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Atomic structure analysis of crystalline materials is a paramount endeavor in both chemical and material sciences. This sophisticated technique necessitates not only a solid foundation in crystallography but also a profound comprehension of the intricacies of the accompanying software, posing a significant challenge in meeting the rigorous daily demands. For the first time, we confront this challenge head-on by harnessing the power of deep learning for ultra-precise structural analysis at the full-atom level. To validate the performance of the model, named CrystalX, we employed a vast dataset comprising over 50,000 X-ray diffraction measurements derived from authentic experiments, demonstrating performance that is commensurate with human experts and adept at deciphering intricate geometric patterns. Remarkably, CrystalX revealed that even peer-reviewed publications can harbor errors that are stealthy to human scrutiny, yet CrystalX adeptly rectifies them. This deep learning model revolutionizes the time frame for crystal structure analysis, slashing it down to seconds. It has already been successfully applied in the structure analysis of newly discovered compounds in the latest research without human intervention. Overall, CrystalX marks the beginning of a new era in automating routine structural analysis within self-driving laboratories.

Scientific discovery contributes largely to human society's prosperity, and recent progress shows that LLMs could potentially catalyze this process. However, it is still unclear whether LLMs can discover novel and valid hypotheses in chemistry. In this work, we investigate this central research question: Can LLMs automatically discover novel and valid chemistry research hypotheses given only a chemistry research background (consisting of a research question and/or a background survey), without limitation on the domain of the research question? After extensive discussions with chemistry experts, we propose an assumption that a majority of chemistry hypotheses can be resulted from a research background and several inspirations. With this key insight, we break the central question into three smaller fundamental questions. In brief, they are: (1) given a background question, whether LLMs can retrieve good inspirations; (2) with background and inspirations, whether LLMs can lead to hypothesis; and (3) whether LLMs can identify good hypotheses to rank them higher. To investigate these questions, we construct a benchmark consisting of 51 chemistry papers published in Nature, Science, or a similar level in 2024 (all papers are only available online since 2024). Every paper is divided by chemistry PhD students into three components: background, inspirations, and hypothesis. The goal is to rediscover the hypothesis, given only the background and a large randomly selected chemistry literature corpus consisting the ground truth inspiration papers, with LLMs trained with data up to 2023. We also develop an LLM-based multi-agent framework that leverages the assumption, consisting of three stages reflecting the three smaller questions. The proposed method can rediscover many hypotheses with very high similarity with the ground truth ones, covering the main innovations., Comment: Code and Benchmark are available at https://github.com/ZonglinY/MOOSE-Chem.git

This paper presents an advanced mathematical problem-solving framework, LLaMA-Berry, for enhancing the mathematical reasoning ability of Large Language Models (LLMs). The framework combines Monte Carlo Tree Search (MCTS) with iterative Self-Refine to optimize the reasoning path and utilizes a pairwise reward model to evaluate different paths globally. By leveraging the self-critic and rewriting capabilities of LLMs, Self-Refine applied to MCTS (SR-MCTS) overcomes the inefficiencies and limitations of conventional step-wise and greedy search algorithms by fostering a more efficient exploration of solution spaces. Pairwise Preference Reward Model~(PPRM), inspired by Reinforcement Learning from Human Feedback (RLHF), is then used to model pairwise preferences between solutions, utilizing an Enhanced Borda Count (EBC) method to synthesize these preferences into a global ranking score to find better answers. This approach addresses the challenges of scoring variability and non-independent distributions in mathematical reasoning tasks. The framework has been tested on general and advanced benchmarks, showing superior performance in terms of search efficiency and problem-solving capability compared to existing methods like ToT and rStar, particularly in complex Olympiad-level benchmarks, including GPQA, AIME24 and AMC23.

