Anisotropic Mixed-Norm Hardy Spaces Cleanthous, G.; Georgiadis, A. G.; Nielsen, M.
The Journal of geometric analysis,
10/2017, Letnik:
27, Številka:
4
Journal Article
Recenzirano
We introduce and explore Hardy spaces defined by mixed Lebesgue norms and anisotropic dilations. We prove that the definitions of these spaces in terms of smooth, non-tangential, auxiliary, grand, ...and Poisson maximal operators coincide. We also study the relation between anisotropic mixed-norm Hardy spaces and mixed-norm Lebesgue spaces.
We deal with homogeneous Besov and Triebel–Lizorkin spaces in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian ...localization and the Markov property. The class of almost diagonal operators on the associated sequence spaces is developed and it is shown that this class is an algebra. The boundedness of almost diagonal operators is utilized for establishing smooth molecular and atomic decompositions for the above homogeneous Besov and Triebel–Lizorkin spaces. Spectral multipliers for these spaces are established as well.
We prove boundedness of pseudodifferential operators on anisotropic mixed‐norm Besov and Triebel–Lizorkin spaces. Our proof relies only on general maximal function estimates and provides a new ...perspective even in the case of spaces without mixed norms. Moreover, we cover the case of Fourier multipliers on the above mentioned spaces. As application we establish boundedness of pseudodifferential operators and Fourier multipliers on anisotropic mixed‐norm Sobolev spaces.
Although recanalization is the goal of thrombolysis, it is well recognized that it fails to improve outcome of acute stroke in a subset of patients. Our aim was to assess the rate of and factors ...associated with "futile recanalization," defined by absence of clinical benefit from recanalization, following endovascular treatment of acute ischemic stroke.
Data from 6 studies of acute ischemic stroke treated with mechanical and/or pharmacologic endovascular treatment were analyzed. "Futile recanalization" was defined by the occurrence of unfavorable outcome (mRS score of > or = 3 at 1-3 months) despite complete angiographic recanalization (Qureshi grade 0 or TIMI grade 3).
Complete recanalization was observed in 96 of 270 patients treated with IA thrombolysis. Futile recanalization was observed in 47 (49%). In univariate analysis, patients with futile recanalization were older (73 +/- 11 versus 58 +/- 15 years, P < .0001) and had higher median initial NIHSS scores (19 versus 14, P < .0001), more frequent BA occlusion (17% versus 4%, P = .049), less frequent MCA occlusion (53% versus 76%, P = .032), and a nonsignificantly higher rate of symptomatic hemorrhagic complications (2% versus 9%, P = .2). In logistic regression analysis, futile recanalization was positively associated with age > 70 years (OR, 4.4; 95% CI, 1.9-10.5; P = .0008) and initial NIHSS score 10-19 (OR, 3.8; 95% CI, 1.7-8.4; P = .001), and initial NIHSS score > or = 20 (OR, 64.4; 95% CI, 28.8-144; P < .0001).
Futile recanalization is a relatively common occurrence following endovascular treatment, particularly among elderly patients and those with severe neurologic deficits.
We consider Hörmander type symbols on a family of spaces associated with non-negative self-adjoint operators, and we prove boundedness of the corresponding pseudodifferential operators on both ...classical and non-classical Besov and Triebel–Lizorkin spaces. Consequently, this also covers the case of Sobolev spaces. As an application, we obtain boundedness of spectral multipliers on the mentioned spaces.
Abstract The aim of this study was to evaluate the efficacy of heparin-bonded vascular grafts to offer improved outcomes compared to standard prosthetic grafts in access surgery. A systematic review ...and meta-analysis was performed and 8 studies (7 observational studies and one randomized controlled trial) were included. The pooled 6-month and 1-year primary patency was not significantly different between heparin-bonded arterio-venous (AV) grafts and standard prosthetic AV grafts in seven studies reporting on 1209 access procedures. The assisted primary patency and secondary patency at 1-year was not significantly different either. In conclusion heparin-bonded AV grafts offer no distinct advantage over standard prosthetic AV grafts and their preferential use in access surgery cannot be recommended based on the available evidence. The heparin-bonded vascular grafts introduced for hemodialysis access in 2006, contain heparin molecules covalently bonded to the graft luminal surface by a proprietary endpoint attachment mechanism (Carmeda BioActive Surface, Carmeda AB, Stockholm, Sweden), which anchors the heparin molecule to the graft surface while preserving the intrinsic bioactive property of heparin. This covalent attachment of heparin provides a stable non leaching heparin surface of the graft, which has the theoretical advantage to prevent clotting and to increase patency 1 . Improved patency was observed in such heparin-bonded grafts (HB-PTFE) compared to standard synthetic grafts (S-PTFE) in a canine model,2 however, controversy remains as to whether they offer improved patency rates compared to S-PTFE AV (arteriovenous) grafts and the results of existing comparative studies are contradictory 1. The aim of this systematic review and meta-analysis was to summarize the currently available evidence and investigate potential benefits of HB-PTFE AV grafts compared with S-PTFE AV grafts.
Homogeneous mixed-norm Triebel–Lizorkin spaces are introduced and studied with the use of a discrete wavelet transformation, the so-called
φ
-transform. This extends the classical
φ
-transform ...approach introduced by Frazier and Jawerth to the setting of mixed-norm spaces. Moreover, the theory of the
φ
-transform is enhanced through a precise definition of the synthesis operator, in terms of a Pettis integral, and a number of rigorous results for this operator. Especially its terms can always be summed in any order, without changing the resulting distribution.
