In high-dimensional data analysis, testing the significance of certain features in a model often resorts to projecting data onto relevant linear subspaces, which intrinsically possess a separable covariance structure. This paper presents a unified approach to such inferences in high-dimensional scenarios via separable sample covariance matrices. Two classic likelihood ratio tests are explored: the first for assessing the significance of coefficients in a multivariate multiple linear regression model, and the second for testing the equality of several covariance matrices. Our results demonstrate that the limiting distributions of these test statistics differ significantly from the Gaussian case, depending both on the moment parameters of the population and on the eigenspaces of the projection matrices. Our methodology is based on a joint central limit theorem for linear spectral statistics of correlated separable sample covariance matrices.
Observing few-photon optomechanical effects remains a significant challenge in optomechanical systems. To investigate intrinsic radiation-pressure-induced nonlinear effects in the few-photon regime, it is essential to strengthen the interaction between a few photons and a finite number of phonons. In this work, we enhance the radiation-pressure nonlinearity by introducing a two-laser coherent driving scheme together with an enhanced cross-Kerr nonlinearity, resulting in a setup that can be effectively described within a circuit QED platform. By properly tuning the two driving laser fields and the cross-Kerr interaction so that the effective optomechanical coupling becomes real, we theoretically establish a symmetric optomechanical model in which the photon and phonon modes exhibit analogous fluctuation dynamics. Within this framework, we analyze the optimal reciprocal transport of the input laser field and identify the critical boundary associated with the onset of different coupling regimes. We also compare the optical signal scattering behavior in both dissipative equilibrium and nonequilibrium symmetric optomechanical systems, with and without non-rotating-wave contributions. Our work provides a controllable route to enhance optomechanical coupling, extending into the ultrastrong-coupling regime, and opens opportunities for exploring few-photon optomechanical effects.
Growing populations and food demand have driven cropland expansion, but this has resulted in a decline in soil quality and posed major threats to global biodiversity. Arbuscular mycorrhizal (AM) fungi form symbiotic associations with most terrestrial plants, enhancing the adaptive capacity of these plants in adverse environments and playing a crucial role in maintaining soil health. However, the global impact of land reclamation on AM fungi and its driving factors remains unclear, creating a critical knowledge gap for sustainable land use. Based on 501 paired observations from 94 publications, we conducted a global meta-analysis to explore the impacts of land reclamation on AM fungi and the roles of climate, vegetation types and agricultural management practices in this process. Land reclamation significantly reduced the AM fungal spore density (-50.98%), richness (-23.86%) and diversity (-8.41%). Compared with forest reclamation, grassland reclamation has a greater negative impact on AM fungi. Forest reclamation has a greater negative impact on AM fungi in areas with a mean annual precipitation of 1000-1500 mm and a mean annual temperature (MAT) >20 degrees C. Grassland reclamation has a greater negative impact on AM fungi in areas with MAT <8 degrees C. In addition, we found that in reclaimed cropland, crop rotation, no tillage and organic fertilizer application effectively alleviated the negative impact of land reclamation on AM fungi spore density and species richness. Although the increase of soil available phosphorus induced by land reclamation reduces AM fungal spore density and richness, climate factors have a higher explanatory power for AM fungal variation. Synthesis and applications. The present results suggest that sustainable land management strategies should consider the effect of local climate and vegetation types on AM fungi to support the development of local land use related policies. In addition, the use of beneficial management practices is crucial for protecting underground biodiversity and maintaining soil health. These findings highlight the influence of global land use changes on underground microbial function and diversity and provide valuable insights for sustainable land management practices for biodiversity conservation and ecosystem health maintenance.
In this paper, we investigate biphoton generation via spontaneous four-wave mixing in Doppler-broadened atomic vapors. Thermal motion breaks the zero-temperature symmetry between copropagating and counterpropagating geometries and introduces competition between the biphoton generation rate and propagation loss. A temperature-dependent pump-detuning scheme restores an approximate mirror symmetry between the frequency-resolved responses of the two geometries, yielding nearly identical biphoton generation rates and correlation strengths over a broad temperature range. We find that increasing atomic thermal velocity drives the temporal correlation function from damped oscillations at low temperatures to a purely exponential decay at higher temperatures by enhancing decoherence and pushing the effective Rabi frequency into the imaginary regime. This behavior is captured analytically through the temperature-dependent modification of the poles governing the oscillatory correlations. The generated biphotons retain strong nonclassical character, accompanied by spectral narrowing and temperature-induced temporal broadening. Numerical simulations incorporating Doppler averaging validate these predictions, quantify the model's accuracy, and confirm that the same qualitative trends persist at higher optical depths. These results identify a simple and tunable route to narrowband biphoton generation in warm vapors, with direct relevance to quantum memories and long-distance quantum communication.
The development of efficient, stable, and cost-effective single-atom catalysts (SACs) is crucial for advancing sustainable energy technologies such as water splitting and metal-air batteries. Two-dimensional (2D) metal phthalocyanine sheets (s-MPc) present a promising platform with their well-defined, high-density active sites, but comprehensive screening for their bifunctional catalytic activity and electrochemical stability is lacking. Herein, we conducted a systematic first-principles density functional theory (DFT) study to screen a series of s-MPc (M = Sc to Zn) as trifunctional electrocatalysts for the hydrogen evolution reaction (HER), oxygen evolution reaction (OER), and oxygen reduction reaction (ORR). Our stability analysis, based on formation energy, dissolution potential, and surface Pourbaix diagrams, identifies s-VPc, s-MnPc, s-FePc, s-CoPc, s-NiPc, and s-CuPc as electrochemically stable across all pH conditions. Catalysts' performance evaluation reveals distinct optimal candidates: s-MnPc and s-VPc exhibit superior HER activity with near-optimal hydrogen adsorption energies (Delta G H*), while s-VPc and s-CuPc demonstrated outstanding OER performance with low overpotentials of 0.41 and 0.49 V, respectively, rivaling IrO2. For the ORR, s-CoPc and s-MnPc emerge as the most active, with low overpotentials comparable to those of the Pt(111) surface. Consequently, we identify s-VPc as an excellent bifunctional catalyst for the HER/OER and s-CoPc and s-CuPc for the OER/ORR. Supervised machine learning (ML) is employed on a set of atomic and electronic descriptors to classify the efficiency of s-MPc sheets for the HER/OER/ORR, with the KNN model demonstrating superior predictive performance. This work not only highlights specific high-performance s-MPc candidates but also establishes a robust computational framework for the design and screening of durable, high-activity single-atom electrocatalysts.