This paper primarily investigates the effect of the tilt of corner cube reflector (CCR) arrays on lunar laser ranging (LLR). A mathematical model was established to study the random errors caused by the tilt of the CCR arrays. The study found that, ideally, when the laser ranging pulse width is 10 picoseconds or less, it is possible to distinguish from which specific corner cubes within the CCR array each peak in the echo signal originates. Consequently, partial data from the echo can be extracted for signal processing, significantly reducing random errors and improving the single-shot precision of LLR. The distance obtained by extracting part of the echo can be reduced to the center position of the array, thereby providing multiple higher-precision ranging results from each measurement. This not only improves the precision of LLR but also increases the data volume. A simulation experiment based on the 1.2 m laser ranging system at Yunnan Observatories was conducted. By extracting one peak for signal processing, the single-shot precision improved from 32.24 mm to 2.52 mm, validating the theoretical analysis results. Finally, an experimental laser ranging system based on a 53 cm binocular telescope system was established for ground experiments. The experimental results indicated that the echo signal could identify the tilt state of the CCR array. By extracting the peak returned by the central CCR for signal processing, the ranging precision was greatly improved. Through theoretical analyses, simulation experiments, and ground experiments, a solution to reduce the random errors caused by the tilt of the CCR array was provided. This offers an approach to enhance the single-shot precision of future LLR and provides a reference for upgrading ground-based equipment at future laser ranging stations.

Large Language Models (LLMs) have achieved remarkable success and have been applied across various scientific fields, including chemistry. However, many chemical tasks require the processing of visual information, which cannot be successfully handled by existing chemical LLMs. This brings a growing need for models capable of integrating multimodal information in the chemical domain. In this paper, we introduce \textbf{ChemVLM}, an open-source chemical multimodal large language model specifically designed for chemical applications. ChemVLM is trained on a carefully curated bilingual multimodal dataset that enhances its ability to understand both textual and visual chemical information, including molecular structures, reactions, and chemistry examination questions. We develop three datasets for comprehensive evaluation, tailored to Chemical Optical Character Recognition (OCR), Multimodal Chemical Reasoning (MMCR), and Multimodal Molecule Understanding tasks. We benchmark ChemVLM against a range of open-source and proprietary multimodal large language models on various tasks. Experimental results demonstrate that ChemVLM achieves competitive performance across all evaluated tasks. Our model can be found at https://huggingface.co/AI4Chem/ChemVLM-26B., Comment: 11 pages, updated version

Machine learning interatomic potentials (MLIPs) have been widely used to facilitate large scale molecular simulations with ab initio level accuracy. However, MLIP-based molecular simulations frequently encounter the issue of collapse due to decreased prediction accuracy for out-of-distribution (OOD) data. To mitigate this issue, it is crucial to enrich the training set with active learning, where uncertainty estimation serves as an effective method for identifying and collecting OOD data. Therefore, a feasible method for uncertainty estimation in MLIPs is desired. The existing methods either require expensive computations or compromise prediction accuracy. In this work, we introduce evidential deep learning for interatomic potentials (eIP) with a physics-inspired design. Our experiments demonstrate that eIP consistently generates reliable uncertainties without incurring notable additional computational costs, while the prediction accuracy remains unchanged. Furthermore, we present an eIP-based active learning workflow, where eIP is used not only to estimate the uncertainty of molecular data but also to perform uncertainty-driven dynamics simulations. Our findings show that eIP enables efficient sampling for a more diverse dataset, thereby advancing the feasibility of MLIP-based molecular simulations.

