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Let $Q(G)=D(G)+A(G)$ be the signless Laplacian matrix of a simple graph $G$, where $D(G)$ and $A(G)$ are the degree diagonal matrix and the adjacency matrix of $G$, respectively. The largest eigenvalue of $Q(G)$, denoted by $q(G)$, is called the signless Laplacian spectral radius of $G$. Let $\theta(l_{1},l_{2},l_{3})$ denote the theta graph which consists of two vertices connected by three internally disjoint paths with length $l_{1}$, $l_{2}$ and $l_{3}$. Let $F_{n}$ be the friendship graph consisting of $\frac{n-1}{2}$ triangles which intersect in exactly one common vertex for odd $n\geq3$ and obtained by hanging an edge to the center of $F_{n-1}$ for even $n\geq4$. Let $S_{n,k}$ denote the graph obtained by joining each vertex of $K_{k}$ to $n-k$ isolated vertices. Let $S_{n,k}^{+}$ denote the graph obtained by adding an edge to the two isolated vertices of $S_{n,k}$. In this paper, firstly, we show that if $G$ is $\theta(1,2,2)$-free, then $q(G)\leq q(F_{n})$, unless $G\cong F_{n}$. Secondly, we show that if $G$ is $\theta(1,2,3)$-free, then $q(G)\leq q(S_{n,2})$, unless $G\cong S_{n,2}$. Finally, we show that if $G$ is $\{\theta(1,2,2),F_{5}\}$-free, then $q(G)\leq q(S_{n,1}^{+})$, unless $G\cong S_{n,1}^{+}$., Comment: 12pages, 3 figures

A graph $G$ is $F$-free if $G$ does not contain $F$ as a subgraph. Let $\mathcal{G}(m, F)$ denote the family of $F$-free graphs with $m$ edges and without isolated vertices. Let $S_{n,k}$ denote the graph obtained by joining every vertex of $K_{k}$ to $n-k$ isolated vertices and $S_{n,k}^{t}$ denote the graph obtained from $S_{n-t,k}$ by attaching $t$ pendant vertices to the maximal degree vertex of $S_{n-t,k}$, respectively. Denote by $H_{n}$ the fan graph obtain from $n-1$-vertex path plus a vertex adjacent to each vertex of the path. Particularly, the graph $H_{5}$ is also known as the gem. Zhang and Wang [Discrete Math. 347(2024)114171] and Yu, Li and Peng [arXiv: 2404. 03423] showed that every gem-free graph $G$ with $m$ edges satisfies $\rho(G)\leq \rho(S_{\frac{m+3}{2},2})$. In this paper, we show that if $G\in \mathcal{G}(m, H_{5})\setminus S_{\frac{m+3}{2},2}$ be a graph of odd size $m\geq23$, then $\rho(G)\leq \rho(S_{\frac{m+5}{2},2}^{2})$, and equality holds if and only if $G\cong S_{\frac{m+5}{2},2}^{2}$., Comment: 10pages. arXiv admin note: text overlap with arXiv:2411.05304

The $Q$-index of graph $G$ is the largest eigenvalue of the signless Laplacian matrix of $G$. Wang [Discrete Appl. Math. 356(2024)] proved the sharp upper bounds on the $Q$-index of leaf-free graphs with given size and characterized the corresponding extremal graphs. A graph is $2$ leaves-free if it has no two pendent vertices. In this paper, we give sharp upper bounds on the $Q$-index of 2 leaves-free graphs with given size and characterize the corresponding extremal graphs., Comment: 21 pages, 5 figures

A graph $G$ is $F$-free if $G$ does not contain $F$ as a subgraph. Let $\rho(G)$ be the spectral radius of a graph $G$. Let $\theta(1,p,q)$ denote the theta graph, which is obtained by connecting two distinct vertices with three internally disjoint paths with lengths $1, p, q$, where $p\leq q$. Let $S_{n,k}$ denote the graph obtained by joining every vertex of $K_{k}$ to $n-k$ isolated vertices and $S_{n,k}^{-}$ denote the graph obtained from $S_{n,k}$ by deleting an edge incident to a vertex of degree $k$, respectively. In this paper, we show that if $\rho(G)\geq\rho(S_{\frac{m+4}{2},2}^{-})$ for a graph $G$ with even size $m\geq 92$, then $G$ contains a $\theta(1,3,3)$ unless $G\cong S_{\frac{m+4}{2},2}^{-}$., Comment: 14pages, 1 figures. arXiv admin note: text overlap with arXiv:2410.07721 by other authors

