overall user experience of the system. We conducted an online empirical study (N = 100) by employing a mixed-method approach that utilized a between-subjects design for the variable of PG (with vs. without) and a within-subjects design for RD (book recommendations vs. job recommendations). The findings reveal that PG can substantially enhance the system's explainability, adaptability, perceived ease of use, and transparency. Moreover, users are inclined to perceive a greater sense of novelty and demonstrate a higher propensity to engage with and try recommended items in the context of book recommendations as opposed to job recommendations. Furthermore, the influence of PG on certain user experience metrics and interactive behaviors appears to be modulated by the recommendation domain, as evidenced by the interaction effects between the two examined factors. This work contributes to the user-centered evaluation of ChatGPT-based CRS by investigating two prominent factors and offers practical design guidance.

cs.HC↗

arXiv2024

On the Determination of Stellar Mass and Binary Fraction of Open Clusters within 500 pc from the Sun

We investigated the stellar mass function and the binary fraction of 114 nearby open clusters (OCs) using the high-precision photometric data from Gaia Data Release 3 (Gaia DR3). We estimated the mass of member stars by using a ridge line (RL) that is better in line with the observed color-magnitude diagram (CMD), thus obtaining more accurate stellar mass and binary mass ratio ($q$) at the low-mass region. By analyzing the present-day mass function (PDMF) of star clusters, we found that 108 OCs follow a two-stage power-law distribution, whereas 6 OCs present a single power-law PDMF. Subsequently, we fitted the high(low)-mass index of PDMF ($dN/dm \propto m^{-α}$), denoted as $α_{\rm h}$($α_{\rm l}$), and segmentation point $m_{\rm c}$. For our cluster sample, the median values of $α_{\rm h}$ and $α_{\rm l}$ are 2.65 and 0.95, respectively, which are approximately consistent with the initial mass function (IMF) results provided by Kroupa (2001). We utilized the cumulative radial number distribution of stars with different masses to quantify the degree of mass segregation. We found a significant positive correlation between the state of dynamical evolution and mass segregation in OCs. We also estimated the fraction of binary stars with $q \geq 0.5$, ranging from 6% to 34% with a median of 17%. Finally, we provided a catalog of 114 nearby cluster properties, including the total mass, the binary fraction, the PDMF, and the dynamical state.

astro-ph.SR↗

arXiv2024

Boosting MLPs with a Coarsening Strategy for Long-Term Time Series Forecasting

Deep learning methods have been exerting their strengths in long-term time series forecasting. However, they often struggle to strike a balance between expressive power and computational efficiency. Resorting to multi-layer perceptrons (MLPs) provides a compromising solution, yet they suffer from two critical problems caused by the intrinsic point-wise mapping mode, in terms of deficient contextual dependencies and inadequate information bottleneck. Here, we propose the Coarsened Perceptron Network (CP-Net), featured by a coarsening strategy that alleviates the above problems associated with the prototype MLPs by forming information granules in place of solitary temporal points. The CP-Net utilizes primarily a two-stage framework for extracting semantic and contextual patterns, which preserves correlations over larger timespans and filters out volatile noises. This is further enhanced by a multi-scale setting, where patterns of diverse granularities are fused towards a comprehensive prediction. Based purely on convolutions of structural simplicity, CP-Net is able to maintain a linear computational complexity and low runtime, while demonstrates an improvement of 4.1% compared with the SOTA method on seven forecasting benchmarks.

cs.LG↗

arXiv2024

Quantitative convergence in relative entropy for a moderately interacting particle system on $\mathbb{R}^d$

This article shows how to combine the relative entropy method by D. Bresch, P.-E. Jabin, and Z. Wang in arXiv:1706.09564, arXiv:1906.04093 and the regularized $L^2(\mathbb{R}^d)$-estimate by Oelschläger (Probability theory and related fields, 1987) to prove a strong propagation of chaos result for the viscous porous medium equation from a moderately interacting particle system in $L^\infty(0,T; L^1(\mathbb{R}^d))$-norm. In the moderate interacting setting, the interacting potential is a smoothed Dirac Delta distribution, however, current results regarding the relative entropy methods for singular potentials do not apply. The result holds on $\mathbb{R}^d$ for any dimension $d\geq 1$ and provides a quantitative result where the rate of convergence depends on the moderate scaling parameter and the dimension $d\geq 1$. Additionally, the presented method can be adapted for moderately interacting systems for which a certain convergence probability holds -- thus a propagation of chaos result in relative entropy can be obtained for kernels approximating Coulomb potentials.

