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In 2017, Zhang et al. proposed a question (not open problem) and two open problems in [IEEE TIT 63 (8): 5336--5349, 2017] about constructing bent functions by using Rothaus' construction. In this note, we prove that the sufficient conditions of Rothaus' construction are also necessary, which answers their question. Besides, we demonstrate that the second open problem, which considers the iterative method of constructing bent functions by using Rothaus' construction, has only a trivial solution. It indicates that all bent functions obtained by using Rothaus' construction iteratively can be generated from the direct sum of an initial bent function and a quadratic bent function. This directly means that Zhang et al.'s construction idea makes no contribution to the construction of bent functions. To compensate the weakness of their work, we propose an iterative construction of bent functions by using a secondary construction in [DCC 88: 2007--2035, 2020].

In this paper, we begin by establishing local well-posedness for the semilinear regular Euler-Poisson-Darboux-Tricomi equation. Subsequently, we derive a lifespan estimate with the Strauss index given by $p=p_{S}(n+\frac{\mu}{m+1}, m)$ for any $\delta>0$, where $\delta$ is a parameter to describe the interplay between damping and mass. This is achieved through the construction of a new test function derived from the Gaussian hypergeometric function and a second-order ordinary differential inequality, as proven by Zhou \cite{Zhou2014}. Additionally, we extend our analysis to prove a blow-up result with the index $p=\max\{p_{S}(n+\frac{\mu}{m+1}, m), p_{F}((m+1)n+\frac{\mu-1-\sqrt\delta}{2})\}$ by applying Kato$^{\prime}$s Lemma ( i.e., Lemma \ref{katolemma} ), specifically in the case of $\delta=1$., Comment: 24 pages

In this paper, we study the stochastic multi-armed bandit problem with graph feedback. Motivated by applications in clinical trials and recommendation systems, we assume that two arms are connected if and only if they are similar (i.e., their means are close to each other). We establish a regret lower bound for this problem under the novel feedback structure and introduce two upper confidence bound (UCB)-based algorithms: Double-UCB, which has problem-independent regret upper bounds, and Conservative-UCB, which has problem-dependent upper bounds. Leveraging the similarity structure, we also explore a scenario where the number of arms increases over time (referred to as the \emph{ballooning setting}). Practical applications of this scenario include Q\&A platforms (e.g., Reddit, Stack Overflow, Quora) and product reviews on platforms like Amazon and Flipkart, where answers (or reviews) continuously appear, and the goal is to display the best ones at the top. We extend these two UCB-based algorithms to the ballooning setting. Under mild assumptions, we provide regret upper bounds for both algorithms and discuss their sub-linearity. Furthermore, we propose a new version of the corresponding algorithms that do not rely on prior knowledge of the graph's structural information and provide regret upper bounds. Finally, we conduct experiments to validate the theoretical results., Comment: arXiv admin note: substantial text overlap with arXiv:2405.11171

Incomplete knowledge of metabolic processes hinders the accuracy of GEnome-scale Metabolic models (GEMs), which in turn impedes advancements in systems biology and metabolic engineering. Existing gap-filling methods typically rely on phenotypic data to minimize the disparity between computational predictions and experimental results. However, there is still a lack of an automatic and precise gap-filling method for initial state GEMs before experimental data and annotated genomes become available. In this study, we introduce CLOSEgaps, a deep learning-driven tool that addresses the gap-filling issue by modeling it as a hyperedge prediction problem within GEMs. Specifically, CLOSEgaps maps metabolic networks as hypergraphs and learns their hyper-topology features to identify missing reactions and gaps by leveraging hypothetical reactions. This innovative approach allows for the characterization and curation of both known and hypothetical reactions within metabolic networks. Extensive results demonstrate that CLOSEgaps accurately gap-filling over 96% of artificially introduced gaps for various GEMs. Furthermore, CLOSEgaps enhances phenotypic predictions for 24 GEMs and also finds a notable improvement in producing four crucial metabolites (Lactate, Ethanol, Propionate, and Succinate) in two organisms. As a broadly applicable solution for any GEM, CLOSEgaps represents a promising model to automate the gap-filling process and uncover missing connections between reactions and observed metabolic phenotypes.

Few-shot action recognition is an emerging field in computer vision, primarily focused on meta-learning within the same domain. However, challenges arise in real-world scenario deployment, as gathering extensive labeled data within a specific domain is laborious and time-intensive. Thus, attention shifts towards cross-domain few-shot action recognition, requiring the model to generalize across domains with significant deviations. Therefore, we propose a novel approach, ``Distillation from Mixed-Source Domain", tailored to address this conundrum. Our method strategically integrates insights from both labeled data of the source domain and unlabeled data of the target domain during the training. The ResNet18 is used as the backbone to extract spatial features from the source and target domains. We design two branches for meta-training: the original-source and the mixed-source branches. In the first branch, a Domain Temporal Encoder is employed to capture temporal features for both the source and target domains. Additionally, a Domain Temporal Decoder is employed to reconstruct all extracted features. In the other branch, a Domain Mixed Encoder is used to handle labeled source domain data and unlabeled target domain data, generating mixed-source domain features. We incorporate a pre-training stage before meta-training, featuring a network architecture similar to that of the first branch. Lastly, we introduce a dual distillation mechanism to refine the classification probabilities of source domain features, aligning them with those of mixed-source domain features. This iterative process enriches the insights of the original-source branch with knowledge from the mixed-source branch, thereby enhancing the model's generalization capabilities. Our code is available at URL: \url{https://xxxx/xxxx/xxxx.git}

