Search

Mass distribution of black holes identified through X-ray emission suggests a paucity of black holes in the mass range of 3 to 5 solar masses. Modified theories have been devised to explain this mass gap, and it is suggested that natal kicks during supernova explosion can more easily disrupt binaries with lower mass black holes. Although recent LIGO observations reveal the existence of compact remnants within this mass gap, the question of whether low-mass black holes can exist in binaries remains a matter of debate. Such a system is expected to be noninteracting without X-ray emission, and can be searched for using radial velocity and astrometric methods. Here we report Gaia DR3 3425577610762832384, a wide binary system including a red giant star and an unseen object, exhibiting an orbital period of approximately 880 days and near-zero eccentricity. Through the combination of radial velocity measurements from LAMOST and astrometric data from Gaia DR2 and DR3 catalogs, we determine a mass of $3.6^{+0.8}_{-0.5}$ $M_{\odot}$ of the unseen component. This places the unseen companion within the mass gap, strongly suggesting the existence of binary systems containing low-mass black holes. More notably, the formation of its surprisingly wide circular orbit challenges current binary evolution and supernova explosion theories., Comment: Published in Nature Astronomy, see https://www.nature.com/articles/s41550-024-02359-9

Neural operators are effective tools for solving parametric partial differential equations (PDEs). They can predict solutions of PDEs with different initial and boundary conditions, as well as different input functions. The recently proposed Wavelet Neural Operator (WNO) utilizes the time-frequency localization of wavelets to capture spatial manifolds effectively. While WNO has shown promise as an operator learning method, it only parameterizes neural network weights under higher-order wavelet factorization. This approach avoids noise interference but may result in insufficient extraction of high-frequency features from the data. In this study, we propose a new network architecture called U-WNO. It incorporates the U-Net path and residual shortcut into the wavelet layer to enhance the extraction of high-frequency features and improve the learning of spatial manifolds. Additionally, we introduce the Adaptive Activation Function into the wavelet layer to address the spectral bias of the neural network. The effectiveness of U-WNO is demonstrated through numerical experiments on various problems, including the Burgers equation, Darcy flow, Navier-Stokes equation, Allen-Cahn equation, Non-homogeneous Poisson equation, and Wave advection equation. This study also includes a comparative analysis of existing operator learning frameworks., Comment: 24 pages, 13 figures, 3 tables

Changing-look Active Galactic Nuclei (CL AGN) exhibit drastic variations in broad emission lines (BELs), the mechanism of which remains unclear. Expanding the sample of CL AGN is helpful to reveal the mechanism. This study aims to identify more CL AGNs by cross-matching spectroscopic data from the Sloan Digital Sky Survey (SDSS) and the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST). Our approach to identify CL AGN candidates is based on the automatic spectral fitting, followed by detailed visual inspections. Through this method, we present a sample of 88 CL AGNs, in which 77 sources being newly discovered. Within this sample, 59 CL AGNs primarily show the variability of the H$\beta$ line, 22 exhibit changes in both the H$\beta$ and H$\alpha$ lines, and 7 mainly display variations in the H$\alpha$ line. Our findings reveal that the sequence of appearance and disappearance of the BELs aligns with the known CL sequence. We estimate the black hole mass and Eddington ratio for these CL AGNs, which range from $2.5\times 10^6$ to $8.0\times 10^8 M_\odot$ and from 0.001 to 0.13, respectively. The Eddington ratio is lower than that of most typical AGNs, and is consistent with the results of previous studies on CL AGN. Our results support the hypothesis that the CL behavior is driven by the state transitions of the accretion disk., Comment: 14 pages, 4 figures, to be submitted

