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This book aims to provide a brief overview of recent advancements in the theory of inverse problems for stochastic partial differential equations. In order to keep the content concise, we will only discuss the inverse problems of two typical classes of stochastic partial differential equations: second-order stochastic parabolic equations and secondorder stochastic hyperbolic equations. The main tool for studying these inverse problem is Carleman estimate. We do not intend to pursue any general treatment of the Carleman estimates themselves and choose direct arguments based on basic stochastic calculus, rather than more general sophisticated methods. As this field is still developing and there are many challenging issues to be addressed, the purpose of this book is not to serve as a comprehensive summary, but rather to spark interest and encourage further exploration in this area among readers. We prefer to present results that, from our perspective, include fresh and promising ideas. In cases where a complete mathematical theory is lacking, we only provide the available results. We do not intend for the current book to be encyclopedic in any sense, and the references are limited.

This article studies the problem of distributed formation control for multiple robots by using onboard ultra wide band (UWB) ranging and inertial odometer (IO) measurements. Although this problem has been widely studied, a fundamental limitation of most works is that they require each robot's pose and sensor measurements are expressed in a common reference frame. However, it is inapplicable for nonholonomic robot formations due to the practical difficulty of aligning IO measurements of individual robot in a common frame. To address this problem, firstly, a concurrent-learning based estimator is firstly proposed to achieve relative localization between neighboring robots in a local frame. Different from most relative localization methods in a global frame, both relative position and orientation in a local frame are estimated with only UWB ranging and IO measurements. Secondly, to deal with information loss caused by directed communication topology, a cooperative localization algorithm is introduced to estimate the relative pose to the leader robot. Thirdly, based on the theoretical results on relative pose estimation, a distributed formation tracking controller is proposed for nonholonomic robots. Both gazebo physical simulation and real-world experiments conducted on networked TurtleBot3 nonholonomic robots are provided to demonstrate the effectiveness of the proposed method., Comment: 11 pages, 12 figures

The $\lambda$-differential operators and modified $\lambda$-differential operators are generalizations of classical differential operators. This paper introduces the notions of $\lambda$-differential Poisson ($\lambda$-DP for short) algebras and modified $\lambda$-differential Poisson ($\lambda$-mDP for short) algebras as generalizations of differential Poisson algebras. The $\lambda$-DP algebra is proved to be closed under tensor product, and a $\lambda$-DP algebra structure is provided on the cohomology algebra of the $\lambda$-DP algebra. These conclusions are also applied to $\lambda$-mDP algebras and their modules. Finally, the universal enveloping algebras of $\lambda$-DP algebras are generalized by constructing a $\mathcal{P}$-triple. Three isomorphisms among opposite algebras, tensor algebras and the universal enveloping algebras of $\lambda$-DP algebras are obtained.

In this work, we examine the classical and quantum Seiberg-Witten curves of 5d N = 1 SCFTs and their 4d limits. The 5d theories we consider are Seiberg's theories of type $E_{6,7,8}$, which serve as the UV completions of 5d SU(2) gauge theories with 5, 6, or 7 flavors. Their classical curves can be constructed using the five-brane web construction [1]. We also use it to re-derive their quantum curves [2], by employing a q-analogue of the Frobenius method in the style of [3]. This allows us to compare the reduction of these 5d curves with the 4d curves, i.e. Seiberg-Witten curves of the Minahan-Nemeschansky theories and their quantization, which have been identified in [4] with the spectral curves of rank-1 complex crystallographic elliptic Calogero-Moser systems., Comment: 22 pages

Long-duration gamma-ray bursts (GRBs) are thought to be from core collapse of massive stars, and a rapidly spinning magnetar or black hole may be formed as the central engine. The extended emission in the prompt emission, flares and plateaus in X-ray afterglow, are proposed to be as the signature of central engine re-activity. However, the directly evidence from observations of identifying the central engines remain an open question. In this paper, we systemically search for long-duration GRBs that consist of bumps in X-ray afterglow detected by Swift/XRT, and find that the peak time of the X-ray bumps exhibit bimodal distribution (defined as early and late bumps) with division line at $t=7190$ s. Although we cannot rule out that such a bimodality arises from selection effects. We proposed that the long-duration GRBs with an early (or late) bumps may be originated from the fall-back accretion onto a new-born magnetar (or black hole). By adopting MCMC method to fit the early (or late) bumps of X-ray afterglow with the fall-back accretion of magnetar (or black hole), it is found that the initial surface magnetic filed and period of magnetars for most early bumps are clustered around $5.88\times10^{13}$ G and $1.04$ ms, respectively. Meanwhile, the derived accretion mass of black hole for late bumps is range of $[4\times10^{-4}, 1.8\times10^{-2}]~M_{\odot}$, and the typical fall-back radius is distributed range of $[1.04, 4.23]\times 10^{11}$ cm which is consistent with the typical radius of a Wolf-Rayet star. However, we also find that the fall-back accretion magnetar model is disfavored by the late bumps, but the fall-back accretion of black hole model can not be ruled out to interpret the early bumps of X-ray afterglow., Comment: 14 pages, 5 figures, accepted for publication in MNRAS

Geometric estimation is required for scene understanding and analysis in panoramic 360{\deg} images. Current methods usually predict a single feature, such as depth or surface normal. These methods can lack robustness, especially when dealing with intricate textures or complex object surfaces. We introduce a novel multi-task learning (MTL) network that simultaneously estimates depth and surface normals from 360{\deg} images. Our first innovation is our MTL architecture, which enhances predictions for both tasks by integrating geometric information from depth and surface normal estimation, enabling a deeper understanding of 3D scene structure. Another innovation is our fusion module, which bridges the two tasks, allowing the network to learn shared representations that improve accuracy and robustness. Experimental results demonstrate that our MTL architecture significantly outperforms state-of-the-art methods in both depth and surface normal estimation, showing superior performance in complex and diverse scenes. Our model's effectiveness and generalizability, particularly in handling intricate surface textures, establish it as a new benchmark in 360{\deg} image geometric estimation. The code and model are available at \url{https://github.com/huangkun101230/360MTLGeometricEstimation}., Comment: 18 pages, this paper is accepted by Computational Visual Media Journal (CVMJ) but not pushlished yet

Carbon dots (CDs) shows great application potential with their unique and excellent performances. Coal and its derivatives are rich in aromatic ring structure, which is suitable for preparing CDs in microstructure. Coal burning dust from coal-fired power plants can be utilized as a rich resource to separate and extract CDs. It has been shown in our results that there have two main possible mechanisms for the formation of CDs in coal burning dust. One is the self-assembly of polycyclic aromatic hydrocarbons contained in coal or produced by incomplete combustion of coal. The other mechanism is that the bridge bonds linking different aromatic structures in coal are breaking which would form CDs with different functional groups when the coals are burning at high temperature. Under violet light excitation at 310-340 nm or red light at 610-640 nm, CDs extracted from coal burning dust can emit purple fluorescence around 410 nm. The mechanism of up-conversion fluorescence emission of CDs is due to a two-photon absorption process. The recycling of CDs from coal burning dust from coal-fired power plants are not only good to protect environment but also would be helpful for mass production of CDs.

