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The Doppler beaming effect, induced by the reflex motion of stars, introduces flux modulations and serves as an efficient method to photometrically determine mass functions for a large number of close binary systems, particularly those involving compact objects. In order to convert observed beaming-flux variations into a radial-velocity curve, precise determination of the beaming factor is essential. Previously, this factor was calculated as a constant, assuming a power-law profile for stellar spectra. In this study, we present a novel approach to directly compute this factor. Our new method not only simplifies the computation, especially for blue bands and cool stars, but also enables us to evaluate whether the relationship between beaming flux and radial velocity can be accurately described as linear. We develop a python code and compute a comprehensive beaming-factor table for commonly used filter systems covering main-sequence, subgiant, and giant stars, as well as hot subdwarf and white dwarf stars. Both the code and our table are archived and publicly available at http://doi.org/10.5281/zenodo.13049419., Comment: 10 pages, 5 figures, 1 table. Accepted by ApJ

A number of modified gravity theories (e.g., $f(R)$-gravity) lead to a Yukawa-like metric in the weak field limit which can be described by two Yukawa parameters, i.e., the strength $\kappa$ and the length scale $\lambda$. The S-stars, orbiting around the supermassive black hole in the Galactic Center, are unique probes to test these gravity theories in relatively strong gravitational field. The Newtonian Yukawa gravity potential or a simple approximation to the Yukawa metric was usually adopted in previous studies when using the orbital motion of S-stars to constrain such modified gravity theories, which may be not sufficiently accurate considering recent and future high resolution observations. In this paper, we first derive the Post-Newtonian (PN) Yukawa motion equation at the 2PN order, and then investigate the high order effects on the orbital motions by comparison with those from the Newtonian Yukawa gravity potential. We further obtain constraints on $\kappa$ by using the observations on the orbital motions of several S-stars (i.e., S2, S38, and S55). Our results show that the current observations of these stars are compatible with the General Relativity and $\kappa$ can be constrained to $|\kappa|<0.01$ with $95\%$ confidence if $\lambda\in(100,250)$\,AU. We also estimate the possible improvements (about an order of magnitude or more) to the constraints by future higher resolution observations and the inclusion of closer S-stars, such as S4716., Comment: 15 pages, 8 figures, accepted for publication in Phys. Rev. D

Let $\{X_{\alpha}\}$ be a family of random variables following a certain type of distributions with finite expectation $\mathbf{E}[X_{\alpha}]$ and finite variance ${\rm Var}(X_{\alpha})$, where $\alpha$ is a parameter. Motivated by the recent paper of Hollom and Portier (arXiv: 2306.07811v1), we study the anti-concentration function $(0, \infty)\ni y\to \inf_{\alpha}\mathbf{P}\left(|X_{\alpha}-\mathbf{E}[X_{\alpha}]|\geq y \sqrt{{\rm Var}(X_{\alpha})}\right)$ and find its explicit expression. We show that, for certain familiar families of distributions, including uniform distributions, exponential distributions, non-degenerate Gaussian distributions and student's $t$-distribution, the anti-concentration function is not identically zero, while for some other familiar families of distributions, including binomial, Poisson, negative binomial, hypergeometric, Gamma, Pareto, Weibull, log-normal and Beta distributions, the anti-concentration function is identically zero., Comment: 15 pages

In this paper, we study the asymptotic behavior of the number of rarely visited edges (i.e., edges that visited only once) of a simple symmetric random walk on $\mathbb{Z}$. Let $\alpha(n)$ be the number of rarely visited edges up to time $n$. First, we evaluate $\mathbb{E}(\alpha(n))$, show that $n\to \mathbb{E}(\alpha(n))$ is non-decreasing in $n$ and that $\lim\limits_{n\to+\infty}\mathbb{E}(\alpha(n))=2$. Then we study the asymptotic behavior of $\mathbb{P} (\alpha(n)>a(\log n)^2)$ for any $a>0$ and use it to show that there exists a constant $C\in(0,+\infty)$ such that $\limsup\limits_{n\to+\infty}\frac{\alpha(n)}{(\log n)^2}=C$ almost surely.

The study of complex networks has significantly advanced our understanding of community structures which serves as a crucial feature of real-world graphs. Detecting communities in graphs is a challenging problem with applications in sociology, biology, and computer science. Despite the efforts of an interdisciplinary community of scientists, a satisfactory solution to this problem has not yet been achieved. This review article delves into the topic of community detection in graphs, which serves as a thorough exposition of various community detection methods from perspectives of modularity-based method, spectral clustering, probabilistic modelling, and deep learning. Along with the methods, a new community detection method designed by us is also presented. Additionally, the performance of these methods on the datasets with and without ground truth is compared. In conclusion, this comprehensive review provides a deep understanding of community detection in graphs.

