The depth and the attracting centre for a continuous map on a fuzzy metric interval

[EN] Let I be a fuzzy metric interval and f be a continuous map from I to I. Denote by R(f), Ω(f) and ω(x, f) the set of recurrent points of f, the set of non-wandering points of f and the set of ω- limit points of x under f, respectively. Write ω(f) = ∪x∈Iω(x, f), ωn+1(f) = ∪x∈ωn(f)ω(x, f) and Ωn+1(f) = Ω(f|Ωn(f)) for any positive integer n. In this paper, we show that Ω2(f) = R(f) and the depth of f is at most 2, and ω3(f) = ω2(f) and the depth of the attracting centre of f is at most 2.Project supported by NNSF of China (11761011, 71862003) and NSF of Guangxi (2018GXNSFAA294010) and SF of Guangxi University of Finance and Economics (2019QNB10).Sun, T.; Li, L.; Su, G.; Han, C.; Xia, G. (2020). The depth and the attracting centre for a continuous map on a fuzzy metric interval. Applied General Topology. 21(2):285-294. https://doi.org/10.4995/agt.2020.13126OJS285294212A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Sys. 64 (1994), 395-399. https://doi.org/10.1016/0165-0114(94)90162-7M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets Sys. 27 (1989), 385-389. https://doi.org/10.1016/0165-0114(88)90064-4V. Gregori and J. J. Miñana, Some remarks on fuzzy contractive mappings, Fuzzy Sets Sys. 251 (2014), 101-103. https://doi.org/10.1016/j.fss.2014.01.002V. Gregori and J. J. Miñana, On fuzzy Ψ-contractive sequences and fixed point theorems, Fuzzy Sets Sys. 300 (2016), 93-101. https://doi.org/10.1016/j.fss.2015.12.010V. Gregori and A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets Sys. 125 (2002), 245-252. https://doi.org/10.1016/S0165-0114(00)00088-9X. Hu, Z. Mo and Y. Zhen, On compactnesses of fuzzy metric spaces (Chinese), J. Sichuan Norm. Univer. (Natur. Sei.) 32 (2009), 184-187.I. Kramosil and J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika 11 (1975), 336-344.C. Li and Y. Zhang, On connectedness of the Hausdorff fuzzy metric spaces, Italian J. Pure Appl. Math. 42 (2019), 458-466.D. Mihet, Fuzzy Ψ-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets Sys. 159 (2008), 739-744. https://doi.org/10.1016/j.fss.2007.07.006D. Mihet, A note on fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets Sys. 251 (2014), 83-91. https://doi.org/10.1016/j.fss.2014.04.010J. Rodríguez-López and S. Romaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets Sys. 147 (2004), 273-283. https://doi.org/10.1016/j.fss.2003.09.007B. Schweizer and A. Sklar, Statistical metrics paces, Pacif. J. Math. 10 (1960), 385-389. https://doi.org/10.2140/pjm.1960.10.313Y. Shen, D. Qiu and W. Chen, Fixed point theorems in fuzzy metric spaces, Appl. Math. Letters 25 (2012), 138-141. https://doi.org/10.1016/j.aml.2011.08.002D. Wardowski, Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy Sets Sys. 222 (2013), 108-114. https://doi.org/10.1016/j.fss.2013.01.012D. Zheng and P. Wang, On probabilistic Ψ-contractions in Menger probabilistic metric spaces, Fuzzy Sets Sys. 350 (2018), 107-110. https://doi.org/10.1016/j.fss.2018.02.011D. Zheng and P. Wang, Meir-Keeler theorems in fuzzy metric spaces, Fuzzy Sets Sys. 370 (2019), 120-128. https://doi.org/10.1016/j.fss.2018.08.01

Presenilin-Dependent Receptor Processing Is Required for Axon Guidance

SummaryThe Alzheimer's disease-linked gene presenilin is required for intramembrane proteolysis of amyloid-β precursor protein, contributing to the pathogenesis of neurodegeneration that is characterized by loss of neuronal connections, but the role of Presenilin in establishing neuronal connections is less clear. Through a forward genetic screen in mice for recessive genes affecting motor neurons, we identified the Columbus allele, which disrupts motor axon projections from the spinal cord. We mapped this mutation to the Presenilin-1 gene. Motor neurons and commissural interneurons in Columbus mutants lacking Presenilin-1 acquire an inappropriate attraction to Netrin produced by the floor plate because of an accumulation of DCC receptor fragments within the membrane that are insensitive to Slit/Robo silencing. Our findings reveal that Presenilin-dependent DCC receptor processing coordinates the interplay between Netrin/DCC and Slit/Robo signaling. Thus, Presenilin is a key neural circuit builder that gates the spatiotemporal pattern of guidance signaling, thereby ensuring neural projections occur with high fidelity

Characterization of Pulmonary Metastases in Children With Hepatoblastoma Treated on Children\u27s Oncology Group Protocol AHEP0731 (The Treatment of Children With All Stages of Hepatoblastoma): A Report From the Children\u27s Oncology Group.