Relativistic polarized electron beams can find applications in broad areas of fundamental physics. Here, we propose for the first time that electron spin polarization can be realized efficiently via collective beam-target interactions. When a relativistic unpolarized electron beam is incident onto the surface of a solid target with a grazing angle, strong magnetic fields are induced at the target surface due to the formation of a high reflux of target electrons. This results in violent beam self-focusing and corresponding beam density increase via magnetic pinching. The pinched dense beam in turn further enhances the magnetic fields to the level of a few Giga-Gauss, which is high enough to trigger strong synchrotron radiation of ultrarelativistic electrons. During the interaction, electron spin polarization develops along the magnetic field direction, which is achieved via radiative spin flips in the quantum radiation-dominated regime. As a consequence, the incident electron beam can be effectively polarized via the spin-dependent radiation reaction, for example, the mean polarization of electrons with energy less than 2 GeV can reach above 50% for an initial 5GeV beam. This provides a robust way for the development of polarized electron sources.

We report two binary systems, LAMOST J035540+381550 (hereafter J035540) and LAMOST J035916+400732 (hereafter J035916), identified through the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) low-resolution survey (LRS). Each of these two systems contains an M-type star orbiting with a invisible compact object candidate. Follow-up spectroscopic observations of Palomar 200-inch telescope (P200) enhance radial velocity measurements. We use radial velocities from LAMOST and P200, as well as light curves from Zwicky Transient Facility (ZTF) to constrain orbital parameters. The masses of the visible M-type stars are estimated by fitting the MIST isochrones and SEDs. The mass functions for the unseen companions are: $0.22\pm 0.01 M_{\odot}$ for J035540 and $0.16\pm 0.01 M_{\odot}$ for J035916. With the orbital and stellar parameters derived above and assuming the orbital inclination is 90 degree (edge-on), we find that the minimum masses of the invisible companions exceeds that of the visible stars. The single-lined feature and the dynamical evidence suggest the presence of compact objects. J035540's ZTF light curve, modeled with PHOEBE, yields a compact object mass of $0.70^{+0.12}_{-0.05} M_{\odot}$. For J035916, ellipsoidal modulation analysis constrains the light curve amplitude, yielding a compact object mass range of $0.57-0.90 M_{\odot}$. The mass estimates indicate that both are likely white dwarfs. These findings underscore the efficiency of optical time-domain surveys and dynamical methods in identifying faint, massive white dwarfs, along with other compact objects in binaries., Comment: 12 pages, 9 figures, accepted for publication in MNRAS

In this paper, we bridge Variational Autoencoders (VAEs) [17] and kernel density estimations (KDEs) [25 ],[23] by approximating the posterior by KDEs and deriving an upper bound of the Kullback-Leibler (KL) divergence in the evidence lower bound (ELBO). The flexibility of KDEs makes the optimization of posteriors in VAEs possible, which not only addresses the limitations of Gaussian latent space in vanilla VAE but also provides a new perspective of estimating the KL-divergence in ELBO. Under appropriate conditions [ 9],[3 ], we show that the Epanechnikov kernel is the optimal choice in minimizing the derived upper bound of KL-divergence asymptotically. Compared with Gaussian kernel, Epanechnikov kernel has compact support which should make the generated sample less noisy and blurry. The implementation of Epanechnikov kernel in ELBO is straightforward as it lies in the "location-scale" family of distributions where the reparametrization tricks can be directly employed. A series of experiments on benchmark datasets such as MNIST, Fashion-MNIST, CIFAR-10 and CelebA further demonstrate the superiority of Epanechnikov Variational Autoenocoder (EVAE) over vanilla VAE in the quality of reconstructed images, as measured by the FID score and Sharpness[27].

The stellar spectra from LAMOST Medium Resolution Survey can be used to search for compact objects in binaries. The LAMOST DR10 catalog includes > 980, 000 targets with multiple medium resolution spectra. We select the targets with large or rapid radial velocity variation, and obtained an input-sample of 1822 sources. We use light curves and spectra to identify and exclude eclipsing binaries and double-lined spectroscopic binaries in the input-sample. We finally derive a catalog of 89 candidates with well-folded radial velocity, which are all single-lined spectroscopic binaries, indicating an unseen companion residing in each system. The mass function of each system can be well constrained based on the radial velocity curve. In our sample, 26 sources have mass function higher than 0.1 $M_{\odot}$, among which 18 sources have ellipsoidal type light curves. In our opinion, compact objects are likely existent in all these 26 binaries, which are worth follow-up identification., Comment: 20 pages, 10 figures, accepted for publication in ApJ

