Dirac-boson stars

In this paper, we construct \textit{Dirac-boson stars} (DBSs) model composed of a scalar field and two Dirac fields. The scalar field and both Dirac fields are in the ground state. We consider the solution families of the DBSs for the synchronized frequency $\tilde{\omega}$ and the nonsynchronized frequency $\tilde{\omega}_D$ cases, respectively. We find several different solutions when the Dirac mass $\tilde{\mu}_D$ and scalar field frequency $\tilde{\omega}_S$ are taken in some particular ranges. In contrast, no similar case has been found in previous studies of multistate boson stars. Moreover, we discuss the characteristics of each type of solution family of the DBSs and present the relationship between the ADM mass $M$ of the DBSs and the synchronized frequency $\tilde{\omega}$ or the nonsynchronized frequency $\tilde{\omega}_D$. Finally, we calculate the binding energy $E_B$ of the DBSs and investigate the relationship of $E_B$ with the synchronized frequency $\tilde{\omega}$ or the nonsynchronized frequency $\tilde{\omega}_D$.Comment: 26 pages, 12 figure

Verifying Safety of Neural Networks from Topological Perspectives

Neural networks (NNs) are increasingly applied in safety-critical systems such as autonomous vehicles. However, they are fragile and are often ill-behaved. Consequently, their behaviors should undergo rigorous guarantees before deployment in practice. In this paper, we propose a set-boundary reachability method to investigate the safety verification problem of NNs from a topological perspective. Given an NN with an input set and a safe set, the safety verification problem is to determine whether all outputs of the NN resulting from the input set fall within the safe set. In our method, the homeomorphism property and the open map property of NNs are mainly exploited, which establish rigorous guarantees between the boundaries of the input set and the boundaries of the output set. The exploitation of these two properties facilitates reachability computations via extracting subsets of the input set rather than the entire input set, thus controlling the wrapping effect in reachability analysis and facilitating the reduction of computation burdens for safety verification. The homeomorphism property exists in some widely used NNs such as invertible residual networks (i-ResNets) and Neural ordinary differential equations (Neural ODEs), and the open map is a less strict property and easier to satisfy compared with the homeomorphism property. For NNs establishing either of these properties, our set-boundary reachability method only needs to perform reachability analysis on the boundary of the input set. Moreover, for NNs that do not feature these properties with respect to the input set, we explore subsets of the input set for establishing the local homeomorphism property and then abandon these subsets for reachability computations. Finally, some examples demonstrate the performance of the proposed method.Comment: 25 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:2210.0417

Safety Verification for Neural Networks Based on Set-boundary Analysis

Neural networks (NNs) are increasingly applied in safety-critical systems such as autonomous vehicles. However, they are fragile and are often ill-behaved. Consequently, their behaviors should undergo rigorous guarantees before deployment in practice. In this paper we propose a set-boundary reachability method to investigate the safety verification problem of NNs from a topological perspective. Given an NN with an input set and a safe set, the safety verification problem is to determine whether all outputs of the NN resulting from the input set fall within the safe set. In our method, the homeomorphism property of NNs is mainly exploited, which establishes a relationship mapping boundaries to boundaries. The exploitation of this property facilitates reachability computations via extracting subsets of the input set rather than the entire input set, thus controlling the wrapping effect in reachability analysis and facilitating the reduction of computation burdens for safety verification. The homeomorphism property exists in some widely used NNs such as invertible NNs. Notable representations are invertible residual networks (i-ResNets) and Neural ordinary differential equations (Neural ODEs). For these NNs, our set-boundary reachability method only needs to perform reachability analysis on the boundary of the input set. For NNs which do not feature this property with respect to the input set, we explore subsets of the input set for establishing the local homeomorphism property, and then abandon these subsets for reachability computations. Finally, some examples demonstrate the performance of the proposed method.Comment: 19 pages, 7 figure

A GPU-Accelerated Moving-Horizon Algorithm for Training Deep Classification Trees on Large Datasets

Decision trees are essential yet NP-complete to train, prompting the widespread use of heuristic methods such as CART, which suffers from sub-optimal performance due to its greedy nature. Recently, breakthroughs in finding optimal decision trees have emerged; however, these methods still face significant computational costs and struggle with continuous features in large-scale datasets and deep trees. To address these limitations, we introduce a moving-horizon differential evolution algorithm for classification trees with continuous features (MH-DEOCT). Our approach consists of a discrete tree decoding method that eliminates duplicated searches between adjacent samples, a GPU-accelerated implementation that significantly reduces running time, and a moving-horizon strategy that iteratively trains shallow subtrees at each node to balance the vision and optimizer capability. Comprehensive studies on 68 UCI datasets demonstrate that our approach outperforms the heuristic method CART on training and testing accuracy by an average of 3.44% and 1.71%, respectively. Moreover, these numerical studies empirically demonstrate that MH-DEOCT achieves near-optimal performance (only 0.38% and 0.06% worse than the global optimal method on training and testing, respectively), while it offers remarkable scalability for deep trees (e.g., depth=8) and large-scale datasets (e.g., ten million samples).Comment: 36 pages (13 pages for the main body, 23 pages for the appendix), 7 figure

