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Abstract We provide high-probability bounds on the condition number of random feature matrices. In particular, we show that if the complexity ratio $N/m$, where $$N$$ is the number of neurons and $$m$$ is the number of data samples, scales like $$\log ^{-1}(N)$$ or $$\log (m)$$, then the random feature matrix is well-conditioned. This result holds without the need of regularization and relies on establishing various concentration bounds between dependent components of the random feature matrix. Additionally, we derive bounds on the restricted isometry constant of the random feature matrix. We also derive an upper bound for the risk associated with regression problems using a random feature matrix. This upper bound exhibits the double descent phenomenon and indicates that this is an effect of the double descent behaviour of the condition number. The risk bounds include the underparameterized setting using the least squares problem and the overparameterized setting where using either the minimum norm interpolation problem or a sparse regression problem. For the noiseless least squares or sparse regression cases, we show that the risk decreases as $$m$$ and $$N$$ increase. The risk bound matches the optimal scaling in the literature and the constants in our results are explicit and independent of the dimension of the data. 

Abstract Carbon nanomaterials, specifically carbon dots and carbon nitrides, play a crucial role as heterogeneous photoinitiators in both radical and cationic polymerization processes. These recently introduced materials offer promising solutions to the limitations of current homogeneous systems, presenting a novel approach to photopolymerization. This review highlights the preparation and photocatalytic performance of these nanomaterials, emphasizing their application in various polymerization techniques, including photoinduced i) free radical, ii) RAFT, iii) ATRP, and iv) cationic photopolymerization. Additionally, it discusses their potential in addressing contemporary challenges and explores prospects in this field. Moreover, carbon nitrides, in particular, exhibit exceptional oxygen tolerance, underscoring their significance in radical polymerization processes and allowing their applications such as 3D printing, surface modification of coatings, and hydrogel engineering. 

Underground Nuclear Astrophysics Experiment in China (JUNA) has been commissioned by taking the advantage of the ultra-low background in Jinping underground lab. High current mA level 400 KV accelerator with an ECR source and BGO detectors were commissioned. JUNA studies directly a number of nuclear reactions important to hydrostatic stellar evolution at their relevant stellar energies. In the first quarter of 2021, JUNA performed the direct measurements of 25 Mg(p, γ ) 26 Al, 19 F(p, α ) 16 O, 13 C( α ,n) 16 O and 12 C( α , γ ) 16 O near the Gamow window. The experimental results reflect the potential of JUNA with higher statistics, precision and sensitivity of the data. The preliminary results of JUNA experiment and future plan are given.