In this paper, we study the multi-rigidity problem in rational homogeneous spaces. A Schubert class is called multi-rigid if every multiple of it can only be represented by a union of Schubert varieties. We prove the multi-rigidity of Schubert classes in rational homogeneous spaces. In particular, we characterize the multi-rigid Schubert classes in partial flag varieties of type A, B and D. Moreover, for a general rational homogeneous space $G/P$, we deduce the rigidity and multi-rigidity from the corresponding generalized Grassmannians (correspond to maximal parabolics). When $G$ is semi-simple, we also deduce the rigidity and multi-rigidity from the simple cases., Comment: 39 pages

The stochastic gravitational wave background (SGWB) consists of an incoherent collection of waves from both astrophysical and cosmological sources. To distinguish the SGWB from noise, it is essential to verify its quadrupolar nature, exemplified by the cross-correlations among pairs of pulsars within a pulsar timing array, commonly referred to as the Hellings-Downs curve. We extend the concept of quadrupolar correlations to pairs of general gravitational wave detectors, classified by their antenna responses. This study involves space-based missions such as the laser interferometers LISA, Taiji, and TianQin, along with atom interferometers like AEDGE/MAGIS. We calculate modulations in their correlations due to orbital motions and relative orientations, which are characteristic markers for identifying the quadrupolar nature of the SGWB. Our findings identify optimal configurations for these missions, offer forecasts for the time needed to identify the quadrupolar nature of the SGWB, and are applicable to both space-space and space-terrestrial correlations., Comment: 19 pages, 6 figures

In response to the demand for real-time performance and control quality in industrial Internet of Things (IoT) environments, this paper proposes an optimization control system based on deep reinforcement learning and edge computing. The system leverages cloud-edge collaboration, deploys lightweight policy networks at the edge, predicts system states, and outputs controls at a high frequency, enabling monitoring and optimization of industrial objectives. Additionally, a dynamic resource allocation mechanism is designed to ensure rational scheduling of edge computing resources, achieving global optimization. Results demonstrate that this approach reduces cloud-edge communication latency, accelerates response to abnormal situations, reduces system failure rates, extends average equipment operating time, and saves costs for manual maintenance and replacement. This ensures real-time and stable control.

Dark photons, as a minimal extension of the Standard Model through an additional Abelian gauge group, may propagate relativistically across the galaxy, originating from dark matter decay or annihilation, thereby contributing to a galactic dark photon background. The generation of dark photons typically favors certain polarization modes, which are dependent on the interactions between dark matter and dark photons. We introduce a framework in which a resonant cavity is utilized to detect and differentiate these polarizations, leveraging the daily variation in expected signals due to the anisotropic distribution of dark photons and the rotation of the Earth. We conduct an experimental search using superconducting radio-frequency cavities, noted for their exceptionally high quality factors, proving them to be effective telescopes for observing galactic dark photons. This approach establishes the most stringent limits yet on the kinetic mixing coefficient between dark photons and electromagnetic photons, thereby unveiling a novel avenue for the indirect search for dark matter via multi-messenger astronomy., Comment: 16 pages, 3 figures, accepted version in Science Bulletin

A Schubert class is called rigid if it can only be represented by Schubert varieties. The rigid Schubert classes have been classified in Grassmannians and orthogonal Grassmannians. In this paper, we study the rigidity problem in partial flag varieties (type A) and orthogonal partial flag varieties (type B and type D). In particular, we give numerical conditions that ensure a Schubert class is rigid., Comment: 36 pages

This study explores the dynamic relationship between online discourse, as observed in tweets, and physical hate crimes, focusing on marginalized groups. Leveraging natural language processing techniques, including keyword extraction and topic modeling, we analyze the evolution of online discourse after events affecting these groups. Examining sentiment and polarizing tweets, we establish correlations with hate crimes in Black and LGBTQ+ communities. Using a knowledge graph, we connect tweets, users, topics, and hate crimes, enabling network analyses. Our findings reveal divergent patterns in the evolution of user communities for Black and LGBTQ+ groups, with notable differences in sentiment among influential users. This analysis sheds light on distinctive online discourse patterns and emphasizes the need to monitor hate speech to prevent hate crimes, especially following significant events impacting marginalized communities.

