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Assume interest is in sampling from a probability distribution $\mu$ defined on $(\mathsf{Z},\mathscr{Z})$. We develop a framework to construct sampling algorithms taking full advantage of numerical integrators of ODEs, say $\psi\colon\mathsf{Z}\rightarrow\mathsf{Z}$ for one integration step, to explore $\mu$ efficiently and robustly. The popular Hybrid/Hamiltonian Monte Carlo (HMC) algorithm [Duane, 1987], [Neal, 2011] and its derivatives are example of such a use of numerical integrators. However we show how the potential of integrators can be exploited beyond current ideas and HMC sampling in order to take into account aspects of the geometry of the target distribution. A key idea is the notion of integrator snippet, a fragment of the orbit of an ODE numerical integrator $\psi$, and its associate probability distribution $\bar{\mu}$, which takes the form of a mixture of distributions derived from $\mu$ and $\psi$. Exploiting properties of mixtures we show how samples from $\bar{\mu}$ can be used to estimate expectations with respect to $\mu$. We focus here primarily on Sequential Monte Carlo (SMC) algorithms, but the approach can be used in the context of Markov chain Monte Carlo algorithms as discussed at the end of the manuscript. We illustrate performance of these new algorithms through numerical experimentation and provide preliminary theoretical results supporting observed performance.

We achieve high detectivity terahertz sensing using a silicon nitride nanomechanical resonator functionalized with a metasurface absorber. High performances are achieved by striking a fine balance between the frequency stability of the resonator, and its responsivity to absorbed radiation. Using this approach, we demonstrate a detectivity $D^*=3.4\times10^9~\mathrm{cm\cdot\sqrt{Hz}/W}$ and a noise equivalent power $\mathrm{NEP}=36~\mathrm{pW/\sqrt{Hz}}$ that outperform the best room-temperature on-chip THz detectors (i.e., pyroelectrics). Our optical absorber consists of a 1-mm diameter metasurface, which currently enables a 0.5-3 THz detection range but can easily be scaled to other frequencies in the THz and infrared ranges. In addition to demonstrating high-performance terahertz sensing, our work unveils an important fundamental trade-off between high frequency stability and high responsivity in thermal-based nanomechanical radiation sensors.

The quantum geometric tensor (QGT) characterizes the complete geometric properties of quantum states, with the symmetric part being the quantum metric, and the antisymmetric part being the Berry curvature. We propose a generic Hamiltonian with global degenerate ground states, and give a general relation between the corresponding non-Abelian quantum metric and unit Bloch vector. This enables us to construct the relation between the non-Abelian quantum metric and Berry or Euler curvature. To be concrete, we present and study two topological semimetal models with global degenerate bands under CP and $C_2T$ symmetries, respectively. The topological invariants of these two degenerate topological semimetals are the Chern number and Euler class, respectively, which are calculated from the non-Abelian quantum metric with our constructed relations. Based on the adiabatic perturbation theory, we further obtain the relation between the non-Abelian quantum metric and the energy fluctuation. Such a non-adiabatic effect can be used to extract the non-Abelian quantum metric, which is numerically demonstrated for the two models of degenerate topological semimetals. Finally, we discuss the quantum simulation of the model Hamiltonians with cold atoms., Comment: 14 pages,5 figures

We investigate the CP violation in the decay process $\bar B_{s} \rightarrow \phi(\rho,\omega) P \rightarrow K^{+}K^{-}P$ by considering the interference effects of $\phi\rightarrow K^{+}K^{-}$, $\rho\rightarrow K^{+}K^{-}$ and $\omega\rightarrow K^{+}K^{-}$ within the framework of perturbative QCD method (P refers to $\pi$, K, $\eta$ and $\eta'$ pseudoscalar mesons, respectively). We analyse the mixings of $\phi-\rho^{0}$, $\phi-\omega$ and $\omega-\rho^{0}$ and provide the amplitudes of the quasi-two-body decay processes. The CP violation for $\bar B_{s} \rightarrow K^{+}K^{-} P$ decay process is obvious at the ranges of the three vector mesons interferences. Meanwhile, the localised CP violation can be found for comparing with the experiment results from three-body decay process at the LHC in the near future.