Variability of active galactic nuclei (AGNs) has long been servicing as an essential avenue of exploring the accretion physics of black hole (BH). There are two commonly used methods for analyzing AGN variability. First, the AGN variability, characterized by the structure function (SF) of a single band, can be well described by a damped random walk (DRW) process on timescales longer than ~weeks, shorter than which departures have been reported. Second, the color variation (CV) between two bands behaves timescale-dependent, raising challenges to the widely accepted reprocessing scenario. However, both the departure from the DRW process and the timescale-dependent CV are hitherto limited to AGNs, mainly quasars, at the supermassive scale. Here, utilizing the high-cadence multi-wavelength monitoring on NGC 4395 harboring an intermediate-mass BH, we unveil at the intermediate-mass scale for the first time, prominent departures from the DRW process at timescales shorter than ~hours in all three nights and bands, and plausible timescale-dependent CVs in the two longest nights of observation. Furthermore, comparing SFs of NGC 4395 to four AGNs at the supermassive scale, we suggest a new scaling relation between the timescale (\uptau; across nearly three orders of magnitude) and the BH mass (M_BH): \uptau \propto M^\gamma_BH where the exponent \gamma is likely ~ 0.6 - 0.8. This exponent differs from most previous measurements, but confirms a few and is consistent with a recent theoretical prediction, suggesting a similar accretion process in AGNs across different mass scales., Comment: 22 pages, 12 figures, Accepted by ApJ

We derive the quantum thermodynamics of quantum Brownian motion from the exact solution of its reduced density matrix. We start from the total equilibrium thermal state between the Brownian particle and its reservoir, and solve analytically and exactly the reduced density matrix of the system by taking the partial trace over all the reservoir states. We find that the reduced Hamiltonian and the reduced partition function of the Brownian motion must be renormalized significantly, as shown in the general nonperturbative renormalization theory of quantum thermodynamics for open quantum systems we developed recently [Phys. Rev. Res. 4, 023141 (2022)]. The reduced Hamiltonian contains not only a frequency shift but also a squeezing pairing interaction, where a momentum-dependent potential is generated naturally from the strong coupling between the Brownian particle and the reservoir, after traced over all the reservoir states. The resulting exact reduced density matrix of the Brownian motion is given by a squeezing thermal state. Moreover, beyond the weak coupling limit, in order to obtain correctly the reduced partition function of the Brownian motion, one must take into account the non-negligible changes of the reservoir state induced by the system-reservoir coupling. Using the exact solutions of the reduced density matrix, the reduced Hamiltonian as well as the reduced partition function of the Brownian motion, we show that the controversial results obtained from the different definitions of internal energy and the issue of the negative heat capacity in the previous studies of strong-coupling quantum thermodynamics are resolved., Comment: 21 pages, 5 figures

Static IR drop analysis is a fundamental and critical task in chip design since the IR drop will significantly affect the design's functionality, performance, and reliability. However, the process of IR drop analysis can be time-consuming, potentially taking several hours. Furthermore, in the process of fixing violations, it is frequently imperative to do IR drop analysis iteratively, hence exacerbating the computational burden associated with the analysis. Therefore, a fast and accurate IR drop prediction is paramount for reducing the overall time invested in chip design. In this paper, we propose a global and local attention-based Inception U-Net for static IR drop estimation. Our U-Net incorporates components from the Transformer, CBAM, and Inception architectures to enhance its feature capture capability at different scales and improve the accuracy of predicted IR drop. Experimental results demonstrate that our proposed algorithm can achieve the best results among the winning teams of the ICCAD 2023 contest and the state-of-the-art algorithms., Comment: 7 pages, 8 figures