Purpose To determine whether the pattern of lung nodules in children with metastatic hepatoblastoma (HB) correlates with outcome. Methods Thirty-two patients with metastatic HB were enrolled on Children\u27s Oncology Group Protocol AHEP0731 and treated with vincristine and irinotecan (VI). Responders to VI received two additional cycles of VI intermixed with six cycles of cisplatin/fluorouracil/vincristine/doxorubicin (C5VD), and nonresponders received six cycles of C5VD alone. Patients were imaged after every two cycles and at the conclusion of therapy. All computed tomography scans and pathology reports were centrally reviewed, and information was collected regarding lung nodule number, size, laterality, timing of resolution, and pulmonary surgery. Results Among the 29 evaluable patients, only 31% met Response Evaluation Criteria in Solid Tumors (RECIST) for measurable metastatic disease. The presence of measurable disease by RECIST, the sum of nodule diameters greater than or equal to the cumulative cohort median size, bilateral disease, and ≥ 10 nodules were each associated with an increased risk for an event-free survival event ( P = .48, P = .08, P = .065, P = .03, respectively), with nodule number meeting statistical significance. Ten patients underwent pulmonary resection/metastasectomy at various time points, the benefit of which could not be determined because of small patient numbers. Conclusion Children with metastatic HB have a poor prognosis. Overall tumor burden may be an important prognostic factor for these patients. Lesions that fail to meet RECIST size criteria (ie, those \u3c 10 mm) at diagnosis may contain viable tumor, whereas residual lesions at the end of therapy may constitute eradicated tumor/scar tissue. Patients may benefit from risk stratification on the basis of the burden of lung metastatic disease at diagnosis

The association between gene polymorphisms in voltage-gated potassium channels Kv2.1 and Kv4.2 and susceptibility to autism spectrum disorder

BackgroundAutism spectrum disorder (ASD) is a heritable form of neurodevelopmental disorder that arises through synaptic dysfunction. Given the involvement of voltage-gated potassium (Kv) channels in the regulation of synaptic plasticity, we aimed to explore the relationship between the genetic variants in the KCNB1 and KCND2 genes (encoding Kv2.1 and Kv4.2, respectively) and the risk of developing ASD.MethodsA total of 243 patients with ASD and 243 healthy controls were included in the present study. Sixty single nucleotide polymorphisms (SNPs) (35 in KCNB1 and 25 in KCND2) were genotyped using the Sequenom Mass Array.ResultsThere were no significant differences in the distribution of allele frequencies and genotype frequencies in KCNB1 between cases and controls. However, the differences were significant in the allelic distribution of KCND2 rs1990429 (pBonferroni < 0.005) and rs7793864 (pBonferroni < 0.005) between the two groups. KCND2 rs7800545 (pFDR = 0.045) in the dominant model and rs1990429 (pFDR < 0.001) and rs7793864 (pFDR < 0.001) in the over-dominant model were associated with ASD risk. The G/A genotype of rs1990429 in the over-dominant model and the G/A–G/G genotype of rs7800545 in the dominant model were correlated with lower severity in the Autism Diagnostic Interview-Revised (ADI–R) restricted repetitive behavior (RRB) domain.ConclusionOur results provide evidence that KCND2 gene polymorphism is strongly associated with ASD susceptibility and the severity of RRB

Integrated Bioinformatic Analysis of a Competing Endogenous RNA Network Reveals a Prognostic Signature in Endometrial Cancer

In endometrial carcinoma, the clinical outcome directly correlates with the TNM stage, but the lack of sufficient information prevents accurate prediction. The molecular mechanism underlying the competing endogenous RNA (ceRNA) hypothesis has not been investigated in endometrial cancer. Multi-bioinformatic analyses, including differentially expressed gene analysis, ceRNA network construction, Cox regression analysis, function enrichment analysis, and protein-protein network analysis, were performed on the sequence data acquired from The Cancer Genome Atlas (TCGA) data bank. A ceRNA network comprising 366 mRNAs, 27 microRNAs (miRNAs), and 66 long non-coding RNAs (lncRNAs) was established. Survival analysis performed with the univariate Cox regression analysis revealed nine lncRNAs with prognostic power in endometrial carcinoma. In multivariate Cox regression analysis, a signature comprising LINC00491, LINC00483, ADARB2-AS1, and C8orf49 showed remarkable prognostic power. Risk score and neoplasm status, but not TNM stage, were independent prognostic factors of endometrial carcinoma. A ceRNA network comprising differentially expressed mRNAs, miRNAs, and lncRNAs may reveal the molecular events involved in the progression of endometrial carcinoma. In addition, the signature with prognostic value may discriminate patients with increased risk for poor outcome, which may allow physicians to take accurate decisions

