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We extend the result on the top eigenvalue of the i.i.d.\ matrix with fixed perturbations by Tao to random perturbations. In particular, we consider a setup that $\mathbf{M}=\mathbf{W}+\lambda\mathbf{u}\mathbf{u}^*$ with $\mathbf{W}$ drawn from a Ginibre Orthogonal Ensemble and the perturbation $\mathbf{u}$ drawn uniformly from $\mathcal{S}^{d-1}$. We provide several asymptotic properties about the eigenvalues and the top eigenvector of the random matrix, which can not be obtained trivially from the deterministic perturbation case. We also apply our results to extend the work of Max Simchowitz, which provides an optimal lower bound for approximating the eigenspace of a symmetric matrix. We present a \textit{query complexity} lower bound for approximating the eigenvector of any asymmetric but diagonalizable matrix $\mathbf{M}$ corresponding to the largest eigenvalue. We show that for every $\operatorname{gap}\in (0,1/2]$ and large enough dimension $d$, there exists a random matrix $\mathbf{M}$ with $\operatorname{gap}(\mathbf{M})=\Omega(\operatorname{gap})$, such that if a matrix-vector query product algorithm can identity a vector $\hat{\mathbf{v}}$ which satisfies $\left\|\hat{\mathbf{v}}-\mathbf{v}_1(\mathbf{M}) \right\|_2^2\le \operatorname{const}\times \operatorname{gap}$, it needs at least $\mathcal{O}\left(\frac{\log d}{\operatorname{gap}}\right)$ queries of matrix-vector products. In the inverse polynomial accuracy regime where $\epsilon \ge \frac{1}{\operatorname{poly}(d)}$, the complexity matches the upper bounds $\mathcal{O}\left(\frac{\log(d/\epsilon)}{\operatorname{gap}}\right)$, which can be obtained via the power method. As far as we know, it is the first lower bound for computing the eigenvector of an asymmetric matrix, which is far more complicated than in the symmetric case.

The two-dimensional (2D) homogeneous electron gas (HEG) is a fundamental model in quantum many-body physics. It is important to theoretical and computational studies, where exchange-correlation energies computed in it serve as the foundation for density-functional calculations. It is also of direct relevance to a variety of experimental settings, especially with the rapid recent growth in 2D materials and moir\'e systems. In these experiments, metallic gates are often present, which screen the Coulomb interaction between electrons. The effect of the screening can qualitatively change the behavior of the 2D HEG, and requires accurate many-body computations to capture. In this work, we perform state-of-the-art diffusion Monte Carlo (DMC) calculations in the 2D HEG subjected to symmetric dual-gate screening. We systematically compute the correlation energy across a range of densities and gate separations for both spin unpolarized and fully polarized systems. A global fit is obtained for the correlation energy, using these data and imposing various limiting behaviors obtained from perturbation analysis. The new functional will allow density-functional calculations to be performed for a variety of realistic experimental setups which can accurately account for the presence of gates. We also investigate how the gate screening affects the bulk modulus, pair correlation function, and the structure factor of the 2D HEG, which can potentially be probed in experiments., Comment: 11 pages, 7 figures in the main text

Precipitation nowcasting plays a pivotal role in socioeconomic sectors, especially in severe convective weather warnings. Although notable progress has been achieved by approaches mining the spatiotemporal correlations with deep learning, these methods still suffer severe blurriness as the lead time increases, which hampers accurate predictions for extreme precipitation. To alleviate blurriness, researchers explore generative methods conditioned on blurry predictions. However, the pairs of blurry predictions and corresponding ground truth need to be generated in advance, making the training pipeline cumbersome and limiting the generality of generative models within blur modes that appear in training data. By rethinking the blurriness in precipitation nowcasting as a blur kernel acting on predictions, we propose an unsupervised postprocessing method to eliminate the blurriness without the requirement of training with the pairs of blurry predictions and corresponding ground truth. Specifically, we utilize blurry predictions to guide the generation process of a pre-trained unconditional denoising diffusion probabilistic model (DDPM) to obtain high-fidelity predictions with eliminated blurriness. A zero-shot blur kernel estimation mechanism and an auto-scale denoise guidance strategy are introduced to adapt the unconditional DDPM to any blurriness modes varying from datasets and lead times in precipitation nowcasting. Extensive experiments are conducted on 7 precipitation radar datasets, demonstrating the generality and superiority of our method.

