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A bounded subset of a (finite or infinite dimensional) normed linear space is said to be complete (or diametrically complete) if it cannot be enlarged without increasing its diameter. Any bounded subset A of a normed linear space is contained in a complete set having the same diameter, which is called a completion of A. We survey characterizations, basic properties, facts about structure of the interior and boundary, and the asymmetry of complete sets. Different methods to obtain completions of bounded sets are presented. Moreover, the structure of the space of complete sets endowed with the Hausdorff metric and relations of this set family to related set families and notions are discussed. For example, we mean here sets of constant width, balls, reduced sets, sets of constant diameter, and sets of constant radius.

The electrical performance and relaxation behavior of Na+ doped BaBiNb5O15 compound were investigated. The grain conductivity of the BaBi0.96Na0.04Nb5O15-δ compound is 4.71 × 10−5 S/cm at 763 K, which is an order of magnitude lower than the parent sample at the same measuring temperature. The highest total conductivity of the BaBi0.96Na0.04Nb5O15-δ and BaBiNb5O15 sample can reach 1.12 × 10−4 S/cm and 4.0 × 10−5 S/cm at 643 K, respectively, which indicates that the slight Na+ doping can improve the total conductivity. A dielectric relaxation peak related to thermal activation was observed. The activation energy values are E = 0.47 eV for BaBiNb5O15 sample, and E = 0.49 eV for BaBi0.96Na0.04Nb5O15-δ sample, which indicates that the relaxation activation energy increases with the Bi3+ ions partially replaced by Na+ ions in the BaBiNb5O15 compound. In addition, the oxygen relaxation peak position shifts to the low-frequency direction, which indicates that Na+ ions doping causes the decrease of oxygen vacancy mobility. The lower oxygen vacancy mobility results in the lower grain conductivity in the BaBi0.96Na0.04Nb5O15-δ sample. After aging for the different time at 773 K, the excellent thermal stability of the BaBi0.96Na0.04Nb5O15-δ sample can be found.

Sr2+ ion-doped BBN-based oxygen ion conductors were systematically investigated. When using the two-step sintering method, the bulk and total conductivities of the BBN-Sr2-TS sample are enhanced by one and two orders of magnitude, respectively.

Supplementary Figure and Table Legends. List of supporting information

Supplementary Fig. S1-S9. Supplementary Fig. S1. miR-195 expression is significantly reduced in both human PCa cells and tissues; Supplementary Fig. S2. Kaplan-Meier analyses of biochemical recurrence (BCR)-free survival, non-metastatic BCR-free, survival overall survival and non-metastatic survival of prostate cancer (PCa) patients based on miR-195 expression in Taylor dataset; Supplementary Fig. S3. Knockdown of miR-195 expression enhances invasion, migration, but inhibits apoptosis of LNCaP and DU145 cells; Supplementary Fig. S4. The inhibition of miR-195 enhances tumor growth, angiogenesis and invasion in vivo; Supplementary Fig. S5. Top ten enriched KEGG pathways (A) and gene ontology (GO) biological processes (B) involved by differentially-expressed proteins induced by miR-195; Supplementary Fig. S6. The knockdown of RPS6KB1 could imitate the tumor suppressive effects of miR-195; Supplementary Fig. S7. The re-expression and knockdown of RPS6KB1 could respectively rescue and imitate the tumor suppressive effects of miR-195; Supplementary Fig. S8. Reverse correlation between miR-195 and RPS6KB1 expression in human PCa tissues; Supplementary Fig. S9. MMP-9, VEGF, BAD and E-cadherin function as downstream effectors of miR-195-RPS6KB1 axis.

Supplementary Tab S1-S9. Supplementary Tab. S1. Follow-up clinicopathological information of patients from MGH cohort; Supplementary Tab. S2. ligonucleotide Sequence for all the primers used in the study; Supplementary Tab.S3. The antibodies used in this study; Supplementary Tab.S4. Associations of miR-195 and RPS6KB1 protein expression with clinicopathological features of prostate cancer (PCa) patients; Supplementary Tab.S5. Prognostic value of miR-195 expression for the biochemical recurrence-free survival in univariate and multivariate analysis by Cox Regression; Supplementary Tab. S6 Differentially expressed proteins detected by iTRAQ; Supplementary Tab. S7 Canonical pathways analysis by IPA; Supplementary Tab. S8 Diseases and bio functions analysis by IPA; Supplementary Tab.S9. Prognostic value of RPS6KB1 expression for the biochemical recurrence-free survival in univariate and multivariate analysis by Cox Regression.

