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The emergence of Large Language Models (LLMs) has necessitated the adoption of parallel training techniques, involving the deployment of thousands of GPUs to train a single model. Unfortunately, we have found that the efficiency of current parallel training is often suboptimal, largely due to the following two main issues. Firstly, hardware failures are inevitable, leading to interruptions in the training tasks. The inability to quickly identify the faulty components results in a substantial waste of GPU resources. Secondly, since GPUs must wait for parameter synchronization to complete before proceeding to the next round of computation, network congestions can greatly increase the waiting time for GPUs. To address these challenges, this paper introduces a communication-driven solution, namely the C4. The key insights of C4 are two folds. First, in parallel training, collective communication exhibits periodic and homogeneous characteristics, so any anomalies are certainly due to some form of hardware malfunction. By leveraging this feature, C4 can rapidly identify the faulty components, swiftly isolate the anomaly, and restart the task, thereby avoiding resource wastage caused by delays in anomaly detection. Second, the predictable communication model of collective communication, involving few large flows, allows C4 to efficiently execute traffic planning, substantially reducing network congestion. C4 has been extensively implemented across our production systems, cutting error-induced overhead by roughly 30% and enhancing runtime performance by about 15% for certain applications with moderate communication costs.

In this paper, we introduce the concepts of $\omega$-limit sets and pseudo orbits for a tree-shift defined on a Markov-Cayley tree, extending the results of tree-shifts defined on $d$-trees [5,6]. Firstly, we establish the relationships between $\omega$-limit sets and we introduce a modified definition of $\omega$-limit set based on complete prefix sets (Theorems 1.4 and 1.9). Secondly, we introduce the concept of projected pseudo orbits and investigate the concept of the shadowing property (Theorems 1.12 and 1.14).

Human Activity Recognition (HAR) has become increasingly popular with ubiquitous computing, driven by the popularity of wearable sensors in fields like healthcare and sports. While Convolutional Neural Networks (ConvNets) have significantly contributed to HAR, they often adopt a frame-by-frame analysis, concentrating on individual frames and potentially overlooking the broader temporal dynamics inherent in human activities. To address this, we propose the intra- and inter-frame attention model. This model captures both the nuances within individual frames and the broader contextual relationships across multiple frames, offering a comprehensive perspective on sequential data. We further enrich the temporal understanding by proposing a novel time-sequential batch learning strategy. This learning strategy preserves the chronological sequence of time-series data within each batch, ensuring the continuity and integrity of temporal patterns in sensor-based HAR.

We investigate self-excited axisymmetric oscillations of a lean premixed methane--air V-flame in a laminar annular jet. The flame is anchored near the rim of the centrebody, forming an inverted cone, while the strongest vorticity is concentrated along the outer shear layer of the annular jet. Consequently, the reaction and vorticity dynamics are largely separated, except where they coalesce near the flame tip. The global eigenmodes corresponding to the linearised reacting flow equations around the steady base state are computed in an axisymmetric setting. We identify an arc branch of eigenmodes exhibiting strong oscillations at the flame tip. The associated eigenvalues are robust with respect to domain truncation and numerical discretisation, and they become destabilised as the Reynolds number increases. The frequency of the leading eigenmode is found to correspond to the Lagrangian disturbance advection time from the nozzle outlet to the flame tip. Nonlinear time-resolved simulation further reveals notable hysteresis phenomena in the subcritical regime prior to instability. Hence, even when the flame is linearly stable, perturbations of sufficient amplitude can trigger limit-cycle oscillations and higher-dimensional dynamics sustained by nonlinear feedback. A Monte Carlo simulation of passive tracers in the unsteady flame suggests a nonlinear non-local instability mechanism. Notably, linear analysis of the subcritical time-averaged limit-cycle state yields eigenvalues that do not match the nonlinear periodic oscillation frequencies, attributed to the fundamentally nonlinear dynamics of the subcritical V-flame instability, where the dichromatic, non-local interaction cannot be approximated as a simple distortion of the mean flow.

We obtain the entropy and the surface entropy of the axial products on $\mathbb{N}^d$ and the $d$-tree $T^d$ of two types of systems: the subshift and the multiplicative subshift.