C$_4$H and $c$-C$_3$H$_2$, as unsaturated hydrocarbon molecules, are important for forming large organic molecules in the interstellar medium. We present mapping observations of C$_4$H ($N$=9$-8$) lines, $c$-C$_3$H$_2$ ($J_{Ka,Kb}$=2$_{1,2}$-1$_{0,1}$) %at 85338.894 MHz and H$^{13}$CO$^+$ ($J$=1$-0$) %at 86754.2884 MHz toward 19 nearby cold molecular cores in the Milky Way with the IRAM 30m telescope. C$_4$H 9--8 was detected in 13 sources, while $c$-C$_3$H$_2$ was detected in 18 sources. The widely existing C$_4$H and $c$-C$_3$H$_2$ molecules in cold cores provide material to form large organic molecules. Different spatial distributions between C$_4$H 9--8 and $c$-C$_3$H$_2$ 2--1 were found. The relative abundances of these three molecules were obtained under the assumption of local thermodynamic equilibrium conditions with a fixed excitation temperature. The abundance ratio of C$_4$H to $c$-C$_3$H$_2$ ranged from 0.34 $\pm$ 0.09 in G032.93+02 to 4.65 $\pm$ 0.50 in G008.67+22. A weak correlation between C$_4$H/H$^{13}$CO$^+$ and $c$-C$_3$H$_2$/H$^{13}$CO$^+$ abundance ratios was found, with a correlation coefficient of 0.46, which indicates that there is no tight astrochemical connection between C$_4$H and $c$-C$_3$H$_2$ molecules., Comment: 17 pages, 2 figures

Dense outflowing gas, traced by transitions of molecules with large dipole moment, is important for understanding mass loss and feedback of massive star formation. HCN 3-2 and HCO$^+$ 3-2 are good tracers of dense outflowing molecular gas, which are closely related to active star formation. In this study, we present on-the-fly (OTF) mapping observations of HCN 3-2 and HCO$^+$ 3-2 toward a sample of 33 massive star-forming regions using the 10-m Submillimeter Telescope (SMT). With the spatial distribution of line wings of HCO$^+$ 3-2 and HCN 3-2, outflows are detected in 25 sources, resulting in a detection rate of 76$\%$. The optically thin H$^{13}$CN and H$^{13}$CO$^+$ 3-2 lines are used to identify line wings as outflows and estimate core mass. The mass $M_{out}$, momentum $P_{out}$, kinetic energy $E_{K}$, force $F_{out}$ and mass loss rate $\dot M_{out}$ of outflow and core mass, are obtained for each source. A sublinear tight correlation is found between the mass of dense molecular outflow and core mass, with an index of $\sim$ 0.8 and a correlation coefficient of 0.88., Comment: 22 pages, 5 figures, 4 tables, accepted in AJ

This paper introduces the MCT Self-Refine (MCTSr) algorithm, an innovative integration of Large Language Models (LLMs) with Monte Carlo Tree Search (MCTS), designed to enhance performance in complex mathematical reasoning tasks. Addressing the challenges of accuracy and reliability in LLMs, particularly in strategic and mathematical reasoning, MCTSr leverages systematic exploration and heuristic self-refine mechanisms to improve decision-making frameworks within LLMs. The algorithm constructs a Monte Carlo search tree through iterative processes of Selection, self-refine, self-evaluation, and Backpropagation, utilizing an improved Upper Confidence Bound (UCB) formula to optimize the exploration-exploitation balance. Extensive experiments demonstrate MCTSr's efficacy in solving Olympiad-level mathematical problems, significantly improving success rates across multiple datasets, including GSM8K, GSM Hard, MATH, and Olympiad-level benchmarks, including Math Odyssey, AIME, and OlympiadBench. The study advances the application of LLMs in complex reasoning tasks and sets a foundation for future AI integration, enhancing decision-making accuracy and reliability in LLM-driven applications.

Machine learning interatomic potentials (MLIPs) enable more efficient molecular dynamics (MD) simulations with ab initio accuracy, which have been used in various domains of physical science. However, distribution shift between training and test data causes deterioration of the test performance of MLIPs, and even leads to collapse of MD simulations. In this work, we propose an online Test-time Adaptation Interatomic Potential (TAIP) framework to improve the generalization on test data. Specifically, we design a dual-level self-supervised learning approach that leverages global structure and atomic local environment information to align the model with the test data. Extensive experiments demonstrate TAIP's capability to bridge the domain gap between training and test dataset without additional data. TAIP enhances the test performance on various benchmarks, from small molecule datasets to complex periodic molecular systems with various types of elements. Remarkably, it also enables stable MD simulations where the corresponding baseline models collapse.