Purpose: To investigate the involvement of hsa-miRNA-195-5p (miR-195) in progression and prognosis of human prostate cancer.Experimental Design: qRT-PCR was performed to detect miR-195 expression in both prostate cancer cell lines and clinical tissue samples. Its clinical significance was statistically analyzed. The roles of miR-195 and its candidate target gene, ribosomal protein S6 kinase, 70 kDa, polypeptide 1 (RPS6KB1) in prostate cancer progression were confirmed on the basis of both in vitro and in vivo systems.Results: miR-195 downregulation in prostate cancer tissues was significantly associated with high Gleason score (P = 0.001), positive metastasis failure (P < 0.001), and biochemical recurrence (BCR, P < 0.001). Survival analysis identified miR-195 as an independent prognostic factor for BCR-free survival of prostate cancer patients (P = 0.022). Then, we confirmed the tumor suppressive role of miR-195 through prostate cancer cell invasion, migration, and apoptosis assays in vitro, along with tumor xenograft growth, angiogenesis, and invasion in vivo according to both gain-of-function and loss-of-function experiments. In addition, RPS6KB1 was identified as a novel direct target of miR-195 through proteomic expression profiling combined with bioinformatic target prediction and luciferase reporter assay. Moreover, the reexpression and knockdown of RPS6KB1 could respectively rescue and imitate the effects induced by miR-195. Importantly, RPS6KB1 expression was closely correlated with aggressive progression and poor prognosis in prostate cancer patients as opposed to miR-195. Furthermore, we identified MMP-9, VEGF, BAD, and E-cadherin as the downstream effectors of miR-195–RPS6KB1 axis.Conclusion: The newly identified miR-195–RPS6KB1 axis partially illustrates the molecular mechanism of prostate cancer progression and represents a novel potential therapeutic target for prostate cancer treatment. Clin Cancer Res; 21(21); 4922–34. ©2015 AACR.

Supplementary Methods

This article has been retracted. Please see the Retraction Notice for more detail: https://doi.org/10.1186/s12943-017-0615-x.

Alternative splicing of pre-mRNAs is an important gene regulatory mechanism shaping the transcriptome. AtMC1 is an Arabidopsis thaliana type I metacaspase that positively regulates the hypersensitive response. Here, we found that AtMC1 is involved in the regulation of plant immunity to the bacterial pathogen Pseudomonas syringae pv. tomato DC3000 and is physically associated with Sm-like4 (LSM4), which is involved in pre-mRNA splicing. AtMC1 and LSM4 protein levels both increased with their coexpression as compared with their separate expression in vivo. Like AtMC1, LSM4 negatively regulates plant immunity to P. syringae pv. tomato DC3000 infection. By RNA sequencing, AtMC1 was shown to modulate the splicing of many pre-mRNAs, including 4CL3, which is a negative regulator of plant immunity. Thus, AtMC1 plays a regulatory role in pre-mRNA splicing, which might contribute to AtMC1-mediated plant immunity. [Formula: see text] Copyright © 2021 The Author(s). This is an open access article distributed under the CC BY-NC-ND 4.0 International license .

Background The incidence of bladder cancer (BCa) in male is approximately three to four times higher than in female, but the oncological outcomes in female patients with BCa are significantly worse than in male patients. Although many biomarkers have been identified in recent decades to predict the prognosis of BCa patients, few of them are able to distinguish the prognosis of BCa patients with gender difference. Aromatase encoded by the CYP19A1 gene catalyzes the conversion of androgens to estrogens. In this study, we investigate the prognosis significance of CYP19A1 expression considering the gender difference in BCa patients from four available public databases. Methods Four available public databases of BCa, including GSE13507, TCGA-BLCA, E-MTAB-4321, and E-MTAB-1803, were utilized in this analysis. The overall survival (OS) and progression-free survival (PFS) in different stages and genders were evaluated using the Kaplan-Meier analysis based on the optimal cut-off values of CYP19A1 expression. Then, Gene Set Enrichment Analysis (GSEA) were further performed to explore the potential biologic pathways by altering CYP19A1 expression in BCa patients. Results The results showed that patients with high CYP19A1 expression had a poorer outcome compared with those with low expression in both BCa cohorts in general. Higher CYP19A1 expression in male patients were significantly associated with shorter survival for either non-muscle-invasive bladder cancer (NMIBC) or muscle-invasive bladder cancer (MIBC). However, female NMIBC patients with high CYP19A1 expression were identified to have a better prognosis, whereas high CYP19A1 expression in female MIBC patients were significantly associated with poorer survival. The result of the GSEA showed that different outcomes in female and male patients with NMIBC were related to the interaction of CYP19A1 and the cell-cycle-related pathways. Conclusions These findings demonstrated that CYP19A1 expression might have a potential role in distinguishing the prognosis of female BCa patients dependent on tumor stage. Our results provide new insights for aromatase-mediated BCa therapy.