Different from most of the formation strategies where robots require unique labels to identify topological neighbors to satisfy the predefined shape constraints, we here study the problem of identity-less distributed shape formation in homogeneous swarms, which is rarely studied in the literature. The absence of identities creates a unique challenge: how to design appropriate target formations and local behaviors that are suitable for identity-less formation shape control. To address this challenge, we propose the following novel results. First, to avoid using unique identities, we propose a dynamic formation description method and solve the formation consensus of robots in a locally distributed manner. Second, to handle identity-less distributed formations, we propose a fully distributed control law for homogeneous swarms based on locally sensed information. While the existing methods are applicable to simple cases where the target formation is stationary, ours can tackle more general maneuvering formations such as translation, rotation, or even shape deformation. Both numerical simulation and flight experiment are presented to verify the effectiveness and robustness of our proposed formation strategy.

In this paper, we propose OpenSatMap, a fine-grained, high-resolution satellite dataset for large-scale map construction. Map construction is one of the foundations of the transportation industry, such as navigation and autonomous driving. Extracting road structures from satellite images is an efficient way to construct large-scale maps. However, existing satellite datasets provide only coarse semantic-level labels with a relatively low resolution (up to level 19), impeding the advancement of this field. In contrast, the proposed OpenSatMap (1) has fine-grained instance-level annotations; (2) consists of high-resolution images (level 20); (3) is currently the largest one of its kind; (4) collects data with high diversity. Moreover, OpenSatMap covers and aligns with the popular nuScenes dataset and Argoverse 2 dataset to potentially advance autonomous driving technologies. By publishing and maintaining the dataset, we provide a high-quality benchmark for satellite-based map construction and downstream tasks like autonomous driving., Comment: NeurIPS 2024 D&B Track. Project Page:https://opensatmap.github.io/

Building a comprehensive catalog of galaxy clusters is a fundamental task for the studies on the structure formation and galaxy evolution. In this paper, we present COSMIC (Cluster Optical Search using Machine Intelligence in Catalogs), an algorithm utilizing machine learning techniques to efficiently detect galaxy clusters. COSMIC involves two steps, including the identification of the brightest cluster galaxies and the estimation of the cluster richness. We train our models on the galaxy data from the Sloan Digital Sky Survey and WHL galaxy cluster catalog. Validated to a test data in the region of northern Galactic cap, COSMIC algorithm demonstrates a high completeness when cross-matching with previous cluster catalogs. Richness comparison with previous optical and X-ray measurements also demonstrated a tight correlation. Our methodology showcases robust performance in galaxy cluster detection and holds promising prospects for applications in upcoming large-scale surveys., Comment: 22 pages, 18 figures. Accepted for publication in APJS

Here we investigate the internal sublattice symmetry, and thus the enriched topological classification of bosonic Bogoliubov excitations of thermodynamically stable free-boson systems with non-vanishing particle-number-nonconserving terms. Specifically, we show that such systems well described by the bosonic Bogoliubov-de Gennes Hamiltonian can be in general reduced to particle-number-conserving (single-particle) ones. Building upon this observation, the sublattice symmetry is uncovered with respect to an excitation energy, which is usually hidden in the bosonic Bogoliubov-de Gennes Hamiltonian. Thus, we obtain an additional topological class, i.e., class AIII, which enriches the framework for the topological threefold way of free-boson systems. Moreover, a construction is proposed to show a category of systems respecting such a symmetry. For illustration, we resort to a one-dimensional (1D) prototypical model to demonstrate the topological excitation characterized by a winding number or symplectic polarization. By introducing the correlation function, we present an approach to measure the topological invariant. In addition, the edge excitation together with its robustness to symmetry-preserving disorders is also discussed., Comment: 18 pages, 4 figures

We develop an approach for calculating heavy quark effective theory (HQET) light-cone distribution amplitudes (LCDAs) by employing a sequential effective theory methodology. The theoretical foundation of the framework is established, elucidating how the quasi distribution amplitudes (quasi DAs) with three scales can be utilized to compute HQET LCDAs. We provide theoretical support for this approach by demonstrating the rationale behind devising a hierarchical ordering for the three involved scales, discussing the factorization at each step, clarifying the underlying reason for obtaining HQET LCDAs in the final phase, and addressing potential theoretical challenges. The lattice QCD simulation aspect is explored in detail, and the computations of quasi DAs are presented. We employ three fitting strategies to handle contributions from excited states and extract the bare matrix elements. For renormalization purposes, we apply hybrid renormalization schemes at short and long distance separations. To mitigate long-distance perturbations, we perform an extrapolation in $\lambda= z\cdot P^z$ and assess the stability against various parameters. After two-step matching, our results for HQET LCDAs are found in agreement with existing model parametrizations. The potential phenomenological implications of the results are discussed, shedding light on how these findings could impact our understanding of the strong interaction dynamics and physics beyond the standard model. It should be noted, however, that systematic uncertainties have not been accounted for yet., Comment: 27 pages, 23 figures

