Can virtual tourism aid in the recovery of tourism industry in the COVID-19 pandemic?

The COVID-19 pandemic has imposed tremendous impacts on the tourism industry worldwide. The tourism sector can take advantage of the new technology (e.g., virtual tourism), to respond to the challenges. This study aims to explore how virtual tourism can aid the recovery of tourism industry. We explore this through a mixed-method approach. Our results show that the use of virtual tourism can be partially explained by the theory of planned behavior. Virtual tourism has a strong influence on people’s onsite destination choices and can be used as an effective marketing tool. Virtual tourism can be an entertainment activity to bring immersed experience without being actually in the destinations, and thus reinforce stay-at-home order. Even after the pandemic is over, people still show willingness to use virtual tourism for diverse purposes. Virtual tourism can also help promote sustainable tourism by reducing unnecessary greenhouse gas emissions and enhance “virtual accessibility” especially for the elderly and disabled with limited mobility

Simpler and Higher Lower Bounds for Shortcut Sets

We provide a variety of lower bounds for the well-known shortcut set problem: how much can one decrease the diameter of a directed graph on $n$ vertices and $m$ edges by adding $O(n)$ or $O(m)$ of shortcuts from the transitive closure of the graph. Our results are based on a vast simplification of the recent construction of Bodwin and Hoppenworth [FOCS 2023] which was used to show an $\widetilde{\Omega}(n^{1/4})$ lower bound for the $O(n)$-sized shortcut set problem. We highlight that our simplification completely removes the use of the convex sets by B\'ar\'any and Larman [Math. Ann. 1998] used in all previous lower bound constructions. Our simplification also removes the need for randomness and further removes some log factors. This allows us to generalize the construction to higher dimensions, which in turn can be used to show the following results. For $O(m)$-sized shortcut sets, we show an $\Omega(n^{1/5})$ lower bound, improving on the previous best $\Omega(n^{1/8})$ lower bound. For all $\varepsilon > 0$, we show that there exists a $\delta > 0$ such that there are $n$-vertex $O(n)$-edge graphs $G$ where adding any shortcut set of size $O(n^{2-\varepsilon})$ keeps the diameter of $G$ at $\Omega(n^\delta)$. This improves the sparsity of the constructed graph compared to a known similar result by Hesse [SODA 2003]. We also consider the sourcewise setting for shortcut sets: given a graph $G=(V,E)$, a set $S\subseteq V$, how much can we decrease the sourcewise diameter of $G$, $\max_{(s, v) \in S \times V, \text{dist}(s, v) < \infty} \text{dist}(s,v)$ by adding a set of edges $H$ from the transitive closure of $G$? We show that for any integer $d \ge 2$, there exists a graph $G=(V, E)$ on $n$ vertices and $S \subseteq V$ with $|S| = \widetilde{\Theta}(n^{3/(d+3)})$, such that when adding $O(n)$ or $O(m)$ shortcuts, the sourcewise diameter is $\widetilde{\Omega}(|S|^{1/3})$.Comment: To appear in SODA 2024. Abstract shortened to fit arXiv requirement

Freeze-in Dark Matter via Lepton Portal: Hubble Tension and Stellar Cooling

We propose a new freeze-in dark matter candidate which feebly couples to the standard model charged leptons. The feeble interactions allow it (i) to freeze-in from the Standard Model thermal bath with its relic density being either a fraction or the entirety of the observed dark matter density and (ii) to radiatively decay to two photons in the dark matter mass ranges of order keV scale with lifetime larger than the age of Universe. These features make this model a realistic realization of dark matter with late-time decay to reduce Hubble tension. We show the best-fit value of H_{0}=68.31(69.34) km s^{-1}Mpc^{-1} in light of Planck 2018+BAO(+LSS)+Pantheon data sets. We then use stellar cooling data to place constraints on the parameter space favored by the Hubble tension. While the universal coupling scenario is excluded, the hierarchical coupling scenario can be tested by future observations of white dwarfs after a careful look into photon inverse decay, Primakoff and Bremsstrahlung emission of the dark matter in various stellar systems. The viable parameter space may be linked to anomalies in future X-ray telescopes.Comment: 21 pages, 8 figure