Artificial intelligence (AI) technology has demonstrated remarkable potential in drug dis-covery, where pharmacokinetics plays a crucial role in determining the dosage, safety, and efficacy of new drugs. A major challenge for AI-driven drug discovery (AIDD) is the scarcity of high-quality data, which often requires extensive wet-lab work. A typical example of this is pharmacokinetic experiments. In this work, we develop a physical formula enhanced mul-ti-task learning (PEMAL) method that predicts four key parameters of pharmacokinetics simultaneously. By incorporating physical formulas into the multi-task framework, PEMAL facilitates effective knowledge sharing and target alignment among the pharmacokinetic parameters, thereby enhancing the accuracy of prediction. Our experiments reveal that PEMAL significantly lowers the data demand, compared to typical Graph Neural Networks. Moreover, we demonstrate that PEMAL enhances the robustness to noise, an advantage that conventional Neural Networks do not possess. Another advantage of PEMAL is its high flexibility, which can be potentially applied to other multi-task machine learning scenarios. Overall, our work illustrates the benefits and potential of using PEMAL in AIDD and other scenarios with data scarcity and noise.

This paper introduces a novel dynamical model, building upon the existing dynamical model for Deimos in the current numerical ephemerides, which only encompasses the simple libration effects of Deimos. The study comprehensively incorporates the rotational dynamics of Deimos influenced by the torque exerted by the major celestial bodies (Mars, the Sun) in the solar system within the inertial space. Consequently, a full dynamical model is formulated to account for the complete coupling between the rotation and orbit of Deimos. Simultaneously, employing precision orbit determination methods used for artificial satellites, we develop an adjustment model for fitting data to the complete model. The 12-order Adams--Bashforth--Moulton (ABM) integration algorithm is employed to synchronously integrate the 12 state variables of the full model to obtain the orbit of Deimos. Numerical simulation results indicate that the full dynamical model and adjustment model are stable and reliable. Compared to the simple model, the polar axis of Deimos in the inertial space exhibits a more complex oscillation in the full model. This work further advances the current dynamical model for Deimos and establishes the foundational model for the generation of a new set of precise numerical ephemerides for Deimos.

Large Language Models (LLMs) have demonstrated exceptional performance in biochemical tasks, especially the molecule caption translation task, which aims to bridge the gap between molecules and natural language texts. However, previous methods in adapting LLMs to the molecule-caption translation task required extra domain-specific pre-training stages, suffered weak alignment between molecular and textual spaces, or imposed stringent demands on the scale of LLMs. To resolve the challenges, we propose In-Context Molecule Adaptation (ICMA), as a new paradigm allowing LLMs to learn the molecule-text alignment from context examples via In-Context Molecule Tuning. Specifically, ICMA incorporates the following three stages: Hybrid Context Retrieval, Post-retrieval Re-ranking, and In-context Molecule Tuning. Initially, Hybrid Context Retrieval utilizes BM25 Caption Retrieval and Molecule Graph Retrieval to retrieve informative context examples. Additionally, we also propose Post-retrieval Re-ranking with Sequence Reversal and Random Walk to further improve the quality of retrieval results. Finally, In-Context Molecule Tuning unlocks the in-context molecule learning capability of LLMs with retrieved examples and adapts the parameters of LLMs for the molecule-caption translation task. Experimental results demonstrate that ICMT can empower LLMs to achieve state-of-the-art or comparable performance without extra training corpora and intricate structures, showing that LLMs are inherently in-context molecule learners.

