Stability of Gorenstein flat categories with respect to a semidualizing module

In this paper, we first introduce $\mathcal {W}_F$-Gorenstein modules to establish the following Foxby equivalence: \xymatrix@C=80pt{\mathcal {G}(\mathcal {F})\cap \mathcal {A}_C(R) \ar@[r]^{C\otimes_R-} & \mathcal {G}(\mathcal {W}_F) \ar@[l]^{\textrm{Hom}_R(C,-)}} where $\mathcal {G}(\mathcal {F})$, $\mathcal {A}_C(R)$ and $\mathcal {G}(\mathcal {W}_F)$ denote the class of Gorenstein flat modules, the Auslander class and the class of $\mathcal {W}_F$-Gorenstein modules respectively. Then, we investigate two-degree $\mathcal {W}_F$-Gorenstein modules. An $R$-module $M$ is said to be two-degree $\mathcal {W}_F$-Gorenstein if there exists an exact sequence \mathbb{G}_\bullet=\indent ...\longrightarrow G_1\longrightarrow G_0\longrightarrow G^0\longrightarrow G^1\longrightarrow... in $\mathcal {G}(\mathcal {W}_F)$ such that $M \cong$ \im(G_0\rightarrow G^0) and that $\mathbb{G}_\bullet$ is Hom$_R(\mathcal {G}(\mathcal {W}_F),-)$ and $\mathcal {G}(\mathcal {W}_F)^+\otimes_R-$ exact. We show that two notions of the two-degree $\mathcal {W}_F$-Gorenstein and the $\mathcal {W}_F$-Gorenstein modules coincide when R is a commutative GF-closed ring.Comment: 18 page

Representations over diagrams of abelian categories I: Global structure and homological objects

Representations over diagrams of abelian categories unify quite a few notions appearing widely in literature such as representations of categories, presheaves of modules over categories, representations of species, etc. In this series of papers we study them systematically, characterizing special homological objects in representation category and constructing various structures (such as model structures and Wandhuasen category strcutres) on it. In the first paper we investigate the Grothendieck structure of the representation category, describe important functors and adjunction relations between them, and characterize special homological objects. These results lay a foundation for our future works.Comment: We reorganize the work in the original version as a series of papers, and this is the first on

A flat model structure on functor categories

In this paper we construct a flat model structure on the category $_{{\mathcal{Q}},A}{\rm Mod}$ of additive functors from a preadditive category ${\mathcal{Q}}$ satisfying certain conditions to the module category $_{A}{\rm Mod}$, whose homotopy category is the ${\mathcal{Q}}$-shaped derived category introduced by Holm and Jorgensen.Comment: 11 pages. Any comments are very welcom

Screening Acute HIV Infections among Chinese Men Who Have Sex with Men from Voluntary Counseling & Testing Centers

Recent studies have shown the public health importance of identifying acute HIV infection (AHI) in the men who have sex with men (MSM) of China, which has a much higher risk of HIV transmission. However, cost-utility analyses to guide policy around AHI screening are lacking.An open prospective cohort was recruited among MSM living in Liaoning Province, Northeast China. Blood samples and epidemiological information were collected every 10 weeks. Third-generation ELISA and rapid test were used for HIV antibody screening, western blot assay (WB) served for assay validation. Antibody negative specimens were tested with 24 mini-pool nucleic acid amplification testing (NAAT). Specimens with positive ELISA but negative or indeterminate WB results were tested with NAAT individually without mixing. A cost-utility analysis of NAAT screening was assessed. Among the 5,344 follow-up visits of 1,765 MSM in 22 months, HIV antibody tests detected 114 HIV chronic infections, 24 seroconverters and 21 antibody indeterminate cases. 29 acute HIV infections were detected with NAAT from 21 antibody indeterminate and 1,606 antibody negative cases. The HIV-1 prevalence and incidence density were 6.6% (95% CI: 5.5–7.9) and 7.1 (95% CI: 5.4–9.2)/100 person-years, respectively. With pooled NAAT and individual NAAT strategy, the cost of an HIV transmission averted was $1,480. The addition of NAAT after HIV antibody tests had a cost-utility ratio of$3,366 per gained quality-adjusted life year (QALY). The input-output ratio of NAAT was about 1∶16.9.The HIV infections among MSM continue to rise at alarming rates. Despite the rising cost, adding pooled NAAT to the HIV antibody screening significantly increases the identification of acute HIV infections in MSM. Early treatment and target-oriented publicity and education programs can be strengthened to decrease the risk of HIV transmission and to save medical resources in the long run

STABILITY OF GORENSTEIN FLAT CATEGORIES WITH RESPECT TO A SEMIDUALIZING MODULE

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Tumour Calcification and Calciphylaxis in End-Stage Renal Disease

Although soft tissue and vascular calcifications are common in CKD and progress as an independent risk factor of all-cause mortality, tumour calcification and calciphylaxis are uncommon in patients with end-stage renal disease (ESRD). Here, we discuss a rare case of a patient with tumour calcification complicated with calciphylaxis developed septic shock from infection. Our patient is a 57-year-old man in his late stage of renal disease who presented with a huge mass at the right hip and necrotic cutaneous ulcers on the lower legs followed by local and systemic infection and death due to septic shock