On convergence of Weak Thresholding Greedy Algorithm in

For any 0<t<1 we construct a Weak Thresholding Greedy Algorithm with weakness parameter t which converges in L¹(0,1) with respect to the Haar system, i. e. the Haar system is a ‘good non quasi-greedy basis’.     

含分布及非线性离散时滞Volterra积分系统的近最优控制

研究由关于状态为(仿射)线性的兼含分布及非线性离散时滞Volterra积分方程系统、紧控制域约束和控制与状态分离型目标泛函构成的最优控制问题.证明了近最优控制的必要条件和充分条件,并将之用于求近最优控制的算法设计.     

关于三 I FMT问题的若干注记

指出了在经典逻辑学中,M T是M P的等价形式;明确了三I FM T是与三I FM P不同的算法,且三I FM P与三I FM T这两种算法是对偶算法,表明三I算法的两个组成部分在理论上是和谐的。指出了如果在Fuzzy推理中模仿M T而计算FM T的解,则会回到FM P问题。     

扰动值模糊推理的三I算法

以D2上的三角模及其伴随为基础,给出了扰动值模糊推理的三I算法,为模糊信息处理的方法和应用提供了新的理论基础。     

目标表面可见光谱BRDF的实验测量及优化建模

介绍了一种用双向反射分布函数测定仪进行目标双向反射分布函数测量的方法。运用该测量系统在可见光谱区域对样片进行了实验测量,然后对BRDF实验数据进行谱积分预处理,结合BRDF五参数半经验统计模型,利用遗传模拟退火算法,获取样片的BRDF模型参数,并获得了三维空间的BRDF分布。结果表明,获得的可见光谱BRDF模型能准确反映材料的光散射特性,符合工程要求。     

A Compound Algorithm of Denoising Using Second-Order and Fourth-Order Partial Differential Equations

In this paper, we propose a compound algorithm for the image restoration. The algorithm is a convex combination of the ROF model and the LLT model with a parameter function 6. The numerical experiments demonstrate that our compound algorithm is efficient and preserves the main advantages of the two models. In particular, the errors of the compound algorithm in L2 norm between the exact images and corresponding restored images are the smallest among the three models. For images with strong noises, the restored images of the compound algorithm are the best in the corresponding restored images. The proposed algorithm combines the fixed point method, an improved AMG method and the Krylov acceleration. It is found that the combination of these methods is efficient and robust in the image restoration.     

Evolutionary Algorithm Directed Synthesis of Mixed Anion Compounds LaF2X (X=Br,I) and LaFI2

Mixed-anion compounds have attracted growing attentions, but their synthesis is challenging, making a rational search desirable. Here, we explored LaF₃-LaX₃ (X=Cl, Br, I) system using ab initio structure searches based on evolutionary algorithms, and predicted LaF₂X and LaFX₂ (X=Br, I), which are respectively isostructural with LaHBr₂ and YH₂I, consisting of layered La-F blocks with single and double ordered honeycomb lattices, separated by van der Waals gaps. We successfully synthesized these compounds: LaF₂Br and LaFI₂ crystallize in the predicted structure, while LaF₂I is similar to the predicted one but with different layer stacking. LaF₂I exhibits fluoride ion conductivity comparable to that of non-doped LaF₃, and has the potential to show better ionic conductivity upon appropriate doping, given the theoretically lower diffusion energy barrier and the presence of soft iodine anions. This study shows the structure prediction using evolutionary algorithms will accelerate the discovery of mixed-anion compounds in future, in particular those with an ordered anion arrangement.     

A Screening Protocol for Exploring Loop Length Requirements for the Formation of a Three Cytosine-Cytosine+ Base-Paired i-Motif

DNA sequences containing at least four runs of repetitive cytosines can fold into tetra-helical structures called i-Motifs (iMs). The interest in these DNA secondary structures is increasing due to their therapeutical and technological applications. Still, limited knowledge of their folding requirements is currently available. We developed a novel step-by-step pipeline for the systematic screening of putative iM-forming model sequences. Focusing on structures comprising only three cytosine-cytosine⁺ base pairs, we investigated what the minimal lengths of the loops required for formation of an intra-molecular iM are. Our data indicate that two and three nucleotides are required to connect the strands through the minor and majorgrooves of the iM, respectively. Additionally, they highlight an asymmetric behavior according to the distribution of the cytosines. Specifically, no sequence containing a single cytosine in the first and third run was able to fold into intra-molecular iMs with the same stability of those formed when the first and the third run comprise two cytosines. This knowledge represents a step forward toward the development of prediction tools for the proper identification of biologically functional iMs, as well as for the rational design of these secondary structures as technological devices.     

Computational Evolution Of New Catalysts For The Morita–Baylis–Hillman Reaction**

We present a de novo discovery of an efficient catalyst of the Morita–Baylis–Hillman (MBH) reaction by searching chemical space for molecules that lower the estimated barrier of the rate-determining step using a genetic algorithm (GA) starting from randomly selected tertiary amines. We identify 435 candidates, virtually all of which contain an azetidine N as the catalytically active site, which is discovered by the GA. Two molecules are selected for further study based on their predicted synthetic accessibility and have predicted rate-determining barriers that are lower than that of a known catalyst. Azetidines have not been used as catalysts for the MBH reaction. One suggested azetidine is successfully synthesized and showed an eightfold increase in activity over a commonly used catalyst. We believe this is the first experimentally verified de novo discovery of an efficient catalyst using a generative model.