Large language models (LLMs) have made impressive progress in chemistry applications. However, the community lacks an LLM specifically designed for chemistry. The main challenges are two-fold: firstly, most chemical data and scientific knowledge are stored in structured databases, which limits the model's ability to sustain coherent dialogue when used directly. Secondly, there is an absence of objective and fair benchmark that encompass most chemistry tasks. Here, we introduce ChemLLM, a comprehensive framework that features the first LLM dedicated to chemistry. It also includes ChemData, a dataset specifically designed for instruction tuning, and ChemBench, a robust benchmark covering nine essential chemistry tasks. ChemLLM is adept at performing various tasks across chemical disciplines with fluid dialogue interaction. Notably, ChemLLM achieves results comparable to GPT-4 on the core chemical tasks and demonstrates competitive performance with LLMs of similar size in general scenarios. ChemLLM paves a new path for exploration in chemical studies, and our method of incorporating structured chemical knowledge into dialogue systems sets a new standard for developing LLMs in various scientific fields. Codes, Datasets, and Model weights are publicly accessible at https://hf.co/AI4Chem, Comment: 9 pages, 5 figures

In this paper, we systematically summarize and enhance the understanding of weak convergence and functional limits of record numbers in discrete-time random walks under Spitzer's condition, and extend these findings to $\sigma$--record numbers using similar methods. Additionally, we identify a sufficient condition for the existence of functional limits for record numbers in continuous-time random walks. Finally, we derive corresponding results for large deviations, moderate deviations, and laws of the iterated logarithm pertaining to record numbers in discrete-time random walks., Comment: 15 pages

Utilizing the extended Huygens-Fresnel principle and the Rytov approximation, the analytical formula for the propagation of a partially coherent electromagnetic hyperbolic-sine-Gaussian vortex beam (PCEShVB) in anisotropic atmospheric turbulence has been theoretically derived. Detailed studies have been conducted on the evolution characteristics of average intensity, the degree of coherence (DOC) and the degree of polarization (DOP) of the beam in turbulence. The results show that during propagation, the intensity distribution of the beam will exhibit a spiral structure, and the overall distribution of light spots will rotate in a direction related to the sign of the topological charge. The DOC distribution of PCEShVB will display a pattern reminiscent of beam interference fringes with an increase in propagation distance, with the number of 'interference fringes' greatly impacted by the hyperbolic sine parameter. Furthermore, PCEShVB with large initial coherent length and hyperbolic sine parameter will increase the degree of separation of the spots and yield a large DOP. Finally, for the validation of the theoretical findings, the random phase screen method was employed to simulate the propagation of PCEShVB through anisotropic atmospheric turbulence. The studies revealed a consistent alignment between the simulation results and the theoretical predictions.

To understand the relation between NH$_2$D and its physical environment, we mapped ortho-NH$_2$D $1_{11}^s-1_{01}^a$ at 85.9 GHz toward 24 Galactic late-stage massive star-forming regions with Institut de Radioastronomie Millim$ \'e$trique (IRAM) 30-m telescope. Ortho-NH$_2$D $1_{11}^s-1_{01}^a$ was detected in 18 of 24 sources. Comparing with the distribution of H$^{13}$CN 1-0 as a dense gas tracer and radio recombination line H42$\alpha$, ortho-NH$_2$D $1_{11}^s-1_{01}^a$ present complex and diverse spatial distribution in these targets. 11 of the 18 targets, present a different distribution between ortho-NH$_2$D $1_{11}^s-1_{01}^a$ and H$^{13}$CN 1-0, while no significant difference between these two lines can be found in the other 7 sources, mainly due to limited spatial resolution and sensitivity. Moreover, with H42$\alpha$ tracing massive young stellar objects, ortho-NH$_2$D $1_{11}^s-1_{01}^a$ seems to show a relatively weak emission near the massive young stellar objects., Comment: 30 pages, 20 figures, 4 tables. Accepted to MNRAS