Ego-centric queries, focusing on a target vertex and its direct neighbors, are essential for various applications. Enabling such queries on graphs owned by mutually distrustful data providers, without breaching privacy, holds promise for more comprehensive results. In this paper, we propose GORAM, a graph-oriented data structure that enables efficient ego-centric queries on federated graphs with strong privacy guarantees. GORAM is built upon secure multi-party computation (MPC) and ensures that no single party can learn any sensitive information about the graph data or the querying keys during the process. However, achieving practical performance with privacy guaranteed presents a challenge. To overcome this, GORAM is designed to partition the federated graph and construct an Oblivious RAM(ORAM)-inspired index atop these partitions. This design enables each ego-centric query to process only a single partition, which can be accessed fast and securely. To evaluate the performance of GORAM, we developed a prototype querying engine on a real-world MPC framework. We conduct a comprehensive evaluation with five commonly used queries on both synthetic and real-world graphs. Our evaluation shows that all benchmark queries can be completed in just 58.1 milliseconds to 35.7 seconds, even on graphs with up to 41.6 million vertices and 1.4 billion edges. To the best of our knowledge, this represents the first instance of processing billion-scale graphs with practical performance on MPC.

Data assimilation is a vital component in modern global medium-range weather forecasting systems to obtain the best estimation of the atmospheric state by combining the short-term forecast and observations. Recently, AI-based data assimilation approaches have attracted increasing attention for their significant advantages over traditional techniques in terms of computational consumption. However, existing AI-based data assimilation methods can only handle observations with a specific resolution, lacking the compatibility and generalization ability to assimilate observations with other resolutions. Considering that complex real-world observations often have different resolutions, we propose the \textit{\textbf{Fourier Neural Processes}} (FNP) for \textit{arbitrary-resolution data assimilation} in this paper. Leveraging the efficiency of the designed modules and flexible structure of neural processes, FNP achieves state-of-the-art results in assimilating observations with varying resolutions, and also exhibits increasing advantages over the counterparts as the resolution and the amount of observations increase. Moreover, our FNP trained on a fixed resolution can directly handle the assimilation of observations with out-of-distribution resolutions and the observational information reconstruction task without additional fine-tuning, demonstrating its excellent generalization ability across data resolutions as well as across tasks.

The spin Coulomb drag effect, arising from the exchange of momentum between electrons of opposite spins, plays a crucial role in the spin transport of interacting electron systems. This effect leads to the emergence of a spin mass and the finite lifetime of spin currents, posing challenges for the accurate description of spin dynamics. Using the state-of-the-art Variational Diagrammatic Monte Carlo approach, we investigate the spin-resolved exchange-correlation (XC) kernel in the three-dimensional uniform electron gas. Our analysis reveals a distinct nature in the spin response, characterized by a $1/q^2$ divergence in the spin XC kernel at finite frequencies. This so-called ultranonlocal behavior, stemming from the spin Coulomb drag effect, is absent in the charge channel. By extracting precise values for the spin mass enhancement factor, we observe a trend of increasing enhancement with decreasing electron density. Furthermore, we find compelling evidence for the suppression of spin diffusion at low temperatures, characterized by vanishing inverse relaxation times. These findings deepen our understanding of the intricate relation between the Coulomb interaction and the spin transport, providing valuable insights for the development of accurate density functional approximations and the advancement of spintronics and quantum technologies., Comment: 8 pages, 5 figures

We present a generalization of the discrete Lehmann representation (DLR) to three-point correlation and vertex functions in imaginary time and Matsubara frequency. The representation takes the form of a linear combination of judiciously chosen exponentials in imaginary time, and products of simple poles in Matsubara frequency, which are universal for a given temperature and energy cutoff. We present a systematic algorithm to generate compact sampling grids, from which the coefficients of such an expansion can be obtained by solving a linear system. We show that the explicit form of the representation can be used to evaluate diagrammatic expressions involving infinite Matsubara sums, such as polarization functions or self-energies, with controllable, high-order accuracy. This collection of techniques establishes a framework through which methods involving three-point objects can be implemented robustly, with a substantially reduced computational cost and memory footprint.