Existing reconstruction-based novel view synthesis methods for driving scenes focus on synthesizing camera views along the recorded trajectory of the ego vehicle. Their image rendering performance will severely degrade on viewpoints falling out of the recorded trajectory, where camera rays are untrained. We propose FreeVS, a novel fully generative approach that can synthesize camera views on free new trajectories in real driving scenes. To control the generation results to be 3D consistent with the real scenes and accurate in viewpoint pose, we propose the pseudo-image representation of view priors to control the generation process. Viewpoint transformation simulation is applied on pseudo-images to simulate camera movement in each direction. Once trained, FreeVS can be applied to any validation sequences without reconstruction process and synthesis views on novel trajectories. Moreover, we propose two new challenging benchmarks tailored to driving scenes, which are novel camera synthesis and novel trajectory synthesis, emphasizing the freedom of viewpoints. Given that no ground truth images are available on novel trajectories, we also propose to evaluate the consistency of images synthesized on novel trajectories with 3D perception models. Experiments on the Waymo Open Dataset show that FreeVS has a strong image synthesis performance on both the recorded trajectories and novel trajectories. Project Page: https://freevs24.github.io/, Comment: Project Page: https://freevs24.github.io/

In this paper, we investigate an inverse Cauchy problem for a stochastic hyperbolic equation. A Lipschitz type observability estimate is established using a pointwise Carleman identity. By minimizing the constructed Tikhonov-type functional, we obtain a regularized approximation to the problem. The properties of the approximation are studied by means of the Carleman estimate and Riesz representation theorem. Leveraging kernel-based learning theory, we simulate numerical algorithms based on the proposed regularization method. These reconstruction algorithms are implemented and validated through several numerical experiments, demonstrating their feasibility and accuracy.

The Willmore Problem seeks the surface in $\mathbb{S}^3\subset\mathbb{R}^4$ of a given topological type minimizing the squared-mean-curvature energy $W = \int |H_{\mathbb{R}^4}|^2 = area + \int |H_{\mathbb{S}^3}|^2$. The longstanding Willmore Conjecture that the Clifford torus minimizes $W$ among genus-$1$ surfaces is now a theorem of Marques and Neves [22], but the general conjecture \cite[12] that Lawson's [18] minimal surface $\xi_{g,1}\subset\mathbb{S}^3$ minimizes $W$ among surfaces of genus $g>1$ remains open. Here we prove this conjecture under the additional assumption that the competitor surfaces $M\subset\mathbb{S}^3$ share the ambient symmetries $\widehat{G}_{g,1}$ of $\xi_{g,1}$. In fact, we show each Lawson surface $\xi_{m,k}$ satisfies the analogous $W$-minimizing property under a smaller symmetry group $\widetilde{G}_{m,k}=\widehat{G}_{m,k}\cap SO(4)$. We also describe a genus 2 example where known methods do not ensure the existence of a $W$-minimizer among surfaces with its symmetry., Comment: 16 pages, 8 figures. This supersedes our previous paper arXiv:2103.09432

Based on astrometric measurements and spectral analysis from $Gaia$ DR3, two quiescent black hole (BH) binaries, $Gaia$ BH1 and BH2, have been identified. Their origins remain controversial, particularly for $Gaia$ BH1. By considering a rapidly rotating ($\omega/\omega_{\rm crit} = 0.8$) and strongly magnetized ($B_{\rm 0} = 5000$ G) merger product, we find that, at typical Galactic metallicity, the merger product can undergo efficient chemically homogeneous evolution (CHE). This results in the merger product having a significantly smaller radius during its evolution compared to that of a normally evolving massive star. Under the condition that the initial triple stability is satisfied, we use the Multiple Stellar Evolution (MSE) code and the MESA code to identify an initial hierarchical triple that can evolve into $Gaia$ BH1. It initially consists of three stars with masses of 9.03 $M_{\odot}$, 3.12 $M_{\odot}$, and 1 $M_{\odot}$, with inner and outer orbital periods of 2.21 days and 121.92 days, and inner and outer eccentricities of 0.41 and 0.45, respectively. This triple initially experiences triple evolution dynamics instability (TEDI) followed by Roche lobe overflow (RLOF). During RLOF, the inner orbit shrinks, and tidal effects gradually suppress the TEDI. Eventually, the inner binary undergoes a merger through contact (or collision). Finally, using models of rapidly rotating and strongly magnetic stars, along with standard core-collapse supernova (SN) or failed supernova (FSN) models, we find that a PMB consisting of an 12.11 $M_{\odot}$ merger product and a 1 $M_{\odot}$ companion star (originally an outer tertiary) can avoid RLOF. After a SN or FSN with a low ejected mass of $\sim$0.22 $M_{\odot}$ and a low kick velocity ($46^{+25}_{-33}$ ${\rm km/s}$ or $9^{+16}_{-8}$ ${\rm km/s}$), the PMB can form $Gaia$ BH1 in the Galactic disk., Comment: 11 pages, 3 figures, Accepted to APJL

In June 2023, multiple pulsar timing array collaborations provided evidence for the existence of a stochastic gravitational wave background. Scalar induced gravitational waves (SIGWs), as one of the most likely sources of stochastic gravitational waves, have received widespread attention. When primordial curvature perturbations on small scales are sufficiently large, \acp{PBH} inevitably form, concurrently producing SIGWs with significant observable effects. These SIGWs can serve as an additional radiation component, influencing the relativistic degrees of freedom $N_{\text{eff}}$. Taking into account primordial non-Gaussianity, we study the energy density spectrum of SIGWs up to the third order and use the current observational data of $N_{\text{eff}}$ to constrain small-scale primordial curvature perturbations and the abundance of \acp{PBH}.

The prompt emission mechanism of gamma-ray bursts (GRBs) is a long-standing open question, and GRBs have been considered as potential sources of high-energy neutrinos. Despite many years of search for the neutrino events associated with GRBs from IceCube, there were no results. However, the absence of search results for neutrino provides a unique opportunity to constrain the parameter space of GRB-jet models. In this paper, we chose four peculiar GRBs with two different types of jet composition to investigate neutrino emission. It is found that only GRB 211211A could be well constrained within the dissipative photosphere model. By adopting the specific parameters of the photosphere, one can obtain \(\varepsilon _{p } \text{/} \varepsilon _{e }<8\) for \(f_{p}>0.2\) from GRB 211211A. For the ICMART model, we can effectively constrain neither GRB 230307A nor GRB 080916C. Moreover, we also investigate the detection prospects of high-energy neutrinos from GRBs, and find that it is difficult to detect at least one high-energy neutrino associated with GRBs from the ICMART model even during the IceCube-Gen2 operation. For the GRB 211211A-like events, it is possible to detect at least one neutrino coincident with the gravitational wave during the IceCube-Gen2 operation, if such an event is originated from mergers of compact stars within the photosphere dissipation., Comment: 15 pages, 10 figures, accepted for publication in ApJ

