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The multilayer perceptron (MLP), a fundamental paradigm in current artificial intelligence, is widely applied in fields such as computer vision and natural language processing. However, the recently proposed Kolmogorov-Arnold Network (KAN), based on nonlinear additive connections, has been proven to achieve performance comparable to MLPs with significantly fewer parameters. Despite this potential, the use of a single activation function space results in reduced performance of KAN and related works across different tasks. To address this issue, we propose an activation space Selectable KAN (S-KAN). S-KAN employs an adaptive strategy to choose the possible activation mode for data at each feedforward KAN node. Our approach outperforms baseline methods in seven representative function fitting tasks and significantly surpasses MLP methods with the same level of parameters. Furthermore, we extend the structure of S-KAN and propose an activation space selectable Convolutional KAN (S-ConvKAN), which achieves leading results on four general image classification datasets. Our method mitigates the performance variability of the original KAN across different tasks and demonstrates through extensive experiments that feedforward KANs with selectable activations can achieve or even exceed the performance of MLP-based methods. This work contributes to the understanding of the data-centric design of new AI paradigms and provides a foundational reference for innovations in KAN-based network architectures., Comment: 12 pages, 6 figures. The code for this work will be released soon

In this note, we study a Serrin-type partially overdetermined problem proposed by Guo-Xia (Calc. Var. Partial Differential Equations 58: no. 160, 2019. https://doi.org/10.1007/s00526-019-1603-3, and prove a rigidity result that characterizes capillary spherical caps in a half ball.

In this paper, we first prove a rigidity result for a Serrin-type partially overdetermined problem in the half-space, which gives a characterization of capillary spherical caps by the overdetermined problem. In the second part, we prove quantitative stability results for the Serrin-type partially overdetermined problem, as well as capillary almost constant mean curvature hypersurfaces in the half-space.

As a significant application of the duality theory between real Hardy spaces $H^1(\mathbb{R}^n)$ and $\mathrm{BMO}(\mathbb{R}^n)$, Fefferman and Stein developed a representation theorem for $\mathrm{BMO}(\mathbb{R}^n)$ by utilizing the Riesz transforms $(n\geq 1)$. L. Carleson provided a constructive proof for the case $n=1$. In this article, we propose a representation theorem for $\mathrm{VMO}(\mathbb{S})$ using Carleson's construction and demonstrate a representation theorem for $\mathrm{VMO}(\mathbb{R}^n)$ through an iterative process. Additionally, we provide a brand-new characterization of $\mathrm{VMO}$ as an application of our results.

Let $\{(p_n, \mathcal{D}_n, L_n)\}$ be a sequence of Hadamard triples on $\mathbb{R}$. Suppose that the associated Cantor-Moran measure $$ \mu_{\{p_n,\mathcal{D}_n\}}=\delta_{p_1^{-1}\mathcal{D}_1}\ast\delta_{(p_2p_1)^{-1}\mathcal{D}_2}\ast\cdots, $$ where $\sup_n\{|p_n^{-1}d|:d\in \mathcal{D}_n\}<\infty$ and $\sup\#\mathcal{D}_n<\infty$. It has been observed that the spectrality of $\mu_{\{p_n,D_n\}}$ is determined by equi-positivity. A significant problem is what kind of Moran measures can satisfy this property. In this paper, we introduce the conception of \textit{Double Points Condition Set} (\textit{DPCS}) to characterize the equi-positivity equivalently. As applications of our characterization, we show that all singularly continuous Cantor-Moran measures are spectral. For the absolutely continuous case, we study Fuglede's Conjecture on Cantor-Moran set. We show that the equi-positivity of $\mu_{\{p_n,D_n\}}$ implies the tiling of its support, and the reverse direction holds under certain conditions., Comment: 34 pages

