Cyclic P\'olya Ensembles on the Unitary Matrices and their Spectral Statistics

The framework of spherical transforms and P\'olya ensembles is of utility in deriving structured analytic results for sums and products of random matrices in a unified way. In the present work, we will carry over this framework to study products of unitary matrices. Those are not distributed via the Haar measure, but still are drawn from distributions where the eigenvalue and eigenvector statistics factorise. They include the circular Jacobi ensemble, known in relation to the Fisher-Hartwig singularity in the theory of Toeplitz determinants, as well as the heat kernel for Brownian motion on the unitary group. We define cyclic P\'olya frequency functions and show their relation to the cyclic P\'olya ensembles, give a uniqueness statement for the corresponding weights, and derive the determinantal point processes of the eigenvalue statistics at fixed matrix dimension. An outline is given of problems one may encounter when investigating the local spectral statistics

Modular development of deep potential for complex solid solutions

The multicomponent oxide solid solution is a versatile platform to tune the delicate balance between competing spin, charge, orbital, and lattice degrees of freedom for materials design and discovery. The development of compositionally complex oxides with superior functional properties has been largely empirical and serendipitous, in part due to the exceedingly complex chemistry and structure of solid solutions that span a range of length scales. The classical molecular dynamics (MD), as a powerful statistical method to investigate materials properties over large spatial and temporal scales, often plays a secondary role in computer-aided materials discovery because of the limited availability and accuracy of classical force fields. Here, we introduce the strategy of ``modular developing deep potential" (ModDP) that enables a systematic development and improvement of deep neural network-based model potential, termed as deep potential, for complex solid solutions with minimum human intervention. The converged training database associated with an end-member material is treated as an independent module and is reused to train the deep potential of solid solutions via a concurrent learning procedure. We apply ModDP to obtain classical force fields of two technologically important solid solutions, Pb$_x$Sr$_{1-x}$TiO$_3$ and Hf$_x$Zr$_{1-x}$O$_2$. For both materials systems, a single model potential is capable of predicting various properties of solid solutions including temperature-driven and composition-driven phase transitions over a wide range of compositions. In particular, the deep potential of Pb$_x$Sr$_{1-x}$TiO$_3$ reproduces a few known topological textures such as polar vortex lattice and electric dipole waves in PbTiO$_3$/SrTiO$_3$ superlattices, paving the way for MD investigations on the dynamics of topological structures in response to external stimuli.Comment: 32 pages, 9 figure

Causal-Based Supervision of Attention in Graph Neural Network: A Better and Simpler Choice towards Powerful Attention

Recent years have witnessed the great potential of attention mechanism in graph representation learning. However, while variants of attention-based GNNs are setting new benchmarks for numerous real-world datasets, recent works have pointed out that their induced attentions are less robust and generalizable against noisy graphs due to lack of direct supervision. In this paper, we present a new framework which utilizes the tool of causality to provide a powerful supervision signal for the learning process of attention functions. Specifically, we estimate the direct causal effect of attention to the final prediction, and then maximize such effect to guide attention attending to more meaningful neighbors. Our method can serve as a plug-and-play module for any canonical attention-based GNNs in an end-to-end fashion. Extensive experiments on a wide range of benchmark datasets illustrated that, by directly supervising attention functions, the model is able to converge faster with a clearer decision boundary, and thus yields better performances

A universal interatomic potential for perovskite oxides

With their celebrated structural and chemical flexibility, perovskite oxides have served as a highly adaptable material platform for exploring emergent phenomena arising from the interplay between different degrees of freedom. Molecular dynamics (MD) simulations leveraging classical force fields, commonly depicted as parameterized analytical functions, have made significant contributions in elucidating the atomistic dynamics and structural properties of crystalline solids including perovskite oxides. However, the force fields currently available for solids are rather specific and offer limited transferability, making it time-consuming to use MD to study new materials systems since a new force field must be parameterized and tested first. The lack of a generalized force field applicable to a broad spectrum of solid materials hinders the facile deployment of MD in computer-aided materials discovery (CAMD). Here, by utilizing a deep-neural network with a self-attention scheme, we have developed a unified force field that enables MD simulations of perovskite oxides involving 14 metal elements and conceivably their solid solutions with arbitrary compositions. Notably, isobaric-isothermal ensemble MD simulations with this model potential accurately predict the experimental phase transition sequences for several markedly different ferroelectric oxides, including a 6-element ternary solid solution, Pb(In$_{1/2}$Nb$_{1/2}$)O$_3$--Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$--PbTiO$_3$. We believe the universal interatomic potential along with the training database, proposed regression tests, and the auto-testing workflow, all released publicly, will pave the way for a systematic improvement and extension of a unified force field for solids, potentially heralding a new era in CAMD.Comment: 18 pages, 4 figure

