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Shiqing Zhang

Publications and source records attributed to Shiqing Zhang.

At least 19 recordsLinked to original sources
arXiv2026

MVG-KAN: Multi-View Geo-Wind Guided KAN for PM$_{2.5}$ Forecasting

Accurate short-term PM$_{2.5}$ forecasting is important for public health protection, air-quality early warning, and urban environmental management. However, PM$_{2.5}$ variation is driven by multiple coupled factors, including stable periodic changes induced by human activities and meteorological regularity, station-specific short-term concentration evolution, and meteorology-driven pollutant dispersion among monitoring stations. Existing spatio-temporal forecasting methods may capture station relationships to some extent, but distance-only, correlation-based, or purely adaptive graphs are often insufficient to comprehensively represent these heterogeneous factors, especially wind-direction-dependent pollutant transport. To address this problem, we propose a Multi-View Geo-Wind Guided KAN model for PM$_{2.5}$ forecasting, named \textbf{MVG-KAN}, which models station-level PM$_{2.5}$ evolution from three complementary views: local periodic regularity, station-wise residual temporal dynamics, and meteorological-environment-guided spatial dispersion. Specifically, the periodic-residual forecasting backbone first separates stable daily and weekly patterns from non-periodic residual variations. A Geo-Wind Graph is constructed by combining geographic distance decay with wind-direction- and wind-speed-aware transport, providing a lightweight physically motivated directed spatial prior for residual propagation among stations. In addition, a temporal Kolmogorov-Arnold network (TKAN) residual head is then introduced to learn station-wise nonlinear autoregressive correction from de-periodized PM$_{2.5}$ residuals and historical multi-pollutant sequences, thereby enhancing the modeling of local residual inertia and pollutant co-variation.

cs.AI↗
arXiv2026

Stability of geodesic-ray data, horofunctions, and rectifiability of fixed-shape slices in the Newtonian \(N\)-body problem

For the Newtonian \(N\)-body problem at nonnegative energy, we study solution sets selected by the Jacobi--Maupertuis variational principle and by the associated stationary Hamilton--Jacobi equation. We prove a compactness/stability theorem for classical initial data generating geodesic rays: limits in the ambient phase space remain collision-free, generate geodesic rays, and carry locally relatively compact normalized Busemann functions. The limiting horofunction of normalized Busemann functions yields a viscosity solution of the limiting stationary equation. For a fixed collision-free hyperbolic limit shape \(a\), we also prove closedness of the corresponding slice of geodesic-ray data. Finally, after passing to the reduced configuration space \(X\), we show that this fixed-shape slice is countably \(d(N-1)\)-rectifiable in phase space and has Hausdorff dimension exactly \(d(N-1)\). Thus the paper combines phase-space compactness of calibrated minimizing motions with a geometric-measure description of a fixed-shape Hamilton--Jacobi calibrated slice.

math.AP↗
arXiv2026

Decoupled Hierarchical Distillation for Multimodal Emotion Recognition

Human multimodal emotion recognition (MER) seeks to infer human emotions by integrating information from language, visual, and acoustic modalities. Although existing MER approaches have achieved promising results, they still struggle with inherent multimodal heterogeneities and varying contributions from different modalities. To address these challenges, we propose a novel framework, Decoupled Hierarchical Multimodal Distillation (DHMD). DHMD decouples each modality's features into modality-irrelevant (homogeneous) and modality-exclusive (heterogeneous) components using a self-regression mechanism. The framework employs a two-stage knowledge distillation (KD) strategy: (1) coarse-grained KD via a Graph Distillation Unit (GD-Unit) in each decoupled feature space, where a dynamic graph facilitates adaptive distillation among modalities, and (2) fine-grained KD through a cross-modal dictionary matching mechanism, which aligns semantic granularities across modalities to produce more discriminative MER representations. This hierarchical distillation approach enables flexible knowledge transfer and effectively improves cross-modal feature alignment. Experimental results demonstrate that DHMD consistently outperforms state-of-the-art MER methods, achieving 1.3\%/2.4\% (ACC$_7$), 1.3\%/1.9\% (ACC$_2$) and 1.9\%/1.8\% (F1) relative improvement on CMU-MOSI/CMU-MOSEI dataset, respectively. Meanwhile, visualization results reveal that both the graph edges and dictionary activations in DHMD exhibit meaningful distribution patterns across modality-irrelevant/-exclusive feature spaces.