Peptide-like molecule, which has a close connection with the origin of life, has been detected in universe. Mapping observations of HCONH$_2$ and CH$_3$CONH$_2$, two simplest peptide-like molecules, are performed towards Sagittarius B2 (Sgr B2) complex with the IRAM 30m telescope. Seven transitions of HCONH$_2$ and five transitions of CH$_3$CONH$_2$ are used in analysis. The spatial distribution of excitation temperature and column density of HCONH$_2$ in the molecular envelope of Sgr B2 are obtained by the rotation diagrams. Assuming the same excitation temperature as HCONH$_2$, the column densities of CH$_3$CONH$_2$ are also calculated. The results show that excitation temperature ranges from 6 K to 46 K in the molecular envelope of Sgr B2. The abundance ratio between HCONH$_2$ and CH$_3$CONH$_2$ are calculated to explore the relationship among them, as well as HNCO mentioned in our pervious research. The abundance ratio of CH$_3$CONH$_2$/HCONH$_2$ varies from 10% to 20%, while that of HCONH$_2$/HNCO ranges from 1.5% to 10%. CH$_3$CONH$_2$ is enhanced with respect to HCONH$_2$ in the northwest region of Sgr B2. One transition of H$^{13}$CONH$_2$ is detected toward 12 positions of Sgr B2, from which a $^{12}$C/$^{13}$C ratio of 28.7 is obtained. A time-dependent chemical model with a short duration of X-ray burst is used to explain the observed abundances of HCONH$_2$ and CH$_3$CONH$_2$, with the best fitting result at T$\rm_{dust}$ = 53-56 K. More chemical reactions are required to be included into the model since the modeled abundance is lower than the observed one at the observed T$\rm_{dust}$.

Machine learning interatomic potentials (MLIPs) enables molecular dynamics (MD) simulations with ab initio accuracy and has been applied to various fields of physical science. However, the performance and transferability of MLIPs are limited by insufficient labeled training data, which require expensive ab initio calculations to obtain the labels, especially for complex molecular systems. To address this challenge, we design a novel geometric structure learning paradigm that consists of two stages. We first generate a large quantity of 3D configurations of target molecular system with classical molecular dynamics simulations. Then, we propose geometry-enhanced self-supervised learning consisting of masking, denoising, and contrastive learning to better capture the topology and 3D geometric information from the unlabeled 3D configurations. We evaluate our method on various benchmarks ranging from small molecule datasets to complex periodic molecular systems with more types of elements. The experimental results show that the proposed pre-training method can greatly enhance the accuracy of MLIPs with few extra computational costs and works well with different invariant or equivariant graph neural network architectures. Our method improves the generalization capability of MLIPs and helps to realize accurate MD simulations for complex molecular systems.

Protostellar outflows are considered a signpost of star formation. These outflows can cause shocks in the molecular gas and are typically traced by the line wings of certain molecules. HNCO (4--3) has been regarded as a shock tracer because of the high abundance in shocked regions. Here we present the first imaging results of HNCO (4--3) line wings toward nine sources in a sample of twenty three massive star-forming regions using the IRAM 30\,m telescope. We adopt the velocity range of the full width of HC$_{3}$N (10--9) and H$^{13}$CO$^+$ (1--0) emissions as the central emission values, beyond which the emission from HNCO (4--3) is considered to be from line wings. The spatial distributions of the red- and/or blue-lobes of HNCO (4--3) emission nicely associate with those lobes of HCO$^{+}$ (1--0) in most of the sources. High intensity ratios of HNCO (4--3) to HCO$^+$ (1--0) are obtained in the line wings. The derived column density ratios of HNCO to HCO$^+$ are consistent with those previously observed towards massive star-forming regions. These results provide direct evidence that HNCO could trace outflow in massive star-forming regions. This work also implies that the formation of some HNCO molecules is related to shock, either on the grain surface or within the shocked gas., Comment: 18 pages, 4 tables, 4 figures, and accepted for publication in ApJ