math.AP↗

arXiv2024

Emergence of Cooperation in Two-agent Repeated Games with Reinforcement Learning

Cooperation is the foundation of ecosystems and the human society, and the reinforcement learning provides crucial insight into the mechanism for its emergence. However, most previous work has mostly focused on the self-organization at the population level, the fundamental dynamics at the individual level remains unclear. Here, we investigate the evolution of cooperation in a two-agent system, where each agent pursues optimal policies according to the classical Q-learning algorithm in playing the strict prisoner's dilemma. We reveal that a strong memory and long-sighted expectation yield the emergence of Coordinated Optimal Policies (COPs), where both agents act like Win-Stay, Lose-Shift (WSLS) to maintain a high level of cooperation. Otherwise, players become tolerant toward their co-player's defection and the cooperation loses stability in the end where the policy all Defection (All-D) prevails. This suggests that tolerance could be a good precursor to a crisis in cooperation. Furthermore, our analysis shows that the Coordinated Optimal Modes (COMs) for different COPs gradually lose stability as memory weakens and expectation for the future decreases, where agents fail to predict co-player's action in games and defection dominates. As a result, we give the constraint to expectations of future and memory strength for maintaining cooperation. In contrast to the previous work, the impact of exploration on cooperation is found not be consistent, but depends on composition of COMs. By clarifying these fundamental issues in this two-player system, we hope that our work could be helpful for understanding the emergence and stability of cooperation in more complex scenarios in reality.

physics.soc-ph↗

arXiv2024

Near-Field Positioning and Attitude Sensing Based on Electromagnetic Propagation Modeling

Positioning and sensing over wireless networks are imperative for many emerging applications. However, since traditional wireless channel models over-simplify the user equipment (UE) as a point target, they cannot be used for sensing the attitude of the UE, which is typically described by the spatial orientation. In this paper, a comprehensive electromagnetic propagation modeling (EPM) based on electromagnetic theory is developed to precisely model the near-field channel. For the noise-free case, the EPM model establishes the non-linear functional dependence of observed signals on both the position and attitude of the UE. To address the difficulty in the non-linear coupling, we first propose to divide the distance domain into three regions, separated by the defined Phase ambiguity distance and Spacing constraint distance. Then, for each region, we obtain the closed-form solutions for joint position and attitude estimation with low complexity. Next, to investigate the impact of random noise on the joint estimation performance, the Ziv-Zakai bound (ZZB) is derived to yield useful insights. The expected Cramér-Rao bound (ECRB) is further provided to obtain the simplified closed-form expressions for the performance lower bounds. Our numerical results demonstrate that the derived ZZB can provide accurate predictions of the performance of estimators in all signal-to-noise ratio (SNR) regimes. More importantly, we achieve the millimeter-level accuracy in position estimation and attain the 0.1-level accuracy in attitude estimation.

cs.IT↗

arXiv2024

Exploration of morphological coherence in open clusters with a "core-shell'' structure

The study of their morphological coherence allows us to obtain a better understanding of the morphological evolution of open clusters. We employed the ellipsoid fitting method to delineate the 3D spatial structure of the sample clusters while using the morphological dislocation (MD) defined in our previous work and the ellipticity ratio (ER) of the clusters' inner and outer structures to characterize the morphological coherence of the sample clusters. The results show an inverse correlation between the ER of the sample clusters and the number of their members, indicating that sample clusters with a much more elliptical external morphology than internal shape generally tend to host a large number of members. Meanwhile, a slight shrinking of the MD of the sample clusters with their members' number may shed light on the significant role of the gravitational binding of the sample clusters in maintaining their morphological stability. Moreover, there are no correlations between the MD and ER of the sample clusters and their age. They are also not significantly correlated with the X-axis, the Y-axis, their orbital eccentricities, and the radial and vertical forces on them. However, the ER of the sample clusters displays some fluctuations in the distributions between it and the above covariates, implying that the morphologies of the sample clusters are sensitive to the external environment if sample effects are not taken into account. Finally, the analysis of the 3D spatial shapes of sample clusters with a small ER or a large ER demonstrates that the number of members lays an important foundation for forming a dense internal system for sample clusters. At the same time, the MD of the sample clusters can serve well as an indicator of their morphological stability, which is built upon a certain amount of member stars.

astro-ph.GA↗

arXiv2024

HarmonyBatch: Batching multi-SLO DNN Inference with Heterogeneous Serverless Functions