We calculate the Minkowski and Hausdorff dimensions of affine multiplicative subshifts on $\mathbb{N}$.

We present a novel, deep-learning based method -- dubbed Galactic-Seismology Substructures and Streams Hunter, or GS$^{3}$ Hunter for short, to search for substructures and streams in stellar kinematics data. GS$^{3}$ Hunter relies on a combined application of Siamese Neural Networks to transform the phase space information and the K-means algorithm for the clustering. As a validation test, we apply GS$^{3}$ Hunter to a subset of the Feedback in Realistic Environments (FIRE) cosmological simulations. The stellar streams and substructures thus identified are in good agreement with corresponding results reported earlier by the FIRE team. In the same vein, we apply our method to a subset of local halo stars from the Gaia Early Data Release 3 and GALAH DR3 datasets, and recover several, previously known dynamical groups, such as Thamnos 1+2, Hot Thick Disk, ED-1, L-RL3, Helmi 1+2, and Gaia-Sausage-Enceladus, Sequoia, VRM, Cronus, Nereus. Finally, we apply our method without fine-tuning to a subset of K-giant stars located in the inner halo region, obtained from the LAMOST Data Release 5 (DR5) dataset. We recover three, previously known structures (Sagittarius, Hercules-Aquila Cloud, and the Virgo Overdensity), but we also discover a number of new substructures. We anticipate that GS$^{3}$ Hunter will become a useful tool for the community dedicated to the search of stellar streams and structures in the Milky Way (MW) and the Local group, thus helping advance our understanding of the stellar inner and outer halos, and of the assembly and tidal stripping history in and around the MW., Comment: 41 pages, 34 figures, 3 tables. Accepted for Publication in the Astrophysical Journal

This paper features an analog of Sanov's theorem for finite-state Markov chains indexed by rooted d-trees, obtained via the method of types in the classical analysis of large deviations. Along with the theorem comes two applications: an almost-sure type convergence of sample means and a formula for the Hausdorff dimension of the symbolic space associated with the irreducible Markov chain.

Unique zero thermal expansion (ZTE) materials are valuable for use in precision instruments, including electronics, aerospace parts, and engines. However, most ZTE materials have a temperature range less than 1000 K under which they do not expand. In this study, we present a uniaxial ZTE in the low-cost Mn2OBO3 with a thermal expansion coefficient of $\alpha$= -1.7$\times$10^(-7) K-1 along the [h00] direction from 3.5 to 1250 K. The monoclinic structure of Mn2OBO3 remains stable over the entire temperature range in ambient conditions. Considerable thermal contraction on the BO3 trigonal planar and thermal expansion on the MnO6 octahedra combine to produce uniaxial ZTE. No charge order-disorder transition, which could cause thermal contraction, was observed up to 1250 K.

The realistic rendering of woven and knitted fabrics has posed significant challenges throughout many years. Previously, fiber-based micro-appearance models have achieved considerable success in attaining high levels of realism. However, rendering such models remains complex due to the intricate internal scatterings of hundreds of fibers within a yarn, requiring vast amounts of memory and time to render. In this paper, we introduce a new framework to capture aggregated appearance by tracing many light paths through the underlying fiber geometry. We then employ lightweight neural networks to accurately model the aggregated BSDF, which allows for the precise modeling of a diverse array of materials while offering substantial improvements in speed and reductions in memory. Furthermore, we introduce a novel importance sampling scheme to further speed up the rate of convergence. We validate the efficacy and versatility of our framework through comparisons with preceding fiber-based shading models as well as the most recent yarn-based model., Comment: 12 pages, 10 figures, 3 tables