Reduced projection method for quasiperiodic Schr\"{o}dinger eigenvalue problems

This paper presents a reduced algorithm to the classical projection method for the solution of $d$-dimensional quasiperiodic problems, particularly Schr\"{o}dinger eigenvalue problems. Using the properties of the Schr\"{o}dinger operator in higher-dimensional space via a projection matrix of size $d\times n$, we rigorously prove that the generalized Fourier coefficients of the eigenfunctions decay exponentially along a fixed direction associated with the projection matrix. An efficient reduction strategy of the basis space is then proposed to reduce the degrees of freedom from $O(N^{n})$ to $O(N^{n-d}D^d)$, where $N$ is the number of Fourier grids in one dimension and the truncation coefficient $D$ is much less than $N$. Correspondingly, the computational complexity of the proposed algorithm for solving the first $k$ eigenpairs using the Krylov subspace method decreases from $O(kN^{2n})$ to $O(kN^{2(n-d)}D^{2d})$. Rigorous error estimates of the proposed reduced projection method are provided, indicating that a small $D$ is sufficient to achieve the same level of accuracy as the classical projection method. We present numerical examples of quasiperiodic Schr\"{o}dinger eigenvalue problems in one and two dimensions to demonstrate the accuracy and efficiency of our proposed method.Comment: 20 pages, 9 figure

AnchorFace: An Anchor-based Facial Landmark Detector Across Large Poses

Facial landmark localization aims to detect the predefined points of human faces, and the topic has been rapidly improved with the recent development of neural network based methods. However, it remains a challenging task when dealing with faces in unconstrained scenarios, especially with large pose variations. In this paper, we target the problem of facial landmark localization across large poses and address this task based on a split-and-aggregate strategy. To split the search space, we propose a set of anchor templates as references for regression, which well addresses the large variations of face poses. Based on the prediction of each anchor template, we propose to aggregate the results, which can reduce the landmark uncertainty due to the large poses. Overall, our proposed approach, named AnchorFace, obtains state-of-the-art results with extremely efficient inference speed on four challenging benchmarks, i.e. AFLW, 300W, Menpo, and WFLW dataset. Code will be available at https://github.com/nothingelse92/AnchorFace.Comment: To appear in AAAI 202

Pythagoras Superposition Principle for Localized Eigenstates of 2D Moir\'e Lattices

Moir\'e lattices are aperiodic systems formed by a superposition of two periodic lattices with a relative rotational angle. In optics, the photonic moir\'e lattice has many promising mysteries such as its ability to localize light, thus attracting much attention to exploring features of such a structure. One fundamental research area for photonic moir\'e lattices is the properties of eigenstates, particularly the existence of localized eigenstates and the localization-to-delocalization transition in the energy band structure. Here we propose an accurate algorithm for the eigenproblems of aperiodic systems by combining plane wave discretization and spectral indicator validation under the higher-dimensional projection, allowing us to explore energy bands of fully aperiodic systems. A localization-delocalization transition regarding the intensity of the aperiodic potential is observed and a novel Pythagoras superposition principle for localized eigenstates of 2D moir\'e lattices is revealed by analyzing the relationship between the aperiodic and its corresponding periodic eigenstates. This principle sheds light on exploring the physics of localizations for moir\'e lattice.Comment: 7 pages, 3 figure

Modelling centrifugal membrane deployment of solar sails with the discrete element method

Spin-stabilized solar sails have been extensively studied in recent years. In this paper, a DEM-based approach is proposed for dynamic analysis of the centrifugal deployment of solar sails. In order to validate the proposed approach, the deployment of a small-scale solar sail similar to “IKAROS” is studied. The membrane is discretised into a number of particles, with no physical contact between them. Non-contact interaction is introduced to model in-plane stiffness of the membrane. In order to improve the accuracy, additional forces are applied to the mass particles to model buckling strength, crease stiffness, air drag and damping. The predicted results of the membrane deployment are compared with the experimental data and numerical results in the literature