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1. Coupled matrix–matrix and coupled tensor–matrix completion methods for predicting drug–target interactions

   https://doi.org/10.1093/bib/bbaa025  

   Bagherian, Maryam ; Kim, Renaid B ; Jiang, Cheng ; Sartor, Maureen A ; Derksen, Harm ; Najarian, Kayvan ( March 2020 , Briefings in Bioinformatics)

   Abstract Predicting the interactions between drugs and targets plays an important role in the process of new drug discovery, drug repurposing (also known as drug repositioning). There is a need to develop novel and efficient prediction approaches in order to avoid the costly and laborious process of determining drug–target interactions (DTIs) based on experiments alone. These computational prediction approaches should be capable of identifying the potential DTIs in a timely manner. Matrix factorization methods have been proven to be the most reliable group of methods. Here, we first propose a matrix factorization-based method termed ‘Coupled Matrix–Matrix Completion’ (CMMC). Next, in order to utilize more comprehensive information provided in different databases and incorporate multiple types of scores for drug–drug similarities and target–target relationship, we then extend CMMC to ‘Coupled Tensor–Matrix Completion’ (CTMC) by considering drug–drug and target–target similarity/interaction tensors. Results: Evaluation on two benchmark datasets, DrugBank and TTD, shows that CTMC outperforms the matrix-factorization-based methods: GRMF, $L_{2,1}$-GRMF, NRLMF and NRLMF$\beta $. Based on the evaluation, CMMC and CTMC outperform the above three methods in term of area under the curve, F1 score, sensitivity and specificity in a considerably shorter run time.
2. Weight-adjusted discontinuous Galerkin methods: Matrix-valued weights and elastic wave propagation in heterogeneous media: Weight-adjusted discontinuous Galerkin methods: Matrix-valued weights and elastic wave propagation in heterogeneous media

   https://doi.org/10.1002/nme.5720  

   Chan, Jesse ( March 2018 , International Journal for Numerical Methods in Engineering)
3. Influence of the amyloid dye Congo red on curli, cellulose, and the extracellular matrix in E. coli during growth and matrix purification

   https://doi.org/10.1007/s00216-016-9868-2  

   Reichhardt, Courtney ; McCrate, Oscar A. ; Zhou, Xiaoxue ; Lee, Jessica ; Thongsomboon, Wiriya ; Cegelski, Lynette ( November 2016 , Analytical and Bioanalytical Chemistry)
4. Numerically stable coded matrix computations via circulant and rotation matrix embeddings

   https://doi.org/10.1109/ISIT45174.2021.9517750  

   Ramamoorthy, Aditya ; Tang, Li ( July 2021 , 2021 IEEE International Symposium on Information Theory (ISIT))
5. Some matrix properties preserved by generalized matrix functions

   https://doi.org/10.1515/spma-2019-0003  

   Benzi, Michele ; Huang, Ru ( January 2019 , Special Matrices)

   Abstract Generalized matrix functions were first introduced in [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra, 1(2), 1973, pp. 163-171]. Recently, it has been recognized that these matrix functions arise in a number of applications, and various numerical methods have been proposed for their computation. The exploitation of structural properties, when present, can lead to more efficient and accurate algorithms. The main goal of this paper is to identify structural properties of matrices which are preserved by generalized matrix functions. In cases where a given property is not preserved in general, we provide conditions on the underlying scalar function under which the property of interest will be preserved by the corresponding generalized matrix function.