In this study we estimate the stellar ages of LAMOST DR8 Red Giant Branch (RGB) stars based on the Gradient Boosting Decision Tree algorithm (GBDT). We used 2,643 RGB stars extracted from the APOKASC-2 astero-seismological catalog as training data-set. After selecting the parameterses ([$\alpha$/Fe], [C/Fe], T$_{eff}$, [N/Fe], [C/H], log g) highly correlated with age using GBDT, we apply the same GBDT method to the new catalog of more than 590,000 stars classified as RGB stars. The test data-set shows that the median relative error is around 11.6$\%$ for the method. We also compare the predicted ages of RGB stars with other studies (e.g., based on APOGEE), and find systematic differences. The final uncertainty is about 15 to 30$\%$ compared to open clusters' ages. Then we present the spatial distribution of the RGB sample having an age determination, which could recreate the expected result, and discuss systematic biases. All these diagnostics show that one can apply the GBDT method to other stellar samples to estimate atmospheric parameters and age., Comment: 17 pages, 17 figures, Accepted for publication in The Astrophysical Journal

Attenuation correction (AC) is essential for the generation of artifact-free and quantitatively accurate positron emission tomography (PET) images. However, AC of PET faces challenges including inter-scan motion and erroneous transformation of structural voxel-intensities to PET attenuation-correction factors. Nowadays, the problem of AC for quantitative PET have been solved to a large extent after the commercial availability of devices combining PET with computed tomography (CT). Meanwhile, considering the feasibility of a deep learning approach for PET AC without anatomical imaging, this paper develops a PET AC method, which uses deep learning to generate continuously valued CT images from non-attenuation corrected PET images for AC on brain PET imaging. Specifically, an invertible network combined with the variable augmentation strategy that can achieve the bidirectional inference processes is proposed for synthetic CT generation (IVNAC). To evaluate the performance of the proposed algorithm, we conducted a comprehensive study on a total of 1440 data from 37 clinical patients using comparative algorithms (such as Cycle-GAN and Pix2pix). Perceptual analysis and quantitative evaluations illustrate that the invertible network for PET AC outperforms other existing AC models, which demonstrates the potential of the proposed method and the feasibility of achieving brain PET AC without CT.

The application of asymmetric drift (AD) tomography across different populations provides valuable insights into the kinematics, dynamics, and rotation curves of the Galactic disk. By leveraging common stars identified in both the LAMOST and Gaia surveys, alongside Gaia DR3's circular velocity curve, we conducted a qualitative exploration of asymmetric drift distributions within the Galactic disk spanning distances from 8 to 16 kpc. In the R-Z plane, we observed that the asymmetric drift is minimal near the mid-plane of the Galactic disk and gradually increases with vertical distance, resulting in a distinctive ``horn" shape. Additionally, our analysis revealed that populations with higher [$\alpha$/Fe] ratios exhibit greater asymmetric drift compared to those with lower [$\alpha$/Fe] ratios. Specifically, we found the asymmetric drift around the solar location to be approximately 6 km s$^{-1}$, with a median value of 16 km s$^{-1}$ across the entire sample. Notably, the median asymmetric drift in the northern region of the Galactic disk (20 km s$^{-1}$) surpasses that in the southern region (13 km s$^{-1}$), with errors remaining within 2 km s$^{-1}$. Furthermore, our investigation into mono-age stellar populations unveiled that older stellar populations tend to exhibit larger asymmetric drift and velocity dispersion, aligning closely with predictions from previous numerical models. Finally, based on chemical compositions, we observed that the median asymmetric drift of the thick disk significantly exceeds that of the thin disk and found that star formation within the thick disk primarily occurred earlier than 8-10 billion years, whereas the thin disk's predominant star formation period spanned 6-8 billion years ago., Comment: 14 pages and 17 figures. The Open Journal of Astrophysics. AD analysis is the key target and the time scale picture of the milky way disk are also revealed here in another point of view, see the Fig. 9

Intrinsic magnetic topological insulators have emerged as a promising platform to study the interplay between topological surface states and ferromagnetism. This unique interplay can give rise to a variety of exotic quantum phenomena, including the quantum anomalous Hall effect and axion insulating states. Here, utilizing molecular beam epitaxy (MBE), we present a comprehensive study of the growth of high-quality MnBi2Te4 thin films on Si (111), epitaxial graphene, and highly ordered pyrolytic graphite substrates. By combining a suite of in-situ characterization techniques, we obtain critical insights into the atomic-level control of MnBi2Te4 epitaxial growth. First, we extract the free energy landscape for the epitaxial relationship as a function of the in-plane angular distribution. Then, by employing an optimized layer-by-layer growth, we determine the chemical potential and Dirac point of the thin film at different thicknesses. Overall, these results establish a foundation for understanding the growth dynamics of MnBi2Te4 and pave the way for the future applications of MBE in emerging topological quantum materials., Comment: 20 pages, 4 figures

