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关键词： Extension dimension   Weak resolution dimension   Homological invariants   Radical layer length   Ring extensions   Recollements  

摘要： Let A be an abelian category having enough projective objects and enough injective objects. We prove that if A admits an additive generating object, then the extension dimension and the weak resolution dimension of A are identical, and they are at most the representation dimension of A minus two. By using it, for a right Morita ring Lambda, we establish the relation between the extension dimension of the category mod Lambda of finitely generated right Lambda-modules and the representation dimension as well as the right global dimension of Lambda. In particular, we give an upper bound for the extension dimension of mod Lambda in terms of the projective dimension of certain class of simple right Lambda-modules and the radical layer length of Lambda. In addition, we investigate the behavior of the extension dimension under some ring extensions and recollements.

关键词： Commutative ring   Derived category   t-Structure   Cosilting complex  

摘要： We classify all compactly generated t-structures in the unbounded derived category of an arbitrary commutative ring, generalizing the result of Alonso Tarrio et al. (J Algebra 324(3):313-346, 2010) for noetherian rings. More specifically, we establish a bijective correspondence between the compactly generated t-structures and infinite filtrations of the Zariski spectrum by Thomason subsets. Moreover, we show that in the case of a commutative noetherian ring, any bounded below homotopically smashing t-structure is compactly generated. As a consequence, all cosilting complexes are classified up to equivalence.

关键词： A skew category algebra   A simple algebra   A left Noetherian algebra   A semiprime algebra  

摘要： We study a new (large) class of algebras (that was introduced in Bavula in Math Comput Sci 11(34):253-268, 2017)-the skew category algebras. Any such an algebra C(sigma) is constructed from a category C and a functor sigma from the category C to the category of algebras. Criteria are given for the algebra C(sigma) to be simple or left Noetherian or right Noetherian or semiprime or have 1.

关键词： Super-modular categories   Spin modular categories   Classification by rank   Fermionic quotient  

摘要： We pursue a classification of low-rank super-modular categories parallel to that of modular categories. We classify all super-modular categories up to rank = 6, and spin modular categories up to rank = 11. In particular, we show that, up to fusion rules, there is exactly one non-split super-modular category of rank 2, 4 and 6, namely PSU(2)(4k+ 2) for k = 0,1 and 2. This classification is facilitated by adapting and extending well-known constraints from modular categories to super-modular categories, such as Verlinde and Frobenius-Schur indicator formulae.

关键词： abelian categories   cocompleteness  

摘要： An example of a cocomplete abelian category that is not complete is constructed.

关键词： Non-invasive follicular thyroid neoplasm with papillary-like nuclear features (NIFTP)   Risk of malignancy (ROM)   Thyroid cancer   Bethesda system  

摘要： In 2016, Nikiforov et al. (JAMA Oncol 2:1023-1029, 2016) proposed replacing the term "non-invasive encapsulated follicular variant of papillary thyroid carcinoma" (FVPTC) with the term "non-invasive follicular thyroid neoplasm with papillary-like nuclear features" (NIFTP). In 2018, to avoid the misdiagnosis of papillary thyroid cancer as NIFTP, the authors proposed changes to the criteria for NIFTP classification. Some previous studies evaluated the impact of NIFTP on the risk of malignancy (ROM) in the fine-needle aspiration cytology (FNAC) diagnostic categories according to the Bethesda System for Reporting Thyroid Cytopathology (TBSRTC). However, little is known about the influence of an NIFTP diagnosis on ROM on the basis of the revised criteria. The aim of this study was to assess the influence of NIFTP on ROM using the revised diagnostic criteria. The present study included 998 thyroid nodules that were diagnosed and resected at the same medical center. All specimens with a diagnosis of cancer were reviewed to identify NIFTP according to the revised 2018 criteria. Additionally, molecular diagnostics were performed to detect the BRAF p.V600E mutation and TERT promoter mutations in all the NIFTP cases. The number of cases that met the revised criteria was determined, and the ROM was calculated in each of the FNAC diagnostic categories. Only five cases (2.3% of all papillary thyroid carcinoma diagnoses) were considered NIFTP, according to the 2018 criteria. With respect to the FNAC category, one case was a follicular neoplasm or suspicious for a follicular neoplasm (FN/SFN), three cases were suspicious for malignancy (SM), and one case was malignant (M). The ROM decreased in each of the Bethesda categories (0.7% in FN/SFN, 4.3% in SM, and 0.5% in M) when a diagnosis of NIFTP was taken into account. These reductions were not statistically significant. These data indicate that the NIFTP entity has very little impact on ROM for the diagnostic categories of the Bethe