Nonlocal effective interactions are inherent to non-relativistic quantum many-body systems, but their systematic resummation poses a significant challenge known as the ``vertex problem" in many-body perturbation theory. We introduce a renormalization scheme based on a projection-based renormalization condition that selectively resums the most essential nonlocal contributions to the effective interaction vertex, avoiding the computational complexity of the full vertex function. This enables us to derive a renormalized Feynman diagrammatic series with large parameters canceled by counter-diagrams, efficiently generated using a perturbative expansion of the parquet equations and computed using a diagrammatic Monte Carlo algorithm. Applying our approach to a 3D Yukawa Fermi liquid, we demonstrate that the renormalized perturbation theory remains predictive even in the strongly correlated regime and uncover significant sign cancellations between different channels contributing to the scattering amplitude. Our work establishes a novel framework for investigating strong correlations in quantum many-body systems, offering a systematic approach to explore nonlocal theories for challenging systems like the electron liquid in material science., Comment: 13 pages, 7 figures

We conducted an eye-tracking user study with 13 participants to investigate the influence of stimulus-question ordering and question modality on participants using visual question-answering (VQA) tasks. We examined cognitive load, task performance, and gaze allocations across five distinct experimental designs, aiming to identify setups that minimize the cognitive burden on participants. The collected performance and gaze data were analyzed using quantitative and qualitative methods. Our results indicate a significant impact of stimulus-question ordering on cognitive load and task performance, as well as a noteworthy effect of question modality on task performance. These findings offer insights for the experimental design of controlled user studies in visualization research., Comment: Accepted at ETVIS 2024

We present a time domain method to solve quantum scattering by an arbitrary potential of finite range. The scattering wave function in full space can be obtained, including the near field, the mid field (i.e. Fresnel region) and the far field. This is achieved by extending several techniques of FDTD computational electrodynamics into the quantum realm. The total-field/scattered-field scheme naturally incorporates the incidence source condition. The wave function in the internal model, including the interaction region and the close near field, is directly computed through PSTD/FDTD iterations. The quantum version of surface equivalence theorem is proven and links the wave function in the external free space to the PSTD/FDTD solution in the internal model. Parallel implementation of PSTD based on overlapping domain decomposition and FFT on local Fourier-basis is briefly discussed. These building blocks unite into a numerical system that provides a general, robust solver to potential scattering problems. Its accuracy is verified by the established partial wave method, by comparing the predictions of both on the central square potential scattering. Further investigations show the far-field solution is inadequate for simulating Fresnel-region effects.

We propose a computational graph representation of high-order Feynman diagrams in Quantum Field Theory (QFT), applicable to any combination of spatial, temporal, momentum, and frequency domains. Utilizing the Dyson-Schwinger and parquet equations, our approach effectively organizes these diagrams into a fractal structure of tensor operations, significantly reducing computational redundancy. This approach not only streamlines the evaluation of complex diagrams but also facilitates an efficient implementation of the field-theoretic renormalization scheme, crucial for enhancing perturbative QFT calculations. Key to this advancement is the integration of Taylor-mode automatic differentiation, a key technique employed in machine learning packages to compute higher-order derivatives efficiently on computational graphs. To operationalize these concepts, we develop a Feynman diagram compiler that optimizes diagrams for various computational platforms, utilizing machine learning frameworks. Demonstrating this methodology's effectiveness, we apply it to the three-dimensional uniform electron gas problem, achieving unprecedented accuracy in calculating the quasiparticle effective mass at metal density. Our work demonstrates the synergy between QFT and machine learning, establishing a new avenue for applying AI techniques to complex quantum many-body problems.

Surface roughness and dielectric properties are crucial in characterizing radar backscattering from bare soil surfaces. However, their estimation depends on the surface size of the sampling profile, and the complex relative permittivity is disturbed by different dielectric spectrum models. Hence, it is desirable to know how the uncertainty associated with roughness and complex relative permittivity propagates to radar backscattering coefficients. To identify the extent to which the uncertainty propagates, we examined the roughness sample variance and bias of complex relative permittivity. Then, we evaluated the error of radar backscattering coefficients as a function of incident angle, frequency, and polarization induced by each of the two uncertainty sources and their coupling. The results help interpret the discrepancy among model predictions and in-situ measurements and suggest a minimum surface size to estimate the RMS height and correlation length to confine the radar backscattering coefficients' error.

