Minimum rankgeneralized adjacency matrixskew-adjacency matrixdeterminanttransitive tournamentLet F be a field and suppose a := ( a 1 , a 2 , ) is a sequence of non-zero elements in F . For a tournament T on [ n ] , associate the n × n symmetric matrix M T ( a ) (resp.skew-...
full-rank factorizationminordeterminantdeterminantal representationIn this paper, we introduce a full-rank representation of the generalized inverse A T , S ( 2 ) of a given complex matrix A, which is based on an arbitrary full-rank decomposition of G, where G is a matrix such that R ( G...
1) I understand if the determinant of matrix is not 0 than it has a full rank. So i solved the matrix of the determinant: det(A) = 0 so i was looking for alfa that makes det(A) = 0; Is my assumption here correct ? 2) I had no clue how to solve the second part so i cal...
Triple-negative breast cancer (TNBC) is a subtype of breast cancer with higher aggressiveness and poorer outcomes. Recently, long non-coding RNAs (lncRNAs) have become the crucial gene regulators in the progression of human cancers. However, the function
The cancer microbiota was considered the main risk factor for cancer progression. We had proved that Fusobacterium periodonticum (F.p) was higher abundance in Esophageal cancer(EC)tissues. Bioinformation analysis found that BCT was a key virulence protei
Peak bone mass (PBM) is another important determinant of osteoporosis [13]. GSE7158, including circulating monocytes from 14 subjects with extremely high Peak bone mass (PBM) and 12 subjects with low PBM, were enrolled as validation data, which were analyzed based on the GPL570 [HG-U133-...
Single-cell RNA sequencing reveals stromal evolution into LRRC15 + myofibroblasts as a determinant of patient response to cancer immunotherapy. Cancer Disc. 2020;10:232–53. Ospelt C, Gay S, Klein K. Epigenetics in the pathogenesis of RA. Semin Immunopathol. 2017;39:409–19. Article PubMed ...
Besides, matrix-metalloproteinases (MMPs), which were closely related to the cancer cells invasion and metastasis, were downregulated by EZH2 knockdown [34]. An in vivo experiment proves the important role of EZH2 in cancer cells metastasis. In control melanoma model mice, melanoma-positive lymph ...
The operator |·||·| represents the absolute value of a scalar or the determinant of a matrix or the number of elements in a set. The operators 𝔼{·}E{·}, Re{·}Re{·}, and 𝑠𝑣𝑑(·)svd(·) refer to taking the expectation, real part, and singular value decomposition ...
As the interest in coalbed methane (CBM) discovery has grown, deep low-rank coal has emerged as a center of inquiry due to its numerous CBM resources [1]. China possesses abundant low-rank CBM deposits, of which the deep CBM resources with a burial depth of more than 1000 m account for...