Designing an effective representation learning method for multimodal sentiment analysis tasks is a crucial research direction. The challenge lies in learning both shared and private information in a complete modal representation, which is difficult with uniform multimodal labels and a raw feature fusion approach. In this work, we propose a deep modal shared information learning module based on the covariance matrix to capture the shared information between modalities. Additionally, we use a label generation module based on a self-supervised learning strategy to capture the private information of the modalities. Our module is plug-and-play in multimodal tasks, and by changing the parameterization, it can adjust the information exchange relationship between the modes and learn the private or shared information between the specified modes. We also employ a multi-task learning strategy to help the model focus its attention on the modal differentiation training data. We provide a detailed formulation derivation and feasibility proof for the design of the deep modal shared information learning module. We conduct extensive experiments on three common multimodal sentiment analysis baseline datasets, and the experimental results validate the reliability of our model. Furthermore, we explore more combinatorial techniques for the use of the module. Our approach outperforms current state-of-the-art methods on most of the metrics of the three public datasets.

Trends of miniaturized devices and quantum interference electronics lead to the long desire of Fano interference in single-molecule junctions, here, which is successfully demonstrated using the 2,7-di(4-pyridyl)-9,9'-spirobifluorene molecule with a long backbone group and a short side group. Experimentally, the two electrically coupled groups are found to contribute to two blurred degenerate points in the differential conductance mapping. This forms a characteristic non-centrosymmetric double-crossing feature, with distinct temperature response for each crossing. Theoretically, we describe the practical in-junction electron transmission using a new two-tunnelling-channel coupling model and obtain a working formula with a Fano term and a Breit-Wigner term. The formula is shown to provide a good fit for all the mapping data and their temperature dependence in three dimensions, identifying the Fano component. Our work thus forms a complete set of evidence of the Fano interference in a single-molecule junction induced by two-tunnelling-channel coupling transport. Density functional theory calculations are used to corroborate this new physics., Comment: 13 pages (main text), 4000 Words (main text), 5 figures

In this work, we propose a distributionally robust stochastic model predictive control (DR-SMPC) algorithm to address the problem of two-sided chance constrained discrete-time linear system corrupted by additive noise. The prevalent mechanism to cope with two-sided chance constraints is the so-called risk allocation approach, which conservatively approximates the two-sided chance constraints with two single chance constraints by applying the Boole's inequality. In this proposed DR-SMPC framework, an exact tractable second-order cone (SOC) approach is adopted to abstract the two-sided chance constraints by considering the first and second moments of the noise. The proposed DR-SMPC algorithm is able to guarantee that the worst-case probability of violating both the upper and lower limits of safety constraints is within the pre-specified maximum probability (PsMP). By flexibly adjusting this PsMP, the feasible region of the initial states can be increased for the SMPC problem. The recursive feasibility and convergence of the proposed DR-SMPC are established rigorously by introducing binary initialization strategy of nominal state. Simulation studies of two practical cases are conducted to demonstrate the effectiveness of the proposed DR-SMPC algorithm., Comment: 14 pages, 6 figures

Motivated by the recently proposed dual control for exploration and exploitation (DCEE) concept, this paper presents a Multi-Step DCEE (MS-DCEE) framework with guaranteed convergence for autonomous search of a source of airborne dispersion. Different from the existing stochastic model predictive control (SMPC) algorithm and informative path planning (IPP) approaches, the proposed MS-DCEE approach uses the current and future input to not only drive the agent towards the estimated source location (exploitation) but also reduce its estimation uncertainty (exploration) by actively learning the operational environment. Unknown source target position, together with unknown environment, impose significant challenges in establishing the recursive feasibility and the convergence of the proposed algorithm. To address them, with the help of the property of Bayesian estimation, we develop a two-step approach where the unbiasedness of the mean estimation is assumed first and then the randomness of the mean estimate under each collected information sequence is accounted. Based on that, we develop a MS-DCEE scheme with suitable terminal ingredients where recursive feasibility and convergence are guaranteed. Two simulation scenarios are conducted, which show that the proposed MS-DCEE algorithm outperforms the SMPC, the IPP and the single-step DCEE approaches in terms of searching successful rates and efficiency., Comment: 4 figures

While the rapid progress of deep learning fuels end-to-end reinforcement learning (RL), direct application, especially in high-dimensional space like robotic scenarios still suffers from low sample efficiency. Therefore State Representation Learning (SRL) is proposed to specifically learn to encode task-relevant features from complex sensory data into low-dimensional states. However, the pervasive implementation of SRL is usually conducted by a decoupling strategy in which the observation-state mapping is learned separately, which is prone to over-fit. To handle such problem, we summarize the state-of-the-art (SOTA) SRL sub-tasks in previous works and present a new algorithm called Policy Optimization via Abstract Representation which integrates SRL into the policy optimization phase. Firstly, We engage RL loss to assist in updating SRL model so that the states can evolve to meet the demand of RL and maintain a good physical interpretation. Secondly, we introduce a dynamic loss weighting mechanism so that both models can efficiently adapt to each other. Thirdly, we introduce a new SRL prior called domain resemblance to leverage expert demonstration to improve SRL interpretations. Finally, we provide a real-time access of state graph to monitor the course of learning. Experiments indicate that POAR significantly outperforms SOTA RL algorithms and decoupling SRL strategies in terms of sample efficiency and final rewards. We empirically verify POAR to efficiently handle tasks in high dimensions and facilitate training real-life robots directly from scratch., Comment: 19 pages