Two-color laser induced plasma filamentation in air could serve as tabletop sources of broadband terahertz (THz) pulses. Ubiquitous air in the earth facilitates its widespread utilities, particularly, in wireless communication and remote sensing, exploiting the unique advantage of the air-based scheme that the THz sources can be delivered over standoff distances via the pump laser propagation in air. However, the THz emission pattern inevitably has a conical angular profile with a dip in the propagation axis, therefore, THz energy concentration, propagation directionality, and accuracy of signal demodulation are significantly impaired, greatly limiting its direct applications. Here, we successfully eliminate the unfavorable conical profile by experiments and meanwhile enhance THz directionality and intensity by 17 folds by use of abruptly-autofocusing laser beams. Our theory and simulations show that these observations are attributed to efficient suppression of the dephasing effect appearing in previous investigations with ordinary Gaussian laser beams. This scheme is easily accessible since the abruptly-autofocusing beam can be achieved by imposing a spatial light modulator on the input Gaussian beam. This study solves a long-standing problem in the two-color laser scheme and clarifies the underlying physics of the conical angular profile formation., Comment: 22 pages, 4 figures, 1 table

The structure of quantum mechanics forbids a bipartite scenario for masking quantum information, however, it allows multipartite maskers. The Latin squares are found to be closely related to a series of tripartite maskers. This adds another item, significantly different from the original no-cloning theorem, to the no-go theorems. On the other hand, anyonic excitations in two dimensions exhibit exotic collective behaviors of quantum physics, and open the avenue of fault-tolerant topological quantum computing. Here, we give the Latin-square construction of Abelian and Ising anyons %of in the Kitaev model and study the maskable space configuration in anyonic space. The circling and braiding of Kitaev anyons are masking operations on extended hyperdisks in anyonic space. We also realize quantum information masking in a teleportation way in the Kitaev Ising anyon model., Comment: 7 pages, 4 figures

Entanglement is the most striking but also most weird property in quantum mechanics, even though it has been confirmed by many experiments over decades through the criterion of violating Bell's inequality. However, a fundamental questions arisen from EPR paradox is still not fully understood, that is, why and how entanglement emerges in quantum realm but not in classical world. In this paper, we investigate the quantum dynamics of two photonic modes (or any two bosonic modes) coupled to each other through a beam splitting. Such a coupling fails to produce two-mode entanglement. We also start with an initially separable pure state for the two modes, namely, there are no entanglement and statistic probability feature to begin with. By solving the quantum equation of motion exactly without relying on the probabilistic interpretation, we find that when the initial wave function of one mode is different from a wave packet obeying the minimum Heisenberg uncertainty (which corresponds to a well-defined classically particle), the causality in the time-evolution of each mode is internally broken. It also leads to the emergence of quantum entanglement between the two modes. The lack of causality is the nature of statistics. The Bell's theorem only rules out the existence of local hidden variables in the probabilistic interpretation of quantum mechanics. It is the breaking of internal causality in the dynamical evolution of subsystems that induces the probabilistic nature of quantum mechanics, even though the dynamical evolution of the whole system completely obey the deterministic Schr\"{o}dinger equation. This conclusion is valid for all quantum systems. It provides a fundamental origin of the probabilistic feature within the deterministic framework of quantum mechanics., Comment: 14 pages, 3 figure (typos are corrected and 2 figures are added)

We present TMMLU+, a new benchmark designed for Traditional Chinese language understanding. TMMLU+ is a multi-choice question-answering dataset with 66 subjects from elementary to professional level. It is six times larger and boasts a more balanced subject distribution than its predecessor, Taiwan Massive Multitask Language Understanding (TMMLU). We also benchmark closed-source models and 26 open-weight Chinese large language models (LLMs) of parameters ranging from 1.8B to 72B on the proposed TMMLU+. Our findings reveal that (1.) Traditional Chinese models still trail behind their Simplified Chinese counterparts, highlighting a need for more focused advancements in LLMs catering to Traditional Chinese. (2.) Current LLMs still fall short of human performance in average scores, indicating a potential need for future research to delve deeper into social science and humanities subjects. (3.) Among all the tokenization compression metrics examined, we identify that only the fertility score uniquely demonstrates strong correlations with our benchmark results. We foresee that TMMLU+ will pinpoint areas for future model improvement, thereby narrowing the gap between machine and human linguistic capabilities and supporting researchers in developing Traditional Chinese LLMs. Our dataset, along with the benchmark source code, is accessible at huggingface.co/datasets/ikala/tmmluplus.