In the paper, we study the semilinear wave equation involving the nonlinear damping $g(u_t) $ and nonlinearity $f(u)$. Under the wider ranges of exponents of $g$ and $f$, the well-posedness of the weak solution is achieved by establishing a priori space-time estimates. Then, the existence of the global attractor in the naturally phase space $H^1_0(\Omega)\times L^2(\Omega)$ is obtained. Moreover, we prove that the global attrator is regular, that is, the global attractor is a bounded subset of $(H^2(\Omega)\cap H^1_0(\Omega))\times H^1_0(\Omega)$., Comment: 33 pages

Defect engineering is promising to tailor the physical properties of two-dimensional (2D) semiconductors for function-oriented electronics and optoelectronics. Compared with the extensively studied 2D binary materials, the origin of defects and their influence on physical properties of 2D ternary semiconductors have not been clarified. In this work, we thoroughly studied the effect of defects on the electronic structure and optical properties of few-layer hexagonal Znln2S4 via versatile spectroscopic tools in combination with theoretical calculations. It has been demonstrated that the Zn-In anti-structural defects induce the formation of a series of donor and acceptor levels inside the bandgap, leading to rich recombination paths for defect emission and extrinsic absorption. Impressively, the emission of donor-acceptor pair (DAP) in Znln2S4 can be significantly tailored by electrostatic gating due to efficient tunability of Fermi level (Ef). Furthermore, the layer-dependent dipole orientation of defect emission in Znln2S4 was directly revealed by back focal plane (BFP) imagining, where it presents obviously in-plane dipole orientation within a dozen layers thickness of Znln2S4. These unique features of defects in Znln2S4 including extrinsic absorption, rich recombination paths, gate tunability and in-plane dipole orientation will definitely benefit to the advanced orientation-functional optoelectronic applications.

The initial and boundary conditions of the Galactic star formation in molecular clouds are not well understood. In an effort to shed new light on this long-standing problem, we measured properties of dense cores and filamentary structures in the Vela C molecular cloud, observed with Herschel. We applied the getsf extraction method to separate the components of sources and filaments from each other and their backgrounds, before detecting, measuring, and cataloging the structures. The cores and filamentary structures constitute 40% of the total mass of Vela C, most of the material is in the low-density molecular background cloud. We selected 570 reliable cores, of which 149 are the protostellar cores and 421 are the starless cores. Almost 78% of the starless cores were identified with the gravitationally bound prestellar cores. The exponent of the CMF (alpha = 1.35) is identical to that of the Salpeter IMF. We selected 68 filaments with at least one side that appeared not blended with adjacent structures. The filament widths are in the range of 0.15 pc to 0.63 pc, and have a median value of W = 0.3(0.11) pc. The surface densities of filaments are well correlated with their contrasts and linear densities. Within uncertainties of the filament instability criterion, many filaments may well be both supercritical and subcritical. A large fraction of filaments may definitely be considered supercritical, in which are found 94 prestellar cores, 83 protostellar cores, and only 1 unbound starless core. Taking into account the uncertainties, the supercritical filaments contain only prestellar and protostellar cores. Our findings support the idea that there exists a direct relationship between the CMF and IMF and that filaments play a key role in the formation of prestellar cores, which is consistent with the previous Herschel results., Comment: 15 pages, 12 figures, 3 tables, accepted for publication in A&A

This paper proposes a novel method for depth completion, which leverages multi-view improved monitored distillation to generate more precise depth maps. Our approach builds upon the state-of-the-art ensemble distillation method, in which we introduce a stereo-based model as a teacher model to improve the accuracy of the student model for depth completion. By minimizing the reconstruction error of a target image during ensemble distillation, we can avoid learning inherent error modes of completion-based teachers. We introduce an Attention-based Sparse-to-Dense (AS2D) module at the front layer of the student model to enhance its ability to extract global features from sparse depth. To provide self-supervised information, we also employ multi-view depth consistency and multi-scale minimum reprojection. These techniques utilize existing structural constraints to yield supervised signals for student model training, without requiring costly ground truth depth information. Our extensive experimental evaluation demonstrates that our proposed method significantly improves the accuracy of the baseline monitored distillation method., Comment: 7 pages, 8 figures, references added