We introduce a new task called *entity-centric question generation* (ECQG), motivated by real-world applications such as topic-specific learning, assisted reading, and fact-checking. The task aims to generate questions from an entity perspective. To solve ECQG, we propose a coherent PLM-based framework GenCONE with two novel modules: content focusing and question verification. The content focusing module first identifies a focus as "what to ask" to form draft questions, and the question verification module refines the questions afterwards by verifying the answerability. We also construct a large-scale open-domain dataset from SQuAD to support this task. Our extensive experiments demonstrate that GenCONE significantly and consistently outperforms various baselines, and two modules are effective and complementary in generating high-quality questions., Comment: Accepted to the Findings of EMNLP 2023. Camera-ready version

Real-time measurement of relative humidity (RH) is important to many physical, chemical, and biological processes. However, in processes that involve harsh conditions such as high temperatures, strong electromagnetic interferences, and complex spatial constraints, conventional electrical sensors often fall short due to their intrinsic limitations. Here, we developed an optical lossy-mode-resonance (LMR) RH sensor based on the SnO2 film coated D-shaped fiber tip. Thanks to the high-temperature endurance and electromagnetic interference immunity, the developed optical fiber-tip sensor is ideal for RH sensing in critical environments, such as in the microwave drying process. Furthermore, unlike other reported in-line LMR sensors, our sensor is located at the D-shaped fiber tip with a probe-like form factor, allowing it to be readily implemented in a spatially confined environment. We have developed a custom fabrication setup for the novel D-shaped LMR fiber-tip sensor. The LMR signal from the sensor was experimentally characterized. The lossy mode resonances are understood by the finite element analysis, the results of which agree well with the experimental measurements. The fiber-tip sensor had a linear RH response between 6.1% to 75.0% and a resolution better than 4.0% RH. The fiber-tip sensor demonstrated a response time and reversibility comparable to that of commercial electrical sensors. The novel D-shaped fiber-tip LMR RH sensor developed in this work will benefit many applications that require RH monitoring in a harsh environment. Furthermore, our innovative D-shaped fiber tip design can be readily applied to LMR-based fiber sensors in general. This will allow the design's advantages of small footprint and agile maneuverability to benefit a wide range of LMR fiber sensing applications beyond RH sensing., Comment: 9 pages, 5 figures

Despite the significant progress in 6-DoF visual localization, researchers are mostly driven by ground-level benchmarks. Compared with aerial oblique photography, ground-level map collection lacks scalability and complete coverage. In this work, we propose to go beyond the traditional ground-level setting and exploit the cross-view localization from aerial to ground. We solve this problem by formulating camera pose estimation as an iterative render-and-compare pipeline and enhancing the robustness through augmenting seeds from noisy initial priors. As no public dataset exists for the studied problem, we collect a new dataset that provides a variety of cross-view images from smartphones and drones and develop a semi-automatic system to acquire ground-truth poses for query images. We benchmark our method as well as several state-of-the-art baselines and demonstrate that our method outperforms other approaches by a large margin.

Self-supervised learning enables networks to learn discriminative features from massive data itself. Most state-of-the-art methods maximize the similarity between two augmentations of one image based on contrastive learning. By utilizing the consistency of two augmentations, the burden of manual annotations can be freed. Contrastive learning exploits instance-level information to learn robust features. However, the learned information is probably confined to different views of the same instance. In this paper, we attempt to leverage the similarity between two distinct images to boost representation in self-supervised learning. In contrast to instance-level information, the similarity between two distinct images may provide more useful information. Besides, we analyze the relation between similarity loss and feature-level cross-entropy loss. These two losses are essential for most deep learning methods. However, the relation between these two losses is not clear. Similarity loss helps obtain instance-level representation, while feature-level cross-entropy loss helps mine the similarity between two distinct images. We provide theoretical analyses and experiments to show that a suitable combination of these two losses can get state-of-the-art results. Code is available at https://github.com/guijiejie/ICCL., Comment: This paper is accepted by IEEE Transactions on Image Processing

With the rapid development of smart manufacturing, edge computing-oriented microservice platforms are emerging as an important part of production control. In the containerized deployment of microservices, layer sharing can reduce the huge bandwidth consumption caused by image pulling, and chain sharing can reduce communication overhead caused by communication between microservices. The two sharing methods use the characteristics of each microservice to share resources during deployment. However, due to the limited resources of edge servers, it is difficult to meet the optimization goals of the two methods at the same time. Therefore, it is of critical importance to realize the improvement of service response efficiency by balancing the two sharing methods. This paper studies the optimal microservice deployment strategy that can balance layer sharing and chain sharing of microservices. We build a problem that minimizes microservice image pull delay and communication overhead and transform the problem into a linearly constrained integer quadratic programming problem through model reconstruction. A deployment strategy is obtained through the successive convex approximation (SCA) method. Experimental results show that the proposed deployment strategy can balance the two resource sharing methods. When the two sharing methods are equally considered, the average image pull delay can be reduced to 65% of the baseline, and the average communication overhead can be reduced to 30% of the baseline.

