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Accurate crystal structure determination is critical across all scientific disciplines involving crystalline materials. However, solving and refining inorganic crystal structures from powder X-ray diffraction (PXRD) data is traditionally a labor-intensive and time-consuming process that demands substantial expertise. In this work, we introduce PXRDGen, an end-to-end neural network that determines crystal structures by learning joint structural distributions from experimentally stable crystals and their PXRD, producing atomically accurate structures refined through PXRD data. PXRDGen integrates a pretrained XRD encoder, a diffusion/flow-based structure generator, and a Rietveld refinement module, enabling the solution of structures with unparalleled accuracy in a matter of seconds. Evaluation on MP-20 inorganic dataset reveals a remarkable matching rate of 82% (1 sample) and 96% (20 samples) for valid compounds, with Root Mean Square Error (RMSE) approaching the precision limits of Rietveld refinement. PXRDGen effectively tackles key challenges in XRD, such as the precise localization of light atoms, differentiation of neighboring elements, and resolution of overlapping peaks. Overall, PXRDGen marks a significant advancement in the automated determination of crystal structures from powder diffraction data.

Learning to represent and simulate the dynamics of physical systems is a crucial yet challenging task. Existing equivariant Graph Neural Network (GNN) based methods have encapsulated the symmetry of physics, \emph{e.g.}, translations, rotations, etc, leading to better generalization ability. Nevertheless, their frame-to-frame formulation of the task overlooks the non-Markov property mainly incurred by unobserved dynamics in the environment. In this paper, we reformulate dynamics simulation as a spatio-temporal prediction task, by employing the trajectory in the past period to recover the Non-Markovian interactions. We propose Equivariant Spatio-Temporal Attentive Graph Networks (ESTAG), an equivariant version of spatio-temporal GNNs, to fulfill our purpose. At its core, we design a novel Equivariant Discrete Fourier Transform (EDFT) to extract periodic patterns from the history frames, and then construct an Equivariant Spatial Module (ESM) to accomplish spatial message passing, and an Equivariant Temporal Module (ETM) with the forward attention and equivariant pooling mechanisms to aggregate temporal message. We evaluate our model on three real datasets corresponding to the molecular-, protein- and macro-level. Experimental results verify the effectiveness of ESTAG compared to typical spatio-temporal GNNs and equivariant GNNs., Comment: The paper has been published to the conference of NeurIPS 2023

In this paper, we prove in a very weak regularity setting existence and uniqueness of quasi-stationary distributions as well as exponential convergence towards the quasi-stationary distribution for the generalized Langevin and the Nos{\'e}-Hoover processes, two processes which are widely used in molecular dynamics. The case of singular potentials is considered. With the techniques used in this work, we are also able to greatly improve existing results on quasi-stationary distributions for the kinetic Langevin process to a weak regularity setting.

Geometric graph is a special kind of graph with geometric features, which is vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections, making them ineffectively processed by current Graph Neural Networks (GNNs). To tackle this issue, researchers proposed a variety of Geometric Graph Neural Networks equipped with invariant/equivariant properties to better characterize the geometry and topology of geometric graphs. Given the current progress in this field, it is imperative to conduct a comprehensive survey of data structures, models, and applications related to geometric GNNs. In this paper, based on the necessary but concise mathematical preliminaries, we provide a unified view of existing models from the geometric message passing perspective. Additionally, we summarize the applications as well as the related datasets to facilitate later research for methodology development and experimental evaluation. We also discuss the challenges and future potential directions of Geometric GNNs at the end of this survey.

In the paper, we introduce the maximum entropy estimator based on 2-dimensional empirical distribution of the observation sequence of hidden Markov model , when the sample size is big: in that case computing the maximum likelihood estimator is too consuming in time by the classical Baum-Welch EM algorithm. We prove the consistency and the asymptotic normality of the maximum entropy estimator in a quite general framework, where the asymptotic covariance matrix is explicitly estimated in terms of the 2-dimensional Fisher information. To complement it, the 2-dimensional relative entropy is skillfully used to study the hypotheses testing problem. Furthermore, we propose 2-dimensional maximum entropy algorithm for finding the maximum entropy estimator, which works for very large observation dataset and large hidden states set. Some numerical examples are furnished and commented for illustrating our theoretical results.

Taiji-1 is the first technology demonstration satellite of the Taiji program of China's space-borne gravitational wave antenna. After the demonstration of the key individual technologies, Taiji-1 continues collecting the data of the precision orbit determinations, satellite attitudes, and non-conservative forces exerted on the S/C. Therefore, during its free-fall, Taiji-1 can be viewed as operating in the high-low satellite-to-satellite tracking mode of a gravity recovery mission. In this work, we have selected and analyzed the one month data from Taiji-1's observations, and developed the techniques to resolve the long term interruptions and disturbances in the data due to the scheduled technology demonstration experiments. The first global gravity model \texttt{TJGM-r1911}, that independently derived from China's own satellite mission, is successfully built from Taiji-1's observations. Compared with gravity models from CHAMP and other satellite gravity missions, the accuracy discrepancies exist, which is mainly caused by the data discontinuity problem. As the extended free-falling phase been approved, Taiji-1 could serve as a gravity recovery mission for China since 2022 and it will provide us the independent measurement of both the static and the monthly time-variable global gravity field., Comment: 17 pages, 15 figures