Short gamma-ray bursts (SGRBs) with extended emission (EE) are composed of initial main emission (ME) with a short-hard spike, followed by a long-lasting EE. Whether the ME and EE originated from the same origin or not, as well as the jet composition, remains an open question. In this paper, we present a systematic analysis of 36 gamma ray bursts (GRBs) in our sample, which are identified as the category of SGRBs with EE as observed by Fermi/Gamma-ray Burst Monitor. By extracting time-integrated spectra of ME and EE with cutoff power-law or Band models for our sample, we find that 20 out of 36 SGRBs have $\alpha$ values that exceed the death line (e.g., -2/3) of synchrotron emission within either ME or EE phases, and we suggest that the quasi-thermal component should exist in the prompt emission. Then, we extract the time-resolved spectra of our samples, but only four GRBs are bright enough to extract the time-resolved spectra. We find that both thermal and nonthermal emissions do exist in the prompt emission of those four bright GRBs, which suggests that a hybrid jet (e.g., matter and Poynting-flux outflow) in GRBs should exist. Moreover, strong positive correlations (e.g., $F_{\rm tot}-\Gamma$ and $F_{\rm tot}-kT$) in the time-resolved spectra of ME and EE for those four GRBs have been discovered. This indicates that the spectral evolution of both ME and EE seem to share similar behavior, possibly from the same physical origin., Comment: 30 pages, 9 figures and 11 tables, matched with the published verison

Let $(S,\mathcal{F})$ be a foliated surface over the complex number of general type, i.e., the Kodaira dimension $\mathrm{Kod}(\mathcal{F})=2$. We study the geometry of the canonical map $\varphi$ of the foliated surface $(S,\mathcal{F})$, and prove several boundedness results on the canonical map $\varphi$, generalizing Beauville's beautiful work on the canonical maps of algebraic surfaces to foliated surfaces. As an application, we prove three Noether type inequalities for $(S,\mathcal{F})$ depending on the Kodaira dimension of the surface $S$., Comment: Comments are welcome. arXiv admin note: text overlap with arXiv:2404.16293

In this paper, we address the shape formation problem for massive robot swarms in environments where external localization systems are unavailable. Achieving this task effectively with solely onboard measurements is still scarcely explored and faces some practical challenges. To solve this challenging problem, we propose the following novel results. Firstly, to estimate the relative positions among neighboring robots, a concurrent-learning based estimator is proposed. It relaxes the persistent excitation condition required in the classical ones such as least-square estimator. Secondly, we introduce a finite-time agreement protocol to determine the shape location. This is achieved by estimating the relative position between each robot and a randomly assigned seed robot. The initial position of the seed one marks the shape location. Thirdly, based on the theoretical results of the relative localization, a novel behavior-based control strategy is devised. This strategy not only enables adaptive shape formation of large group of robots but also enhances the observability of inter-robot relative localization. Numerical simulation results are provided to verify the performance of our proposed strategy compared to the state-of-the-art ones. Additionally, outdoor experiments on real robots further demonstrate the practical effectiveness and robustness of our methods.

Impact dynamics are crucial for estimating the growth patterns of NFT projects by tracking the diffusion and decay of their relative appeal among stakeholders. Machine learning methods for impact dynamics analysis are incomprehensible and rigid in terms of their interpretability and transparency, whilst stakeholders require interactive tools for informed decision-making. Nevertheless, developing such a tool is challenging due to the substantial, heterogeneous NFT transaction data and the requirements for flexible, customized interactions. To this end, we integrate intuitive visualizations to unveil the impact dynamics of NFT projects. We first conduct a formative study and summarize analysis criteria, including substitution mechanisms, impact attributes, and design requirements from stakeholders. Next, we propose the Minimal Substitution Model to simulate substitutive systems of NFT projects that can be feasibly represented as node-link graphs. Particularly, we utilize attribute-aware techniques to embed the project status and stakeholder behaviors in the layout design. Accordingly, we develop a multi-view visual analytics system, namely NFTracer, allowing interactive analysis of impact dynamics in NFT transactions. We demonstrate the informativeness, effectiveness, and usability of NFTracer by performing two case studies with domain experts and one user study with stakeholders. The studies suggest that NFT projects featuring a higher degree of similarity are more likely to substitute each other. The impact of NFT projects within substitutive systems is contingent upon the degree of stakeholders' influx and projects' freshness., Comment: 25 pages, 13 figures, 3 tables, accepted by IEEE Transactions on Visualization and Computer Graphics (2024)

A graph $G$ $=$ $(V,E)$ is vertex-pancyclic if for every vertex $u$ and any integer $l$ ranging from $3$ to $|V|$, $G$ contains a cycle $C$ of length $l$ such that $u$ is on $C$. A bipartite graph $G$ $=$ $(V,E)$ is vertex-bipancyclic if for every vertex $u$ and any even integer $l$ ranging from $4$ to $|V|$, $G$ contains a cycle $C$ of length $l$ such that $u$ is on $C$. The simplified shuffle-cube and the balanced shuffle-cube, which are two variants of the shuffle-cube and are superior to shuffle-cube in terms of vertex-transitivity. In this paper, we show that the $n$-dimensional simplified shuffle-cube is vertex-pancyclic for $n\geqslant 6$, and the $n$-dimensional balanced shuffle-cube is vertex-bipancyclic for $n\geqslant 2$.

