185 research outputs found
Nonoscillatory solutions for super-linear Emden–Fowler type dynamic equations on time scales
Nonoscillatory solutions for super-linear Emden-Fowler type dynamic equations on time scales
In this paper, we consider the following Emden-Fowler type dynamic equations on time scales
\begin{equation*}
\big(a(t)|x^\Delta(t)|^\alpha \operatorname{sgn}
x^\Delta(t)\big)^\Delta+b(t)|x(t)|^\beta \operatorname{sgn}x(t)=0,
\end{equation*}
when . The classification of the nonoscillatory solutions are investigated and some necessary and sufficient conditions of the existence of oscillatory and nonoscillatory solutions are given by using the Schauder-Tychonoff fixed point theorem. Three possibilities of two classes of double integrals which are not only related to the coefficients of the equation but also linked with the classification of the nonoscillatory solutions and oscillation of solutions are put forward. Moreover, an important property of the intermediate solutions on time scales is indicated. At last, an example is given to illustrate our main results
Numerical simulation and manifold learning for the vibration of molten steel draining from a ladle
To ensure the purity of molten steel and maintain the continuity of casting, the slag detection utilizing vibration signals has been widely applied in the continuous casting. Due to the non-stationary and non-linear flow behavior of molten steel, it is hard to construct a reliable criterion to identify the slag entrapment from the vibration signals. In this paper, a numerical simulation model is built to reveal the flow process of molten steel draining from a ladle. By the analysis of the volume fraction, path line and velocity field, the flow state at the moment of slag outflowing is captured. According to the simulated results, a method based on the manifold learning is proposed to deal with the vibration signals. Firstly, the non-stationary vibration signals are decomposed into sub-bands by the continuous wavelet transform and the energy of the signal component at each wavelet scale is calculated to constitute the high dimensional feature space. Then, a manifold learning algorithm called local target space alignment (LTSA) is employed to extract the non-linear principal manifold of the feature space. Finally, the abnormal spectral energy distribution caused by slag entrapment is indicated by the one-dimensional principal manifold. The proposed method is evaluated by the vibration acceleration signals acquired from a steel ladle of 60Â tons. Results show that the slag entrapment is exactly and timely identified
Automatic artifacts removal from epileptic EEG using a hybrid algorithm
Electroencephalogram (EEG) examination plays a very important role in the diagnosis of disorders related to epilepsy in clinic. However, epileptic EEG is often contaminated with lots of artifacts such as electrocardiogram (ECG), electromyogram (EMG) and electrooculogram (EOG). These artifacts confuse EEG interpretation, while rejecting EEG segments containing artifacts probably results in a substantial data loss and it is very time-consuming. The purpose of this study is to develop a novel algorithm for removing artifacts from epileptic EEG automatically. The collected multi-channel EEG data are decomposed into statistically independent components with Independent Component Analysis (ICA). Then temporal and spectral features of each independent component, including Hurst exponent, skewness, kurtosis, largest Lyapunov exponent and frequency-band energy extracted with wavelet packet decomposition, are calculated to quantify the characteristics of different artifact components. These features are imported into trained support vector machine to determine whether the independent components represent EEG activity or artifactual signals. Finally artifact-free EEGs are obtained by reconstructing the signal with artifact-free components. The method is evaluated with EEG recordings acquired from 15 epilepsy patients. Compared with previous work, the proposed method can remove artifacts such as baseline drift, ECG, EMG, EOG, and power frequency interference automatically and efficiently, while retaining important features for epilepsy diagnosis such as interictal spikes and ictal segments
On the Mathematics of RNA Velocity II: Algorithmic Aspects
In a previous paper [CSIAM Trans. Appl. Math. 2 (2021), 1-55], the authors
proposed a theoretical framework for the analysis of RNA velocity, which is a
promising concept in scRNA-seq data analysis to reveal the cell
state-transition dynamical processes underlying snapshot data. The current
paper is devoted to the algorithmic study of some key components in RNA
velocity workflow. Four important points are addressed in this paper: (1) We
construct a rational time-scale fixation method which can determine the global
gene-shared latent time for cells. (2) We present an uncertainty quantification
strategy for the inferred parameters obtained through the EM algorithm. (3) We
establish the optimal criterion for the choice of velocity kernel bandwidth
with respect to the sample size in the downstream analysis and discuss its
implications. (4) We propose a temporal distance estimation approach between
two cell clusters along the cellular development path. Some illustrative
numerical tests are also carried out to verify our analysis. These results are
intended to provide tools and insights in further development of RNA velocity
type methods in the future.Comment: 32 pages, 5 figure
Unmasked Teacher: Towards Training-Efficient Video Foundation Models
Video Foundation Models (VFMs) have received limited exploration due to high
computational costs and data scarcity. Previous VFMs rely on Image Foundation
Models (IFMs), which face challenges in transferring to the video domain.
