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 $\alpha<\beta$. 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

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

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 60 tons. Results show that the slag entrapment is exactly and timely identified

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

Dynamic Indoor Fingerprinting Localization based on Few-Shot Meta-Learning with CSI Images

While fingerprinting localization is favored for its effectiveness, it is hindered by high data acquisition costs and the inaccuracy of static database-based estimates. Addressing these issues, this letter presents an innovative indoor localization method using a data-efficient meta-learning algorithm. This approach, grounded in the ``Learning to Learn'' paradigm of meta-learning, utilizes historical localization tasks to improve adaptability and learning efficiency in dynamic indoor environments. We introduce a task-weighted loss to enhance knowledge transfer within this framework. Our comprehensive experiments confirm the method's robustness and superiority over current benchmarks, achieving a notable 23.13\% average gain in Mean Euclidean Distance, particularly effective in scenarios with limited CSI data.Comment: 5 pages,7 figure