Band gap energy of an organic molecule can be reduced by intermolecular interaction enhancement, and thus, certain polycyclic aromatic hydrocarbons (PAHs), which are insulators with wide band gaps, are expected to undergo insulator-metal transitions by simple compression. Such a pressure-induced electronic transition can be exploited to transform non-metallic organic materials into states featuring intriguing electronic characteristics such as high-temperature superconductivity. Numerous attempts have been made to metalize various small PAHs, but so far only pressure-induced amorphization well below the megabar region was observed. The wide band gap energy of the small PAHs and low chemical stability under simple compression are the bottlenecks. We have investigated the band gap energy evolution and the crystal structural compression of the large PAH molecules, where the band gap energy is significantly reduced by increasing the number of {\pi}-electrons and improved chemical stability with fully benzenoid molecular structure. Herein, we present a pressure-induced transition in dicoronylene, C48H20, an insulator at ambient conditions that transforms into a semi-metallic state above 23.0 GPa with a three-order-of-magnitude reduction in resistivity. In-situ UV-visible absorption, transport property measurement, Raman spectroscopy, X-ray diffraction and density functional theory calculations were performed to provide tentative explanations to the alterations in its electronic structure at high pressure. The discovery of an electronic transition at pressures well below the megabar is a promising step towards realization of a single component purely hydrocarbon molecular metal in the near future., Comment: 22 pages, 5 figures

Let $S/R$ be a Frobenius extension with $_RS_R$ centrally projective over $R$. We show that if $_R\omega$ is a Wakamatsu tilting module then so is $_SS\otimes_R\omega$, and the natural ring homomorphism from the endomorphism ring of $_R\omega$ to the endomorphism ring of $_SS\otimes_R\omega$ is a Frobenius extension in addition that pd$(\omega_T)$ is finite, where $T$ is the endomorphism ring of $_R\omega$. We also obtain that the relative $n$-torsionfreeness of modules is preserved under Frobenius extensions. Furthermore, we give an application, which shows that the generalized G-dimension with respect to a Wakamatsu module is invariant under Frobenius extensions., Comment: arXiv admin note: text overlap with arXiv:2301.01903

In this paper, we consider the adaptive linear quadratic Gaussian control problem, where both the linear transformation matrix of the state $A$ and the control gain matrix $B$ are unknown. The proposed adaptive optimal control only assumes that $(A, B)$ is stabilizable and $(A, Q^{1/2})$ is detectable, where $Q$ is the weighting matrix of the state in the quadratic cost function. This condition significantly weakens the classic assumptions used in the literature. To tackle this problem, a weighted least squares algorithm is modified by using random regularization method, which can ensure uniform stabilizability and uniform detectability of the family of estimated models. At the same time, a diminishing excitation is incorporated into the design of the proposed adaptive control to guarantee strong consistency of the desired components of the estimates. Finally, by utilizing this family of estimates, even if not all components of them converge to the true values, it is demonstrated that a certainty equivalence control with such a diminishing excitation is optimal for an ergodic quadratic cost function.

We investigate the first and second order cosmological perturbation equations in f(R) modified gravity theory and provide the equation of motion of second order scalar induced gravitational waves. We find that the effects of modified gravity not only change the form of the equation of motion of second order scalar induced gravitational waves but also contribute an additional anisotropic stress tensor, composed of first order scalar perturbations, to the source term of the gravitational waves. We calculate the energy density spectrum of second order scalar induced gravitational waves in the HS model. Utilizing current pulsar timing array observational data, we perform a rigorous Bayesian analysis of the parameter space of the HS model., Comment: Accepted for publication in JCAP on 2024 November 11

This research aims to investigate the effects of information cocooning on group mood changes caused by information spreading. The simulation of the realistic network evolution process is realized at the structural level by building a network evolution model based on individual viewpoints. Abstracting the accuracy of the real intelligent recommendation process by setting RA (Recommended Accuracy). By analyzing the information cocoon effect due to the recommendation in the comment section, we provide the structural basis of spreading for the dynamics model. A dynamics model of emotion spreading is developed to explore the trend of individual emotion spreading and to quantify the change of group emotion. Through experiments and analysis, this paper concludes that the information cocoon has a positive effect on the stability of group emotions, and that the H-CAC (Hidden Comment Area Cocoon) structure exists widely in real online social networks, and can produce a protective "harbor" effect in the competition of public opinion and cognitive games. The validity of the model is verified by comparison with real cases and generalization ability experiments. This work provides a multi-perspective analysis and visualization, providing more quantitative results. The research is expected to provide new perspectives and tools for understanding the reality of information cocooning and expanding the scenarios of its use.

Gravitational waves induced by primordial perturbations serve as crucial probes for studying the early universe, providing a significant window into potential new physics during cosmic evolution. Due to the potentially large amplitudes of primordial perturbations on small scales, the contributions of high-order cosmological perturbations are highly significant. We propose a vertex approach applicable to the study of induced gravitational waves for arbitrary higher orders. Using the vertex approach and tree diagrams, we can directly derive the explicit expressions of higher-order induced gravitational waves without involving the complex and lengthy calculations of higher-order cosmological perturbations. Correlations between different tree diagrams correspond to the loop diagrams of two-point correlation functions of induced gravitational waves. Our investigation reveals that one-particle reducible diagrams impact tensor-scalar induced gravitational waves while leaving scalar induced gravitational waves unaffected.

In this work, we have investigated the strong decays for low-lying excited states of doubly charmed and bottom baryons in the constituent quark model. Our results indicate that some $\lambda-$mode $\Xi_{cc/bb}(1P)$ and $\Omega_{cc/bb}(1P)$ states are relatively narrow, which are very likely to be discovered by future experiments. The light meson emissions for the low-lying $\rho-$mode states are highly suppressed due to the orthogonality of wave functions between initial and final states. Moreover, the strong decay behaviors for doubly charmed and bottom baryons preserve the heavy superflavor symmetry well, where the small violation originates from the finite heavy quark masses and different phase spaces. We hope that present theoretical results for undiscovered doubly charmed and bottom baryons can provide helpful information for future experiments and help us better understand the heavy quark symmetry., Comment: 9 pages, 2 figures, comments and suggestions are welcome

Predicting high-growth firms has attracted increasing interest from the technological forecasting and machine learning communities. Most existing studies primarily utilize financial data for these predictions. However, research suggests that a firm's research and development activities and its network position within technological ecosystems may also serve as valuable predictors. To unpack the relative importance of diverse features, this paper analyzes financial and patent data from 5,071 firms, extracting three categories of features: financial features, technological features of granted patents, and network-based features derived from firms' connections to their primary technologies. By utilizing ensemble learning algorithms, we demonstrate that incorporating financial features with either technological, network-based features, or both, leads to more accurate high-growth firm predictions compared to using financial features alone. To delve deeper into the matter, we evaluate the predictive power of each individual feature within their respective categories using explainable artificial intelligence methods. Among non-financial features, the maximum economic value of a firm's granted patents and the number of patents related to a firms' primary technologies stand out for their importance. Furthermore, firm size is positively associated with high-growth probability up to a certain threshold size, after which the association plateaus. Conversely, the maximum economic value of a firm's granted patents is positively linked to high-growth probability only after a threshold value is exceeded. These findings elucidate the complex predictive role of various features in forecasting high-growth firms and could inform technological resource allocation as well as investment decisions., Comment: 26 pages, 9 figures