cs.CV↗
arXiv2025

The existence and stability of viscosity solutions to perturbed contact Hamilton-Jacobi equations

We consider a contact Hamiltonian $H(x,p,u)$ with certain dependence on the contact variable $u$. If $u_{-}$ is a viscosity solution of the contact Hamilton-Jacobi equation \[H(x,D_{x}u(x),u(x))=0,\quad x\in M,\] and $u_{-}$ is locally Lyapunov asymptotically stable, we will prove that the perturbed equation \[H(x,D_{x}u(x),u(x))+\varepsilon P(x,D_{x}u(x),u(x))=0,\quad x\in M,\] does exist viscosity solution $u_{-}^{\varepsilon}$ which converges uniformly to $u_{-}$, as perturbation parameter $\varepsilon$ converges to 0. Moreover, we give a case that in a neighborhood of viscosity solution $u_-$, the perturbed equation has an unique viscosity solution $u_{-}^{\varepsilon}$. Furthermore, $u_{-}^{\varepsilon}$ keeps locally Lyapunov asymptotically stability.

math.AP↗
arXiv2024

Weak Compactness Criterion in $ W^{k, 1} $ with an Existence Theorem of Minimizers

There is a rich theory of existence theorems for minimizers over reflexive Sobolev spaces (ex. Eberlein-Šmulian theorem). However, the existence theorems for many variational problems over non-reflexive Sobolev spaces remain underexplored. In this paper, we investigate various examples of functionals over non-reflexive Sobolev spaces. To do this, we prove a weak compactness criterion in $W^{k,1}$ that generalizes the Dunford-Pettis theorem, which asserts that relatively weakly compact subsets of $ L^1 $ coincide with equi-integrable families. As a corollary, we also extend an existence theorem of minimizers from reflexive Sobolev spaces to non-reflexive ones. This work is also benefited and streamlined by various concepts in category theory.

math.FA↗
arXiv2024

On the uniqueness of the strictly convex quadrilateral central configuration with a fixed angle

The conjecture of the existence and the uniqueness of the strictly convex quadrilateral central configuration for the Newtonian 4-body problem is one of the most-talked open problems in the study of the classical n-body problems in celestial mechanics. MacMillan and Bartky first gave its general existence in the 1930s and a particular case for its uniqueness. Still, the general case has yet to be solved perfectly since it was considered by Sim'{o} and Yoccoz in the 1980s and was first mentioned by Albouy and Fu in 2008 in the formal publication. Using coordinates of mutual distances and Morse's critical point theory, we give the (at most) uniqueness of the planar strictly convex 4-body central configuration when the angle of one pair of the opposite sides is given.

math-ph↗
arXiv2024

On the uniqueness of the planar 5-body central configuration with a trapezoidal convex hull

To apply Morse's critical point theory, we use mutual distances as coordinates to discuss a kind of central configuration of the planar Newtonian 5-body problem with a trapezoidal convex hull, i.e., four of the five bodies are located at the vertices of a trapezoid, and the fifth one is located on one of the parallel sides. We show that there is at most one central configuration of this geometrical shape for a given cyclic order of the five bodies along the convex hull.

math.DS↗
arXiv2024

LMVD: A Large-Scale Multimodal Vlog Dataset for Depression Detection in the Wild

Depression can significantly impact many aspects of an individual's life, including their personal and social functioning, academic and work performance, and overall quality of life. Many researchers within the field of affective computing are adopting deep learning technology to explore potential patterns related to the detection of depression. However, because of subjects' privacy protection concerns, that data in this area is still scarce, presenting a challenge for the deep discriminative models used in detecting depression. To navigate these obstacles, a large-scale multimodal vlog dataset (LMVD), for depression recognition in the wild is built. In LMVD, which has 1823 samples with 214 hours of the 1475 participants captured from four multimedia platforms (Sina Weibo, Bilibili, Tiktok, and YouTube). A novel architecture termed MDDformer to learn the non-verbal behaviors of individuals is proposed. Extensive validations are performed on the LMVD dataset, demonstrating superior performance for depression detection. We anticipate that the LMVD will contribute a valuable function to the depression detection community. The data and code will released at the link: https://github.com/helang818/LMVD/.

cs.CV↗
arXiv2024

Approximation analysis for the minimization problem of difference-of-convex functions with Moreau envelopes

