Matrix Li-Yau-Hamilton estimates under Ricci Flow and parabolic frequency

In this paper we prove matrix Li-Yau-Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Ricci flow. We then apply such estimates to establish the monotonicity of parabolic frequencies up to correction factors. As applications, we obtain some unique continuation results under the nonnegativity of sectional or complex sectional curvature.Comment: 37 pages. All comments are welcom

Accurate Reconstruction of Molecular Phylogenies for Proteins Using Codon and Amino Acid Unified Sequence Alignments (CAUSA)

Based on molecular clock hypothesis, and neutral theory of molecular evolution, molecular phylogenies have been widely used for inferring evolutionary history of organisms and individual genes. Traditionally, alignments and phylogeny trees of proteins and their coding DNA sequences are constructed separately, thus often different conclusions were drawn. Here we present a new strategy for sequence alignment and phylogenetic tree reconstruction, codon and amino acid unified sequence alignment (CAUSA), which aligns DNA and protein sequences and draw phylogenetic trees in a unified manner. We demonstrated that CAUSA improves both the accuracy of multiple sequence alignments and phylogenetic trees by solving a variety of molecular evolutionary problems in virus, bacteria and mammals. Our results support the hypothesis that the molecular clock for proteins has two pointers existing separately in DNA and protein sequences. It is more accurate to read the molecular clock by combination (additive) of these two pointers, since the ticking rates of them are sometimes consistent, sometimes different. CAUSA software were released as Open Source under GNU/GPL license, and are downloadable free of charge from the website www.dnapluspro.com

Trend-Based SAC Beam Control Method with Zero-Shot in Superconducting Linear Accelerator

The superconducting linear accelerator is a highly flexiable facility for modern scientific discoveries, necessitating weekly reconfiguration and tuning. Accordingly, minimizing setup time proves essential in affording users with ample experimental time. We propose a trend-based soft actor-critic(TBSAC) beam control method with strong robustness, allowing the agents to be trained in a simulated environment and applied to the real accelerator directly with zero-shot. To validate the effectiveness of our method, two different typical beam control tasks were performed on China Accelerator Facility for Superheavy Elements (CAFe II) and a light particle injector(LPI) respectively. The orbit correction tasks were performed in three cryomodules in CAFe II seperately, the time required for tuning has been reduced to one-tenth of that needed by human experts, and the RMS values of the corrected orbit were all less than 1mm. The other transmission efficiency optimization task was conducted in the LPI, our agent successfully optimized the transmission efficiency of radio-frequency quadrupole(RFQ) to over $85\%$ within 2 minutes. The outcomes of these two experiments offer substantiation that our proposed TBSAC approach can efficiently and effectively accomplish beam commissioning tasks while upholding the same standard as skilled human experts. As such, our method exhibits potential for future applications in other accelerator commissioning fields