We investigate the steady-state transport characteristics of a quantum dot system consisting of a single energy level embedded between two reservoirs under the influence of both the temperature gradient and bias voltage. Within tailored parameter regimes, the system can exhibit three counterintuitive transport phenomena of anomalous thermodiffusion, absolute negative mobility and reverse heat transport respectively. These counterintuitive phenomena do not violate the second law of thermodynamics. Moreover, absolute negative mobility and reverse heat transport can be identified by a reversible energy level. These anomalous transports are different from thermoelectric transports and provide different perspectives for a more comprehensive understanding of the transport characteristics of quantum systems., Comment: 16 pages, 9 figures

The modeling and manipulation of 3D scenes captured from the real world are pivotal in various applications, attracting growing research interest. While previous works on editing have achieved interesting results through manipulating 3D meshes, they often require accurately reconstructed meshes to perform editing, which limits their application in 3D content generation. To address this gap, we introduce a novel single-image-driven 3D scene editing approach based on 3D Gaussian Splatting, enabling intuitive manipulation via directly editing the content on a 2D image plane. Our method learns to optimize the 3D Gaussians to align with an edited version of the image rendered from a user-specified viewpoint of the original scene. To capture long-range object deformation, we introduce positional loss into the optimization process of 3D Gaussian Splatting and enable gradient propagation through reparameterization. To handle occluded 3D Gaussians when rendering from the specified viewpoint, we build an anchor-based structure and employ a coarse-to-fine optimization strategy capable of handling long-range deformation while maintaining structural stability. Furthermore, we design a novel masking strategy to adaptively identify non-rigid deformation regions for fine-scale modeling. Extensive experiments show the effectiveness of our method in handling geometric details, long-range, and non-rigid deformation, demonstrating superior editing flexibility and quality compared to previous approaches., Comment: 10 pages, 12 figures

Recently, the detection of a coherent radio flash associated with short-duration GRB 201006A, occurring 76.6 minutes after the burst, has attracted great attention. However, the physical origin of the coherent radio flash remains under debate. By reanalyzing its data observed by Fermi and Swift, we find that an early radio afterglow as the physical origin of the radio flash can be ruled out, but the coherent radio emission seems to be consistent with the hypothesis of a supramassive magnetar as the central engine collapsing into a black hole. Within this scenario, the derived magnetar surface magnetic field ($B_{\rm p}$) and the initial spin period ($P_{\rm 0}$) fall into a reasonable range but require a preferable low value of $\eta_{\rm R} = 10^{-7}$ or $10^{-6}$. Moreover, the calculated low-$\varepsilon$ value and $E_{\rm \gamma,iso}-E_{\rm p}$ correlation of GRB 201006A also supports the progenitor which is from the merger of compact stars. We also discuss the non-detected kilonova emission associated with GRB 201006A, and then compare with its upper limits of optical observations., Comment: 14 pages, 7 figures, matched with the published verison

In this paper, a triggered Batch Least-Squares Identifier (BaLSI) based adaptive safety control scheme is proposed for uncertain systems with potentially conflicting control objectives and safety constraints. A relaxation term is added to the Quadratic Programs (QP) combining the transformed Control Lyapunov Functions (CLFs) and Control Barrier Functions (CBFs), to mediate the potential conflict. The existing Lyapunov-based adaptive schemes designed to guarantee specific properties of the Lyapunov functions, may grow unboundedly under the effects of the relaxation term. The adaptive law is designed by processing system inputs and outputs, to avoid unbounded estimates and overparameterization problems in the existing results. A safetytriggered condition is presented, based on which the forward invariant property of the safe set is shown and Zeno behavior can be excluded. Simulation results are presented to demonstrate the effectiveness of the proposed adaptive control scheme., Comment: 11 pages, 10 fidures

In this paper, we are concerned with the three dimensional Euler equations driven by an additive stochastic forcing. First, we construct global H\"{o}lder continuous (stationary) solutions in $C(\mathbb{R};C^{\vartheta})$ space for some $\vartheta>0$ via a different method from \cite{LZ24}. Our approach is based on applying stochastic convex integration to the construction of Euler flows in \cite{DelSze13} to derive uniform moment estimates independent of time. Second, for any divergence-free H\"{o}lder continuous initial condition, we show the existence of infinitely many global-in-time probabilistically strong and analytically weak solutions in $L^p_{\rm{loc}}([0,\infty);C^{\vartheta'}) \cap C_{\rm{loc}}([0,\infty);H^{-1})$ for all $p\in [1,\infty)$ and some $\vartheta'>0$., Comment: 40 pages

We analyze the frequencies of three known roAp stars, TIC 96315731, TIC 72392575, and TIC 318007796, using the light curves from the Transiting Exoplanet Survey Satellite (TESS). For TIC 96315731, the rotational and pulsational frequencies are $0.1498360\,\mathrm{d}^{-1}$ and $165.2609\,\mathrm{d}^{-1}$, respectively. In the case of TIC 72392575, the rotational frequency is $0.25551\,\mathrm{d}^{-1}$. We detect a quintuplet of pulsation frequencies with a center frequency of $135.9233\,\mathrm{d}^{-1}$, along with two signals within the second pair of rotational sidelobes of the quintuplet separated by the rotation frequency. These two signals may correspond to the frequencies of a dipole mode. In TIC 318007796, the rotational and pulsational frequencies are $0.2475021\,\mathrm{d}^{-1}$, $192.73995\,\mathrm{d}^{-1}$, and $196.33065\,\mathrm{d}^{-1}$, respectively. Based on the oblique pulsator model, we calculate the rotation inclination $\left( i \right)$ and magnetic obliquity angle $\left( \beta \right)$ for the stars, which provides the geometry of the pulsation modes. Combining the phases of the frequency quintuplets, the pulsation amplitude and phase modulation curves, and the results of spherical harmonic decomposition, we conclude that the pulsation modes of frequency quintuplets in TIC 96315731, TIC 72392575, and TIC 318007796 correspond to distorted dipole mode, distorted quadrupole mode, and distorted dipole mode, respectively.