In this work the minimization problem for the difference of convex (DC) functions is studied by using Moreau envelopes and the descent method with Moreau gradient is employed to approximate the numerical solution. The main regularization idea in this work is inspired by Hiriart-Urruty [14], Moudafi[17], regularize the components of the DC problem by adapting the different parameters and strategic matrices flexibly to evaluate the whole DC problem. It is shown that the inertial gradient method as well as the classic gradient descent scheme tend towards an approximation stationary point of the original problem.

math.OC↗
arXiv2023

Stacked central configurations with a homogeneous potential in $\mathbb{R}^3$

In this paper we generalize some results in \cite{Yu2021} concerning stacked central configurations. We can deal with the general homogeneous potential $U_α$ (containing the vortex case) in $\mathbb{R}^3$. We give the admissible set of $α$ for a convex central configuration (with respect to the Newtonian potential i.e. $α=3$). We discuss some properties of the regular $n$-gon co-circular central configurations. We also find that the stacked property is particular for central configurations by studying the S-balanced configuration case.

math.DS↗
arXiv2023

On Geodesic Rays of Newtonian Gravitational Systems

In this paper, we focus on the set of geodesics rays of the Newtonian N-body problem. We find that the limits of geodesic rays are also geodesic rays, hence they are not dense in the space of initial conditions. As a result, there are many motions whose domain is the half real line has non-negative total energy, and they are not geodesic rays, the set of such motions has positive measure, we think this set gives a large space to accommodate many solutions with "bad" behaviors. As an application of weak KAM theory for N-body problem, we give a brief proof of the existence of complete parabolic orbit starting from any given initial position.

math.DS↗
arXiv2022

A N-body problem with weak force potential through Hamilton-Jacobi equation approach

This paper we consider for the N-body problem with potential 1/rα (0 < α < 1) the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. Here E is the Euclidean space where the bodies moving and is the norm induced by the inner product. The energy level h > 0 of the motion can also be chosen arbitrarily. We use the global viscosity solutions for the Hamilton-Jacobi equation H (x, dxu) = h and geodesics.

math.AP↗
arXiv2022

Some nonlinear characterizations of reflexive Banach spaces

It is well known that in the calculus of variations and in optimization there exist many formulations of the fundamental propositions on the attainment of the infima of sequentially weakly lower semicontinuous coercive functions on reflexive Banach spaces. By either some constructive skills or the regularization skill by inf--convolutions we show in this paper that all these formulations together with their important variants are equivalent to each other and equivalent to the reflexivity of the underlying space. Motivated by this research, we also give a characterization for a normed space to be finite dimensional: a normed space is finite dimensional iff every continuous real--valued function defined on each bounded closed subset of this space can obtain its minimum, namely the converse of the classical Weierstrass theorem also holds true.

math.FA↗
arXiv2021

On the convergence and applications of the inertial-like method for null-point problems

In this paper, we propose two novel inertial-like algorithms for solving the split common null point problem (SCNPP) with respect to set-valued maximal operators. The features of the presented algorithm are using new inertial structure (i.e, the design of the new inertial-like method does neither involve computation of the norm of the difference between $x_n$ and $x_{n-1}$ in advance, nor need to consider the special value of the inertial parameter $θ_n$ to make the condition $\sum_{n=1}^\infty α_n\|x_n-x_{n-1}\|^2<\infty$ valid) and the selection of the step-sizes does not need prior knowledge of operator norms. Numerical experiments are presented to illustrate the performance of the algorithms.

math.NA↗
arXiv2021

A Generalized Mountain Pass Lemma with a Closed Subset for Locally Lipschitz Functionals

The classical Mountain Pass Lemma of Ambrosetti-Rabinowitz has been studied, extended and modified in several directions. Notable examples would certainly include the generalization to locally Lipschitz functionals by K.C. Chang, analyzing the structure of the critical set in the mountain pass theorem in the works of Hofer, Pucci-Serrin and Tian, and the extension by Ghoussoub-Preiss to closed subsets in a Banach space with recent variations. In this paper, we utilize the generalized gradient of Clarke and Ekeland's variatonal principle to generalize the Ghoussoub-Preiss's Theorem in the setting of locally Lipschitz functionals. We give an application to periodic solutions of Hamiltonian systems.

math.CA↗