Multiplication and Composition in Weighted Modulation Spaces

We study the existence of the product of two weighted modulation spaces. For this purpose we discuss two different strategies. The more simple one allows transparent proofs in various situations. However, our second method allows a closer look onto associated norm inequalities under restrictions in the Fourier image. This will give us the opportunity to treat the boundedness of composition operators.Comment: 49 page

Caffeic acid phenethyl ester decreases acute pneumonitis after irradiation in vitro and in vivo

BACKGROUND: Lung cancer is relatively resistant to radiation treatment and radiation pneumonitis is a major obstacle to increasing the radiation dose. We previously showed that Caffeic acid phenethyl ester (CAPE) induces apoptosis and increases radiosensitivity in lung cancer. To determine whether CAPE, an antioxidant and an inhibitor of NF-kappa B, could be a useful adjuvant agent for lung cancer treatment, we examine the effects of CAPE on irradiated normal lung tissue in this study. METHODS: We compared the effects of CAPE on cytotoxicity and intracellular oxidative stress in normal lung fibroblast and a lung cancer cell line. For in vivo analysis, whole thorax radiation (single dose 10 Gy and 20 Gy) was delivered to BALB/c male mice with or without CAPE pretreatment. NF- kappaB activation and the expression levels of acute inflammatory cytokines were evaluated in mice after irradiation. RESULTS: The in vitro studies showed that CAPE cause no significant cytotoxicity in normal lung as compared to lung cancer cells. This is probably due to the differential effect on the expression of NF-kappa B between normal and malignant lung cells. The results from in vivo study showed that CAPE treatment decreased the expression of inflammatory cytokines including IL-1 alpha and beta, IL-6, TNF-alpha and TGF- beta, after irradiation. Moreover, histological and immunochemical data revealed that CAPE decreased radiation- induced interstitial pneumonitis and TGF-beta expression. CONCLUSION: This study suggests that CAPE decreases the cascade of inflammatory responses induced by thoracic irradiation without causing toxicity in normal lung tissue. This provides a rationale for combining CAPE and thoracic radiotherapy for lung cancer treatment in further clinical studies

Caffeic Acid Phenethyl Ester Causes p21Cip1 Induction, Akt Signaling Reduction, and Growth Inhibition in PC-3 Human Prostate Cancer Cells

Caffeic acid phenethyl ester (CAPE) treatment suppressed proliferation, colony formation, and cell cycle progression in PC-3 human prostate cancer cells. CAPE decreased protein expression of cyclin D1, cyclin E, SKP2, c-Myc, Akt1, Akt2, Akt3, total Akt, mTOR, Bcl-2, Rb, as well as phosphorylation of Rb, ERK1/2, Akt, mTOR, GSK3α, GSK3β, PDK1; but increased protein expression of KLF6 and p21Cip1. Microarray analysis indicated that pathways involved in cellular movement, cell death, proliferation, and cell cycle were affected by CAPE. Co-treatment of CAPE with chemotherapeutic drugs vinblastine, paclitaxol, and estramustine indicated synergistic suppression effect. CAPE administration may serve as a potential adjuvant therapy for prostate cancer

Heterogeneous treatment effects of therapeutic-dose heparin in patients hospitalized for COVID-19

Importance Randomized clinical trials (RCTs) of therapeutic-dose heparin in patients hospitalized with COVID-19 produced conflicting results, possibly due to heterogeneity of treatment effect (HTE) across individuals. Better understanding of HTE could facilitate individualized clinical decision-making. Objective To evaluate HTE of therapeutic-dose heparin for patients hospitalized for COVID-19 and to compare approaches to assessing HTE. Design, Setting, and Participants Exploratory analysis of a multiplatform adaptive RCT of therapeutic-dose heparin vs usual care pharmacologic thromboprophylaxis in 3320 patients hospitalized for COVID-19 enrolled in North America, South America, Europe, Asia, and Australia between April 2020 and January 2021. Heterogeneity of treatment effect was assessed 3 ways: using (1) conventional subgroup analyses of baseline characteristics, (2) a multivariable outcome prediction model (risk-based approach), and (3) a multivariable causal forest model (effect-based approach). Analyses primarily used bayesian statistics, consistent with the original trial. Exposures Participants were randomized to therapeutic-dose heparin or usual care pharmacologic thromboprophylaxis. Main Outcomes and Measures Organ support–free days, assigning a value of −1 to those who died in the hospital and the number of days free of cardiovascular or respiratory organ support up to day 21 for those who survived to hospital discharge; and hospital survival. Results Baseline demographic characteristics were similar between patients randomized to therapeutic-dose heparin or usual care (median age, 60 years; 38% female; 32% known non-White race; 45% Hispanic). In the overall multiplatform RCT population, therapeutic-dose heparin was not associated with an increase in organ support–free days (median value for the posterior distribution of the OR, 1.05; 95% credible interval, 0.91-1.22). In conventional subgroup analyses, the effect of therapeutic-dose heparin on organ support–free days differed between patients requiring organ support at baseline or not (median OR, 0.85 vs 1.30; posterior probability of difference in OR, 99.8%), between females and males (median OR, 0.87 vs 1.16; posterior probability of difference in OR, 96.4%), and between patients with lower body mass index (BMI 90% for all comparisons). In risk-based analysis, patients at lowest risk of poor outcome had the highest propensity for benefit from heparin (lowest risk decile: posterior probability of OR >1, 92%) while those at highest risk were most likely to be harmed (highest risk decile: posterior probability of OR <1, 87%). In effect-based analysis, a subset of patients identified at high risk of harm (P = .05 for difference in treatment effect) tended to have high BMI and were more likely to require organ support at baseline. Conclusions and Relevance Among patients hospitalized for COVID-19, the effect of therapeutic-dose heparin was heterogeneous. In all 3 approaches to assessing HTE, heparin was more likely to be beneficial in those who were less severely ill at presentation or had lower BMI and more likely to be harmful in sicker patients and those with higher BMI. The findings illustrate the importance of considering HTE in the design and analysis of RCTs. Trial Registration ClinicalTrials.gov Identifiers: NCT02735707, NCT04505774, NCT04359277, NCT0437258