Deep Neural Network (DNN) inference on serverless functions is gaining prominence due to its potential for substantial budget savings. Existing works on serverless DNN inference solely optimize batching requests from one application with a single Service Level Objective (SLO) on CPU functions. However, production serverless DNN inference traces indicate that the request arrival rate of applications is surprisingly low, which inevitably causes a long batching time and SLO violations. Hence, there is an urgent need for batching multiple DNN inference requests with diverse SLOs (i.e., multi-SLO DNN inference) in serverless platforms. Moreover, the potential performance and cost benefits of deploying heterogeneous (i.e., CPU and GPU) functions for DNN inference have received scant attention. In this paper, we present HarmonyBatch, a cost-efficient resource provisioning framework designed to achieve predictable performance for multi-SLO DNN inference with heterogeneous serverless functions. Specifically, we construct an analytical performance and cost model of DNN inference on both CPU and GPU functions, by explicitly considering the GPU time-slicing scheduling mechanism and request arrival rate distribution. Based on such a model, we devise a two-stage merging strategy in HarmonyBatch to judiciously batch the multi-SLO DNN inference requests into application groups. It aims to minimize the budget of function provisioning for each application group while guaranteeing diverse performance SLOs of inference applications. We have implemented a prototype of HarmonyBatch on Alibaba Cloud Function Compute. Extensive prototype experiments with representative DNN inference workloads demonstrate that HarmonyBatch can provide predictable performance to serverless DNN inference workloads while reducing the monetary cost by up to 82.9% compared to the state-of-the-art methods.

cs.DC↗

arXiv2024

New upper bounds on the number of non-zero weights of constacyclic codes

For any simple-root constacyclic code $\mathcal{C}$ over a finite field $\mathbb{F}_q$, as far as we know, the group $\mathcal{G}$ generated by the multiplier, the constacyclic shift and the scalar multiplications is the largest subgroup of the automorphism group ${\rm Aut}(\mathcal{C})$ of $\mathcal{C}$. In this paper, by calculating the number of $\mathcal{G}$-orbits of $\mathcal{C}\backslash\{\bf 0\}$, we give an explicit upper bound on the number of non-zero weights of $\mathcal{C}$ and present a necessary and sufficient condition for $\mathcal{C}$ to meet the upper bound. Some examples in this paper show that our upper bound is tight and better than the upper bounds in [Zhang and Cao, FFA, 2024]. In particular, our main results provide a new method to construct few-weight constacyclic codes. Furthermore, for the constacyclic code $\mathcal{C}$ belonging to two special types, we obtain a smaller upper bound on the number of non-zero weights of $\mathcal{C}$ by substituting $\mathcal{G}$ with a larger subgroup of ${\rm Aut}(\mathcal{C})$. The results derived in this paper generalize the main results in [Chen, Fu and Liu, IEEE-TIT, 2024]}.

cs.IT↗

arXiv2024

Regularities for solutions to the $L_p$ dual Minkowski problem for unbounded closed sets

Recently, the $L_p$ dual Minkowski problem for unbounded closed convex sets in a pointed closed convex cone was proposed and a weak solution to this problem was provided. In smooth setting, this problem is equivalent to solving the Dirichlet problem for a class of Monge-Ampère type equations. In this paper, we show the existence, regularity and uniqueness of solutions to this Monge-Ampère type equation in the case $p\geq 1$ by studying variational properties for a family of Monge-Ampère functionals. Moreover, the existence and optimal global Hölder regularity in the case $p<1$ and $q\geq n$ is also be discussed.

math.AP↗

arXiv2024

Helical Phononic Modes Induced by a Screw Dislocation

In this study, we investigate a one-dimensional (1D) unidirectional phononic waveguide embedded within a three-dimensional (3D) hexagonal close-packed phononic crystal, achieved by the introduction of a screw dislocation. This approach does not rely on the non-trivial topological characteristics of the 3D crystal. We discover that this dislocation induces a pair of helical modes, characterized by their orthogonal $x$- and $y$-directional displacements being out of phase by 90 degrees, which results in a distinctive rotational motion. These helical modes demonstrate directional propagation, tightly linked to the helicity of the screw dislocation. Through considerations of symmetry, we reveal that the emergence of these helical modes is governed by the symmetry of the screw dislocation itself. Our findings not only provide insights into the interplay between dislocation-induced symmetry and wave propagation in phononic systems but also open new avenues for designing directionally selective waveguides without relying on the crystal's topological properties.

physics.app-ph↗

arXiv2024

Q2A: Querying Implicit Fully Continuous Feature Pyramid to Align Features for Medical Image Segmentation

