Search

We establish a class of pointwise estimates for weak solutions to mixed local and nonlocal parabolic equations involving measure data and merely measurable coefficients via caloric Riesz potentials. Such estimates effectively bound the sizes and oscillations of weak solutions, respectively. The proof relies on demonstrating a new local H\"{o}lder estimate with an optimal $L^q$-Tail for weak solutions to the corresponding homogeneous problem, which remarkably extends the $L^\infty$-Tail in previous work. It is worth mentioning that our main results capture both local and nonlocal features of the double phase parabolic equations and, more importantly, remain valid for SOLA (Solutions Obtained by Limit of Approximations).

In this paper,we consider the solutions of the elliptic double obstacle problems with Orlicz growth involving measure data. Some pointwise estimates for the approximable solutions to these problems are obtained in terms of fractional maximal operators. Furthermore, we establish pointwise and oscillation estimates for the gradients of solutions via the non-linear Wolff potentials, which in turn yield $C^{1,\alpha}$-regularity of solutions., Comment: arXiv admin note: substantial text overlap with arXiv:2104.00260

We study the local H\"{o}lder regularity of weak solutions to the fully fractional parabolic equations involving spatial fractional diffusion and fractional time derivatives of the Marchaud type. It is worth noting that we do not impose boundedness assumptions on the weak solutions and nonhomogeneous terms. Within the space-time nonlocal framework, it is crucial to consider both space-dependent nonlocal tail terms and the first introduced time-dependent nonlocal tail term. By adapting a nonlocal variant of the parabolic De Giorgi iterative technique, we initially establish a priori local boundedness with tail terms for weak solutions and then prove the local H\"{o}lder continuity.

Learning temporal dependencies among targets (TDT) benefits better time series forecasting, where targets refer to the predicted sequence. Although autoregressive methods model TDT recursively, they suffer from inefficient inference and error accumulation. We argue that integrating TDT learning into non-autoregressive methods is essential for pursuing effective and efficient time series forecasting. In this study, we introduce the differencing approach to represent TDT and propose a parameter-free and plug-and-play solution through an optimization objective, namely TDT Loss. It leverages the proportion of inconsistent signs between predicted and ground truth TDT as an adaptive weight, dynamically balancing target prediction and fine-grained TDT fitting. Importantly, TDT Loss incurs negligible additional cost, with only $\mathcal{O}(n)$ increased computation and $\mathcal{O}(1)$ memory requirements, while significantly enhancing the predictive performance of non-autoregressive models. To assess the effectiveness of TDT loss, we conduct extensive experiments on 7 widely used datasets. The experimental results of plugging TDT loss into 6 state-of-the-art methods show that out of the 168 experiments, 75.00\% and 94.05\% exhibit improvements in terms of MSE and MAE with the maximum 24.56\% and 16.31\%, respectively.

In this paper, we consider the solutions to the non-homogeneous double obstacle problems with Orlicz growth involving measure data. After establishing the existence of the solutions to this problem in the Orlicz-Sobolev space, we derive a pointwise gradient estimate for these solutions by Riesz potential, which leads to the result on the $C^1$ regularity criterion.

Channel charting, an unsupervised learning method that learns a low-dimensional representation from channel information to preserve geometrical property of physical space of user equipments (UEs), has drawn many attentions from both academic and industrial communities, because it can facilitate many downstream tasks, such as indoor localization, UE handover, beam management, and so on. However, many previous works mainly focus on charting that only preserves local geometry and use raw channel information to learn the chart, which do not consider the global geometry and are often computationally intensive and very time-consuming. Therefore, in this paper, a novel signature based approach for global channel charting with ultra low complexity is proposed. By using an iterated-integral based method called signature transform, a compact feature map and a novel distance metric are proposed, which enable channel charting with ultra low complexity and preserving both local and global geometry. We demonstrate the efficacy of our method using synthetic and open-source real-field datasets., Comment: accepted by IEEE ICC 2024 Workshops