Long-term exposure to air pollution has been associated with several adverse health effects including cardiovascular, respiratory diseases and cancers. However, underlying molecular alterations ...remain to be further investigated. The aim of this study is to investigate the effects of long-term exposure to air pollutants on (a) average DNA methylation at functional regions and, (b) individual differentially methylated CpG sites. An assumption is that omic measurements, including the methylome, are more sensitive to low doses than hard health outcomes.
This study included blood-derived DNA methylation (Illumina-HM450 methylation) for 454 Italian and 159 Dutch participants from the European Prospective Investigation into Cancer and Nutrition (EPIC). Long-term air pollution exposure levels, including NO2, NOx, PM2.5, PMcoarse, PM10, PM2.5 absorbance (soot) were estimated using models developed within the ESCAPE project, and back-extrapolated to the time of sampling when possible. We meta-analysed the associations between the air pollutants and global DNA methylation, methylation in functional regions and epigenome-wide methylation. CpG sites found differentially methylated with air pollution were further investigated for functional interpretation in an independent population (EnviroGenoMarkers project), where (N=613) participants had both methylation and gene expression data available.
Exposure to NO2 was associated with a significant global somatic hypomethylation (p-value=0.014). Hypomethylation of CpG island's shores and shelves and gene bodies was significantly associated with higher exposures to NO2 and NOx. Meta-analysing the epigenome-wide findings of the 2 cohorts did not show genome-wide significant associations at single CpG site level. However, several significant CpG were found if the analyses were separated by countries. By regressing gene expression levels against methylation levels of the exposure-related CpG sites, we identified several significant CpG-transcript pairs and highlighted 5 enriched pathways for NO2 and 9 for NOx mainly related to the immune system and its regulation.
Our findings support results on global hypomethylation associated with air pollution, and suggest that the shores and shelves of CpG islands and gene bodies are mostly affected by higher exposure to NO2 and NOx. Functional differences in the immune system were suggested by transcriptome analyses.
•We studied the effects of long-term exposure to air pollutants on DNA methylation.•A consistent global hypomethylation was observed for exposure to ambient NO2 and NOx.•This hypomethylation was observed for CpG island's shores, shelves and gene bodies.•No CpG sites were epigenome-wide significant in a combined analysis of a low and high exposed cohort.
Abstract Background The lower extremity is increasingly used as an access site in end-stage renal disease patients. However, reports present conflicting results, creating confusion regarding the ...feasibility and outcomes. Our objective is to review the available literature and analyse the patency rates and complications of various types of lower-extremity arteriovenous access. Methods An Internet-based literature search was performed using MEDLINE to identify all published reports on lower-extremity vascular access. The analysis involved studies comprising at least 10 arteriovenous accesses with both inflow and outflow vessels in the lower extremity, and reporting on patency rates and access-related complications. The weighted mean patency rates were calculated, and the chi-square ( χ2 ) test was used to evaluate the differences in the complication rates in the subgroups of patients identified. Results Three main types of lower-extremity vascular access were identified: the upper thigh prosthetic, the mid-thigh prosthetic and the femoral vein transposition arteriovenous access. There are limited data on saphenous vein loop grafts, which report poor results. The weighted mean primary patency rates at 12 months were 48%, 43% and 83%, respectively. The weighted mean secondary patency rates at 12 months were 69%, 67% and 93%, respectively. Access loss as a result of infection was more common in upper thigh and mid-thigh grafts than femoral vein transposition arteriovenous access (18.40%, 18.33% vs. 1.61%; P < 0.05). Ischaemic complications rates were higher in autologous than prosthetic arteriovenous access (20.97% vs. 7.18%, P < 0.05). Conclusions Lower-extremity vascular access has acceptable results in terms of patency, with femoral vein transposition having better patency rates than femoral grafts. Autologous access is associated with less infective complications, however, at the expense of increased ischaemic complications rates. Further research with randomised trials is required to assess the outcomes of lower-extremity vascular access.
Objective The hemodynamic consequences of misaligned stent-grafts (SG) in fenestrated endografts (EG) have not been adequately studied. Our aim was to study the hemodynamic effects of positional ...variations of SG, investigating the potential influence on the total displacement forces acting on the EG and the shear stress values at the stented segments. Methods This was a computational study. An idealized EG model with two renal fenestrations was computationally reconstructed and centrally extended up to the suprarenal level to treat a suprarenal aneurysm. The misalignment of SG was represented by a variable take-off angle between the SG and the EG centerline axis, corresponding to angles of 90°, 176°, 142°, 38°, and 4°, respectively. Accordingly, the maximum EG displacement forces and the shear stress within the stented segments were calculated, using commercially available software. Results The variable positions of the SG caused no effect on the maximum displacement force acting on the EG, being quite steady and equal to 5.55 N. On the contrary, the values of maximum shear stress acting on the stented segments were influenced by their orientation. The narrow transition zone between the distal end of the mating stent and the target artery showed higher stresses than any other segment. The right-angle take off SG position (90°) was associated with the lowest stresses (12.5 Pa), whereas the highest values were detected at 38° and 142° (16.5 and 16.1 Pa, respectively). The vessel segments distal to the SG exhibited constantly lower stress values (1.9–2.2 Pa) than any other segment. Conclusion We detected differences in the values of shear stress exerted on the stented arteries, depending on different positions that SG can adapt after the deployment of fenestrated EG. The pathophysiologic implication of our findings and their potential association with clinical events deserve further investigation and clinical validation.
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