Linking nutrient strategies with plant size along a grazing gradient: Evidence from Leymus chinensis in a natural pasture

AbstractStudying the changes in nutrient use strategies induced by grazing can provide insight into the process of grassland degradation and is important for improving grassland quality and enhancing ecosystem function. Dominant species in meadow steppe can optimize their use of limiting resources; however, the regulation of nutrient use strategies across grazing gradients is not fully understood. Therefore, in this study, we report an in situ study in which the impact of grazing rates on nutrient use strategies of Leymus chinensis, the dominant plant species in eastern Eurasian temperate steppes, was investigated. We conducted a large randomized controlled experiment (conducted continuously for five years in grassland plots in a natural pasture in Hailar, eastern Mongolia Plateau, China) to assess the effects of grazing rate treatments (0.00, 0.23, 0.34, 0.46, 0.69, and 0.92 adult cattle unit (AU) ha−1) on L. chinensis along a grazing gradient and employed a random sampling approach to compare the accumulation, allocation, and stoichiometry of C, N, and P in leaves and stems. Our findings demonstrated the follows: (i) The height of L. chinensis decreased with an increase in the grazing gradient, and the concentrations of C, N, and P significantly increased; (ii) the accumulation of C, N, and P per individual was negatively correlated with the concentration of aboveground tissues, suggesting that there was a tradeoff in L. chinensis between nutrient accumulation and concentration at the individual scale; (iii) the leaf-to-stem ratio of C, N, and P accumulation increased with grazing intensity, indicating a tradeoff in nutrient allocation and plant size at the individual plant level; and (iv) grazing rates were negatively correlated with the ratios of C:N and C:P in the stem; however, these ratios in leaves significantly increased with grazing intensity. Our findings suggest that L. chinensis in meadow steppe adapts to grazing disturbance through tradeoffs between plant size and nutrient use strategies. Moreover, our results imply that grazing produces a compensatory effect on nutrient use efficiency between the stems and leaves of L. chinensis

Generation of γ\gamma photons with extremely large orbital angular momenta

Vortex $\gamma$ photons, which carry large intrinsic orbital angular momenta (OAM), have significant applications in nuclear, atomic, hadron, particle and astro-physics, but their production remains unclear. In this work, we investigate the generation of such photons from nonlinear Compton scattering of circularly polarized monochromatic lasers on vortex electrons. We develop a quantum radiation theory for ultrarelativistic vortex electrons in lasers by using the harmonics expansion and spin eigenfunctions, which allows us to explore the kinematical characteristics, angular momentum transfer mechanisms, and formation conditions of vortex $\gamma$ photons. The multiphoton absorption of electrons enables the vortex $\gamma$ photons, with fixed polarizations and energies, to exist in mixed states comprised of multiple harmonics. Each harmonic represents a vortex eigenmode and has transverse momentum broadening due to transverse momenta of the vortex electrons. The large topological charges associated with vortex electrons offer the possibility for $\gamma$ photons to carry adjustable OAM quantum numbers from tens to thousands of units, even at moderate laser intensities. $\gamma$ photons with large OAM and transverse coherence length can assist in influencing quantum selection rules and extracting phase of the scattering amplitude in scattering processes.Comment: 7 pages, 4 figure

Transcriptional regulation of SlPYL, SlPP2C, and SlSnRK2 gene families encoding ABA signal core components during tomato fruit development and drought stress

In order to characterize the potential transcriptional regulation of core components of abscisic acid (ABA) signal transduction in tomato fruit development and drought stress, eight SlPYL (ABA receptor), seven SlPP2C (type 2C protein phosphatase), and eight SlSnRK2 (subfamily 2 of SNF1-related kinases) full-length cDNA sequences were isolated from the tomato nucleotide database of NCBI GenBank. All SlPYL, SlPP2C, and SlSnRK2 genes obtained are homologous to Arabidopsis AtPYL, AtPP2C, and AtSnRK2 genes, respectively. Based on phylogenetic analysis, SlPYLs and SlSnRK2s were clustered into three subfamilies/subclasses, and all SlPP2Cs belonged to PP2C group A. Within the SlPYL gene family, SlPYL1, SlPYL2, SlPYL3, and SlPYL6 were the major genes involved in the regulation of fruit development. Among them, SlPYL1 and SlPYL2 were expressed at high levels throughout the process of fruit development and ripening; SlPYL3 was strongly expressed at the immature green (IM) and mature green (MG) stages, while SlPYL6 was expressed strongly at the IM and red ripe (RR) stages. Within the SlPP2C gene family, the expression of SlPP2C, SlPP2C3, and SlPP2C4 increased after the MG stage; SlPP2C1 and SlPP2C5 peaked at the B3 stage, while SlPP2C2 and SlPP2C6 changed little during fruit development. Within the SlSnRK2 gene family, the expression of SlSnRK2.2, SlSnRK2.3, SlSnRK2.4, and SlSnRK2C was higher than that of other members during fruit development. Additionally, most SlPYL genes were down-regulated, while most SlPP2C and SlSnRK2 genes were up-regulated by dehydration in tomato leaf