The weather forecasting system is important for science and society, and significant achievements have been made in applying artificial intelligence (AI) to medium-range weather forecasting. However, existing AI-based weather forecasting models rely on analysis or reanalysis products from traditional numerical weather prediction (NWP) systems as initial conditions for making predictions. Initial states are typically generated by traditional data assimilation components, which are computational expensive and time-consuming. Here we present an AI-based data assimilation model, i.e., Adas, for global weather variables. By introducing the confidence matrix, Adas employs gated convolution to handle sparse observations and gated cross-attention for capturing the interactions between the background and observations. Further, we combine Adas with the advanced AI-based forecasting model (i.e., FengWu) to construct the first end-to-end AI-based global weather forecasting system: FengWu-Adas. We demonstrate that Adas can assimilate global observations to produce high-quality analysis, enabling the system operate stably for long term. Moreover, we are the first to apply the methods to real-world scenarios, which is more challenging and has considerable practical application potential. We have also achieved the forecasts based on the analyses generated by AI with a skillful forecast lead time exceeding that of the IFS for the first time.

Investigating the implications of interlayer coupling on superconductivity is essential for comprehending the intrinsic mechanisms of high temperature superconductors. Van der Waals heterojunctions have attracted extensive research due to their exotic interlayer coupling. Here, we present a natural heterojunction superconductor of 6R-TaS2 that demonstrates a double-dome of superconductivity, in addition to, the reemergence of superconducting under high pressures. Our first principles calculation shows that the first dome of superconductivity in 6R-TaS2 can be attributed to changes in interlayer coupling and charge transfer. The second superconducting dome and the reemergence of superconductivity can be ascribed to changes in the density of states resulting from Fermi surface reconstruction, in which the DOS of T-layer and S p-orbitals play a crucial role. We have reported the first observation in TMDs that non-metallic atoms playing a dominant role in the reemergence of superconducting and the influence of two Lifshitz transitions on superconducting properties.

The planar grasshopper problem, originally introduced in (Goulko & Kent 2017 Proc. R. Soc. A 473, 20170494), is a striking example of a model with long-range isotropic interactions whose ground states break rotational symmetry. In this work we analyze and explain the nature of this symmetry breaking with emphasis on the importance of dimensionality. Interestingly, rotational symmetry is recovered in three dimensions for small jumps, which correspond to the non-isotropic cogwheel regime of the two-dimensional problem. We discuss simplified models that reproduce the symmetry properties of the original system in N dimensions. For the full grasshopper model in two dimensions we obtain quantitative predictions for optimal perturbations of the disk. Our analytical results are confirmed by numerical simulations., Comment: Ancillary files with animations of 3d shapes included

We study critical properties of the entanglement and charge-sharpening measurement-induced phase transitions in a non-unitary quantum circuit evolving with a U(1) conserved charge. Our numerical estimation of the critical properties of the entanglement transition at finite system sizes appears distinct from the generic non-conserving case and percolation. We provide two possible interpretations of this observation: (a) these two transitions occur at different measurement rates in the thermodynamic limit, but at finite system sizes their critical fans overlap and the critical exponents we probed here show a combination of both the criticality. Nonetheless, the multifractal properties of the entanglement transition remain distinct from the generic case without any symmetry, indicating a unique universality class due to the U(1) symmetry. (b) these two transitions occur at the same measurement rate at any length scale. Within this interpretation, our estimation of all the critical exponents are sharply different than the non-conserving case, again confirming the presence of a new universality class due U(1) symmetry. We compute entanglement critical exponents and correlation functions via various ancilla measures, use a transfer matrix for multifractality, and compute correlators associated with charge sharpening to explain these findings. Through these correlators, we also find evidence consistent with the charge-sharpening transition being of the Berezinskii-Kosterlitz-Thouless type (including the predicted ``jump'' in stiffness), which simultaneously argues for a broad critical fan for this transition. As a result, attempts to measure critical properties in this finite-size system will see anomalously large exponents predicted by our numerical analysis., Comment: 12+5 pages, 8+6 figures