arXiv subjects

Weimin Zhang

Publications and source records attributed to Weimin Zhang.

23 records · Page 2Linked to original sources

arXiv2023

Existence and Multiplicity of Solutions for Fractional $p$-Laplacian Equation Involving Critical Concave-convex Nonlinearities

We investigate the following fractional $p$-Laplacian equation \[ \begin{cases} \begin{aligned} (-Δ)_p^s u&=λ|u|^{q-2}u+|u|^{p_s^*-2}u &&\text{in}~Ω,\\ u &=0 &&\text{in}~ \mathbb{R}^n\setminusΩ, \end{aligned} \end{cases} \] where $s\in (0,1)$, $p>q>1$, $n>sp$, $λ>0$, $p_s^*=\frac{np}{n-sp}$ and $Ω$ is a bounded domain (with $C^{1, 1}$ boundary). Firstly, we get a dichotomy result for the existence of positive solution with respect to $λ$. For $p\ge 2$, $p-1 \frac{sp(q+1)}{q+1-p}$, we provide two positive solutions for small $λ$. Finally, without sign constraint, for $λ$ sufficiently small, we show the existence of infinitely many solutions.

math.AP↗

arXiv2023

Correlative Preference Transfer with Hierarchical Hypergraph Network for Multi-Domain Recommendation

Advanced recommender systems usually involve multiple domains (such as scenarios or categories) for various marketing strategies, and users interact with them to satisfy diverse demands. The goal of multi-domain recommendation (MDR) is to improve the recommendation performance of all domains simultaneously. Conventional graph neural network based methods usually deal with each domain separately, or train a shared model to serve all domains. The former fails to leverage users' cross-domain behaviors, making the behavior sparseness issue a great obstacle. The latter learns shared user representation with respect to all domains, which neglects users' domain-specific preferences. In this paper we propose $\mathsf{H^3Trans}$, a hierarchical hypergraph network based correlative preference transfer framework for MDR, which represents multi-domain user-item interactions into a unified graph to help preference transfer. $\mathsf{H^3Trans}$ incorporates two hyperedge-based modules, namely dynamic item transfer (Hyper-I) and adaptive user aggregation (Hyper-U). Hyper-I extracts correlative information from multi-domain user-item feedbacks for eliminating domain discrepancy of item representations. Hyper-U aggregates users' scattered preferences in multiple domains and further exploits the high-order (not only pair-wise) connections to improve user representations. Experiments on both public and production datasets verify the superiority of $\mathsf{H^3Trans}$ for MDR.

cs.IR↗

arXiv2022

UKD: Debiasing Conversion Rate Estimation via Uncertainty-regularized Knowledge Distillation

In online advertising, conventional post-click conversion rate (CVR) estimation models are trained using clicked samples. However, during online serving the models need to estimate for all impression ads, leading to the sample selection bias (SSB) issue. Intuitively, providing reliable supervision signals for unclicked ads is a feasible way to alleviate the SSB issue. This paper proposes an uncertainty-regularized knowledge distillation (UKD) framework to debias CVR estimation via distilling knowledge from unclicked ads. A teacher model learns click-adaptive representations and produces pseudo-conversion labels on unclicked ads as supervision signals. Then a student model is trained on both clicked and unclicked ads with knowledge distillation, performing uncertainty modeling to alleviate the inherent noise in pseudo-labels. Experiments on billion-scale datasets show that UKD outperforms previous debiasing methods. Online results verify that UKD achieves significant improvements.

cs.IR↗

arXiv2021

Unraveling the Unconventional Order of a High-Mobility Indacenodithiophene-Benzothiadiazole Copolymer

A new class of donor-acceptor (D-A) copolymers found to produce high charge carrier mobilities competitive with amorphous silicon ($> 1 cm^{2}V^{-1}s^{-1}$) exhibits the puzzling microstructure of substantial local order, however lacking long-range order and crystallinity previously deemed necessary for achieving high mobility. Here, we demonstrate the application of low-dose transmission electron microscopy to image and quantify the nanoscale and mesoscale organization of an archetypal D-A copolymer across areas comparable to electronic devices (~ $9 μm^{2}$). The local structure is spatially resolved by mapping the backbone (001) spacing reflection, revealing nanocrystallites of aligned polymer chains over nearly the entire film. Analysis of the nanoscale structure of its ordered domains suggests significant short- and medium-range order and preferential grain boundary orientations. Moreover, we provide insights into the rich, interconnected mesoscale organization of this new family of D-A copolymers by analysis of the local orientational spatial autocorrelations.

cond-mat.mtrl-sci↗

arXiv2015

Microscopic properties of degradation-free capped GdN thin films studied by Electron Spin Resonance

The microscopic magnetic properties of high-quality GdN thin films have been investigated by electron spin resonance (ESR) and ferromagnetic resonance (FMR) measurements. Detailed temperature dependence ESR measurements have shown the existence of two ferromagnetic components at lower temperatures which was not clear from the previous magnetization measurements. The temperature, where the resonance shift occurs for the major ferromagnetic component, seems to be consistent with the Curie temperature obtained from the previous magnetization measurement. On the other hand, the divergence of line width is observed around 57 K for the minor ferromagnetic component. The magnetic anisotropies of GdN thin films have been obtained by the analysis of FMR angular dependence observed at 4.2 K. Combining the X-ray diffraction results, the correlation between the magnetic anisotropies and the lattice constants is discussed.

cond-mat.mtrl-sci↗