关键词： Cholangiocarcinoma   Distal bile duct   Stage   Depth   Survival  

摘要： According to the current 8th edition of the American Joint Committee of Cancer (AJCC), the T category of distal cholangiocarcinomas is classified based on the depth of invasion (DOI) (T1, < 5 mm;T2, between 5 and 12 mm;T3, > 12 mm). In consideration of the discrepancies between previous studies about the prognostic significance, we aimed to validate the current AJCC T staging system of distal cholangiocarcinomas. DOI was measured using three different methods: DOI1, DOI2, and DOI3. DOI1 was defined and stratified according to the AJCC 8th edition. DOI2 was measured as the distance from an imaginary curved line approximated along the distorted mucosal surface to the deepest invasive tumor cells. DOI3 was defined as the total tumor thickness. DOI2 and DOI3 were also divided into three categories using the same cut-off points as in the AJCC 8th edition. We compared these three DOI methods to the AJCC 7th edition as well. In contrast with the AJCC 7th edition, all three groups showed a correlation with patients' overall survival. Above all, the DOI2 group demonstrated the best significance in multivariate analysis. However, when the C indices were compared between these groups, differential significance proved to be negligible (DOI1 vs DOI2, p = 0.915;DOI2 vs DOI3, p = 0.057). Therefore, the measurement of DOI does not need to be rigorously and stringently performed. In conclusion, we showed that the current T classification system better correlates with the overall survival of patients with distal cholangiocarcinomas than the previous system.

关键词： Quantale   Quantale-semimodule   Quantale-valued fuzzy automata   Minimizatin   Deteminization   Category  

摘要： The objective of this paper is to introduce quantale-valued (in short Q-valued) fuzzy automata and its categories. The Q-valued fuzzy automaton in order to introduce here differs from the existing studies in the sense that the state-set itself is a quantale semimodule (in short Q-semimodule). Next, we introduce deterministic Q-valued fuzzy automaton and study the determinization of Q-valued fuzzy automata by using of Q-valued power set functor and show the existence of final object in the subcategory of category of deterministic Q-valued fuzzy automata. Finally, we show that the existence of minimal deterministic Q-valued fuzzy automata in the category of deterministic Q-valued fuzzy automata by using functorial maps.

摘要： We study the path category of an inverse semigroup admitting unique maximal idempotents and give an abstract characterization of the inverse semigroups arising from zigzag maps on a left cancellative category. As applications we show that every inverse semigroup is Morita equivalent to an inverse semigroup of zigzag maps and hence the class of Cuntz-Krieger C-algebras of singly aligned categories include the tight C-algebras of all countable inverse semigroups, up to Morita equivalence.

关键词： Pain disorder subtypes   Complex network analysis   Network pharmacology   Cancer pain  

摘要： Chronic pain is highly prevalent and poorly controlled, of which the accurate underlying mechanisms need be further elucidated. Herbal drugs have been widely used for controlling various pain disorders. The systematic integration of pain herbal data resources might be promising to help investigate the molecular mechanisms of pain phenotypes. Here, we integrated large-scale bibliographic literatures and well-established data sources to obtain high-quality pain relevant herbal data (i.e. 426 pain related herbs with their targets). We used machine learning method to identify three distinct herb categories with their specific indications of symptoms, targets and enriched pathways, which were characterized by the efficacy of treatment to the chronic cough related neuropathic pain, the reproduction and autoimmune related pain, and the cancer pain, respectively. We further detected the novel pathophysiological mechanisms of the pain subtypes by network medicine approach to evaluate the interactions between herb targets and the pain disease modules. This work increased the understanding of the underlying molecular mechanisms of pain subtypes that herbal drugs are participating and with the ultimate aim of developing novel personalized drugs for pain disorders.