The aim of sequential pattern mining (SPM) is to discover potentially useful information from a given se-quence. Although various SPM methods have been investigated, most of these focus on mining all of the patterns. However, users sometimes want to mine patterns with the same specific prefix pattern, called co-occurrence pattern. Since sequential rule mining can make better use of the results of SPM, and obtain better recommendation performance, this paper addresses the issue of maximal co-occurrence nonoverlapping sequential rule (MCoR) mining and proposes the MCoR-Miner algo-rithm. To improve the efficiency of support calculation, MCoR-Miner employs depth-first search and backtracking strategies equipped with an indexing mechanism to avoid the use of sequential searching. To obviate useless support calculations for some sequences, MCoR-Miner adopts a filtering strategy to prune the sequences without the prefix pattern. To reduce the number of candidate patterns, MCoR-Miner applies the frequent item and binomial enumeration tree strategies. To avoid searching for the maximal rules through brute force, MCoR-Miner uses a screening strategy. To validate the per-formance of MCoR-Miner, eleven competitive algorithms were conducted on eight sequences. Our experimental results showed that MCoR-Miner outperformed other competitive algorithms, and yielded better recommendation performance than frequent co-occurrence pattern mining. All algorithms and datasets can be downloaded from https://github.com/wuc567/Pattern-Mining/tree/master/MCoR-Miner.

The frequency stability of nanomechanical resonators (NMR) dictates the performance level of many state-of-the-art sensors (e.g., mass, force, temperature, radiation) that relate an external physical perturbation to a resonance frequency shift. While this is obviously of fundamental importance, accurate models and understandings of sources of frequency instability are not always available. The contribution of thermomechanical noise to frequency stability has been well studied in recent years and is often the fundamental performance limitation. Frequency stability limited by thermal fluctuation noise has attracted less interest but is nevertheless of fundamental importance notably in temperature sensing applications. In particular, temperature-sensitive NMR have become promising candidates for replacing traditional bolometers in infrared radiation sensing. However, reaching the ultimate detectivity limit of thermal radiation sensors requires their noise to be dominated by fundamental thermal fluctuation, which has not been demonstrated to date. In this work, we first develop a theoretical model for computing the frequency stability of NMR by considering the effect of both additive phase noise (i.e., thermomechanical, and experimental detection noise) and thermal fluctuation noise in a close-loop frequency tracking scheme. We thereafter validate this model experimentally and observe thermal fluctuation noise in SiN drum resonators of various sizes. Our work shows that by using resonators of specific characteristics--such as high temperature sensitivity, high mechanical quality factors, and high mass-to-thermal-conductance ratio--one can minimize additive phase noise below thermal fluctuation noise. This paves the way for NMR-based radiation sensors that can reach the fundamental detectivity limit of thermal radiation sensing and outperform existing technologies.

Massive young stellar objects (MYSOs) play a crucial role in star formation. Given that MYSOs were previously identified based on the extended structure and the observational data for them is limited, screening the Wide-field Infrared Survey Explorer (WISE) objects showing green features (for the common coding of the 4.6 $\mu$m band as green channel in three-color composite WISE images) will yield more MYSO candidates. Using WISE images in the whole Galactic Plane ($ 0^\circ 60^\circ$. Matching results with various masers show that those three groups of WGOs are at different evolutionary stages. After cross-matching WGOs with published YSO survey catalogs, we infer that $\sim$50% of WGOs are samples of newly discovered YSOs. In addition, 1260 WGOs are associated with Hi-GAL sources, according to physical parameters estimated by spectral energy distribution fitting, of which 231 are classified as robust MYSOs and 172 as candidate MYSOs., Comment: 25 pages, 9 figures, accepted for publication in ApJS

In this work, we study the continual semantic segmentation problem, where the deep neural networks are required to incorporate new classes continually without catastrophic forgetting. We propose to use a structural re-parameterization mechanism, named representation compensation (RC) module, to decouple the representation learning of both old and new knowledge. The RC module consists of two dynamically evolved branches with one frozen and one trainable. Besides, we design a pooled cube knowledge distillation strategy on both spatial and channel dimensions to further enhance the plasticity and stability of the model. We conduct experiments on two challenging continual semantic segmentation scenarios, continual class segmentation and continual domain segmentation. Without any extra computational overhead and parameters during inference, our method outperforms state-of-the-art performance. The code is available at \url{https://github.com/zhangchbin/RCIL}., Comment: Accepted by CVPR 2022