Pitch and meter are two fundamental music features for symbolic music generation tasks, where researchers usually choose different encoding methods depending on specific goals. However, the advantages and drawbacks of different encoding methods have not been frequently discussed. This paper presents a integrated analysis of the influence of two low-level feature, pitch and meter, on the performance of a token-based sequential music generation model. First, the commonly used MIDI number encoding and a less used class-octave encoding are compared. Second, an dense intra-bar metric grid is imposed to the encoded sequence as auxiliary features. Different complexity and resolutions of the metric grid are compared. For complexity, the single token approach and the multiple token approach are compared; for grid resolution, 0 (ablation), 1 (bar-level), 4 (downbeat-level) 12, (8th-triplet-level) up to 64 (64th-note-grid-level) are compared; for duration resolution, 4, 8, 12 and 16 subdivisions per beat are compared. All different encodings are tested on separately trained Transformer-XL models for a melody generation task. Regarding distribution similarity of several objective evaluation metrics to the test dataset, results suggest that the class-octave encoding significantly outperforms the taken-for-granted MIDI encoding on pitch-related metrics; finer grids and multiple-token grids improve the rhythmic quality, but also suffer from over-fitting at early training stage. Results display a general phenomenon of over-fitting from two aspects, the pitch embedding space and the test loss of the single-token grid encoding. From a practical perspective, we both demonstrate the feasibility and raise the concern of easy over-fitting problem of using smaller networks and lower embedding dimensions on the generation task. The findings can also contribute to futural models in terms of feature engineering., Comment: This is a draft before submitted to TISMIR as a journal paper

Reinforcement learning policy evaluation problems are often modeled as finite or discounted/averaged infinite-horizon MDPs. In this paper, we study undiscounted off-policy policy evaluation for absorbing MDPs. Given the dataset consisting of the i.i.d episodes with a given truncation level, we propose a so-called MWLA algorithm to directly estimate the expected return via the importance ratio of the state-action occupancy measure. The Mean Square Error (MSE) bound for the MWLA method is investigated and the dependence of statistical errors on the data size and the truncation level are analyzed. With an episodic taxi environment, computational experiments illustrate the performance of the MWLA algorithm., Comment: 36 pages, 9 figures

We present sensitive observations of NH2D at 110.153599 GHz toward 50 Galactic massive star-forming regions with IRAM 30-m telescope. The NH2D transition is detected toward 36 objects, yielding a detection rate of 72%. Column densities of NH2D, HC3N and C18O for each source are derived by assuming local thermal equilibrium conditions with a fixed excitation temperature. The deuterium ratio of NH$_3$, defined as the abundance ratio of NH2D to NH3, for 19 sources is also obtained with the information of NH3 from the literature. The range of deuterium fractionation bends to be large in the late-stage star-forming regions in this work, with the value from 0.043 to 0.0006. The highest deuterium ratio of NH3 is 0.043 in G081.75+00.78 (DR21). We also find that the deuterium ratio of NH3 increases with the Galactocentric distances and decreases with the line width., Comment: Accepted for publication in MNRAS. 16 pages, 12 figures, 3 tables

Record numbers are basic statistics in random walks, whose deviation principles are not very clear so far. In this paper, the asymptotic probabilities of large and moderate deviations for numbers of weak records in right continuous or left continuous random walks are proved., Comment: A new version is posted by the coauthor in the identifier 1909.09763

TianQin is a planned space-based gravitational wave (GW) observatory consisting of three earth orbiting satellites with an orbital radius of about $10^5~{\rm km}$. The satellites will form a equilateral triangle constellation the plane of which is nearly perpendicular to the ecliptic plane. TianQin aims to detect GWs between $10^{-4}~{\rm Hz}$ and $1~{\rm Hz}$ that can be generated by a wide variety of important astrophysical and cosmological sources, including the inspiral of Galactic ultra-compact binaries, the inspiral of stellar-mass black hole binaries, extreme mass ratio inspirals, the merger of massive black hole binaries, and possibly the energetic processes in the very early universe or exotic sources such as cosmic strings. In order to start science operations around 2035, a roadmap called the 0123 plan is being used to bring the key technologies of TianQin to maturity, supported by the construction of a series of research facilities on the ground. Two major projects of the 0123 plan are being carried out. In this process, the team has created a new generation $17~{\rm cm}$ single-body hollow corner-cube retro-reflector which has been launched with the QueQiao satellite on 21 May 2018; a new laser ranging station equipped with a $1.2~{\rm m}$ telescope has been constructed and the station has successfully ranged to all the five retro-reflectors on the Moon; and the TianQin-1 experimental satellite has been launched on 20 December 2019 and the first round result shows that the satellite has exceeded all of its mission requirements., Comment: 16 pages, 1 figure, invited article to a special section in PTEP