We propose a novel ensemble method called Riemann-Lebesgue Forest (RLF) for regression. The core idea in RLF is to mimic the way how a measurable function can be approximated by partitioning its range into a few intervals. With this idea in mind, we develop a new tree learner named Riemann-Lebesgue Tree (RLT) which has a chance to perform Lebesgue type cutting,i.e splitting the node from response $Y$ at certain non-terminal nodes. We show that the optimal Lebesgue type cutting results in larger variance reduction in response $Y$ than ordinary CART \cite{Breiman1984ClassificationAR} cutting (an analogue of Riemann partition). Such property is beneficial to the ensemble part of RLF. We also generalize the asymptotic normality of RLF under different parameter settings. Two one-dimensional examples are provided to illustrate the flexibility of RLF. The competitive performance of RLF against original random forest \cite{Breiman2001RandomF} is demonstrated by experiments in simulation data and real world datasets.

The combination of mobile edge computing (MEC) and radio frequency-based wireless power transfer (WPT) presents a promising technique for providing sustainable energy supply and computing services at the network edge. This study considers a wireless-powered mobile edge computing system that includes a hybrid access point (HAP) equipped with a computing unit and multiple Internet of Things (IoT) devices. In particular, we propose a novel muti-user cooperation scheme to improve computation performance, where collaborative clusters are dynamically formed. Each collaborative cluster comprises a source device (SD) and an auxiliary device (AD), where the SD can partition the computation task into various segments for local processing, offloading to the HAP, and remote execution by the AD with the assistance of the HAP. Specifically, we aims to maximize the weighted sum computation rate (WSCR) of all the IoT devices in the network. This involves jointly optimizing collaboration, time and data allocation among multiple IoT devices and the HAP, while considering the energy causality property and the minimum data processing requirement of each device. Initially, an optimization algorithm based on the interior-point method is designed for time and data allocation. Subsequently, a priority-based iterative algorithm is developed to search for a near-optimal solution to the multi-user collaboration scheme. Finally, a deep learning-based approach is devised to further accelerate the algorithm's operation, building upon the initial two algorithms. Simulation results show that the performance of the proposed algorithms is comparable to that of the exhaustive search method, and the deep learning-based algorithm significantly reduces the execution time of the algorithm., Comment: Accepted to IEEE Open Journal of the Communications Society

Many studies have shown that high-energy $\gamma$-photon beams can be efficiently generated via nonlinear Compton scattering driven by laser pulses with intensities $> 10^{22}\rm{W/cm^2}$ recently available in laboratories. Here, we propose a laserless scheme to efficiently generate high-energy polarized $\gamma$-photon beams by collision of two ultrarelativistic electron beams. The self-generated field of a dense driving electron beam provides the strong deflection field for the other ultrarelativistic seeding electron beam. A QED Monte Carlo code based on the locally constant field approximation is employed to simulate the collision process, and the polarization properties of produced $\gamma$ photons are investigated. The simulation results and theoretical analysis indicate that the photon polarization, including both linear and circular polarizations, can be tuned by changing the initial polarization of the seeding beam. If an unpolarized seeding beam is used, linearly polarized photons with an average polarization of 55\% can be obtained. If the seeding beam is transversely (longitudinally) polarized, the linear (circular) polarization of photons above 3 GeV can reach 90\% (67\%), which is favorable for highly polarized, high-energy $\gamma$ photon sources., Comment: 12 pages, 8 figures