Identifying causal relations is crucial for a variety of downstream tasks. In additional to observational data, background knowledge (BK), which could be attained from human expertise or experiments, is usually introduced for uncovering causal relations. This raises an open problem that in the presence of latent variables, what causal relations are identifiable from observational data and BK. In this paper, we propose two novel rules for incorporating BK, which offer a new perspective to the open problem. In addition, we show that these rules are applicable in some typical causality tasks, such as determining the set of possible causal effects with observational data. Our rule-based approach enhances the state-of-the-art method by circumventing a process of enumerating block sets that would otherwise take exponential complexity.

Spontaneous symmetry breaking (SSB) is crucial to the occurrence of phase transitions. Once a phase transition occurs, a quantum system presents degenerate eigenstates that lack the symmetry of the Hamiltonian. After crossing the critical point, the system is essentially evolved to a quantum superposition of these eigenstates until decoherence sets in. Despite the fundamental importance and potential applications in quantum technologies, such quantum-mechanical SSB phenomena have not been experimentally explored in many-body systems. We here present an experimental demonstration of the SSB process in the Lipkin-Meshkov-Glick model, governed by the competition between the individual driving and intra-qubit interaction. The model is realized in a circuit quantum electrodynamics system, where 6 Xmon qubits are coupled in an all-to-all manner through virtual photon exchange mediated by a resonator. The observed nonclassical correlations among these qubits in the symmetry-breaking region go beyond the conventional description of SSB, shedding new light on phase transitions for quantum many-body systems., Comment: 27 pages, 18 figures

We present a time-dependent variational approach with the multiple Davydov $D_2$ trial state to simulate the dynamics of light-matter systems when the field is in a coherent state with an arbitrary finite mean photon number. The variational approach captures not only the system dynamics but also the field dynamics and is applicable to a variety of quantum models of light-matter interaction such as the Jaynes-Cummings model, Rabi model, and Dicke model, and is feasible to tackle the multimode quantized fields. By comparison of the variational and semiclassical dynamics of both the system and field, we illustrate that the variational dynamics from the quantum models agrees with those from the corresponding semiclassical models as long as the mean number of photons is sufficiently large. Moreover, we illustrate that in the crossover between the quantum and semiclassical limits, the quantum corrections lead to the collapse of the oscillations in dynamics, which is absent in the semiclassical models. The variational approach provides a unified treatment of light-matter interaction from the quantum to the semiclassical limit., Comment: 14 pages, 8 figures

Precise positioning and navigation information has been increasingly important with the development of the consumer electronics market. Due to some deficits of Global Navigation Satellite System (GNSS), such as susceptible to interferences, integrating of GNSS with additional alternative sensors is a promising approach to overcome the performance limitations of GNSS-based localization systems. Ultra-Wideband (UWB) can be used to enhance GNSS in constructing an integrated localization system. However, most low-cost UWB devices lack a hardware-level time synchronization feature, which necessitates the estimation and compensation of the time-offset in the tightly coupled GNSS/UWB integration. Given the flexibility of probabilistic graphical models, the time-offset can be modeled as an invariant constant in the discretization of the continuous model. This work proposes a novel architecture in which Factor Graph Optimization (FGO) is hybrid with Extend Kalman Filter (EKF) for tightly coupled GNSS/UWB integration with online Temporal calibration (FE-GUT). FGO is utilized to precisely estimate the time-offset, while EKF provides initailization for the new factors and performs time-offset compensation. Simulation-based experiments validate the integrated localization performance of FE-GUT. In a four-wheeled robot scenario, the results demonstrate that, compared to EKF, FE-GUT can improve horizontal and vertical localization accuracy by 58.59\% and 34.80\%, respectively, while the time-offset estimation accuracy is improved by 76.80\%. All the source codes and datasets can be gotten via https://github.com/zhaoqj23/FE-GUT/.

The dynamic mechanism of short range interaction between $u/d$ quarks is still an open and challenging problem. In order to reveal this quark dynamics, we perform a systematic analysis of $NN$, $D_{03}$, and $D_{30}$ systems in the (extended) chiral SU(3) constituent quark models. By comparing results calculated with different models and different parameter sets, the effects of one gluon exchange and vector meson exchange terms are carefully examined. The results indicate that the vector meson exchange interactions dominate the short range interactions between $u/d$ quarks, while the small residual one gluon exchange coupling strength is also allowed., Comment: 8 pages, 2 figures, comments and suggestions are welcome

The environment-induced dissipation of an open system, once thought as a nuisance, can actually lead to emergence of many intriguing phenomena that are absent in an isolated system. Among these, Weyl exceptional rings (WER), extended from point-like singularities, are particularly interesting. Theoretically, a WER was predicted to carry a topological charge with a nonzero Chern number, but it has not been measured so far. We here investigate this topology in a circuit, where the WER is synthesized with a superconducting qubit controllably coupled to a decaying resonator. The high flexibility of the system enables us to characterize its eigenvectors on different manifolds of parameter space. We extract both the quantized Berry phase and Chern number from these eigenvectors. Furthermore, we demonstrate a topological transition triggered by shrinking the size of the manifold$-$a unique feature of the WER., Comment: 15 pages, 10 figures

We present optical photometry for the afterglow of GRB 221009A, in some respects the most extraordinary gamma-ray burst (GRB) ever observed. Good quality in the R-band light curve is obtained, covering 0.32-19.57 days since the Fermi-GBM trigger. We find that a weak bump emerges fromthe declining afterglow at $t \approx 11$ days; a supernova (SN) may be responsible. We use a smooth broken power-law and $^{56}\mathrm{Ni}$ model to fit the light curve. The best-fitting results reveal that the SN ejected a total mass of $M_\mathrm{ej} = 3.70 M_\odot$, a $^{56}\mathrm{Ni}$ mass of $M_\mathrm{Ni} = 0.23 M_\odot$, and a kinetic energy of $E_\mathrm{SN,K} = 2.35 \times 10^{52} \mathrm{erg}$. We also compare GRB 221009A with other GRB-SN events based on a GRB-associated SN sample, and find that only SN 2003lw and SN 2011kl can be obviously revealed in the afterglow of GRB 221009A by setting these objects at its distance. This suggests that a supernova (SN 2022xiw) is possibly obscured by the brighter afterglow emission from GRB 221009A.