Cores and filamentary structures are the prime birthplaces of stars, and play key roles in the process of star formation. Latest advances in the methods of multi-scale source and filament extraction, and in making high-resolution column density map from $Herschel$ multi-wavelength observations enable us to detect the filamentary network structures in highly complex molecular cloud environments. The statistics for physical parameters shows that core mass strongly correlates with core dust temperature, and $M/L$ strongly correlates with $M/T$, which is in line with the prediction of the blackbody radiation, and can be used to trace evolutionary sequence from unbound starless cores to robust prestellar cores. Crest column densities of the filamentary structures are clearly related with mass per unit length ($M_{\rm line}$), but are uncorrelated by three orders ranging from $\sim 10^{20}$ to $\sim 10^{22}$ $ \rm cm^{-2}$ with widths. Full width at half maximum (FWHM) have a median value of 0.15 pc, which is consistent with the 0.1 pc typical inner width of the filamentary structures reported by previous research. We find $\sim $70\% of robust prestellar cores (135/199) embedded in supercritical filaments with $M_{\rm line}>16~M_{\odot}/{\rm pc}$, which implies that the gravitationally bound cores come from fragmentation of supercritical filaments. And on the basis of observational evidences that probability distribution function (PDF) with power-law distribution in the Perseus south is flatter than north, YSO number is significantly less than that in the north, and dust temperature difference. We infer that south region is more gravitationally bound than north region., Comment: 15 pages, 9 figures, accepted for publication in RAA

In this article, we study the influence of long-range Coulomb interaction on three-dimensional second-order topological insulator (TI) by renormalization group theory. We find that both the analysis method and conclusions in the recent Letter Phys. Rev. Lett. {\bf 127}, 176601 (2021) are unreliable. There are two problems in this Letter. Firstly, the characteristic described by the RG flows $m\rightarrow\infty$ and $D\rightarrow0$ can not be used as the criterion for transition from second-order TI to TI, since this characteristic could be essentially not induced by Coulomb interaction but only results from the trivial power counting contribution of fermion action. Indeed, this characteristic is satisfied even for free second-order TI. Second, the flow of $B$ is not paid attention, which is very important and should be seriously studied. In this article, we analyze carefully the corrections for the flows of the model parameters induced by Coulomb interaction. We find that the sign of $m$ changes but the sign of $B$ holds if the initial Coulomb strength is large enough, while the sign of $m$ holds but the sign of $B$ changes if the initial Coulomb strength takes small values. These results indicate that second-order TI is unstable to trivial band insulator not only under strong Coulomb interaction but also under weak Coulomb interaction. We also study the effects of disorder scattering in second-order TI by renormalization group theory. According to the criterion in Phys. Rev. Lett. {\bf 127}, 176601 (2021), weak disorder drives second-order TI to TI. However, we find that second-order TI is robust against weak disorder, since weak disorder does not give qualitative modification for second-order TI. This result is consistent with recent studies based on other methods. Interplay of Coulomb interaction and disorder in second-order TI is also investigated., Comment: 38 pages, 14 figures

To understand the nature of SiO emission, we conducted ACA observations of the SiO (2-1) lines toward 146 massive star-forming regions, as part of the ALMA Three-millimeter Observations of Massive Star-forming regions (ATOMS) survey. We detected SiO emission in 128 (87.7$\%$) sources and identified 171 SiO clumps, 105 of which are spatially separated from 3 mm continuum emission. A large amount of the SiO line profiles (60$\%$) are non-Gaussian. The velocity dispersion of the SiO lines ranges from 0.3 to 5.43 km s$^{-1}$. In 63 sources the SiO clumps are associated with H$_\rm{II}$ regions characterized by H40$\alpha$ emission. We find that 68$\%$ (116) of the SiO clumps are associated with strong outflows. The median velocity dispersion of the SiO line for outflow sources and non-outflow sources is 1.91 km s$^{-1}$ and 0.99 km s$^{-1}$, respectively. These results indicate that outflow activities could be connected to strongly shocked gas. The velocity dispersion and [SiO]/[H$^{13}$CO$^+$] intensity ratio do not show any correlation with the dust temperature and particle number density of clumps. We find a positive correlation between the SiO line luminosity and the bolometric luminosity, implying stronger shock activities are associated with more luminous proto-clusters. The SiO clumps in associations with H$_\rm{II}$ regions were found to show a steeper feature in $L_\rm{sio}$/$L_\rm{bol}$. The SiO line luminosity and the fraction of shocked gas have no apparent evidence of correlation with the evolutionary stages traced by luminosity to mass ratio ($L_\rm{bol}/M$)., Comment: 18 pages, 10 figures