In this paper, we introduce a notion of capillary Schwarz symmetrization in the half-space. It can be viewed as the counterpart of the classical Schwarz symmetrization in the framework of capillary problem in the half-space. A key ingredient is a special anisotropic gauge, which enables us to transform the capillary symmetrization to the convex symmetrization introduced in \cite{AFT97}., Comment: 15 pages

The mobile network operators (MNOs) are looking into economically viable backhaul solutions as alternatives to fiber, specifically the hybrid fiber coaxial networks (HFC). When the latencies from both the wireless and the HFC networks are added together, the result is a noticeable end-to-end system latency, particularly under network congestion. In order to decrease total system latency, we proposed a method to improve upstream user- to-mobile core latency by coordinating the LTE and HFC scheduling in previous papers. In this paper, we implement and optimize the proposed method on a custom LTE and DOCSIS end-to-end system testbed. The testbed uses the OpenAirInterface (OAI) platform for the LTE network, along with Cisco's broadband router cBR-8 that is currently deployed in the HFC networks around the world. Our results show a backhaul latency improvement under all traffic load conditions., Comment: IEEE Wireless Communications and Networking Conference (WCNC), 2018. arXiv admin note: text overlap with arXiv:2211.08292

Visual-Semantic Embedding (VSE) aims to learn an embedding space where related visual and semantic instances are close to each other. Recent VSE models tend to design complex structures to pool visual and semantic features into fixed-length vectors and use hard triplet loss for optimization. However, we find that: (1) combining simple pooling methods is no worse than these sophisticated methods; and (2) only considering the most difficult-to-distinguish negative sample leads to slow convergence and poor Recall@K improvement. To this end, we propose an adaptive pooling strategy that allows the model to learn how to aggregate features through a combination of simple pooling methods. We also introduce a strategy to dynamically select a group of negative samples to make the optimization converge faster and perform better. Experimental results on Flickr30K and MS-COCO demonstrate that a standard VSE using our pooling and optimization strategies outperforms current state-of-the-art systems (at least 1.0% on the metrics of recall) in image-to-text and text-to-image retrieval. Source code of our experiments is available at https://github.com/96-Zachary/vse_2ad.

Spurred by the emerging blockchain technology and increased interest in tokenization, this forecasting research built on extensive literature and aggregated expertise to explore the potential implementation of blockchain-enabled tokenization in infrastructure investment and development. The Delphi-based scenario analysis approach was applied to gather long-term forecasts and assessments of a research panel consisting of 39 experts in blockchain tokenization and infrastructure development on how tokenization will influence the future of infrastructure finance and identify scenarios of potential applications and impact. International experts were segregated into two groups salient to this topical area based on both experience ad self-identification: infrastructure development and blockchain tokenization. Twenty-three projections for 2035, developed from a literature review, case study analysis, and expert interviews, concerning perspectives of both the supply and demand side for the adoption of blockchain tokenization, were assessed in a two-round Delphi analysis. Regulatory, economic, social, and technological perspectives of tokenization were taken into consideration. Assessments were based on both probability and impact of occurrence. Three groups of scenarios resulted from quantitative and qualitative analysis, reflecting agreement and differentiation between both expert groups. The results of this study clearly underlined the potential of tokenization in infrastructure. Uncertainties and barriers confronting the technologies' diffusion were discussed. This study contributes to the transfer of general technical-driven blockchain-enabled tokenization knowledge to infrastructure-specific tokenization knowledge. Long-term strategic planning is supported by this study with the scenario data acting as a starting point for blockchain-related efforts in infrastructure development.

We design the helicity-conservative physics-informed neural network model for the Navier-Stokes equation in the ideal case. The key is to provide an appropriate PDE model as loss function so that its neural network solutions produce helicity conservation. Physics-informed neural network model is based on the strong form of PDE. We compare the proposed Physics-informed neural network model and a relevant helicity-conservative finite element method. We arrive at the conclusion that the strong form PDE is better suited for conservation issues. We also present theoretical justifications for helicity conservation as well as supporting numerical calculations., Comment: 17 pages, 9 figures, 3 tables