There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

BIOE 402. Medical Technology Assessment. 2 or 3 hours. Bioentrepreneur course. Assessment of medical technology in the context of commercialization. Objectives, competition, market share, funding, pricing, manufacturing, growth, and intellectual property; many issues unique to biomedical products. Course Information: 2 undergraduate hours. 3 graduate hours. Prerequisite(s): Junior standing or above and consent of the instructor.

“Bioinformatics” 특집을 내면서

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

A discrete singular convolution (DSC) solver is developed for treating incompressible flows Three different two-dimensional benchmark problems, the Taylor problem, the driven cavity flow, and a periodic shear layer flow, are utilized to test the accuracy, to explore the reliability and to demonstrate the efficiency of the present approach Solution of extremely high accuracy is attained in the analytically solvable Taylor problem The results of treating the other problems are in excellent agreement with those in the literature Copyright © 2002 John Wiley & Sons, Ltd

Numerical solution of incompressible flows by discrete singular convolution

The ability of molecular property prediction is of great significance to drug discovery, human health, and environmental protection. Despite considerable efforts, quantitative prediction of various molecular properties remains a challenge. Although some machine learning models, such as bidirectional encoder from transformer, can incorporate massive unlabeled molecular data into molecular representations via a self-supervised learning strategy, it neglects three-dimensional (3D) stereochemical information. Algebraic graph, specifically, element-specific multiscale weighted colored algebraic graph, embeds complementary 3D molecular information into graph invariants. We propose an algebraic graph-assisted bidirectional transformer (AGBT) framework by fusing representations generated by algebraic graph and bidirectional transformer, as well as a variety of machine learning algorithms, including decision trees, multitask learning, and deep neural networks. We validate the proposed AGBT framework on eight molecular datasets, involving quantitative toxicity, physical chemistry, and physiology datasets. Extensive numerical experiments have shown that AGBT is a state-of-the-art framework for molecular property prediction. Despite considerable efforts, quantitative prediction of various molecular properties remains a challenge. Here, the authors propose an algebraic graph-assisted bidirectional transformer, which can incorporate massive unlabeled molecular data into molecular representations via a self-supervised learning strategy and assisted with 3D stereochemical information from graphs.

/pdf/algebraic-graph-assisted-bidirectional-transformers-for-3db9zv4mvs.pdf

Algebraic graph-assisted bidirectional transformers for molecular property prediction.

DeepMind’s AlphaFold recently demonstrated the potential of deep learning for protein structure prediction. DeepFragLib, a new protein-specific fragment library built using deep neural networks, may have advanced the field to the next stage.

Protein structure prediction beyond AlphaFold

Persistent homology has emerged as a popular technique for the topological simplification of big data, including biomolecular data. Multidimensional persistence bears considerable promise to bridge the gap between geometry and topology. However, its practical and robust construction has been a challenge. We introduce two families of multidimensional persistence, namely pseudo-multidimensional persistence and multiscale multidimensional persistence. The former is generated via the repeated applications of persistent homology filtration to high dimensional data, such as results from molecular dynamics or partial differential equations. The latter is constructed via isotropic and anisotropic scales that create new simiplicial complexes and associated topological spaces. The utility, robustness and efficiency of the proposed topological methods are demonstrated via protein folding, protein flexibility analysis, the topological denoising of cryo-electron microscopy data, and the scale dependence of nano particles. Topological transition between partial folded and unfolded proteins has been observed in multidimensional persistence. The separation between noise topological signatures and molecular topological fingerprints is achieved by the Laplace-Beltrami flow. The multiscale multidimensional persistent homology reveals relative local features in Betti-0 invariants and the relatively global characteristics of Betti-1 and Betti-2 invariants.

Multidimensional persistence in biomolecular data

Protein function and dynamics are closely related to its sequence and structure. However prediction of protein function and dynamics from its sequence and structure is still a fundamental challenge in molecular biology. Protein classification, which is typically done through measuring the similarity be- tween proteins based on protein sequence or physical information, serves as a crucial step toward the understanding of protein function and dynamics. Persistent homology is a new branch of algebraic topology that has found its success in the topological data analysis in a variety of disciplines, including molecular biology. The present work explores the potential of using persistent homology as an indepen- dent tool for protein classification. To this end, we propose a molecular topological fingerprint based support vector machine (MTF-SVM) classifier. Specifically, we construct machine learning feature vectors solely from protein topological fingerprints, which are topological invariants generated during the filtration process. To validate the present MTF-SVM approach, we consider four types of problems. First, we study protein-drug binding by using the M2 channel protein of influenza A virus. We achieve 96% accuracy in discriminating drug bound and unbound M2 channels. Additionally, we examine the use of MTF-SVM for the classification of hemoglobin molecules in their relaxed and taut forms and obtain about 80% accuracy. The identification of all alpha, all beta, and alpha-beta protein domains is carried out in our next study using 900 proteins. We have found a 85% success in this identifica- tion. Finally, we apply the present technique to 55 classification tasks of protein superfamilies over 1357 samples. An average accuracy of 82% is attained. The present study establishes computational topology as an independent and effective alternative for protein classification.

Guo-Wei Wei

Papers

Numerical solution of incompressible flows by discrete singular convolution

Algebraic graph-assisted bidirectional transformers for molecular property prediction.

Protein structure prediction beyond AlphaFold

Multidimensional persistence in biomolecular data

A topological approach for protein classification