Stable transport of laser beams in highly over-dense plasmas is of significance in fast ignition of inertial confinement fusion, relativistic electrons generation, and powerful electromagnetic emission, but hard to realize. Early in 1996, Harris proposed an electromagnetically induced transparency (EIT) mechanism, analogous to the concept in atom physics, to transport a low-frequency (LF) laser in over-dense plasmas aided by a high-frequency pump laser. However, subsequent investigations show that EIT cannot occur in real plasmas with boundaries. Here, our particle-in-cell simulations show that EIT can occur in strongly-relativistic regime and results in stable propagation of a LF laser in bounded plasmas with tens of its critical density. A relativistic three-wave coupling model is developed, and the criteria and frequency passband for EIT occurrence are presented. The passband is sufficiently wide in strongly-relativistic regime, allowing EIT to work sustainably. Nevertheless, it is narrowed to nearly an isolated point in weakly-relativistic regime, which can explain the quenching of EIT in bounded plasmas found in previous investigations.

Seasonal influenza causes on average 425,000 hospitalizations and 32,000 deaths per year in the United States. Forecasts of influenza-like illness (ILI) -- a surrogate for the proportion of patients infected with influenza -- support public health decision making. The goal of an ensemble forecast of ILI is to increase accuracy and calibration compared to individual forecasts and to provide a single, cohesive prediction of future influenza. However, an ensemble may be composed of models that produce similar forecasts, causing issues with ensemble forecast performance and non-identifiability. To improve upon the above issues we propose a novel Cluster-Aggregate-Pool or `CAP' ensemble algorithm that first clusters together individual forecasts, aggregates individual models that belong to the same cluster into a single forecast (called a cluster forecast), and then pools together cluster forecasts via a linear pool. When compared to a non-CAP approach, we find that a CAP ensemble improves calibration by approximately 10% while maintaining similar accuracy to non-CAP alternatives. In addition, our CAP algorithm (i) generalizes past ensemble work associated with influenza forecasting and introduces a framework for future ensemble work, (ii) automatically accounts for missing forecasts from individual models, (iii) allows public health officials to participate in the ensemble by assigning individual models to clusters, and (iv) provide an additional signal about when peak influenza may be near.

During the ultraintense laser interaction with solids (overdense plasmas), the competition between two possible quantum electrodynamics (QED) mechanisms responsible for $e^\pm$ pair production, i.e., linear and nonlinear Breit-Wheeler (BW) processes, remains to be studied. Here, we have implemented the linear BW process via a Monte Carlo algorithm into the QED particle-in-cell (PIC) code YUNIC, enabling us to self-consistently investigate both pair production mechanisms in the plasma environment. By a series of 2D QED-PIC simulations, the transition from the linear to the nonlinear BW process is observed with the increase of laser intensities in the typical configuration of a linearly polarized laser interaction with solid targets. A critical normalized laser amplitude about $a_0\sim$ 400-500 is found under a large range of preplasma scale lengths, below which the linear BW process dominates over the nonlinear BW process. This work provides a practicable technique to model linear QED processes via integrated QED-PIC simulations. Moreover, it calls for more attention to be paid to linear BW pair production in near future 10-PW-class laser-solid interactions., Comment: 8 pages, 3 figures

Existing score distillation methods are sensitive to classifier-free guidance (CFG) scale: manifested as over-smoothness or instability at small CFG scales, while over-saturation at large ones. To explain and analyze these issues, we revisit the derivation of Score Distillation Sampling (SDS) and decipher existing score distillation with the Wasserstein Generative Adversarial Network (WGAN) paradigm. With the WGAN paradigm, we find that existing score distillation either employs a fixed sub-optimal discriminator or conducts incomplete discriminator optimization, resulting in the scale-sensitive issue. We propose the Adversarial Score Distillation (ASD), which maintains an optimizable discriminator and updates it using the complete optimization objective. Experiments show that the proposed ASD performs favorably in 2D distillation and text-to-3D tasks against existing methods. Furthermore, to explore the generalization ability of our WGAN paradigm, we extend ASD to the image editing task, which achieves competitive results. The project page and code are at https://github.com/2y7c3/ASD., Comment: CVPR 2024

