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In this article, we study the n × n matrices over a finite distributive lattice L. By using join irreducible elements in L, we first give some concrete ways to decompose L into a subdirect product of some chains. Also, it is showed that by a subdirect embedding from semiring R to the direct product of semirings R 1, R 2, … , R m , we can give a corresponding subdirect embedding from the matrix semiring M n (R) to semiring . Based on the above results, it is proved that a square matrix over a finite distributive lattice L can be decomposed into the sum of matrices over some special subchains of L. This generalizes and extends the corresponding results obtained by Fan [Z.T. Fan, The Theory and Applications of Fuzzy Matrices, Science Publication, Beijing, 2006 (in Chinese)] and by Zhao et al. [X.Z. Zhao, Y.B. Jun, and F. Ren, The semiring of matrices over a finite chain, Inform. Sci. 178 (2008), pp. 3443–3450]. As some applications, we present a method to calculate the indices and periods of the matrices ove...

The translation hull of semigroups plays an important role in the algebraic theory of semigroups. It is an important tool in the study of ideal extensions.

Because of a complicated metamorphic history, the isotopic systematics of the ultrahigh-pressure (UHP) metamorphic rocks in the Dabie-Sulu belt, east China, appear to be rather different from what were expected. Depending on the degree of retrograde metamorphism and on the retentivity of isotopes, the radiogenic isotopic systematics in the UHP metamorphic rocks yielded a wide range of radiometric ages. Some of these ages are geologically meaningful, but others may not be. In some fine-grained UHP metamorphic rocks, Sm/Nd isotopic systematics appear to be in equilibrium among the UHP phases, showing the best estimate for the age of peak metamorphism at 226 ± 3 Ma. On the other hand, retrograde overprinting often makes the interpretation of isotopic data more difficult. It is common to find that the Sm/Nd and Rb/Sr isotopic systematics among the UHP phases and retrograde phases are not in equilibrium. Regression of isotopic data involving both UHP and retrograde minerals in isotopic correlation diagrams oft...

LetLbe a distributive lattice andMn,q(L)(Mn(L), resp.) the semigroup (semiring, resp.) ofn×q(n×n, resp.) matrices overL. In this paper, we show that if there is a subdirect embedding from distributive latticeLto the direct product∏i=1m‍Liof distributive latticesL1,L2, …,Lm, then there will be a corresponding subdirect embedding from the matrix semigroupMn,q(L)(semiringMn(L), resp.) to semigroup∏i=1m‍Mn,q(Li)(semiring∏i=1m‍Mn(Li), resp.). Further, it is proved that a matrix over a distributive lattice can be decomposed into the sum of matrices over some of its special subchains. This generalizes and extends the decomposition theorems of matrices over finite distributive lattices, chain semirings, fuzzy semirings, and so forth. Finally, as some applications, we present a method to calculate the indices and periods of the matrices over a distributive lattice and characterize the structures of idempotent and nilpotent matrices over it. We translate the characterizations of idempotent and nilpotent matrices over a distributive lattice into the corresponding ones of the binary Boolean cases, which also generalize the corresponding structures of idempotent and nilpotent matrices over general Boolean algebras, chain semirings, fuzzy semirings, and so forth.

Background and objectives: The associations of pathological features with renal outcomes in adult Idiopathic Membranous Nephropathy (IMN) are still controversial. A meta-analysis was performed to assess whether pathological features could independently predict risk of progressive kidney disease in adult IMN patients. Methods: The PubMed database (January 2000 to September 2013) was searched to identify cohort studies of adult IMN patients (≥ 50 patients for each study) in which at least one of the following pathological features was assessed: segmental sclerosis, tubular atrophy/interstitial fibrosis, arteriosclerosis, C3 deposits by immunofluorescence, and the stage or heterogeneity of electron dense deposits by electron microscopy. Renal outcomes included development of renal insufficiency or progression to ESRD. Results: Nine cohort studies were included. A total of 2080 patients with 252 hard endpoints (renal insufficiency or ESRD) were reported. Segmental sclerosis was significantly associated with poor renal outcomes (8 studies with 1622 patients: hazard ratio, 1.59 [95% confidence interval, 1.07-2.37], P=0.02). Tubular atrophy/interstitial fibrosis and arteriosclerosis were also significantly associated with poor renal outcomes (7 studies with 1569 patients: 3.85 [2.16-6.87], P