Comparison of carboplatin versus cisplatin in the treatment of paediatric extracranial malignant germ cell tumours: A report of the Malignant Germ Cell International Consortium.

PURPOSE: To compare the outcomes of paediatric and adolescent extracranial malignant germ cell tumour (GCT) patients treated with either carboplatin or cisplatin on clinical trials conducted by the Children's Oncology Group (COG) and the Children's Cancer and Leukaemia Group (CCLG). METHODS: The Malignant Germ Cell International Consortium (MaGIC) has created a database of the GCT clinical trials conducted since 1983 by COG (United States, Canada and Australia), which used cisplatin-based regimens, and by CCLG (United Kingdom), which used carboplatin-based regimens. Using the parametric cure model, this study compared the overall 4-year event-free survival (EFS), stratified by age, stage, site and the a-priori defined MaGIC 'risk' groups: standard risk ((SR) 1 (EFS >80%; age 80%, age ≥ 11y) and poor risk (PR) (EFS ≤ 70%, age ≥ 11y). RESULTS: Cisplatin-based therapy was used in 620 patients; carboplatin was used in 163 patients. In the overall multivariate cure model, the two regimens did not differ significantly (cisplatin: 4-year EFS 86%; 95% confidence interval (CI) 83-89% versus carboplatin 4-year EFS 86%; 95% CI 79-90%; p = 0.87). No significant differences were noted in stratified analyses by site, stage, age and MaGIC risk groups: SR1 (p = 0.20), SR2 (p = 0.55) or PR (p = 0.72) patients. CONCLUSIONS: In these trials conducted contemporaneously, there is no significant difference in outcome observed overall, or any subset of patients, who were treated with regimens containing cisplatin versus carboplatin These results suggested sufficient equipoise to justify a randomised trial to evaluate the effectiveness of carboplatin versus cisplatin in the treatment of children, adolescents and young adults with standard risk GCT, which is currently underway

Reproducibility and Relative Validity of a Food Frequency Questionnaire Developed for Female Adolescents in Suihua, North China

BACKGROUND: This study aims to evaluate the reproducibility and validity of a food frequency questionnaire (FFQ) developed for female adolescents in the Suihua area of North China. The FFQ was evaluated against the average of 24-hour dietary recalls (24-HRs). METHODOLOGY/PRINCIPAL FINDINGS: A total of 168 female adolescents aged 12 to 18 completed nine three consecutive 24-HRs (one three consecutive 24 HRs per month) and two FFQs over nine months. The reproducibility of the FFQ was estimated using intraclass correlation coefficients (ICCs), and its relative validity was assessed by comparing it with the 24-HRs. The mean values of the 24-HRs were lower than those of the FFQs, except for protein (in FFQ1) and iron (in FFQ2). The ICCs for all nutrients and food groups in FFQ1 and FFQ2 were moderately correlated (0.4-0.8). However, all the ICCs decreased after adjusting for energy. The weighted κ statistic showed moderate agreement (0.40-0.6) for all nutrients and food groups, except for niacin and calcium, which showed poor agreement (0.35). The relative validity results indicate that the crude Spearman's correlation coefficients of FFQ1 and the 24-HRs ranged from 0.41 (for Vitamin C) to 0.65 (for fruit). The coefficients of each nutrient and food group in FFQ2 and the 24-HRs were higher than those in FFQ1 and the 24-HRs, indicating good correlation. Although all energy-adjusted Spearman's correlation coefficients were lower than the crude coefficients, de-attenuation to correct for intra-individual variability improved the correlation coefficients. The weighted κ coefficients of nutrients and food groups ranged from 0.32 for beans to 0.52 for riboflavin in FFQ1 and the 24-HRs, and 0.32 for Vitamin C to 0.54 for riboflavin in FFQ2 and the 24-HRs. CONCLUSION: The FFQ developed for female adolescents in the Suihua area is a reliable and valid instrument for ranking individuals within this study