The deviation principles of record numbers in random walk models have not been completely investigated, especially for the non-nearest neighbor cases. In this paper, we derive the asymptotic probabilities of large and moderate deviations for the number of "weak records"(or "ladder points") in two kinds of one-dimensional non-nearest neighbor random walks. The proofs depend only on the direct analysis of random walks. We illustrate that the traditional method of analyzing the local time of Brownian motions, which is often adopted for the simple random walks, would lead to wrong conjectures for our cases., Comment: 17 Pages

Let $X=\{X(t),t\in\mathrm{R}^N\}$ be a centered real-valued operator-scaling Gaussian random field with stationary increments, introduced by Bierm\'{e}, Meerschaert and Scheffler (Stochastic Process. Appl. 117 (2007) 312-332). We prove that $X$ satisfies a form of strong local nondeterminism and establish its exact uniform and local moduli of continuity. The main results are expressed in terms of the quasi-metric $\tau_E$ associated with the scaling exponent of $X$. Examples are provided to illustrate the subtle changes of the regularity properties., Comment: Published at http://dx.doi.org/10.3150/13-BEJ593 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

It is proved in this paper that Riemann-Liouville processes can arise from the temporal structures of the scaled occupation time fluctuation limits of the site-dependent (d,\alpha,\sigma(x))branching particle systems in the case of 1=d<\alpha<2 and \int_{\R}\sigma(x)\d x<\infty., Comment: 12 pages

Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process. The proof involves the tightness and identification of finite-dimensional distributions., Comment: Published in at http://dx.doi.org/10.3150/10-BEJ319 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

Functional limit theorems for scaled fluctuations of occupation time processes of a sequence of critical branching particle systems in $\R^d$ with anisotropic space motions and strongly degenerated splitting abilities are proved in the cases of critical and intermediate dimensions. The results show that the limit processes are constant measure-valued Wienner processes with degenerated temporal and simple spatial structures., Comment: 15 pages

In this paper, we studied the functional ergodic limits of the site-dependent branching Brownian motions in R. The results show that the limiting processes are non-degenerate if and only if the variance functions of branching laws are integrable. When the functions are integrable, although the limiting processes will vary according to the integrals, they are always positive, infinitely divisible and self-similar, and their marginal distributions are determined by a kind of 1/2-fractional integral equations. As a byproduct, the unique non-negative solutions of the integral equations are explicitly presented by the Levy-measure of the corresponding limiting processes., Comment: 25 pages

We establish limit theorems for re-scaled occupation time fluctuations of a sequence of branching particle systems in $\R^d$ with anisotropic space motion and weakly degenerate splitting ability. In the case of large dimensions, our limit processes lead to a new class of operator-scaling Gaussian random fields with non-stationary increments. In the intermediate and critical dimensions, the limit processes have spatial structures analogous to (but more complicated than) those arising from the critical branching particle system without degeneration considered by Bojdecki et al.{\it Stochastic Process. Appl. 2006}. Due to the weakly degenerate branching ability, temporal structures of the limit processes in all three cases are different from those obtained by Bojdecki et al. .{\it Stochastic Process. Appl. 2006}., Comment: 27pages

Multivariate random fields whose distributions are invariant under operator-scalings in both time-domain and state space are studied. Such random fields are called operator-self-similar random fields and their scaling operators are characterized. Two classes of operator-self-similar stable random fields $X=\{X(t), t \in \R^d\}$ with values in $\R^m$ are constructed by utilizing homogeneous functions and stochastic integral representations., Comment: 27 pages