Void size function (VSF) contains information of the cosmic large-scale structure (LSS), and can be used to derive the properties of dark energy and dark matter. We predict the VSFs measured from the spectroscopic galaxy survey operated by the China Space Station Telescope (CSST), and study the strength of cosmological constraint. We employ a high-resolution Jiutian simulation to get CSST galaxy mock samples based on an improved semi-analytical model. We identify voids from this galaxy catalog using the watershed algorithm without assuming a spherical shape, and estimate the VSFs at different redshift bins from $z=0.5$ to 1.1. We propose a void selection method based on the ellipticity, and assume the void linear underdensity threshold $\delta_{\rm v}$ in the theoretical model is redshift-dependent and set it as a free parameter in each redshift bin. The Markov Chain Monte Carlo (MCMC) method is adopted to implement the constraints on the cosmological and void parameters. We find that the CSST VSF measurement can constrain the cosmological parameters to a few percent level. The best-fit values of $\delta_{\rm v}$ are ranging from $\sim-0.4$ to $-0.1$ as the redshift increases from 0.5 to 1.1, which has a distinct difference from the theoretical calculation with $\delta_{\rm v}\simeq-2.7$ assuming the spherical evolution and using particles as tracer. Our method can provide a good reference for void identification and selection in the VSF analysis of the spectroscopic galaxy surveys., Comment: 10 pages, 7 figures, 3 tables. Accepted for publication in MNRAS

Blockchain has been used in several domains. However, this technology still has major limitations that are largely related to one of its core components, namely the consensus protocol/algorithm. Several solutions have been proposed in literature and some of them are based on the use of Machine Learning (ML) methods. The ML-based consensus algorithms usually waste the work done by the (contributing/participating) nodes, as only winners' ML models are considered/used, resulting in low energy efficiency. To reduce energy waste and improve scalability, this paper proposes an AI-enabled consensus algorithm (named AICons) driven by energy preservation and fairness of rewarding nodes based on their contribution. In particular, the local ML models trained by all nodes are utilised to generate a global ML model for selecting winners, which reduces energy waste. Considering the fairness of the rewards, we innovatively designed a utility function for the Shapley value evaluation equation to evaluate the contribution of each node from three aspects, namely ML model accuracy, energy consumption, and network bandwidth. The three aspects are combined into a single Shapley value to reflect the contribution of each node in a blockchain system. Extensive experiments were carried out to evaluate fairness, scalability, and profitability of the proposed solution. In particular, AICons has an evenly distributed reward-contribution ratio across nodes, handling 38.4 more transactions per second, and allowing nodes to get more profit to support a bigger network than the state-of-the-art schemes.

Mini-app is an emerging form of mobile application that combines web technology with native capabilities. Its features, e.g., no need to download and no installation, have made it popular rapidly. However, privacy issues that violate the laws or regulations are breeding in the swiftly expanding mini-app ecosystem. The consistency between what the mini-app does about the data in the program code and what it declares in its privacy policy description is important. But no work has systematically investigated the privacy problem of the mini-app before. In this paper, to our best knowledge, we are the first to conduct the compliance detection of data practice and policy description in mini-apps. In this paper, we first customize a taint analysis method based on data entity dependency network to adapt to the characteristics of the JavaScript language in the mini-apps. Then, we transform data types and data operations to data practices in program codes and privacy policies, so as to finish a fine-grained consistency matching model.We crawl 100,000 mini-apps on WeChat client in the wild and extract 2,998 with a privacy policy. Among them, only 318 meet the consistency requirements, 2,680 are inconsistent, and the proportion of inconsistencies is as high as 89.4%. The inconsistency in the mini-app is very serious. Based on 6 real-world cases analyzed, in order to reduce this potential data leakage risk, we suggest that the developer should reduce the collection of irrelevant information and the straightforward use of templates, and the platform should provide data flow detection tools and privacy policy writing support.