Background Tripterygium wilfordii Hook F (TwHF), a traditional Chinese herbal medicine used as an immunosuppressive agent, has been prescribed in China for patients with primary nephrotic syndrome (NS) for more than two decades. Although patients with primary NS in China have benefited from TwHF treatment, its properties have not yet been fully understood. Objectives To assess the benefits and harms of TwHF for patients with primary NS. Search methods We searched the Cochrane Renal Group's specialised register (August 2012), Cochrane Register of Controlled Trials (CENTRAL, The Cochrane Library 2012, Issue 8), EMBASE (1966 to August 2012), and MEDLINE (1966 to August 2012). We also searched CBM (Chinese Biological Medical Database) (1978 to November 2010), CNKI (Chinese National Knowledge Infrastructure) (1979 to November 2010), VIP (ChongQing WeiPu Chinese Science and Technology Periodical Database) (1989 to November 2010), WanFang Database (1980 to November 2010), and reference lists of articles (6 November 2010). Selection criteria Only randomised controlled trials (RCTs) were included. Two standardised preparations of TwHF were investigated: ethanol-ethyl acetate extract and chloroform-methanol extract. All other TwHF preparations were excluded because of reported toxicities. Other traditional Chinese herbal medicines were also excluded. All included RCTs had a follow-up of at least three months. Data collection and analysis Data extraction and risk of bias assessment were undertaken independently by two authors. Where details of randomised sequence generation and allocation concealment were absent or inadequately reported, we contacted original study investigators for verification and details of the procedure. For dichotomous outcomes (remission and drug-related adverse events) we used risk ratio (RR) with 95% confidence intervals (95% CI) and mean difference (MD) for continuous outcomes (urinary protein excretion, serum albumin and serum creatinine). Main results Ten studies enrolling 630 participants were included. Overall, the quality of evidence was suboptimal due to the small number of included studies enrolling small numbers of participants; short follow-up in each study; only a few studies in each comparison category; and major concerns with methodological bias. Four studies (293 participants) contributed to the comparison of TwHF versus non-TwHF. TwHF significantly increased complete remission (RR 1.46, 95% CI 1.18 to 1.80) and complete or partial remission (RR 1.26, 95% CI 1.10 to 1.44) without escalating the adverse events profile at the last follow-up (12 to 16 months). Four studies (223 participants) compared TwHF with prednisone. There were no statistically significant differences between complete remission, partial remission, and complete or partial remission. Two studies (114 participants) contributed to the comparison of TwHF versus cyclophosphamide (CPA) at the last follow-up (3 to 12 months). There were no statistically significant differences between complete, partial, or complete or partial remission. One study (46 participants) reported TwHF was associated with a significantly lower serum creatinine compared with CPA (MD -14.00 μmol/L, 95% CI -26.43 to -1.57). No serious adverse events of TwHF were observed. One study (37 participants) reported TwHF was associated with a significantly lower risk of psychosis when compared to prednisone (RR 0.11, 95% CI 0.01 to 0.75), and two studies showed a significantly lower risk of hair loss with TwHF when compared to CPA ((2 studies, 114 participants): RR 0.11, 95% CI 0.02 to 0.59). Authors' conclusions TwHF may have an add-on effect on remission in patients with primary NS. There was insufficient evidence to assess if TwHF was as effective as prednisone or CPA. More methodologically sound and sufficiently powered studies, with adequate follow-up would help to better inform management options for the use of TwHF for primary NS. TwHF should be further directly compared with other widely used immunosuppressive agents after the superiority over placebo or no treatment has been clearly established.

Peripheral artery disease (PAD) may lead to a poor quality of life. Although percutaneous transluminal angioplasty (PTA) is widely used for the treatment of PAD, restenosis remains a major drawback. Hydrogen sulfide (H2S) plays potential roles in many physiological processes, such as vasodilatation and inhibition of smooth muscle cell proliferation. However, little is known regarding its role in arterial restenosis. In this study, we induced atherosclerotic-like lesions in rabbits, and we treated the rabbits with balloon angioplasty (BA) in a similar manner as PTA performed in the clinic. The rabbits were treated with sodium hydrosulfide (NaHS, a donor of H2S) or DL-propargylglycine (PPG, an inhibitor of H2S synthase). Treatment with NaHS significantly inhibited arterial restenosis following BA by reducing the intimal area and the intima/media ratio, while PPG treatment had a tendency to result in more severe restenosis. NaHS treatment significantly reduced smooth muscle cell (SMC) proliferation and elevated SMC apoptosis in the neointima. In contrast, PPG induced a significant increase in SMC proliferation. In conclusion, H2S attenuates the progression of neointimal hyperplasia and inhibits restenosis after BA. This discovery may lead to potential novel therapies, which can improve the prognosis of PAD patients.