Dose verification based on proton-induced positron emitters is a promising quality assurance tool and may leverage the strength of artificial intelligence. To move a step closer towards practical application, the sensitivity analysis of two factors needs to be performed: biological washout and depth selection. selection. A bi-directional recurrent neural network (RNN) model was developed. The training dataset was generated based upon a CT image-based phantom (abdomen region) and multiple beam energies/pathways, using Monte-Carlo simulation (1 mm spatial resolution, no biological washout). For the modeling of biological washout, a simplified analytical model was applied to change raw activity profiles over a period of 5 minutes, incorporating both physical decay and biological washout. For the study of depth selection (a challenge linked to multi field/angle irradiation), truncations were applied at different window lengths (100, 125, 150 mm) to raw activity profiles. Finally, the performance of a worst-case scenario was examined by combining both factors (depth selection: 125 mm, biological washout: 5 mins). The accuracy was quantitatively evaluated in terms of range uncertainty, mean absolute error (MAE) and mean relative errors (MRE). Our proposed AI framework shows good immunity to the perturbation associated with two factors. The detection of proton-induced positron emitters, combined with machine learning, has great potential to implement online patient-specific verification in proton therapy.

Let $\rho(G)$ be the spectral radius of a graph $G$ with $m$ edges. Let $S_{m-k+1}^{k}$ be the graph obtained from $K_{1,m-k}$ by adding $k$ disjoint edges within its independent set. Nosal's theorem states that if $\rho(G)>\sqrt{m}$, then $G$ contains a triangle. Zhai and Shu showed that any non-bipartite graph $G$ with $m\geq26$ and $\rho(G)\geq\rho(S_{m}^{1})>\sqrt{m-1}$ contains a quadrilateral unless $G\cong S_{m}^{1}$ [M.Q. Zhai, J.L. Shu, Discrete Math. 345 (2022) 112630]. Wang proved that if $\rho(G)\geq\sqrt{m-1}$ for a graph $G$ with size $m\geq27$, then $G$ contains a quadrilateral unless $G$ is one of four exceptional graphs [Z.W. Wang, Discrete Math. 345 (2022) 112973]. In this paper, we show that any non-bipartite graph $G$ with size $m\geq51$ and $\rho(G)\geq\rho(S_{m-1}^{2})>\sqrt{m-2}$ contains a quadrilateral unless $G$ is one of three exceptional graphs. Moreover, we show that if $\rho(G)\geq\rho(S_{\frac{m+4}{2},2}^{-})$ for a graph $G$ with even size $m\geq74$, then $G$ contains a $C_{5}^{+}$ unless $G\cong S_{\frac{m+4}{2},2}^{-}$, where $C_{t}^{+}$ denotes the graph obtained from $C_{t}$ and $C_{3}$ by identifying an edge, $S_{n,k}$ denotes the graph obtained by joining each vertex of $K_{k}$ to $n-k$ isolated vertices and $S_{n,k}^{-}$ denotes the graph obtained by deleting an edge incident to a vertex of degree two, respectively., Comment: 16 pages, 4 figures

We classify rigid Schubert classes in orthogonal Grassmannians. More generally, given a representative $X$ of a Schubert class in an orthogonal Grassmannian, we give combinatorial conditions which guarantee that every linear space parametrized by $X$ meets a fixed linear space in the required dimension., Comment: 24 pages

Atomic stabilization is a universal phenomenon that occurs when atoms interact with intense and high-frequency laser fields. In this work, we systematically study the influence of the ponderomotive (PM) force, present around the laser focus, on atomic stabilization. We show that the PM force could induce tunneling and even over-barrier ionization to the otherwise stabilized atoms. Such effect may overweight the typical multiphoton ionization under moderate laser intensities. Our work highlights the importance of an improved treatment of atomic stabilization that includes the influence of the PM force.

We present a mm-scale optical fiber strain sensor to continuously measure the food deformation below the surface during the drying process. The sensor has a soft buffer sleeve, which enables a large measurable deformation range and minimizes the influence on the native food deformation. The sensor performance was investigated both theoretically and experimentally. To demonstrate the application in foods, we embedded the sensor inside fresh banana slices during a 4-hour-long air-drying process, where its wet basis moisture contents dropped from around 80% to 40%. The fiber sensor measurements covered the full normal strain of ~20% of the banana slices and revealed the shell-hardening characteristics in both the spatial and time dependences, by the comparison with the surface strains measured by the computer vision. Our work provides an unprecedented strain sensor that holds a high potential to contribute to improving both fundamental understandings and process monitoring of food drying processes.