1,019 research outputs found
Existence and continuous dependence of mild solutions for fractional abstract differential equations with infinite delay
In this paper, we prove the existence, uniqueness, and continuous dependence of the mild solutions for a class of fractional abstract differential equations with infinite delay. The results are obtained by using the Krasnoselskii's fixed point theorem and the theory of resolvent operators for integral equations
Dirichlet Boundary Value Problems for Second Order -Laplacian Difference Equations
In this paper, the solutions to second order Dirichlet boundary value problems of -Laplacian difference equations are investigated. By using critical point theory, existence and multiplicity results are obtained. The proof is based on the Mountain Pass Lemma in combination with variational techniques
Geometry-aware Line Graph Transformer Pre-training for Molecular Property Prediction
Molecular property prediction with deep learning has gained much attention
over the past years. Owing to the scarcity of labeled molecules, there has been
growing interest in self-supervised learning methods that learn generalizable
molecular representations from unlabeled data. Molecules are typically treated
as 2D topological graphs in modeling, but it has been discovered that their 3D
geometry is of great importance in determining molecular functionalities. In
this paper, we propose the Geometry-aware line graph transformer (Galformer)
pre-training, a novel self-supervised learning framework that aims to enhance
molecular representation learning with 2D and 3D modalities. Specifically, we
first design a dual-modality line graph transformer backbone to encode the
topological and geometric information of a molecule. The designed backbone
incorporates effective structural encodings to capture graph structures from
both modalities. Then we devise two complementary pre-training tasks at the
inter and intra-modality levels. These tasks provide properly supervised
information and extract discriminative 2D and 3D knowledge from unlabeled
molecules. Finally, we evaluate Galformer against six state-of-the-art
baselines on twelve property prediction benchmarks via downstream fine-tuning.
Experimental results show that Galformer consistently outperforms all baselines
on both classification and regression tasks, demonstrating its effectiveness.Comment: 9 pages, 5 figure
Anomalous second-order skin modes in Floquet non-Hermitian systems
The non-Hermitian skin effect under open boundary conditions is widely
believed to originate from the intrinsic spectral topology under periodic
boundary conditions. If the eigenspectra under periodic boundary conditions
have no spectral windings (e.g., piecewise arcs) or a finite area on the
complex plane, there will be no non-Hermitian skin effect with open boundaries.
In this article, we demonstrate another scenario beyond this perception by
introducing a two-dimensional periodically driven model. The effective Floquet
Hamiltonian lacks intrinsic spectral topology and is proportional to the
identity matrix (representing a single point on the complex plane) under
periodic boundary conditions. Yet, the Floquet Hamiltonian exhibits a
second-order skin effect that is robust against perturbations and disorder
under open boundary conditions. We further reveal the dynamical origin of these
second-order skin modes and illustrate that they are characterized by a
dynamical topological invariant of the full time-evolution operator.Comment: 10 pages, 4 figure
What are Public Concerns about ChatGPT? A Novel Self-Supervised Neural Topic Model Tells You
The recently released artificial intelligence conversational agent, ChatGPT,
has gained significant attention in academia and real life. A multitude of
early ChatGPT users eagerly explore its capabilities and share their opinions
on it via social media. Both user queries and social media posts express public
concerns regarding this advanced dialogue system. To mine public concerns about
ChatGPT, a novel Self-Supervised neural Topic Model (SSTM), which formalizes
topic modeling as a representation learning procedure, is proposed in this
paper. Extensive experiments have been conducted on Twitter posts about ChatGPT
and queries asked by ChatGPT users. And experimental results demonstrate that
the proposed approach could extract higher quality public concerns with
improved interpretability and diversity, surpassing the performance of
state-of-the-art approaches
You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptors
In this paper, we propose a novel local descriptor-based framework, called
You Only Hypothesize Once (YOHO), for the registration of two unaligned point
clouds. In contrast to most existing local descriptors which rely on a fragile
local reference frame to gain rotation invariance, the proposed descriptor
achieves the rotation invariance by recent technologies of group equivariant
feature learning, which brings more robustness to point density and noise.
Meanwhile, the descriptor in YOHO also has a rotation equivariant part, which
enables us to estimate the registration from just one correspondence
hypothesis. Such property reduces the searching space for feasible
transformations, thus greatly improves both the accuracy and the efficiency of
YOHO. Extensive experiments show that YOHO achieves superior performances with
much fewer needed RANSAC iterations on four widely-used datasets, the
3DMatch/3DLoMatch datasets, the ETH dataset and the WHU-TLS dataset. More
details are shown in our project page: https://hpwang-whu.github.io/YOHO/.Comment: Accepted by ACM Multimedia(MM) 2022, Project page:
https://hpwang-whu.github.io/YOHO
Vibration signal simulation of planetary gearbox based on motion process modeling
In planetary gearbox, multiple gear pair meshing with each other and the vibration transmission paths from gear meshing points to the fixed sensors are time-varying. Therefore, fault diagnosis of the planetary gearbox is more difficult compared to that of fixed-axis gearbox, in which the vibration signal simulation models are very important. This paper constructs vibration signal models based on motion process modeling. This kind of modeling method is easier to understand compare with other methods which mainly based on the theory or physical laws behind the phenomena. The modeling process was presented in a step-by-step procedure according to the motion process of planetary gearbox. Frequency analysis was also implemented and comprehensive diagram was shown to help understand the result
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