Background Vitamin D insufficiency or deficiency is associated with an altered microbiota in older men. However, the relationship between the gut microbiota and 25-hydroxyvitamin D (25(OH)D) levels remains unknown in postmenopausal women. In this study, fecal microbiota profiles for 88 postmenopausal women in the high 25(OH)D (HVD) group (n = 44) and the low 25(OH)D (LVD) group (n = 44) were determined. An integrated 16S rRNA gene sequencing and liquid chromatography–mass spectrometry (LC–MS)-based metabolomics approach was applied to explore the association of serum 25(OH)D levels with the gut microbiota and fecal metabolic phenotype. Adjustments were made using several statistical models for potential confounding variables identified from the literature. Results The results demonstrated that the community diversity estimated by the Observe, Chao1 and ACE indexes was significantly lower in the LVD group than in the HVD group. Additionally, two kinds of characteristic differences in the microflora were analyzed in the HVD group, and ten kinds of characteristic differences in the microflora were analyzed in the LVD group. We observed that some bacteria belonging to the genera Bifidobacterium, Bacillus, F0332 and Gemella, were enriched in the LVD group, as were other genera, including Lachnoclostridium, UC5_1_2E3, Ruminococcus_gnavus_group and un_f_Lachnospiraceae. Christensenellaceae, Eggerthellaceae and Cloacibacillus were enriched in the HVD group. The L-pyroglutamic acid, inosine, and L-homocysteic acid levels were higher in the HVD group and were negatively correlated with the 1,2-benzenedicarboxylic acid and cholic acid metabolic levels. Conclusions These observations provide a better understanding of the relationships between serum 25(OH)D levels and the fecal microbiota and metabolites in postmenopausal women.

In this paper, we consider the non-recombining trinomial tree pricing model under the volatility, which is a function of time, establish the option pricing model and give the convergence rates of the non-recombining trinomial tree method. In addition, we research the calibration problem of volatility and adopt an exterior penalty method to transform this problem into a nonlinear unconstrained optimization problem. For the optimization problem, we use the quasi-Newton algorithm. Finally, we test our model by numerical examples and options data on the S&P 500 index. The results show the effectiveness of the non-recombining trinomial tree pricing model.

In this paper, we combine the traditional binomial tree and trinomial tree to construct a new alternative tree pricing model, where the local volatility is a deterministic function of time. We then prove the convergence rates of the alternative tree method. The proposed model can price a wide range of derivatives efficiently and accurately. In addition, we research the optimization approach for the calibration of local volatility. The calibration problem can be transformed into a nonlinear unconstrained optimization problem by exterior penalty method. For the optimization problem, we use the quasi-Newton algorithm. Finally, we test our model by numerical examples and options data on the S&P 500 index. Numerical results confirm the excellent performance of the alternative tree pricing model.

Purpose To explore the efficacy and safety of fecal microbiota transplantation (FMT) as a treatment approach for ulcerative colitis (UC), a comprehensive systematic review and meta-analysis of randomized controlled trials was conducted. Methods To collect and evaluate randomized controlled trials of high quality on FMT for UC, we searched a number of databases, including PubMed, Web of Science, Cochrane, Embase, and Medline, for studies published between the establishment of the databases and March 2023. We conducted a meta-analysis of the studies using Review Manager software (version 5.4.1) to determine the differences in rates of remission and adverse reactions between the FMT group and the control group, utilizing the risk ratio (RR) and 95% confidence interval (CI) to combine our findings. Results A total of 13 RCTs on the efficacy of FMT in patients with UC were included in the study, in which 580 patients participated, including 293 patients treated with FMT and 287 control subjects. Meta-analysis revealed that clinical remission was significantly better in the FMT group than in the control group [RR = 1.73; 95% CI = (1.41, 2.12); P < 0.00001]; endoscopic remission was significantly better in the FMT group than in the control group [RR = 1.74; 95% CI = (1.24, 2.44); P = 0.001]. Additionally, there were no significant differences in the incidence of adverse reactions between the two groups [RR = 1.00; 95% CI = (0.86, 1.15); P = 0.96]. Conclusions FMT is an effective treatment for UC with good clinical remission rates and endoscopic remission rates. However, safety remains a concern during treatment and measures must be taken to enhance both safety and success rates.

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