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In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once the voltage reaches a threshold. In this work, the main goal is to establish the convergence relationship between the regularized process and the original one where in the regularized process, the jump mechanism is replaced by a Poisson dynamic, and jump intensity within the classically forbidden domain goes to infinity as the regularization parameter vanishes. On the macroscopic level, the Fokker-Planck equation for the process with random discharges (i.e. Poisson jumps) are defined on the whole space, while the equation for the limit process is on the half space. However, with the iteration scheme, the difficulty due to the domain differences has been greatly mitigated and the convergence for the stochastic process and the firing rates can be established. Moreover, we find a polynomial-order convergence for the distribution by a re-normalization argument in probability theory. Finally, by numerical experiments, we quantitatively explore the rate and the asymptotic behavior of the convergence for both linear and nonlinear models., This is a new version of the existed paper and I should not submit a new one. Please see arXiv:2009.04679

In this work, we are concerned with the Fokker-Planck equations associated with the Nonlinear Noisy Leaky Integrate-and-Fire model for neuron networks. Due to the jump mechanism at the microscopic level, such Fokker-Planck equations are endowed with an unconventional structure: transporting the boundary flux to a specific interior point. While the equations exhibit diversified solutions from various numerical observations, the properties of solutions are not yet completely understood, and by far there has been no rigorous numerical analysis work concerning such models. We propose a conservative and conditionally positivity preserving scheme for these Fokker-Planck equations, and we show that in the linear case, the semi-discrete scheme satisfies the discrete relative entropy estimate, which essentially matches the only known long time asymptotic solution property. We also provide extensive numerical tests to verify the scheme properties, and carry out several sets of numerical experiments, including finite-time blowup, convergence to equilibrium and capturing time-period solutions of the variant models.

Adiponectin, as an important adipocytokine, plays a pivotal role in the regulation of insulin sensitivity and metabolism. It has been reported that circulating adiponectin levels were decreased in women with polycystic ovary syndrome (PCOS). However, the results remained inconsistent. In order to derive a more precise estimation of this relationship, a large meta-analysis was performed in this study. A comprehensive systematic electronic search was conducted in electronic databases PubMed, EMBASE, and Web of Science up to November 30, 2013. Pooled weighted mean differences (WMDs) with 95 % confidence intervals (CIs) were calculated to estimate the strength of the association. A meta-analysis technique was used to study 38 trials involving 1,944 PCOS women and 1,654 healthy controls. Overall pooled adiponectin levels in women with PCOS were significantly reduced compared with healthy controls (WMD −2.67, 95 % CI −3.22 to −2.13; P = 0.000), yet with significant heterogeneity across studies (I2 = 95.9 %, P = 0.000). In subgroup analysis by HOMA-IR ratio and total testosterone ratio, inconsistent results were presented. No single study was found to affect the overall results by sensitivity testing. Meta-regression suggested that BMI might contribute little to the heterogeneity between including studies. Cumulative meta-analysis demonstrated the reliability and stability of the meta-analysis results. No evidence of publication bias was observed. Our meta-analysis suggested that circulating adiponectin levels in women with PCOS were significantly lower than those in healthy controls, which indicated that circulating adiponectin might play a role in the development of PCOS.

The efficacy of probiotics supplementation in children undergoing Helicobacter pylori (H. pylori) eradication therapy remains controversial. This study aimed to meta-analyze whether probiotics supplementation in triple therapy could improve H. pylori eradication rates and reduce therapy-related side effects in children. Electronic databases PubMed and Embase were searched to identify all randomized controlled trials in pediatric patients comparing probiotics supplementation with placebo or no extra intervention in H. pylori eradication therapy. Two authors independently extracted the data. Results were expressed as odds ratios (ORs) and accompanying 95 % confidence intervals (CIs). Stata version 12.0 was used to perform all statistical analyses. Seven studies consisting of 508 pediatric patients were included in our study. The pooled ORs (studies n = 7) of eradication rates by intention-to-treat and per-protocol analysis in the probiotics group versus the control group were 1.96 (95 % CI 1.28–3.02) and 2.25 (95 % CI 1.41–3.57), respectively. The pooled OR (studies n = 5) of incidence of total side effects was 0.32 (95 % CI 0.13–0.79), with significant heterogeneity observed (I2 = 71.9 %). Conclusion: Probiotics supplementation in triple therapy for H. pylori infection may have beneficial effects on eradication and therapy-related side effects, particularly diarrhea, in children.

CR1 polymorphisms have been reported to be associated with late-onset Alzheimer's disease (LOAD) susceptibility. The findings of these studies, however, have been inconsistent. Therefore, we performed a meta-analysis to assess the association between CR1 variants and LOAD susceptibility. We retrieved all relevant studies of the associations between CR1 polymorphisms and the susceptibility to LOAD for the period up to March 30, 2014. The strength of the association between CR1 polymorphisms and LOAD risk was estimated by odds ratios (ORs) and their 95% confidence intervals (CIs). A total of 6 articles were eventually identified with 2752 LOAD cases and 2313 controls for the rs6656401 polymorphism, and 4 studies containing 2547 LOAD cases and 2338 controls were included for the rs3818361 polymorphism. Overall, the pooled data showed that the CR1 rs6656401 polymorphism was significantly associated with LOAD risk in the overall population (A vs. G: OR=1.32, 95%CI=1.17-1.50, P=0.000; AG+AA vs. GG: OR=1.39, 95%CI=1.20-1.61, P=0.000). With respect to the CR1 rs3818361 polymorphism, a statistically significant increased LOAD risk was observed in the overall population (T vs. C: OR=1.24, 95% CI=1.13-1.37, P=0.000; TT+TC vs. CC: OR=1.30, 95% CI=1.15-1.46, P=0.000; TT vs. TC+CC: OR=1.35, 95% CI=1.06-1.71, P=0.014). This meta-analysis demonstrated significant associations of both the CR1 rs6656401 and CR1 rs3818361 polymorphisms with LOAD susceptibility.

