In this paper two kernel density estimators are introduced and investigated. In order to reduce bias, we intuitively subtract an estimated bias term from ordinary kernel density estimator. The second proposed density estimator is a geometric extrapolation of the first bias reduced estimator. Theoretical properties such as bias, variance and mean squared error are investigated for both estimators. To observe their finite sample performance, a Monte Carlo simulation study based on small to moderately large samples is presented.

Background The chronic infection with Helicobacter pylori (H. pylori), especially cytotoxin-associated gene A-positive (CagA+) strains, has been associated with various extragastric disorders. Evaluating the potential impacts of virulence factor CagA on intestine may provide a better understanding of H. pylori pathogenesis such as colitis. The intestinal mucosal barrier is essential for maintaining its integrity and functions. However, how persistent CagA+H. pylori colonization influences barrier disruption and thereby affects chronic colitis is not fully understood. Results Chronic colitis models of CagA+H. pylori-colonized mice treated with 2% Dextran sulphate sodium (DSS) were established to assess the disease activity and pertinent expression of tight junction proteins closely related to mucosal integrity. The aggravating effect of CagA+H. pylori infection on DSS-induced chronic colitis was confirmed in mouse models. In addition, augmented Claudin-2 expression was detected in CagA+H. pylori infection conditions and selected for mechanistic analysis. Next, GES-1 human gastric epithelial cells were cultured with CagA+H. pylori or a recombinant CagA protein, and exosomes isolated from conditioned media were then identified. We assessed the Claudin-2 levels after exposure to CagA+ exosomes, CagA− exosomes, and IFN-γ incubation, revealing that CagA+H. pylori compromised the colonic mucosal barrier and facilitated IFN-γ-induced intestinal epithelial destruction through CagA-containing exosome-mediated mechanisms. Specifically, CagA upregulated Claudin-2 expression at the transcriptional level via a CDX2-dependent mechanism to slow the restoration of wounded mucosa in colitis in vitro. Conclusions These data suggest that exosomes containing CagA facilitate CDX2-dependent Claudin-2 maintenance. The exosome-dependent mechanisms of CagA+H. pylori infection are indispensable for damaging the mucosal barrier integrity in chronic colitis, which may provide a new idea for inflammatory bowel disease (IBD) treatment.

Background: Angiogenesis and vascular dysfunction play important roles in the occurrence and development of Crohn's disease (CD), but relevant mechanistic research is lacking. This paper aimed to use exosomal technology to elucidate the mechanism of vascular abnormalities in CD.Methods: Ultra-high-speed centrifugation was used to extract circulating exosomes. Electron microscopy, particle size, and biomarker detection were used for exome quality control. MicroRNA 21 (miR-21) levels were determined by quantitative polymerase chain reaction (qPCR). Migration abilities and tubule-forming capacity were assessed by wound healing assay, transwell invasion test, and tube formation assay. Exosome biomarkers and pathway protein levels were determined by western blotting.Results: Our data revealed that the circulating exosomes of patients with CD have a remarkable effect on the proliferation and migration of human umbilical vein endothelial cells (HUVECs), and that exosomal miR-21 levels were highly elevated in exosomes derived from the plasma of CD patients. Exosomes derived from CD patients and miR-21 mimic had more powerful migration abilities and tubule-forming capacity than control groups. miR-21 inhibitors significantly blocked the quick migration and tubule formation of HUVECs induced by CD-exosomes. Western blot analysis revealed that circulating exosome miR-21 in HUVECs might weaken negative regulation of phosphoinositide 3-kinase (PI3K)/AKT serine/threonine kinase (AKT) by target-inhibiting phosphatase and tensin homolog (PTEN) and inducing the expression of hypoxia-inducible factor 1-alpha (HIF-1α) and vascular endothelial growth factor (VEGF).Conclusions: Circulating exosomal miR-21 mediates HUVEC proliferation and migration through PTEN/PI3K/AKT in CD. Exosomal miR-21 may be a new biomarker or therapeutic target for the treatment of vascular abnormalities in CD.

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Background: The pathogenesis of Crohn's disease (CD) is unknown; however, angiogenesis is known to play an important role in the disease. The present research suggests that microRNA-21 (miR-21) may play a positive regulatory role in disordered angiogenesis in CD.Methods: C57 wild-type mice were divided into 6 groups. On day 0, all mice in the 2,4,6-trinitrobenzenesulfonic acid (TNBS) group were given an enema at the concentration of TNBS 100 mg/kg mouse body weight (solvent 50% alcohol). In the control group, the enema was performed with 50% alcohol. On day 0, 2, 4, and 6, the mice of the agomir-21 + TNBS group and the agomir control + TNBS group were injected with 200 μL, 5 nmol agomir-21 or agomir control [dissolved in ribonuclease (RNase)-free water] by tail vein injection, while the antagomir-21 + TNBS group and the antagomir control + TNBS group were injected with 200 μL, 20 nmol antagomir-21 or antagomir control (dissolved in RNasefree water). The body weight and disease activity index (DAI) score were recorded daily. The colons were obtained to assess macro and microscopic colon damage. The inferior vena cava and the accompanying abdominal aorta were chosen to detect the protein expression of the phosphatase and tensin homolog (PTEN)/phosphoinositide 3-kinase (PI3K)/serine/threonine kinase (AKT)/vascular endothelial growth factor (VEGF) axis through western blotting. Serum interleukin-1 beta (IL-1β) and tumor necrosis factor alpha (TNF-α) were detected by enzyme-linked immunosorbent assay (ELISA). The distribution and expression of neovascularization were demonstrated by cluster of differentiation 31 (CD31) immunohistochemistry.Results: Compared with the only-TNBS group, the agomir-21 + TNBS group showed significantly severer colitis symptoms and more abnormal vascular hyperplasia, while the antagomir-21 + TNBS group showed symptom relief and reduced vascular hyperplasia. In addition, agomir-21 obviously inhibited the expression of PTEN and activated the PI3K/AKT/VEGF pathway in mice induced by TNBS, while antagomir-21 effectively antagonized this effect.Conclusions: miR-21 can promote the progression of colitis in mice induced by TNBS and aggravate the disordered angiogenesis by regulating the PTEN/PI3K/AKT axis. Intravenous injection of miR-21 antagonists can effectively relieve the symptoms of colitis and inhibit colonic angiogenesis.