Non-Standard Errors

In statistics, samples are drawn from a population in a data-generating process (DGP). Standard errors measure the uncertainty in estimates of population parameters. In science, evidence is generated to test hypotheses in an evidence-generating process (EGP). We claim that EGP variation across researchers adds uncertainty: Non-standard errors (NSEs). We study NSEs by letting 164 teams test the same hypotheses on the same data. NSEs turn out to be sizable, but smaller for better reproducible or higher rated research. Adding peer-review stages reduces NSEs. We further find that this type of uncertainty is underestimated by participants

Prevalence, associated factors and outcomes of pressure injuries in adult intensive care unit patients: the DecubICUs study

Funder: European Society of Intensive Care Medicine; doi: http://dx.doi.org/10.13039/501100013347Funder: Flemish Society for Critical Care NursesAbstract: Purpose: Intensive care unit (ICU) patients are particularly susceptible to developing pressure injuries. Epidemiologic data is however unavailable. We aimed to provide an international picture of the extent of pressure injuries and factors associated with ICU-acquired pressure injuries in adult ICU patients. Methods: International 1-day point-prevalence study; follow-up for outcome assessment until hospital discharge (maximum 12 weeks). Factors associated with ICU-acquired pressure injury and hospital mortality were assessed by generalised linear mixed-effects regression analysis. Results: Data from 13,254 patients in 1117 ICUs (90 countries) revealed 6747 pressure injuries; 3997 (59.2%) were ICU-acquired. Overall prevalence was 26.6% (95% confidence interval [CI] 25.9–27.3). ICU-acquired prevalence was 16.2% (95% CI 15.6–16.8). Sacrum (37%) and heels (19.5%) were most affected. Factors independently associated with ICU-acquired pressure injuries were older age, male sex, being underweight, emergency surgery, higher Simplified Acute Physiology Score II, Braden score 3 days, comorbidities (chronic obstructive pulmonary disease, immunodeficiency), organ support (renal replacement, mechanical ventilation on ICU admission), and being in a low or lower-middle income-economy. Gradually increasing associations with mortality were identified for increasing severity of pressure injury: stage I (odds ratio [OR] 1.5; 95% CI 1.2–1.8), stage II (OR 1.6; 95% CI 1.4–1.9), and stage III or worse (OR 2.8; 95% CI 2.3–3.3). Conclusion: Pressure injuries are common in adult ICU patients. ICU-acquired pressure injuries are associated with mainly intrinsic factors and mortality. Optimal care standards, increased awareness, appropriate resource allocation, and further research into optimal prevention are pivotal to tackle this important patient safety threat

Prevalence, associated factors and outcomes of pressure injuries in adult intensive care unit patients: the DecubICUs study

Funder: European Society of Intensive Care Medicine; doi: http://dx.doi.org/10.13039/501100013347Funder: Flemish Society for Critical Care NursesAbstract: Purpose: Intensive care unit (ICU) patients are particularly susceptible to developing pressure injuries. Epidemiologic data is however unavailable. We aimed to provide an international picture of the extent of pressure injuries and factors associated with ICU-acquired pressure injuries in adult ICU patients. Methods: International 1-day point-prevalence study; follow-up for outcome assessment until hospital discharge (maximum 12 weeks). Factors associated with ICU-acquired pressure injury and hospital mortality were assessed by generalised linear mixed-effects regression analysis. Results: Data from 13,254 patients in 1117 ICUs (90 countries) revealed 6747 pressure injuries; 3997 (59.2%) were ICU-acquired. Overall prevalence was 26.6% (95% confidence interval [CI] 25.9–27.3). ICU-acquired prevalence was 16.2% (95% CI 15.6–16.8). Sacrum (37%) and heels (19.5%) were most affected. Factors independently associated with ICU-acquired pressure injuries were older age, male sex, being underweight, emergency surgery, higher Simplified Acute Physiology Score II, Braden score 3 days, comorbidities (chronic obstructive pulmonary disease, immunodeficiency), organ support (renal replacement, mechanical ventilation on ICU admission), and being in a low or lower-middle income-economy. Gradually increasing associations with mortality were identified for increasing severity of pressure injury: stage I (odds ratio [OR] 1.5; 95% CI 1.2–1.8), stage II (OR 1.6; 95% CI 1.4–1.9), and stage III or worse (OR 2.8; 95% CI 2.3–3.3). Conclusion: Pressure injuries are common in adult ICU patients. ICU-acquired pressure injuries are associated with mainly intrinsic factors and mortality. Optimal care standards, increased awareness, appropriate resource allocation, and further research into optimal prevention are pivotal to tackle this important patient safety threat