The purpose of this study was to conduct a meta-analysis to assess the association between FSHR Asn680Ser polymorphism and ovarian cancer susceptibility.A literature search was conducted in PubMed, Embase and the China National Knowledge Infrastructure (CNKI) for all relevant studies published up to September 2013. The pooled odds ratios (ORs) with the corresponding 95 % confidence intervals (95 % CIs) were calculated to evaluate the association.Four case-control studies including 474 ovarian cancer cases and 659 controls met the inclusion criteria. The pooled analyses showed that FSHR Asn680Ser polymorphism was associated with the risk of ovarian cancer (Ser vs Asn: OR=1.295, 95 % CI 1.057-1.498, P=0.01; Ser/Ser + Asn/Ser vs Asn/Asn: OR=1.611, 95 % CI 1.027-2.528, P=0.038). Subgroup analyses by ethnicity (Caucasian and Asian) further revealed significant associations among Asians (Ser vs Asn: OR=1.386, 95 % CI 1.066-1.802, P=0.015; Ser/Ser + Asn/Ser vs Asn/Asn: OR=1.893, 95 % CI 1.329-2.689, P=0.000) but not Caucasians. There was no obvious risk of publication bias.The meta-analysis suggests that FSHR Asn680Ser polymorphism may be a risk factor for ovarian cancer in Asians. Due to the limited quantity of the included studies, further studies are needed to validate the above conclusions.

This study aimed to derive a more precise estimate of the prognostic significance of S-1-based therapy over S-1 monotherapy in patients with advanced gastric cancer (AGC), including overall survival (OS) time, progression-free survival (PFS) time, objective response rate (ORR), and adverse events (AEs). Studies stratifying OS, PFS, ORR, and AEs in AGC patients in an S-1-based therapy versus an S-1 monotherapy setting were eligible for analysis by systematic computerized PubMed, Embase and Cochrane Library searches. Data from these studies were pooled using STATA package version 11.0. Six studies that investigated outcomes in a total of 913 AGC cases, of which 443 (48.5 %) received S-1-based therapy and 470 (51.5 %) received S-1 monotherapy, were included in the meta-analysis. Median OS and median PFS were significantly prolonged in AGC patients receiving S-1-based therapy compared with those receiving S-1 monotherapy (hazard ratio [HR] 0.83, 95 % confidence interval [CI] 0.71–0.96, P = 0.015, and HR 0.69, 95 % CI 0.60–0.80, P = 0.000, respectively). The ORR favored patients with S-1-based therapy (OR 1.65, 95 % CI 1.34–2.06, P = 0.000). Higher incidence of grade 3/4 neutropenia was found in patients with S-1-based therapy (P = 0.000). For the Asian population, S-1-based therapy significantly improved OS and PFS and enhanced ORR in comparison to S-1 monotherapy. The safety profile was poorer in patients with S-1-based therapy, but could be considerable between the S-1-based therapy and S-1 monotherapy group. Our conclusion needs to be confirmed via high-quality trials and the results need to be reproduced in other regions and populations.

BACKGROUND: Many epidemiological studies have been conducted to explore the association between a single CYP2D6 gene polymorphism and Parkinson's disease (PD) susceptibility. However, the results remain controversial. OBJECTIVES: To clarify the effects of a single CYP2D6 gene polymorphism on the risk of PD, a meta-analysis of all available studies relating to CYP2D6*4 polymorphism and the risk of PD was conducted. METHODS: A comprehensive literature search of PubMed, EMBASE, and the China National Knowledge Infrastructure (CNKI) up to September 1, 2013 was conducted. Data were extracted by two independent authors and pooled odds ratio (OR) with 95% confidence interval (CI) were calculated. Meta-regression, Galbraith plots, subgroup analysis, sensitivity analysis, and publication bias analysis were also performed. RESULTS: Twenty-two separate comparisons consisting of 2,629 patients and 3,601 controls were included in our meta-analysis. The pooled analyses showed a significant association between CYP2D6*4G/A polymorphism and PD risk in all of the comparisons (A vs. G allele: OR = 1.28, 95% CI = 1.14-1.43, P = 0.001; AA vs. GG: OR = 1.43, 95% CI = 1.06-1.93, P = 0.018; AG vs. GG: OR = 1.22, 95% CI = 1.06-1.40, P = 0.006; AG+AA vs. GG: OR = 1.26, 95% CI = 1.10-1.44, P = 0.001; AA vs. AG+GG: OR = 1.37, 95% CI = 1.02-1.83, P = 0.036). In subgroup analysis stratified by ethnicity, significant associations were also demonstrated in Caucasians but not in Asians. No significant association was found in subgroup analysis stratified by age of onset or disease form. CONCLUSIONS: We concluded that the CYP2D6*4G/A polymorphism denotes an increased genetic susceptibility to PD in the overall population, especially in Caucasians. Further large and well-designed studies are needed to confirm this association.