Cross-correlating the data of neutral hydrogen (HI) 21cm intensity mapping with galaxy surveys is an effective method to extract astrophysical and cosmological information. In this work, we investigate the cross-correlation of MeerKAT single-dish mode HI intensity mapping and China Space Station Telescope (CSST) spectroscopic galaxy surveys. We simulate a survey area of $\sim 300$ $\mathrm{deg}^2$ of MeerKAT and CSST surveys at $z=0.5$ using Multi-Dark N-body simulation. The PCA algorithm is applied to remove the foregrounds of HI intensity mapping, and signal compensation is considered to solve the signal loss problem in the HI-galaxy cross power spectrum caused by the foreground removal process. We find that from CSST galaxy auto and MeerKAT-CSST cross power spectra, the constraint accuracy of the parameter product $\Omega_{\rm HI}b_{\rm HI}r_{{\rm HI},g}$ can reach to $\sim1\%$, which is about one order of magnitude higher than the current results. After performing the full MeerKAT HI intensity mapping survey with 5000 deg$^2$ survey area, the accuracy can be enhanced to $<0.3\%$. This implies that the MeerKAT-CSST cross-correlation can be a powerful tool to probe the cosmic HI property and the evolution of galaxies and the Universe., Comment: 18 pages, 11 figures, 3 tables. Accepted for publication in RAA, revised to match the published version

This paper revisits Deep Mutual Learning (DML), a simple yet effective computing paradigm. We propose using R\'{e}nyi divergence instead of the KL divergence, which is more flexible and tunable, to improve vanilla DML. This modification is able to consistently improve performance over vanilla DML with limited additional complexity. The convergence properties of the proposed paradigm are analyzed theoretically, and Stochastic Gradient Descent with a constant learning rate is shown to converge with $\mathcal{O}(1)$-bias in the worst case scenario for nonconvex optimization tasks. That is, learning will reach nearby local optima but continue searching within a bounded scope, which may help mitigate overfitting. Finally, our extensive empirical results demonstrate the advantage of combining DML and R\'{e}nyi divergence, leading to further improvement in model generalization.

A mixed graph $M_{G}$ is the graph obtained from an unoriented simple graph $G$ by giving directions to some edges of $G$, where $G$ is often called the underlying graph of $M_{G}$. In this paper, we introduce two classes of incidence matrices of the second kind of $M_{G}$, and discuss the determinants of these two matrices for rootless mixed trees and unicyclic mixed graphs. Applying these results, we characterize the explicit expressions of various minors for Hermitian (quasi-)Laplacian matrix of the second kind of $M_{G}$. Moreover, we give two sufficient conditions that the absolute values of all the cofactors of Hermitian (quasi-)Laplacian matrix of the second kind are equal to the number of spanning trees of the underlying graph $G$., Comment: 16 pages,7 figures

Given two graphs $G_{1}$ of order $n_{1}$ and $G_{2}$, the neighborhood corona of $G_{1}$ and $G_{2}$, denoted by $G_{1}\bigstar G_{2}$, is the graph obtained by taking one copy of $G_{1}$ and taking $n_{1}$ copies of $G_{2}$, in the meanwhile, linking all the neighbors of the $i$-th vertex of $G_{1}$ with all vertices of the $i$-th copy of $G_{2}$. In our work, we give some conditions that $G_{1}\bigstar G_{2}$ is not periodic. Furthermore, we demonstrate some sufficient conditions for $G_{1}\bigstar G_{2}$ having no perfect state transfer. Some examples are provided to explain our results. In addition, for the reason that the graph admitting perfect state transfer is rare, we also consider pretty good state transfer on neighborhood corona of two graphs. We show some sufficient conditions for $G_{1}\bigstar G_{2}$ admitting pretty good state transfer., Comment: 17 pages

We explore the intriguing effects of underlying star topological structure in the framework of Schelling's segregation model with blocks. The significant consequences exerted by the star topology are both theoretically analysed and numerically simulated with and without introducing a fraction of altruistic agents, respectively. The collective utility of the model with pure egoists alone can be optimized and the optimum stationary state is achieved with the underlying star topology of blocks. More surprisingly, once a proportion of altruists are introduced, the average utility gradually decreases as altruists' fraction increases. This presents a sharp contrast to the results in Schelling's model with lattice topology of blocks. Furthermore, an adding-link mechanism is introduced to bridge the gap between the lattice and the star topologies, and extend our analysis to more general scenarios. A novel scaling law of the average utility function are found for star topology of blocks., Comment: 7 pages, accepted by PRE