Low-dimensional materials are susceptible to electronic instabilities such as charge density waves (CDWs), originating from a divergence in the Lindhard electron response function, combined with a finite electron-phonon coupling strength. In this report, we present a detailed characterisation of the CDW in the quasi-one-dimensional material CuTe, including (1) direct visualization of lattice distortion seen with non-contact atomic force microscopy in real space, (2) the out-of-plane momentum dependency of the CDW gap size of the quasi-1-dimensional bands, by angle-resolved photoemission spectroscopy, (3) coherent dynamics of a photoexcited phonon mode seen by time- and angle-resolved photoemission spectroscopy, with frequency and wavevector q_CDW corresponding to the soft phonon modes predicted by theory. Furthermore, we find that the CDW gap closes through a transient band renormalisation. We thus confirm that, despite the quasi-1D characteristics of CuTe, it hosts inherently 3-dimensional CDWs.

Time and angle-resolved photoemission spectroscopy (trARPES) allows direct mapping of the electronic band structure and its dynamic response on femtosecond timescales. Here, we present a new ARPES system, powered by a new fiber-based femtosecond light source in the vacuum ultraviolet (VUV) range, accessing the complete first Brillouin zone for most materials. We present trARPES data on Au(111), polycrystalline Au, Bi2Se3 and TaTe2, demonstrating an energy resolution of 21 meV with a time resolution of <360 fs, at a high repetition rate of 1 MHz. The system is integrated with an extreme ultraviolet (EUV) high harmonic generation (HHG) beamline, enabling excellent tunability of the time-bandwidth resolution., Comment: The following article has been published in Review of Scientific Instruments. The article can be found at https://doi.org/10.1063/5.0179549

In this work, we calculate the magnetic moment and axial charge of the octet hidden-charm molecular pentaquark family in quark model. The Coleman-Glashow sum-rule for the magnetic moments of pentaquark family is always fulfilled independently of SU(3) symmetry breaking. In the $ 8_{2f} $ flavor representation, the magnetic moments of hidden-charm molecular pentaquark states with spin configuration $J^{P}=\frac{1}{2}^{-}(\frac{1}{2}^{+}\otimes0^{-})$ are all equal to $\mu_{c}=0.38\mu_{N}$. The axial charges of octet hidden-charm molecular pentaquark states are quite small compared to the axial charge of nucleon. The axial charges of the pentaquark states with the spin configuration $J^{P}=\frac{1}{2}^{-}(\frac{1}{2}^{+}\otimes0^{-})$ in $8_{2f}$ flavor representation are all zero.

The multi-armed bandit(MAB) is a classical sequential decision problem. Most work requires assumptions about the reward distribution (e.g., bounded), while practitioners may have difficulty obtaining information about these distributions to design models for their problems, especially in non-stationary MAB problems. This paper aims to design a multi-armed bandit algorithm that can be implemented without using information about the reward distribution while still achieving substantial regret upper bounds. To this end, we propose a novel algorithm alternating between greedy rule and forced exploration. Our method can be applied to Gaussian, Bernoulli and other subgaussian distributions, and its implementation does not require additional information. We employ a unified analysis method for different forced exploration strategies and provide problem-dependent regret upper bounds for stationary and piecewise-stationary settings. Furthermore, we compare our algorithm with popular bandit algorithms on different reward distributions.

Recently, few-shot action recognition has significantly progressed by learning the feature discriminability and designing suitable comparison methods. Still, there are the following restrictions. (a) Previous works are mainly based on visual mono-modal. Although some multi-modal works use labels as supplementary to construct prototypes of support videos, they can not use this information for query videos. The labels are not used efficiently. (b) Most of the works ignore the motion feature of video, although the motion features are essential for distinguishing. We proposed a Consistency Prototype and Motion Compensation Network(CLIP-CP$M^2$C) to address these issues. Firstly, we use the CLIP for multi-modal few-shot action recognition with the text-image comparison for domain adaption. Secondly, in order to make the amount of information between the prototype and the query more similar, we propose a novel method to compensate for the text(prompt) information of query videos when text(prompt) does not exist, which depends on a Consistency Loss. Thirdly, we use the differential features of the adjacent frames in two directions as the motion features, which explicitly embeds the network with motion dynamics. We also apply the Consistency Loss to the motion features. Extensive experiments on standard benchmark datasets demonstrate that the proposed method can compete with state-of-the-art results. Our code is available at the URL: https://github.com/xxx/xxx.git.

In the research field of few-shot learning, the main difference between image-based and video-based is the additional temporal dimension. In recent years, some works have used the Transformer to deal with frames, then get the attention feature and the enhanced prototype, and the results are competitive. However, some video frames may relate little to the action, and only using single frame-level or segment-level features may not mine enough information. We address these problems sequentially through an end-to-end method named "Task-Specific Alignment and Multiple-level Transformer Network (TSA-MLT)". The first module (TSA) aims at filtering the action-irrelevant frames for action duration alignment. Affine Transformation for frame sequence in the time dimension is used for linear sampling. The second module (MLT) focuses on the Multiple-level feature of the support prototype and query sample to mine more information for the alignment, which operates on different level features. We adopt a fusion loss according to a fusion distance that fuses the L2 sequence distance, which focuses on temporal order alignment, and the Optimal Transport distance, which focuses on measuring the gap between the appearance and semantics of the videos. Extensive experiments show our method achieves state-of-the-art results on the HMDB51 and UCF101 datasets and a competitive result on the benchmark of Kinetics and something 2-something V2 datasets. Our code is available at the URL: https://github.com/cofly2014/tsa-mlt.git