Although VideoMAE has trained a robust ViT from limited data, its low-level
reconstruction poses convergence difficulties and conflicts with high-level
cross-modal alignment. This paper proposes a training-efficient method for
temporal-sensitive VFMs that integrates the benefits of existing methods. To
increase data efficiency, we mask out most of the low-semantics video tokens,
but selectively align the unmasked tokens with IFM, which serves as the
UnMasked Teacher (UMT). By providing semantic guidance, our method enables
faster convergence and multimodal friendliness. With a progressive pre-training
framework, our model can handle various tasks including scene-related,
temporal-related, and complex video-language understanding. Using only public
sources for pre-training in 6 days on 32 A100 GPUs, our scratch-built ViT-L/16
achieves state-of-the-art performances on various video tasks. The code and
models will be released at https://github.com/OpenGVLab/unmasked_teacher.Comment: 16 pages, 5 figures, 28 table
MindDiffuser: Controlled Image Reconstruction from Human Brain Activity with Semantic and Structural Diffusion
Reconstructing visual stimuli from brain recordings has been a meaningful and
challenging task. Especially, the achievement of precise and controllable image
reconstruction bears great significance in propelling the progress and
utilization of brain-computer interfaces. Despite the advancements in complex
image reconstruction techniques, the challenge persists in achieving a cohesive
alignment of both semantic (concepts and objects) and structure (position,
orientation, and size) with the image stimuli. To address the aforementioned
issue, we propose a two-stage image reconstruction model called MindDiffuser.
In Stage 1, the VQ-VAE latent representations and the CLIP text embeddings
decoded from fMRI are put into Stable Diffusion, which yields a preliminary
image that contains semantic information. In Stage 2, we utilize the CLIP
visual feature decoded from fMRI as supervisory information, and continually
adjust the two feature vectors decoded in Stage 1 through backpropagation to
align the structural information. The results of both qualitative and
quantitative analyses demonstrate that our model has surpassed the current
state-of-the-art models on Natural Scenes Dataset (NSD). The subsequent
experimental findings corroborate the neurobiological plausibility of the
model, as evidenced by the interpretability of the multimodal feature employed,
which align with the corresponding brain responses.Comment: arXiv admin note: substantial text overlap with arXiv:2303.1413
Harvest Video Foundation Models via Efficient Post-Pretraining
Building video-language foundation models is costly and difficult due to the
redundant nature of video data and the lack of high-quality video-language
datasets. In this paper, we propose an efficient framework to harvest video
foundation models from image ones. Our method is intuitively simple by randomly
dropping input video patches and masking out input text during the
post-pretraining procedure. The patch dropping boosts the training efficiency
significantly and text masking enforces the learning of cross-modal fusion. We
conduct extensive experiments to validate the effectiveness of our method on a
wide range of video-language downstream tasks including various zero-shot
tasks, video question answering, and video-text retrieval. Despite its
simplicity, our method achieves state-of-the-art performances, which are
comparable to some heavily pretrained video foundation models. Our method is
extremely efficient and can be trained in less than one day on 8 GPUs,
requiring only WebVid-10M as pretraining data. We hope our method can serve as
a simple yet strong counterpart for prevalent video foundation models, provide
useful insights when building them, and make large pretrained models more
accessible and sustainable. This is part of the InternVideo project
\url{https://github.com/OpenGVLab/InternVideo}
Effects of the seedling tray overlapping for seed emergence mode on emergence characteristics and growth of rice seedlings
Seedling mode plays a crucial role in the rice production process, as it significantly affects the growth and development of seedlings. Among the various seedling modes, the seedling tray overlapping for seed emergence mode (STOSE mode) has been demonstrated to be effective in enhancing seedling quality. However, the impact of this mode on the germination and growth of seeds with varying plumpness remains uncertain. To investigate the effect of the STOSE mode on seedling emergence characteristics, growth uniformity, and nutrient uptake of seeds with varying plumpness levels, we conducted a study using super early rice Zhongzao 39 (ZZ39) as the test material. The seeds were categorized into three groups: plumped, mixed, and unplumped. The results indicated that the STOSE mode significantly improved the seedling rate for all types of seeds in comparison to the seedling tray nonoverlapping for seed emergence mode (TSR mode). Notably, the unplumped seeds exhibited the most pronounced enhancement effect. The soluble sugar content of the seeds increased significantly after 2 days of sowing under the STOSE mode, whereas the starch content exhibited a significant decrease. Furthermore, the STOSE mode outperformed the TSR mode in several aspects including seedling growth uniformity, aboveground dry matter mass, root traits, and nutrient uptake. Overall, the STOSE mode not only promoted the germination and growth of plumped and mixed seeds but also had a more pronounced impact on unplumped seeds
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