After the successful fusion ignition at National Ignition Facility, seeking for a high-gain fusion scheme becomes the next hot-spot in inertial confinement fusion community. Fast ignition provides an alternative due to its potential to reduce the energy of driven lasers and achieve higher target gain, whose core step is generating fast electron beam using picosecond lasers. The properties of the electron beam, such as energy spectra, determines the succeed heating process and the yield. In this study, with 2D particle-in-cell simulations, we find that the energy transfer ratio would significantly increase, and the energy spectra would be lifted up in the dual-color injecting scheme, where an extra weak low-frequency laser is injected with the main pulse. These phenomena are attributed to the longitudinal electric field modulation in low-density region and electromagnetically-induced-transparency process in the microchannels formed near the critical surface. Our results can be applied to fast ignition schemes and experimental designs of super-hot electron generation with different pulse durations. For example, in the DCI project with a fast ignition scheme, such a dual-color intense picosecond laser facility is under construction to control the fast electron generation and enhance the laser transparency., Comment: 24 pages, 8 figures

Relativistic positron sources with high spin polarization have important applications in nuclear and particle physics and many frontier fields. However, it is challenging to produce dense polarized positrons. Here we present a simple and effective method to achieve such a positron source by directly impinging a relativistic high-density electron beam on the surface of a solid target. During the interaction, a strong return current of plasma electrons is induced and subsequently asymmetric quasistatic magnetic fields as high as megatesla are generated along the target surface. This gives rise to strong radiative spin flips and multiphoton processes, thus leading to efficient generation of copious polarized positrons. With three-dimensional particle-in-cell simulations, we demonstrate the production of a dense highly-polarized multi-GeV positron beam with an average spin polarization above 40% and nC-scale charge per shot. This offers a novel route for the studies of laserless strong-field quantum electrodynamics physics and for the development of high-energy polarized positron sources.

It is very difficult and important to construct Bell inequalities for n-partite, k-settings of measurement, and d-dimensional (n,k,d) systems. Inspired by the iteration formula form of the Mermin-Ardehali-Belinski{\u{\i}}-Klyshko (MABK) inequality, we generalize the multi-component correlation functions for bipartite d-dimensional systems to n-partite ones, and construct the corresponding Bell inequality. The Collins-Gisin-Linden-Massar-Popescu inequality can be reproduced by this way. The most important result is that for prime d the general Bell function in full-correlated multi-component correlation function form for (n,2,d) systems can be reformulated in iteration formula by two full-correlated multi-component Bell functions for (n-1,2,d) systems. As applications, we recover the MABK inequality and the most robust coincidence Bell inequalities for (3,2,3),(4,2,3),(5,2,3), and (3,2,5) Bell scenarios with this iteration formula. This implies that the iteration formula is an efficient way of constructing multi-partite Bell inequalities. In addition, we also give some new Bell inequalities with the same robustness but inequivalent to the known ones.

With the insight of variance-bias decomposition, we design a new hybrid bagging-boosting algorithm named SBPMT for classification problems. For the boosting part of SBPMT, we propose a new tree model called Probit Model Tree (PMT) as base classifiers in AdaBoost procedure. For the bagging part, instead of subsampling from the dataset at each step of boosting, we perform boosted PMTs on each subagged dataset and combine them into a powerful "committee", which can be viewed an incomplete U-statistic. Our theoretical analysis shows that (1) SBPMT is consistent under certain assumptions, (2) Increase the subagging times can reduce the generalization error of SBPMT to some extent and (3) Large number of ProbitBoost iterations in PMT can benefit the performance of SBPMT with fewer steps in the AdaBoost part. Those three properties are verified by a famous simulation designed by Mease and Wyner (2008). The last two points also provide a useful guidance in model tuning. A comparison of performance with other state-of-the-art classification methods illustrates that the proposed SBPMT algorithm has competitive prediction power in general and performs significantly better in some cases.