Belief functions contextual discounting and canonical decompositions

In this article, the contextual discounting of a belief function, a classical discounting generalization, is extended and its particular link with the canonical disjunctive decomposition is highlighted. A general family of correction mechanisms allowing one to weaken the information provided by a source is then introduced, as well as the dual of this family allowing one to strengthen a belief function.     

On weighting two criteria with a parameter in combinatorial optimization problems

Two criteria in a combinatorial problem are often combined in a weighted sum objective using a weighting parameter between 0 and 1. For special problem types, e.g., when one of the criteria is a bottleneck value, efficient algorithms are known that solve for a given value of the weighting parameter.     

完备化Witt代数中自然出现的一些非有限阶化李代数的表示

讨论了完备化Witt代数的三类非有限阶化子代数的不可约非权模的实现,并利用它们的表示得到一些有趣的组合恒等式.     

平板折叠桌的设计模型

根据折叠桌的运动特征,选取折叠桌的四分之一为研究对象,建立任意角度下桌脚点的运动变化模型。考虑到产品稳固性、加工便利性和节约用材三方面对加工参数的影响,对折叠桌进行受力分析,得到多目标组合优化模型,用以确定出折叠桌的最优设计参数。针对用户提出的桌面形状要求,建立桌脚曲线的参数方程。作为模型推广,以椭圆状折叠桌为例,运用Matlab画出了桌脚边缘线在折叠过程中的动态变化示意图。同时,又深入研究Robert van Embricqs的滑动折叠桌,建立了新的桌脚曲线参数方程。最后,运用Matlab对多种形状折叠桌进行仿真,编写多目标优化算法,得出了最优加工参数,并进行了算法描述。     

Structure‐Based Design of Inhibitors of the Aspartic Protease Endothiapepsin by Exploiting Dynamic Combinatorial Chemistry

Structure‐based design (SBD) can be used for the design and/or optimization of new inhibitors for a biological target. Whereas de novo SBD is rarely used, most reports on SBD are dealing with the optimization of an initial hit. Dynamic combinatorial chemistry (DCC) has emerged as a powerful strategy to identify bioactive ligands given that it enables the target to direct the synthesis of its strongest binder. We have designed a library of potential inhibitors (acylhydrazones) generated from five aldehydes and five hydrazides and used DCC to identify the best binder(s). After addition of the aspartic protease endothiapepsin, we characterized the protein‐bound library member(s) by saturation‐transfer difference NMR spectroscopy. Cocrystallization experiments validated the predicted binding mode of the two most potent inhibitors, thus demonstrating that the combination of de novo SBD and DCC constitutes an efficient starting point for hit identification and optimization.     

Fast Epitope Mapping for the Anti‐MUC1 Monoclonal Antibody by Combining a One‐Bead‐One‐Glycopeptide Library and a Microarray Platform

Anti‐MUC1 monoclonal antibodies (mAbs) are powerful tools that can be used to recognize cancer‐related MUC1 molecules, the O‐glycosylation status of which is believed to affect binding affinity. We demonstrate the feasibility of using a rapid screening methodology to elucidate those effects. The approach involves i) “one‐bead‐one‐compound”‐based preparation of bilayer resins carrying glycopeptides on the shell and mass‐tag tripeptides coding O‐glycan patterns in the core, ii) on‐resin screening with an anti‐MUC1 mAb, iii) separating positive resins by utilizing secondary antibody conjugation with magnetic beads, and (iv) decoding the mass‐tag that is detached from the positive resins pool by using mass spectrometric analysis. We tested a small library consisting of 27 MUC1 glycopeptides with different O‐glycosylations against anti‐MUC1 mAb clone VU‐3C6. Qualitative mass‐tag analysis showed that increasing the number of glycans leads to an increase in the binding affinity. Six glycopeptides selected from the library were validated by using a microarray‐based assay. Our screening provides valuable information on O‐glycosylations of epitopes leading to high affinity with mAb.     

Combinatorial Crystal Synthesis: Structural Landscape of Phloroglucinol:1,2‐bis(4‐pyridyl)ethylene and Phloroglucinol:Phenazine

A large number of crystal forms, polymorphs and pseudopolymorphs, have been isolated in the phloroglucinol‐dipyridylethylene (PGL:DPE) and phloroglucinol‐phenazine (PGL:PHE) systems. An understanding of the intermolecular interactions and synthon preferences in these binary systems enables one to design a ternary molecular solid that consists of PGL, PHE, and DPE, and also others where DPE is replaced by other heterocycles. Clean isolation of these ternary cocrystals demonstrates synthon amplification during crystallization. These results point to the lesser likelihood of polymorphism in multicomponent crystals compared to single‐component crystals. The appearance of several crystal forms during crystallization of a multicomponent system can be viewed as combinatorial crystal synthesis with synthon selection from a solution library. The resulting polymorphs and pseudopolymorphs that are obtained constitute a crystal structure landscape.     

TEAD–YAP Interaction Inhibitors and MDM2 Binders from DNA-Encoded Indole-Focused Ugi Peptidomimetics

DNA-encoded combinatorial synthesis provides efficient and dense coverage of chemical space around privileged molecular structures. The indole side chain of tryptophan plays a prominent role in key, or “hot spot”, regions of protein–protein interactions. A DNA-encoded combinatorial peptoid library was designed based on the Ugi four-component reaction by employing tryptophan-mimetic indole side chains to probe the surface of target proteins. Several peptoids were synthesized on a chemically stable hexathymidine adapter oligonucleotide “hexT”, encoded by DNA sequences, and substituted by azide-alkyne cycloaddition to yield a library of 8112 molecules. Selection experiments for the tumor-relevant proteins MDM2 and TEAD4 yielded MDM2 binders and a novel class of TEAD-YAP interaction inhibitors that perturbed the expression of a gene under the control of these Hippo pathway effectors.