BACKGROUND: There have been an increasing number of studies with evidence suggesting that the N-acetyltransferase 1 (NAT1) and N-acetyltransferase 2 (NAT2) genotypes may be implicated in the development of colorectal cancer (CRC) and colorectal adenoma (CRA). So far the published data on this association has remained controversial, however. We performed a meta-analysis of case-cohort and case-control studies using a subset of the published data, with an aim to derive a better understanding of the underlying relationship. METHODS/PRINCIPAL FINDINGS: A literature search was performed using Medline database for relevant studies published through October 31, 2011. A total of 39 publications were selected for this meta-analysis, including 11,724 cases and 16,215 controls for CRC, and 3,701 cases and 5,149 controls for CRA. In our pooled analysis of all these studies, the results of our meta-analysis suggested that the NAT1 genotype was not significantly associated with an elevated CRC risk (OR 0.99, 95% CI 0.91-1.07). We also found that individuals with the rapid NAT2 genotype did have an elevated risk of CRC (OR 1.07, 95% CI 1.01-1.13). There was no evidence for an association between the NAT1 and 2 rapid genotype and an elevated CRA risk (NAT1: OR 1.14, 95% CI 0.99-1.29; NAT2: OR 0.94, 95% CI 0.86-1.03). CONCLUSION: This meta-analysis suggests that individuals with NAT2 genotype had an elevated risk of CRC. There was no evidence for the association between NAT1 and 2 rapid genotype and CRA risk.

The existence of excess Ar in phengites from coesite-bearing ultrahigh-pressure eclogites of the Dabie Mountains and SuLu terrain, China, has been confirmed by dating of minerals using SmNd, RbSr and 40Ar39Ar methods. 40Ar39Ar ages of phengites for two samples studied are much older than the SmNd and RbSr mineral isochron ages: sample QL-1 has RbSr age of 219.5 ± 0.5 Ma, SmNd age of 226.3 ± 4.5 Ma and phengite 40Ar39Ar age of 877.5 ± 15.9 Ma; the corresponding ages for sample Zb-4 are: 223.9 ± 0.9 Ma (RbSr), 228.4 ± 6.0 Ma (SmNd) and 943.3 ± 12.4 Ma (40Ar39Ar, phengite). An age of ∼225 Ma based on the SmNd and RbSr mineral isochron ages is consistent with the time inferred from paleomagnetic and geological data for collision of the North China and Yangtse Blocks and formation of these eclogites. We call for greater caution in 40Ar39Ar dating of phengites from other occurrences of ultrahigh-pressure environments.

Various types of eclogite, including coesite-bearing varieties formed under high-P-high-T conditions (up to 27 kbar, 700–800°C), and glaucophane schist occur in the Dabie Mountains and the SuLu terrane, eastern China. Dating of these high-pressure rocks by the SmNd mineral isochron and 40 Ar 39 Ar method suggests that the occurrence of the high-pressure metamorphism was during the early Triassic. LREE-enriched chondrite-normalized patterns for type-II eclogites and low initial ϵNd of − 14 to − 3 and the 87 Sr 86 Sr-values (0.706–0.710) for various types of eclogites suggest that their protoliths were mainly derived from Precambrian island arc or intraplate basalts in the basement of the Yangtse Block and the enriched pyroxenite layer in alpine peridotite. The P-T-t path of eclogite from the southern Dabie Mountains suggests that the uplift history of eclogite in the Dabie Mountains can be subdivided into two stages: (1) fast uplift driven by thrust during continental-continental collision and deep subduction (at 221 Ma) of the continental crust; (2) later gentle uplift with rise of the Dabie Mountains in the late Jurassic and Cretaceous (at 134 Ma). It is proposed that the collision between the North China Block and Yangtse Block began in the late Permian or early Triassic with a north-dipping subduction zone. This was followed by subduction of the continental crust of the Yangtse Block under the North China Block during the Triassic. These two continental blocks were welded into a single tectonic unit in the late Jurassic or early Cretaceous. Different cooling histories for a coexisting gneiss and eclogite pair from Shima area suggest that the eclogite and their country rocks are not always coherent to each other. Some of them may have been juxtaposed through tectonic processes from different levels.

