Optimal Rate of Kernel Regression in Large Dimensions

We perform a study on kernel regression for large-dimensional data (where the sample size $n$ is polynomially depending on the dimension $d$ of the samples, i.e., $n\asymp d^{\gamma}$ for some $\gamma >0$ ). We first build a general tool to characterize the upper bound and the minimax lower bound of kernel regression for large dimensional data through the Mendelson complexity $\varepsilon_{n}^{2}$ and the metric entropy $\bar{\varepsilon}_{n}^{2}$ respectively. When the target function falls into the RKHS associated with a (general) inner product model defined on $\mathbb{S}^{d}$, we utilize the new tool to show that the minimax rate of the excess risk of kernel regression is $n^{-1/2}$ when $n\asymp d^{\gamma}$ for $\gamma =2, 4, 6, 8, \cdots$. We then further determine the optimal rate of the excess risk of kernel regression for all the $\gamma>0$ and find that the curve of optimal rate varying along $\gamma$ exhibits several new phenomena including the {\it multiple descent behavior} and the {\it periodic plateau behavior}. As an application, For the neural tangent kernel (NTK), we also provide a similar explicit description of the curve of optimal rate. As a direct corollary, we know these claims hold for wide neural networks as well

Overview and prospect of the detection capability of China's first precipitation measurement satellite FY-3G

Based on introducing the technical characteristics of FY-3G, which is China's first precipitation measurement satellite and successfully launched at 09∶36 BT on April 16 in 2023, this paper focuses on the precipitation detection capabilities and application prospect in rainstorm monitoring of FY-3G. The results show that, with an orbit at 407 km and an inclination angle of 50°, and equipped with a dual-frequency Ka/Ku band precipitation measurement radar, microwave, and optical imaging instruments, the FY-3G satellite can detect the three-dimensional structure of disastrous weather systems such as typhoon, heavy rainfall, and other strong convection events in most of China. At the design level, FY-3G has precipitation detection capabilities comparable to the current US Second Generation Global Precipitation Measurement Program (GPM) Core Satellite (GPMCO), but better payload types, quantities, and channel settings compared with the GPMCO satellite. After the service operation, the FY-3G satellite, together with other polar-orbiting meteorological satellites such as FY-3 AM, PM, and EM, as well as high-orbit geostationary satellites, will form the Fengyun precipitation detection constellation system, which will improve the overall precipitation detection capability of the Fengyun Satellite constellation and provide stronger basic support for meteorological disaster prevention and mitigation

Cloud-Assisted Private Set Intersection via Multi-Key Fully Homomorphic Encryption

With the development of cloud computing and big data, secure multi-party computation, which can collaborate with multiple parties to deal with a large number of transactions, plays an important role in protecting privacy. Private set intersection (PSI), a form of multi-party secure computation, is a formidable cryptographic technique that allows the sender and the receiver to calculate their intersection and not reveal any more information. As the data volume increases and more application scenarios emerge, PSI with multiple participants is increasingly needed. Homomorphic encryption is an encryption algorithm designed to perform a mathematical-style operation on encrypted data, where the decryption result of the operation is the same as the result calculated using unencrypted data. In this paper, we present a cloud-assisted multi-key PSI (CMPSI) system that uses fully homomorphic encryption over the torus (TFHE) encryption scheme to encrypt the data of the participants and that uses a cloud server to assist the computation. Specifically, we design some TFHE-based secure computation protocols and build a single cloud server-based private set intersection system that can support multiple users. Moreover, security analysis and performance evaluation show that our system is feasible. The scheme has a smaller communication overhead compared to existing schemes

Targeted Metabolomics Reveals a Protective Role for Basal PPARα in Cholestasis Induced by α‑Naphthylisothiocyanate

α-Naphthylisothiocyanate (ANIT) is an experimental agent used to induce intrahepatic cholestasis. The <i>Ppara</i>-null mouse line is widely employed to explore the physiological and pathological roles of PPARα. However, little is known about how PPARα influences the hepatotoxicity of ANIT. In the present study, wild-type and <i>Ppara</i>-null mice were orally treated with ANIT to induce cholestasis. The serum metabolome of wild-type mice segregated from that of the <i>Ppara</i>-null mice, driven by changes of bile acid (BA) metabolites. Alkaline phosphatase and total BAs were elevated preferentially in <i>Ppara</i>-null mice, which correlated with changes in <i>Cyp7a1</i>, <i>Cyp8b1</i>, <i>Mrp3</i>, <i>Cyp3a11</i>, <i>Cyp2b10</i>, <i>Ugt1a2</i>, and <i>Ugt1a5</i> genes and showed cross-talk between basal PPARα and potentially adaptive pathways. <i>Il6</i>, <i>Tnfa</i>, and target genes in the STAT3 pathway (<i>Socs3</i>, <i>Fga</i>, <i>Fgb</i>, and <i>Fgg</i>) were up-regulated in <i>Ppara</i>-null mice but not in wild-type mice. The JNK pathway was activated in both mouse lines, while NF-κB and STAT3 were activated only in <i>Ppara</i>-null mice. These data suggest protection against cholestasis by basal PPARα involves regulation of BA metabolism and inhibition of NF-κB/STAT3 signaling. Considering studies on the protective effects of both basal and activated PPARα, caution should be exercised when one attempts to draw conclusions in which the PPARα is modified by genetic manipulation, fasting, or activation in pharmacological and toxicological studies