NEW ESTIMATES FOR SINGULAR VALUES OF A MATRIX

New estimates are provided for singular values of a matrix in this paper. These results generalize and improve corresponding estimates for singular values in [4]-[6].     

FS-相容Domain的定向完备化及相关范畴性质

引入FS-相容Domain概念,研究FS-相容Domain的性质,主要结果有：（1）FS-相容Domain的收缩核与连续函数空间还是FS-相容Domain;（2）FS-相容Domain是有限生成上集,从而是Scott紧的;（3）FS-相容Domain的定向完备化是FS-Domaln;（4）有最大元的FS-Domain去掉最大元后是FS-相容Domain;（5）证明了以Scott连续映射为态射,FS-相容Domain为对象的范畴FS-CDOM是笛卡儿闭范畴并以FS-Domain范畴FS-DOM作为满的反射子范畴。     

Quasi profile and directed likelihoods from estimating functions

Frequently, corresponding to a given estimating equation it would be desirable to have a scalar combinant having parametric derivative equal to the estimating function since such a combinant may serve as a quasi log likelihood. In general this cannot be achieved but it is nevertheless possible to define a quasi profile log likelihood and also a quasi directed likelihood, for an arbitrary one-dimensional parameter of interest and with the standard kind of distributional limit behaviour.     

关于块有限无限方阵的非异性

利用有向图给出了块有限无限方阵的概念 ,得到了该类矩阵的置换相似标准形 ,以及该类矩阵非异性的一个充分必要条件 .     

Normative selection of Bayesian networks

This paper presents a Bayesian decision theoretic foundation to the selection of a Bayesian network from data. We introduce the class of disintegrable loss functions to diversify the loss incurred in choosing different models. Disintegrable loss functions can iteratively be built from simple 0-L loss functions over pair-wise model comparisons and decompose the search for the model with minimum risk into a sequence of local searches, thus retaining the modularity of the model selection procedures for Bayesian networks.     

Mutability-Landscape-Guided Engineering of l-Threonine Aldolase Revealing the Prelog Rule in Mediating Diastereoselectivity of C−C Bond Formation

l -threonine aldolase (LTA) catalyzes C−C bond synthesis with moderate diastereoselectivity. In this study, with LTA from Cellulosilyticum sp (CpLTA) as an object, a mutability landscape was first constructed by performing saturation mutagenesis at substrate access tunnel amino acids. The combinatorial active-site saturation test/iterative saturation mutation (CAST/ISM) strategy was then used to tune diastereoselectivity. As a result, the diastereoselectivity of mutant H305L/Y8H/V143R was improved from 37.2 %_syn to 99.4 %_syn. Furthermore, the diastereoselectivity of mutant H305Y/Y8I/W307E was inverted to 97.2 %_anti. Based on insight provided by molecular dynamics simulations and coevolution analysis, the Prelog rule was employed to illustrate the diastereoselectivity regulation mechanism of LTA, holding that the asymmetric formation of the C−C bond was caused by electrons attacking the carbonyl carbon atom of the substrate aldehyde from the re or si face. The study would be useful to expand LTA applications and guide engineering of other C−C bond-forming enzymes.     

Evolving Robust and Interpretable Enzymes for the Bioethanol Industry

Obtaining a robust and applicable enzyme for bioethanol production is a dream for biorefinery engineers. Herein, we describe a general method to evolve an all-round and interpretable enzyme that can be directly employed in the bioethanol industry. By integrating the transferable protein evolution strategy InSiReP 2.0 (In Silico guided Recombination Process), enzymatic characterization for actual production, and computational molecular understanding, the model cellulase PvCel5A (endoglucanase II Cel5A from Penicillium verruculosum) was successfully evolved to overcome the remaining challenges of low ethanol and temperature tolerance, which primarily limited biomass transformation and bioethanol yield. Remarkably, application of the PvCel5A variants in both first- and second-generation bioethanol production processes (i. Conventional corn ethanol fermentation combined with the in situ pretreatment process; ii. cellulosic ethanol fermentation process) resulted in a 5.7–10.1 % increase in the ethanol yield, which was unlikely to be achieved by other optimization techniques.     

Directed Evolution of Piperazic Acid Incorporation by a Nonribosomal Peptide Synthetase**

Engineering of biosynthetic enzymes is increasingly employed to synthesize structural analogues of antibiotics. Of special interest are nonribosomal peptide synthetases (NRPSs) responsible for the production of important antimicrobial peptides. Here, directed evolution of an adenylation domain of a Pro-specific NRPS module completely switched substrate specificity to the non-standard amino acid piperazic acid (Piz) bearing a labile N−N bond. This success was achieved by UPLC-MS/MS-based screening of small, rationally designed mutant libraries and can presumably be replicated with a larger number of substrates and NRPS modules. The evolved NRPS produces a Piz-derived gramicidin S analogue. Thus, we give new impetus to the too-early dismissed idea that widely accessible low-throughput methods can switch the specificity of NRPSs in a biosynthetically useful fashion.     

The path relation for directed planar graphs in rectangles, and its relation to the free diad

In this paper, we define the path relation of a directed graph to be the relation which relates two vertices if there is a path from the first to the second. We study the restriction of this relation to paths from sources to sinks, and consider the question of when two finite graphs embedded in a rectangle give the same relation. We find a set of local changes to these graphs which can be used to get between any two graphs for which this relation is the same. Furthermore, we classify the relations which can arise as this relation for a finite directed graph embedded in a rectangle as the triconvex relations between finite ordinals (defined in this paper).This work originated from some of the author’s work on category theory. It turns out that the category of finite ordinals and relations that can be the path relation of a directed graph embedded in a rectangle, is relevant to the study of diads—introduced by the author as a common generalisation of monads and comonads (note that the terms diad and dyad have been used to mean different things by other authors). More specifically, the referee of one of the author’s papers suggested that it would be useful to identify the category which plays the role for diads that the category of finite ordinals and order-preserving functions plays for monads. It turns out that the category of finite ordinals and relations that can be path relations of graphs embedded in a rectangle, is exactly the category that plays this role.     

Orientable edge colorings of graphs

An edge coloring of a graph is orientable if and only if it is possible to orient the edges of the graph so that the color of each edge is determined by the head of its corresponding oriented arc. The goals of this paper include finding a forbidden substructure characterization of orientable colorings and giving a linear time recognition algorithm for orientable colorings.An edge coloring is lexical if and only if it is possible to number the vertices of the graph so that the color of each edge is determined by its lower endpoint. Lexical colorings are, of course, the orientable colorings in which the underlying orientation is acyclic. Lexical colorings play an important role in Canonical Ramsey theory, and it is this standpoint that motivates the current study.