BACKGROUND: Idiopathic membranous nephropathy (IMN) is the most common form of nephrotic syndrome in adults. The disease shows a benign or indolent course in the majority of patients, with a rate of spontaneous complete or partial remission of nephrotic syndrome as high as 30% or more. Despite this, 30% to 40% of patients progress toward end‐stage kidney disease (ESKD) within five to 15 years. The efficacy and safety of immunosuppression for IMN with nephrotic syndrome are still controversial. This is an update of a Cochrane review first published in 2004. OBJECTIVES: The aim of this review was to evaluate the safety and efficacy of immunosuppressive treatments for adult patients with IMN and nephrotic syndrome. Moreover it was attempted to identify the best therapeutic regimen, when to start immunosuppression and whether the above therapies should be given to all adult patients at high risk of progression to ESKD or only restricted to those with impaired kidney function. SEARCH METHODS: We searched Cochrane Renal Group Specialised Register, Cochrane Central Register of Controlled Trials (CENTRAL), MEDLINE, EMBASE, Chinese databases, reference lists of articles, and clinical trial registries to June 2014. We also contacted principal investigators of some of the studies for additional information. SELECTION CRITERIA: Randomised controlled trials (RCTs) investigating the effects of immunosuppression in adults with IMN and nephrotic syndrome. DATA COLLECTION AND ANALYSIS: Study selection, data extraction, quality assessment, and data synthesis were performed using the Cochrane‐recommended methods. Summary estimates of effect were obtained using a random‐effects model, and results were expressed as risk ratios (RR) and their 95% confidence intervals (CI) for dichotomous outcomes, and mean difference (MD) and 95% CI for continuous outcomes. MAIN RESULTS: Thirty nine studies with 1825 patients were included, 36 of these could be included in our meta‐analyses. The data from two studies could not be extracted and one study was terminated due to poor accrual. Immunosuppression significantly reduced all‐cause mortality or risk of ESKD ((15 studies, 791 patients): RR 0.58 (95% CI 0.36 to 0.95, P = 0.03) and risk of ESKD ((15 studies, 791 patients): RR 0.55, 95% CI 0.31 to 0.95, P = 0.03), increased complete or partial remission ((16 studies, 864 patients): RR 1.31, 95% CI 1.01 to 1.70, P = 0.04), and decreased proteinuria ((9 studies,(393 patients): MD ‐0.95 g/24 h, 95% CI ‐1.81 to ‐0.09, P = 0.03) at the end of follow‐up (range 6 to 120 months). However this regimen was associated with more discontinuations or hospitalisations ((16 studies, 880 studies): RR 5.35, 95% CI 2.19 to 13.02), P = 0.0002). Combined corticosteroids and alkylating agents significantly reduced death or risk of ESKD ((8 studies, 448 patients): RR 0.44, 95% CI 0.26 to 0.75, P = 0.002) and ESKD ((8 studies, 448 patients): RR 0.45, 95% CI 0.25 to 0.81, P = 0.008), increased complete or partial remission ((7 studies, 422 patients): RR 1.46, 95% CI 1.13 to 1.89, P = 0.004) and complete remission ((7 studies, 422 patients): RR 2.32, 95% CI 1.61 to 3.32, P < 0.00001), and decreased proteinuria ((6 studies, 279 patients): MD ‐1.25 g/24 h, 95% CI ‐1.93 to ‐0.57, P = 0.0003) at the end of follow‐up (range 9 to 120 months). In a population with an assumed risk of death or ESKD of 181/1000 patients, this regimen would be expected to reduce the number of patients experiencing death or ESKD to 80/1000 patients (range 47 to 136). In a population with an assumed complete or partial remission of 408/1000 patients, this regimen would be expected to increase the number of patients experiencing complete or partial remission to 596/1000 patients (range 462 to 772). However this combined regimen was associated with a significantly higher risk of discontinuation or hospitalisation due to adverse effects ((4 studies, 303 patients): RR 4.20, 95% CI 1.15 to 15.32, P = 0.03). Whether this combined therapy should be indicated in all adult patients at high risk of progression to ESKD or only restricted to those with deteriorating kidney function still remained unclear. Cyclophosphamide was safer than chlorambucil ((3 studies, 147 patients): RR 0.48, 95% CI 0.26 to 0.90, P = 0.02). There was no clear evidence to support the use of either corticosteroid or alkylating agent monotherapy. Cyclosporine and mycophenolate mofetil failed to show superiority over alkylating agents. Tacrolimus and adrenocorticotropic hormone significantly reduced proteinuria. The numbers of corresponding studies related to tacrolimus, mycophenolate mofetil, adrenocorticotropic hormone, azathioprine, mizoribine, and Tripterygium wilfordii are still too sparse to draw final conclusions. AUTHORS' CONCLUSIONS: In this update, a combined alkylating agent and corticosteroid regimen had short‐ and long‐term benefits on adult IMN with nephrotic syndrome. Among alkylating agents, cyclophosphamide was safer than chlorambucil. This regimen was significantly associated with more withdrawals or hospitalisations. It should be emphasised that the number of included studies with high‐quality design was relatively small and most of included studies did not have adequate follow‐up and enough power to assess the prespecified definite endpoints. Although a six‐month course of alternating monthly cycles of corticosteroids and cyclophosphamide was recommended by the KDIGO Clinical Practice Guideline 2012 as the initial therapy for adult IMN with nephrotic syndrome, clinicians should inform their patients of the lack of high‐quality evidence for these benefits as well as the well‐recognised adverse effects of this therapy. Cyclosporine or tacrolimus was recommended by the KDIGO Clinical Practice Guideline 2012 as the alternative regimen for adult IMN with nephrotic syndrome; however, there was no evidence that calcineurin inhibitors could alter the combined outcome of death or ESKD.