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We introduce the notion of a perfect path for a monomial algebra. We classify indecomposable non-projective Gorenstein-projective modules over the given monomial algebra via perfect paths. We apply the classification to a quadratic monomial algebra and describe explicitly the stable category of its Gorenstein-projective modules.

For each recollement of triangulated categories, there is an epivalence between the middle category and the comma category associated with a triangle functor from the category on the right to the category on the left. For a morphic enhancement of a triangulated category $\\mathcal {T}$, there are three explicit ideals of the enhancing category, whose corresponding factor categories are all equivalent to the module category over $\\mathcal {T}$. Examples related to inflation categories and weighted projective lines are discussed.

For a finite dimensional algebra A, the bounded homotopy category of projective A-modules and the bounded derived category of A-modules are dual to each other via certain categories of locally-finite cohomological functors. We prove that the duality gives rise to a 2-categorical duality between certain strict 2-categories involving bounded homotopy categories and bounded derived categories, respectively. We apply the 2-categorical duality to the study of triangle autoequivalence groups.

Let$R$be a two-sided Noetherian ring, and let$M$be a nilpotent$R$-bimodule, which is finitely generated on both sides. We study Gorenstein homological properties of the tensor ring$T_{R}(M)$. Under certain conditions, the ring$R$is Gorenstein if and only if so is$T_{R}(M)$. We characterize Gorenstein projective$T_{R}(M)$-modules in terms of$R$-modules.

Xiao-Wu Chen,1 Shu-Feng Zhou2 1Department of General Surgery, The First People’s Hospital of Shunde, Southern Medical University, Shunde, Foshan, Guangdong, People’s Republic of China; 2Department of Pharmaceutical Sciences, College of Pharmacy, University of South Florida, Tampa, FL, USA In the recently published paper by Xie et al1 in the journal of Drug Design, Development and Therapy, the authors have evaluated interleukin (IL)-17–driven inflammatory responses in 17 cases of human colon adenocarcinomas, 16 cases of human normal colon tissues adjacent to the resected colon adenocarcinomas, ten cases of human ulcerative colitis tissues from biopsies, and eight cases of human benign colon polyps. The authors have observed that human colon adenocarcinomas contained the highest levels of IL-17, which was significantly higher than the IL-17 level in the adenomas, ulcerative colitis, and normal colon tissues (P<0.01). The levels of IL-17 receptor A (IL-17RA) were also the highest in human colon adenocarcinomas, followed by adenomas and ulcerative colitis. The increased level of IL-17 and IL-17RA was accompanied with increased IL-17–driven inflammatory responses, including activation of extracellular signal-regulated kinase 1/2 and c-Jun N-terminal kinase pathways, increased expression of matrix metalloproteinase (MMP)-9, MMP-7, MMP-2, B-cell lymphoma, and cyclin D1, decreased expression of Bcl-2-associated X protein, and increased expression of vascular endothelial growth factor (VEGF) and VEGF receptor expression that were associated with increased angiogenesis.1 These data suggest that IL-17–driven inflammatory responses contribute to the initiation, growth, development, and metastasis of colon cancer. IL-17 and its related signaling pathways may serve as promising novel targets in the development of drugs for the prevention and treatment of colon cancer.

Few studies have evaluated the usefulness of fecal calprotectin (FC) or magnetic resonance enterography (MRE) in diagnosing active Crohn’s disease (CD) of the small bowel. In the study, we investigated the reliability of FC and MRE in assessing the activity of ileal CD and further explored the relationship between levels of FC and MRE scores. A total of 221 patients were diagnosed with ileal or ileo-colitis CD in our department between July 2012 and October 2016. The global magnetic resonance index of activity (MaRIA) correlated with the simple endoscopic score for CD (SES-CD) (r = 0.527, P = 0.005). When analysed segment-by-segment, a significant correlation was still observed (r = 0.590, P < 0.001). The SES-CD correlated closest with FC (r = 0.503), followed by CRP (r = 0.461), ESR (0.377) and the CDAI (r = 0.320). In receiver operating characteristic (ROC) analyses, the FC cut-off value of mucosal healing was 213.1 μg/g, with 76.1% sensitivity and 66.7% specificity. As for MaRIA, a cut-off value of 6.8 for each segment provided a sensitivity of 100% and a specificity of 79.2%. No agreement between MaRIA and FC levels was found. In conclusion, a combination of FC levels and MaRIA could be effective in monitoring mucosal activity in patients with small bowel CD.