Recent medical image segmentation methods apply implicit neural representation (INR) to the decoder for achieving a continuous coordinate decoding to tackle the drawback of conventional discrete grid-based data representations. However, the INR-based decoder cannot well handle the feature misalignment problem brought about by the naive latent code acquisition strategy in INR. Although there exist many feature alignment works, they all adopt a progressive multi-step aligning paradigm on a discrete feature pyramid, which is incompatible with the continuous one-step characteristics of INR-based decoder, and thus fails to be the solution. Therefore, we propose Q2A, a novel one-step query-based aligning paradigm, to solve the feature misalignment problem in the INR-based decoder. Specifically, for each target coordinate, Q2A first generates several queries depicting the spatial offsets and the cell resolutions of the contextual features aligned to the coordinate, then calculates the corresponding aligned features by feeding the queries into a novel implicit fully continuous feature pyramid (FCFP), finally fuses the aligned features to predict the class distribution. In FCFP, we further propose a novel universal partition-and-aggregate strategy (P&A) to replace the naive interpolation strategy for latent code acquisition in INR, which mitigates the information loss problem that occurs when the query cell resolution is relatively large and achieves an effective feature decoding at arbitrary continuous resolution. We conduct extensive experiments on two medical datasets, i.e. Glas and Synapse, and a universal dataset, i.e. Cityscapes, and they show the superiority of the proposed Q2A.

cs.CV↗

arXiv2024

Age Determination of LAMOST Red Giant Branch stars based on the Gradient Boosting Decision Tree method

In this study we estimate the stellar ages of LAMOST DR8 Red Giant Branch (RGB) stars based on the Gradient Boosting Decision Tree algorithm (GBDT). We used 2,643 RGB stars extracted from the APOKASC-2 astero-seismological catalog as training data-set. After selecting the parameterses ([$α$/Fe], [C/Fe], T$_{eff}$, [N/Fe], [C/H], log g) highly correlated with age using GBDT, we apply the same GBDT method to the new catalog of more than 590,000 stars classified as RGB stars. The test data-set shows that the median relative error is around 11.6$\%$ for the method. We also compare the predicted ages of RGB stars with other studies (e.g., based on APOGEE), and find systematic differences. The final uncertainty is about 15 to 30$\%$ compared to open clusters' ages. Then we present the spatial distribution of the RGB sample having an age determination, which could recreate the expected result, and discuss systematic biases. All these diagnostics show that one can apply the GBDT method to other stellar samples to estimate atmospheric parameters and age.

astro-ph.SR↗

arXiv2024

Enhancing Programming Education with ChatGPT: A Case Study on Student Perceptions and Interactions in a Python Course

The integration of ChatGPT as a supportive tool in education, notably in programming courses, addresses the unique challenges of programming education by providing assistance with debugging, code generation, and explanations. Despite existing research validating ChatGPT's effectiveness, its application in university-level programming education and a detailed understanding of student interactions and perspectives remain limited. This paper explores ChatGPT's impact on learning in a Python programming course tailored for first-year students over eight weeks. By analyzing responses from surveys, open-ended questions, and student-ChatGPT dialog data, we aim to provide a comprehensive view of ChatGPT's utility and identify both its advantages and limitations as perceived by students. Our study uncovers a generally positive reception toward ChatGPT and offers insights into its role in enhancing the programming education experience. These findings contribute to the broader discourse on AI's potential in education, suggesting paths for future research and application.

cs.CY↗

arXiv2024

A fast-rotating blue straggler star in the tidal tail of the open cluster NGC 752

NGC 752 is a famous Galactic open cluster of intermediate age. In recent works, a very long and asymmetric tail was newly revealed. A blue straggler star (BSS) at the periphery of the tidal tail of the cluster has been identified subsequently. We aim to perform a detailed analysis of the newly detected BSS based on the available comprehensive spectroscopic and photometric data. We also explored this BSS's possible formation pathway and age limitation based on the collected spectroscopic and photometric data. We estimated the projected rotational velocity $v\ \mathrm{sin}i$ and the mass of the BSS from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope low-resolution spectra and multiband photometric data from various catalogs, respectively. The newly discovered BSS is confirmed as a genuine member of NGC 752. The lack of ultraviolet excess in the SED and no significant variations in the light curve imply that this BSS is likely a single star ($mass=1.86^{+3.62}_{-0.94}\ M_{\odot}$) formed through stellar mergers. The fast rotation velocity ($v\ \mathrm{sin}i=206.9\pm4.9$~km $\rm s^{-1}$) of the BSS may provide constraints on its age (less than a hundred million years), but more formation details require further investigation.

astro-ph.GA↗