Spontaneous symmetry breaking (SSB) plays a central role in understanding a large variety of phenomena associated with phase transitions, such as superfluid and superconductivity. So far, the transition from a symmetric vacuum to a macroscopically ordered phase has been substantially explored. The process bridging these two distinct phases is critical to understanding how a classical world emerges from a quantum phase transition, but so far remains unexplored in experiment. We here report an experimental demonstration of such a process with a quantum Rabi model engineered with a superconducting circuit. We move the system from the normal phase to the superradiant phase featuring two symmetry-breaking field components, one of which is observed to emerge as the classical reality. The results demonstrate that the environment-induced decoherence plays a critical role in the SSB., Comment: 13 pages,9 figures

We explore the collective Zeno dynamics of giant artificial atoms that are coupled, via multiple coupling points, to a common photonic or acoustic reservoir. In this regime, the establishment of atomic cooperativity and the revivification of exponential decay, are highly intertwined, which is utterly beyond the non-Markovian regime with only retarded backaction. We reveal that giant atoms build up their collective emission smoothly from the decay rate of zero to that predicted by Markovian approximation, and show great disparity between different waveguide QED setups. As a comparison, the step-like growth of instantaneous decay rates in the retardation-only picture has also been shown. All of these theoretical pictures predict the same collective behavior in the long time limit. From a phenomenological standpoint, we observe that the atomic superradiance exhabits significant directional property. In addition, the subradiant photons feature prolonged oscillation in the early stage of collective radiance, where the energy is exchanged remarkably between giant emitters and the field. Our results might be probed in state-of-art waveguide QED experiments, and fundamentally broaden the fields of collective emission in systems with giant atoms., Comment: 14 pages, 6 figures

The source of the Galactic Lithium (Li) has long been a puzzle. With the discovery of Li in novae, extensive research has been conducted. However, there still exists a significant disparity between the observed abundance of lithium in novae and the existing theoretical predictions. Using the Modules for Experiments in Stellar Astrophysics (MESA), we simulate the evolution of nova with element diffusion and appropriately increased the amount of 3^He in the mixtures. Element diffusion enhances the transport efficiency between the nuclear reaction zone and the convective region on the surface of the white dwarf during nova eruptions, which results in more 7^Be to be transmitted to the white dwarf surface and ultimately ejected. Compared to the previous predictions, the abundance of 7^Be in novae simulated in our model significantly increases. And the result is able to explain almost all observed novae. Using the method of population synthesis, we calculate Li yield in the Galaxy. We find that the Galactic occurrence rate of nova is about 130 yr^{-1}, and about 110M Li produced by nova eruption is ejected into the interstellar medium (ISM). About 73\% of Li in the Galactic ISM originates from novae, and approximately 15\%-20\% of the entire Galaxy. It means that novae are the important source of Li in the Galactic., Comment: 12 pages, 4 figures. Accepted for publication in Astrophysical Journal

Genuine multipartite entanglement (GME) is not only fundamental interesting for the study of quantum-to-classical transition, but also is essential for realizing universal quantum computing and quantum networks. Here we investigate the multipartite entanglement (ME) dynamics in a linear chain of N LC resonators interacting optomechanically with a common thermal acoustic reservoir. By presenting the exact analytical solutions of system evolution, we predict the periodic generation of non-Gaussian ME, including the discrete and continuous variables entanglement. Interestingly, the GME is obtained even though the system is in a heat bath. The mechanism relies on the special acoustic environment featuring frequency comb structure. More importantly, our proposed model also allows the periodic generation of entangled multipartite cat states (MCSs), i.e., a typical GHZ state, with high fidelity. This work fundamentally broadens the fields of ME, and have wide applications in implementing thermal-noise-resistant quantum information processing and many-body quantum simulation., Comment: 25 pages, 9 figures

Realizing precise control over multiquanta emission is crucial for quantum information processing, especially when integrated with advanced techniques of manipulating quantum states. Here, by spinning the resonator to induce the Sagnac effect, we can obtain nonreciprocal photon-phonon and photon-magnon super-Rabi oscillations under conditions of optically driving resonance transitions. Opening dissipative channels for such super-Rabi oscillations enables the realization of directional bundle emissions of entangled photon-phonon pairs and photon-magnon pairs by transferring pure multiquanta state to bundled multiquanta outside of the system. This nonreciprocal emission is a flexible switch that can be controlled with precision, and simultaneous emissions of different entangled pairs (such as photon-phonon or photon-magnon pairs) can even emerge but in opposite directions by driving the resonator from different directions. This ability to flexibly manipulate the system allows us to achieve directional entangled multiquanta emitters, and has also potential applications for building hybrid quantum networks and on-chip quantum communications., Comment: 16 pages, 4 figures, accepted by Physical Review Letters

Serialization-based methods, which serialize the 3D voxels and group them into multiple sequences before inputting to Transformers, have demonstrated their effectiveness in 3D object detection. However, serializing 3D voxels into 1D sequences will inevitably sacrifice the voxel spatial proximity. Such an issue is hard to be addressed by enlarging the group size with existing serialization-based methods due to the quadratic complexity of Transformers with feature sizes. Inspired by the recent advances of state space models (SSMs), we present a Voxel SSM, termed as Voxel Mamba, which employs a group-free strategy to serialize the whole space of voxels into a single sequence. The linear complexity of SSMs encourages our group-free design, alleviating the loss of spatial proximity of voxels. To further enhance the spatial proximity, we propose a Dual-scale SSM Block to establish a hierarchical structure, enabling a larger receptive field in the 1D serialization curve, as well as more complete local regions in 3D space. Moreover, we implicitly apply window partition under the group-free framework by positional encoding, which further enhances spatial proximity by encoding voxel positional information. Our experiments on Waymo Open Dataset and nuScenes dataset show that Voxel Mamba not only achieves higher accuracy than state-of-the-art methods, but also demonstrates significant advantages in computational efficiency., Comment: 10 pages, 4 figures