Robust and accurate nuclei centroid detection is important for the understanding of biological structures in fluorescence microscopy images. Existing automated nuclei localization methods face three main challenges: (1) Most of object detection methods work only on 2D images and are difficult to extend to 3D volumes; (2) Segmentation-based models can be used on 3D volumes but it is computational expensive for large microscopy volumes and they have difficulty distinguishing different instances of objects; (3) Hand annotated ground truth is limited for 3D microscopy volumes. To address these issues, we present a scalable approach for nuclei centroid detection of 3D microscopy volumes. We describe the RCNN-SliceNet to detect 2D nuclei centroids for each slice of the volume from different directions and 3D agglomerative hierarchical clustering (AHC) is used to estimate the 3D centroids of nuclei in a volume. The model was trained with the synthetic microscopy data generated using Spatially Constrained Cycle-Consistent Adversarial Networks (SpCycleGAN) and tested on different types of real 3D microscopy data. Extensive experimental results demonstrate that our proposed method can accurately count and detect the nuclei centroids in a 3D microscopy volume.

Deep learning methods have been widely applied to visual and acoustic technology. In this paper, we proposed an odor labeling convolutional encoder-decoder (OLCE) for odor identification in machine olfaction. OLCE composes a convolutional neural network encoder and decoder where the encoder output is constrained to odor labels. An electronic nose was used for the data collection of gas responses followed by a normative experimental procedure. Several evaluation indexes were calculated to evaluate the algorithm effectiveness: accuracy 92.57%, precision 92.29%, recall rate 92.06%, F1-Score 91.96%, and Kappa coefficient 90.76%. We also compared the model with some algorithms used in machine olfaction. The comparison result demonstrated that OLCE had the best performance among these algorithms. In the paper, some perspectives of machine olfactions have been also discussed.

In this paper, we investigate gradient estimate of the Poisson equation and the exponential convergence in the Wasserstein metric $W_{1,d_{l^1}}$, uniform in the number of particles, and uniform-in-time propagation of chaos for the mean-field weakly interacting particle system related to McKean-Vlasov equation. By means of the known approximate componentwise reflection coupling and with the help of some new cost function, we obtain explicit estimates for those three problems, avoiding the technical conditions in the known results. Our results apply when the confinement potential $V$ has many wells, the interaction potential $W$ has bounded second mixed derivative $\nabla^2_{xy}W$ which should be not too big so that there is no phase transition. As an application, we obtain the concentration inequality of the mean-field interacting particle system with explicit and sharp constants, uniform in time. Several examples are provided to illustrate the results.

If Poincar{\'e} inequality has been studied by Bobkov for radial measures, few is known about the logarithmic Sobolev inequalty in the radial case. We try to fill this gap here using different methods: Bobkov's argument and super-Poincar{\'e} inequalities, direct approach via L1-logarithmic Sobolev inequalities. We also give various examples where the obtained bounds are quite sharp. Recent bounds obtained by Lee-Vempala in the logconcave bounded case are refined for radial measures.

We study the long time behaviour of the kinetic Fokker-Planck equation with mean field interaction, whose limit is often called Vlasov-Fkker-Planck equation. We prove a uniform (in the number of particles) exponential convergence to equilibrium for the solutions in the weighted Sobolev space H 1 ($\mu$) with a rate of convergence which is explicitly computable and independent of the number of particles. The originality of the proof relies on functional inequalities and hypocoercivity with Lyapunov type conditions, usually not suitable to provide adimensional results.

In this paper we establish some explicit and sharp estimates of the spectral gap and the log-Sobolev constant for mean field particles system, uniform in the number of particles, when the confinement potential have many local minimums. Our uniform log-Sobolev inequality, based on Zegarlinski's theorem for Gibbs measures, allows us to obtain the exponential convergence in entropy of the McKean-Vlasov equation with an explicit rate constant, generalizing the result of [10] by means of the displacement convexity approach, or [19, 20] by Bakry-Emery technique or the recent [9] by dissipation of the Wasserstein distance.

In this paper, we show that the Ricci curvature lower bound in Ollivier's Wasserstein metric sense of a continuous time jumping Markov process on a graph can be characterized by some optimal coupling generator and provide the construction of this latter. Some previous results of Ollivier for discrete time Markov chains are generalized to the actual continuous time case. We propose a comparison technique with some death-birth process on $\mathbb N$ to obtain some explicit exponential convergence rate, by modifying the metric. A counterpart of Zhong-Yang's estimate is established in the case where the Ricci curvature with repsect to the graph metric is nonnegative. Moreover we show that the Lyapunov function method for the exponential convergence works with some explicit quantitative estimates, once if the Ricci curvature is bounded from below by a negative constant. Finally we present applications to Glauder dynamics under some dynamical versions of the Dobrushin uniqueness condition or of the Dobrushin-Shlosman analyticity condition.