Robust Quadrupedal Locomotion via Risk-Averse Policy Learning

The robustness of legged locomotion is crucial for quadrupedal robots in challenging terrains. Recently, Reinforcement Learning (RL) has shown promising results in legged locomotion and various methods try to integrate privileged distillation, scene modeling, and external sensors to improve the generalization and robustness of locomotion policies. However, these methods are hard to handle uncertain scenarios such as abrupt terrain changes or unexpected external forces. In this paper, we consider a novel risk-sensitive perspective to enhance the robustness of legged locomotion. Specifically, we employ a distributional value function learned by quantile regression to model the aleatoric uncertainty of environments, and perform risk-averse policy learning by optimizing the worst-case scenarios via a risk distortion measure. Extensive experiments in both simulation environments and a real Aliengo robot demonstrate that our method is efficient in handling various external disturbances, and the resulting policy exhibits improved robustness in harsh and uncertain situations in legged locomotion. Videos are available at https://risk-averse-locomotion.github.io/.Comment: 8 pages, 5 figure

Therapeutic effects and mechanism of Atractylodis rhizoma in acute lung injury: Investigation based on an Integrated approach

Acute lung injury (ALI) is characterized by an excessive inflammatory response. Atractylodes lancea (Thunb.) DC. is a traditional chinese medicine with good anti-inflammatory activity that is commonly used clinically for the treatment of lung diseases in China; however, its mechanism of against ALI is unclear. We clarified the therapeutic effects of ethanol extract of Atractylodis rhizoma (EEAR) on lipopolysaccharide (LPS)-induced ALI by evaluation of hematoxylin-eosin (HE) stained sections, the lung wet/dry (W/D) ratio, and levels of inflammatory factors as indicators. We then characterized the chemical composition of EEAR by ultra-performance liquid chromatography and mass spectrometry (UPLC-MS) and screened the components and targets by network pharmacology to clarify the signaling pathways involved in the therapeutic effects of EEAR on ALI, and the results were validated by molecular docking simulation and Western blot (WB) analysis. Finally, we examined the metabolites in rat lung tissues by gas chromatography and mass spectrometry (GC-MS). The results showed that EEAR significantly reduced the W/D ratio, and tumor necrosis factor-α (TNF-α), interleukin-1 beta (IL-1β), interleukin-6 (IL-6) levels in the lungs of ALI model rats. Nineteen components of EEAR were identified and shown to act synergetically by regulating shared pathways such as the mitogen-activated protein kinase (MAPK) and phosphoinositide 3-kinase (PI3K)-protein kinase B (AKT) signaling pathways. Ferulic acid, 4-methylumbelliferone, acetylatractylodinol, atractylenolide I, and atractylenolide III were predicted to bind well to PI3K, AKT and MAPK1, respectively, with binding energies < -5 kcal/mol, although only atractylenolide II bound with high affinity to MAPK1. EEAR significantly inhibited the phosphorylation of PI3K, AKT, p38, and ERK1/2, thus reducing protein expression. EEAR significantly modulated the expression of metabolites such as D-Galactose, D-Glucose, serine and D-Mannose. These metabolites were mainly concentrated in the galactose and amino acid metabolism pathways. In conclusion, EEAR alleviates ALI by inhibiting activation of the PI3K-AKT and MAPK signaling pathways and regulating galactose metabolism, providing a new direction for the development of drugs to treat ALI

Continuous and Discrete-Time Optimal Controls for an Isolated Signalized Intersection

A classical control problem for an isolated oversaturated intersection is revisited with a focus on the optimal control policy to minimize total delay. The difference and connection between existing continuous-time planning models and recently proposed discrete-time planning models are studied. A gradient descent algorithm is proposed to convert the optimal control plan of the continuous-time model to the plan of the discrete-time model in many cases. Analytic proof and numerical tests for the algorithm are also presented. The findings shed light on the links between two kinds of models

Proliferation-Attenuating and Apoptosis-Inducing Effects of Tryptanthrin on Human Chronic Myeloid Leukemia K562 Cell Line in Vitro

Tryptanthrin, a kind of indole quinazoline alkaloid, has been shown to exhibit anti-microbial, anti-inflammation and anti-tumor effects both in vivo and in vitro. However, its biological activity on human chronic myeloid leukemia cell line K562 is not fully understood. In the present study, we investigated the proliferation-attenuating and apoptosis-inducing effects of tryptanthrin on leukemia K562 cells in vitro and explored the underlying mechanisms. The results showed that tryptanthrin could significantly inhibit K562 cells proliferation in a time- and dose-dependent manner as evidenced by MTT assay and flow cytometry analysis. We also observed pyknosis, chromatin margination and the formation of apoptotic bodies in the presence of tryptanthrin under the electron microscope. Nuclei fragmentation and condensation by Hoechst 33258 staining were detected as well. The amount of apoptotic cells significantly increased whereas the mitochondrial membrane potential decreased dramatically after tryptanthrin exposure. K562 cells in the tryptanthrin treated group exhibited an increase in cytosol cyt-c, Bax and activated caspase-3 expression while a decrease in Bcl-2, mito cyt-c and pro-caspase-3 contents. However, the changes of pro-caspase-3 and activated caspase-3 could be abolished by a pan-caspase inhibitor ZVAD-FMK. These results suggest that tryptanthrin has proliferation-attenuating and apoptosis-inducing effects on K562 cells. The underlying mechanism is probably attributed to the reduction in mitochondria membrane potential, the release of mito cyt-c and pro-caspase-3 activation