Let X be a normed linear space. We prove that if the norm on X is almost transitive and if there exists a unit vector u satisfying that, for each point y in the unit ball of X that is isosceles orthogonal to u, there always exists $$\alpha \in (0,1)$$ so that u is isosceles orthogonal to $$\alpha y$$ , then X is an inner product space.

The electrical performance of Ga3+ doping Na0.5Bi0.5TiO3-based oxygen ion conductor was studied. The Na0.52Bi0.47Ti1−xGaxO3−δ (x = 0, 0.01, 0.015, 0.02) samples were fabricated by the means of traditional solid-state reaction. The results of AC impedance measurement show that the bulk conductivity of Na0.52Bi0.47Ti1−xGaxO3−δ samples decrease monotonously with the increase of Ga3+ doping. At 673 K, the bulk conductivity of the Na0.52Bi0.47Ti0.98Ga0.02O3−δ sample is 7.19×10− 4 S/cm, which is lower than that of Na0.52Bi0.47TiO3−δ sample under the identical test temperature. The highest total conductivity emerges in the Na0.52Bi0.47Ti0.99Ga0.01O3−δ sample with 1.387×10− 4 S/cm at 623 K for the Ga3+ doping content of 1 mol%, which demonstrate that a slight of Ga3+ doping supports the enhancement of the total conductivity. A relaxation peak was observed in the Na0.52Bi0.47Ti1−xGaxO3−δ compounds. As the Ga3+ ions were introduced into the Na0.52Bi0.47TiO3−δ compound, there is an increasing trend of the relaxation activation energy educed by the internal friction test. In addition, the oxygen relaxtion height of Na0.52Bi0.47Ti1−xGaxO3−δ samples decreases along with the introduction of the Ga3+ doping, suggesting that the introduction of the Ga3+ leads to the decrease of mobile oxygen vacancy .

There is a compelling need to identify novel genetic variants for papillary thyroid cancer (PTC) susceptibility. The Cancer Genome Atlas (TCGA) data showed associations between SPP1 and SPARC mRNA overexpression and aggressive behaviors of PTC, which prompted us to assess potential associations between genetic variants in these genes and PTC risk. Three highly linked SPARC loci (rs1054204, rs3210714, and rs3549) contributed to reduced PTC risk under a codominant model (odds ratio [OR], 0.79-0.80). Variant CAG alleles at these loci significantly enhanced SPARC transcription activation upon cotransfection with miR-29b and miR-495 when compared to the common alleles GGC (all P 0.05). The three SPARC polymorphisms interacted with SPP1 rs4754, with elevated joint ORs of 2.43, 2.52, and 2.52, respectively. Additionally, interaction between SPP1 rs2358744 and SPARC rs2304052 was observed. Our study revealed associations between SPP1 and SPARC polymorphisms that, individually or in combination, are involved in PTC susceptibility.

To compare the expression levels of Defective In Cullin Neddylation 1 Domain Containing 1 oncogene in prostate cancer tissues and normal prostate tissues, to explore its effect on cancerous cells, and to investigate its underlying mechanisms on such cells in vitro.The cross-sectional study was conducted at Guangdong Key Laboratory of Clinical Molecular Medicine and Diagnostics from Jan 03,2017 to Nov 05,2018, and comprised prostate tissue samples on which immunohistochemistry was used to detect the expression of Defective In Cullin Neddylation 1 Domain Containing 1 oncogene. Short hairpin ribonucleic acid expression plasmid targeting the oncogene was constructed and transferred into prostate cance cell line DU145. The roles of the oncogene in prostate cancer progression were confirmed in vitro. The expression of vimentin and epithelial cadherin influenced by the oncogene were detected using Western blot. Data was analysed using SPSS 24.Of the 80 samples, 3(3.75%) were normal prostate tissues, 7(8.75%) adjacent normal prostate tissues, 20(25%) hyperplasia, and 50(62.5%) prostate cancer tissues. Defective In Cullin Neddylation 1 Domain Containing 1 oncogene expression in prostate cancerous tissues was significantly associated with high Gleason score (p0.001), metastasis (p0.05) and pathological stage (p0.001). The oncogene was found to be an independent prognostic factor for disease-free survival of prostate cancer patients (p=0.0108). In vitro analysis confirmed the tumour promotive role of the oncogene through cell proliferation, invasion and migration assays. Its expression was closely correlated with aggressive progression and poor prognosis in prostate cancer patients (p0.05). Vimentin and epithelial cadherin were affected by the oncogene.Defective In Cullin Neddylation 1 Domain Containing 1 oncogene highly expressed in DU145 and the prostate cancer tissues, which correlated with prognosis.