Most existing MRI reconstruction methods perform tar-geted reconstruction of the entire MR image without tak-ing specific tissue regions into consideration. This may fail to emphasize the reconstruction accuracy on im-portant tissues for diagnosis. In this study, leveraging a combination of the properties of k-space data and the diffusion process, our novel scheme focuses on mining the multi-frequency prior with different strategies to pre-serve fine texture details in the reconstructed image. In addition, a diffusion process can converge more quickly if its target distribution closely resembles the noise distri-bution in the process. This can be accomplished through various high-frequency prior extractors. The finding further solidifies the effectiveness of the score-based gen-erative model. On top of all the advantages, our method improves the accuracy of MRI reconstruction and accel-erates sampling process. Experimental results verify that the proposed method successfully obtains more accurate reconstruction and outperforms state-of-the-art methods.

The strip entropy is studied in this article. We prove that the strip entropy approximation is valid for every ray of a golden-mean tree. This result extends the previous result of [Petersen-Salama, Discrete \& Continuous Dynamical Systems, 2020] on the conventional 2-tree. Lastly, we prove that the strip entropy approximation is valid for eventually periodic rays of a class of Markov-Cayley trees.

Human activity recognition (HAR) is one of the core research themes in ubiquitous and wearable computing. With the shift to deep learning (DL) based analysis approaches, it has become possible to extract high-level features and perform classification in an end-to-end manner. Despite their promising overall capabilities, DL-based HAR may suffer from overfitting due to the notoriously small, often inadequate, amounts of labeled sample data that are available for typical HAR applications. In response to such challenges, we propose ConvBoost -- a novel, three-layer, structured model architecture and boosting framework for convolutional network based HAR. Our framework generates additional training data from three different perspectives for improved HAR, aiming to alleviate the shortness of labeled training data in the field. Specifically, with the introduction of three conceptual layers--Sampling Layer, Data Augmentation Layer, and Resilient Layer -- we develop three "boosters" -- R-Frame, Mix-up, and C-Drop -- to enrich the per-epoch training data by dense-sampling, synthesizing, and simulating, respectively. These new conceptual layers and boosters, that are universally applicable for any kind of convolutional network, have been designed based on the characteristics of the sensor data and the concept of frame-wise HAR. In our experimental evaluation on three standard benchmarks (Opportunity, PAMAP2, GOTOV) we demonstrate the effectiveness of our ConvBoost framework for HAR applications based on variants of convolutional networks: vanilla CNN, ConvLSTM, and Attention Models. We achieved substantial performance gains for all of them, which suggests that the proposed approach is generic and can serve as a practical solution for boosting the performance of existing ConvNet-based HAR models. This is an open-source project, and the code can be found at https://github.com/sshao2013/ConvBoost, Comment: 21 pages

In this paper, we first concentrate on the possible values and dense property of entropies for isotropic and anisotropic axial products of subshifts of finite type (SFTs) on $\mathbb{N}^d$ and $d$-tree $\mathcal{T}_d$. We prove that the entropies of isotropic and anisotropic axial products of SFTs on $\mathbb{N}^d$ are dense in $[0,\infty)$, and the same result also holds for anisotropic axial products of SFTs on $\mathcal{T}_d$. However, the result is no longer true for isotropic axial products of SFTs on $\mathcal{T}_d$. Next, motivated by the work of Johnson, Kass and Madden [16], and Schraudner [28], we establish the entropy formula and structures for full axial extension shifts on $\mathbb{N}^d$ and $\mathcal{T}_d$. Combining the aforementioned results with the findings on the surface entropy for multiplicative integer systems [8] on $\mathbb{N}^d$ enables us to estimate the surface entropy for the full axial extension shifts on $\mathcal{T}_d$. Finally, we extend the results of full axial extension shifts on $\mathcal{T}_d$ to general trees.