Alisertib (ALS) is an investigational potent Aurora A kinase inhibitor currently undergoing clinical trials for the treatment of hematological and non-hematological malignancies. However, its antitumor activity has not been tested in human breast cancer. This study aimed to investigate the effect of ALS on the growth, apoptosis, and autophagy, and the underlying mechanisms in human breast cancer MCF7 and MDA-MB-231 cells. In the current study, we identified that ALS had potent growth-inhibitory, pro-apoptotic, and pro-autophagic effects in MCF7 and MDA-MB-231 cells. ALS arrested the cells in G2/M phase in MCF7 and MDA-MB-231 cells which was accompanied by the downregulation of cyclin-dependent kinase (CDK)1/cell division cycle (CDC) 2, CDK2, and cyclin B1 and upregulation of p21 Waf1/Cip1, p27 Kip1, and p53, suggesting that ALS induces G2/M arrest through modulation of p53/p21/CDC2/cyclin B1 pathways. ALS induced mitochondria-mediated apoptosis in MCF7 and MDA-MB-231 cells; ALS significantly decreased the expression of B-cell lymphoma 2 (Bcl-2), but increased the expression of B-cell lymphoma 2-associated X protein (Bax) and p53-upregulated modulator of apoptosis (PUMA), and increased the expression of cleaved caspases 3 and 9. ALS significantly increased the expression level of membrane-bound microtubule-associated protein 1 light chain 3 (LC3)-II and beclin 1 and induced inhibition of phosphatidylinositol 3-kinase (PI3K)/protein kinase B (Akt)/mammalian target of rapamycin (mTOR) and p38 mitogen-activated protein kinase (MAPK) pathways in MCF7 and MDA-MB-231 cells as indicated by their altered phosphorylation, contributing to the pro-autophagic activities of ALS. Furthermore, treatment with wortmannin markedly downregulated ALS-induced p38 MAPK activation and LC3 conversion. In addition, knockdown of the p38 MAPK gene by ribonucleic acid interference upregulated Akt activation and resulted in LC3-II accumulation. These findings indicate that ALS promotes cellular apoptosis and autophagy in breast cancer cells via modulation of p38 MAPK/Akt/mTOR pathways. Further studies are warranted to further explore the molecular targets of ALS in the treatment of breast cancer.

To an artin algebra with radical square zero, a regular algebra in the sense of von Neumann and a family of invertible bimodules over the regular algebra are associated. These data describe completely, as a triangulated category, the singularity category of the artin algebra. A criterion on the Hom-finiteness of the singularity category is given in terms of the valued quiver of the artin algebra.

We study certain Schur functors which preserve singularity categories of rings and we apply them to study the singularity category of triangular matrix rings. In particular, combining these results with Buchweitz–Happel’s theorem, we can describe singularity categories of certain non-Gorenstein rings via the stable category of maximal Cohen–Macaulay modules. Three concrete examples of finite-dimensional algebras with the same singularity category are discussed.

We investigate the problem when the tensor functor by a bimodule yields a singular equivalence. It turns out that this problem is equivalent to the one when the Hom functor given by the same bimodule induces a triangle equivalence between the homotopy categories of acyclic complexes of injective modules. We give conditions on when a bimodule appears in a pair of bimodules, that defines a singular equivalence with level. We construct an explicit bimodule in a combinatorial manner, which yields a singular equivalence between a quadratic monomial algebra and its associated algebra with radical square zero. Under certain conditions which include the Gorenstein cases, the bimodule does appear in a pair of bimodules defining a singular equivalence with level.