For a convex body K and two positive integers m and l satisfying $$m\le l$$ , we provide a way to dominate the smallest positive number $$\gamma _1$$ such that K can be covered by m translates of $$\gamma _1 K$$ by the infimum of all positive numbers $$\gamma _2$$ such that the set of extreme points of K can be covered by l translates of $$\gamma _2 K$$ .

BACKGROUND AND AIM Single-nucleotide polymorphisms (SNPs) in long non-coding RNAs (lncRNAs) are potential biomarkers for cancer risk, but their association with hepatocellular carcinoma (HCC) is unclear. We examined the association of lncRNA-related SNPs with HCC susceptibility and explored the optimal genetic models for SNPs. METHODS Five candidate SNPs linked with digestive tumors were first genotyped in a screening population of 700 HCC and 2800 control cases. The association between each SNP and HCC risk was estimated by multivariate logistic regression adjusted by sex and age and recorded as odds ratio (OR) with 95% confidence interval. Significant associations were further tested in a validation population with 1140 HCC and 5115 control cases. Finally, the most appropriate genetic models for HCC-associated SNPs were identified using pairwise allele differences; the overall gene effects of each SNP were further evaluated based on optimal genetic models. RESULTS Three candidate SNPs, rs7315438, rs6983267, and rs10795668, showed statistical connections with HCC risk in the discovery stage. Among these, rs7315438 remained steadily significant in the validation stage; rs7315438 and rs10795668 both reached statistical threshold in the combined analysis of both stages. SNP rs7315438 (TC vs TT/CC, OR = 1.410, P

In this study, we investigate the stochastic finite-time $H_{\infty }$H∞ bounded control problem for a class of networked control systems (NCSs) subject to mixed delays, stochastic nonlinearities, and randomly missing measurement. The mixed delays consist of discrete time-varying and distributed delays. The stochastic nonlinearities satisfy statistical means. The missing measurement is modeled by a Bernoulli-distributed random variable. By applying stochastic analysis method we present sufficient conditions guaranteeing the stochastic finite-time boundedness of a closed-loop system with desired $H_{\infty }$H∞ performance level within a finite time interval. Moreover, dynamic output feedback controller can be obtained in terms of a set of matrix inequalities, which can be easily solved by using the cone complementarity linearization method (CCLM). Finally, we provide two numerical examples to illustrate the validity of the proposed design technique.

Alternative splicing (AS) of pre-mRNAs is an important gene regulatory mechanism shaping the transcriptome. AtMC1 is an Arabidopsis thaliana type I metacaspase that positively regulates hypersensitive response (HR). Here, we found that AtMC1 is a negative regulator of plant immunity to the bacterial pathogen Pseudomonas syringae pv. tomato (Pst) DC3000 and is physically associated with Sm-like4 (LSM4), which is involved in pre-mRNA splicing. AtMC1 and LSM4 protein levels both increased with their co-expression as compared with their separate expression in vivo. Like AtMC1, LSM4 negatively regulates plant immunity to Pst DC3000 infection. By RNA-seq, AtMC1 was shown to modulate the splicing of many pre-mRNAs including 4CL3, which is a negative regulator of plant immunity. Moreover, atmc1 mutant plants accumulated microRNAs (miRNAs) such as miR398b, miR399a, miR165a and miR159a at a low level than wild-type Arabidopsis Col-0 plants. Furthermore, AtMC1 affected pri-miRNA processing. RNA immunoprecipitation revealed that AtMC1 interacted with these pri-miRNAs in vivo, suggesting that AtMC1 might suppress their processing by directly binding to them. In addition, we found that MC1-mediated plant immunity is conserved in tomato. Thus, AtMC1 plays a regulatory role in both miRNA expression and pre-mRNA splicing, which might contribute to AtMC1-mediated plant immunity.