A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces

We consider the scalar semilinear heat equation ut−Δu=f(u), where f:[0,∞)→[0,∞) is continuous and non-decreasing but need not be convex. We completely characterise those functions f for which the equation has a local solution bounded in Lq(Ω) for all non-negative initial data u0∈Lq(Ω), when Ω⊂Rd is a bounded domain with Dirichlet boundary conditions. For q∈(1,∞) this holds if and only if limsups→∞s−(1+2q/d)f(s

A note on maximal estimates for stochastic convolutions

In stochastic partial differential equations it is important to have pathwise regularity properties of stochastic convolutions. In this note we present a new sufficient condition for the pathwise continuity of stochastic convolutions in Banach spaces.Comment: Minor correction

A particle system with explosions: law of large numbers for the density of particles and the blow-up time

Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for diffusion/creation/annihilation of particles, we obtain a stong law of large numbers for the density of particles in the supremum norm. The limiting object is a classical solution to the semilinear heat equation u_t =u_{xx} + f(u). If f(u)=u^p, 1<p \le 3, we also obtain a law of large numbers for the explosion time

Association of chronic obstructive pulmonary disease with morbidity and mortality in patients with peripheral artery disease: insights from the EUCLID trial

Background: Patients with chronic obstructive pulmonary disease (COPD) are at increased risk of developing lower extremity peripheral artery disease (PAD) and suffering PAD-related morbidity and mortality. However, the effect and burden of COPD on patients with PAD is less well defined. This post hoc analysis from EUCLID aimed to analyze the risk of major adverse cardiovascular events (MACE) and major adverse limb events (MALE) in patients with PAD and concomitant COPD compared with those without COPD, and to describe the adverse events specific to patients with COPD. Methods: EUCLID randomized 13,885 patients with symptomatic PAD to monotherapy with either ticagrelor or clopidogrel for the prevention of MACE. In this analysis, MACE, MALE, mortality, and adverse events were compared between groups with and without COPD using unadjusted and adjusted Cox proportional hazards model. Results: Of the 13,883 patients with COPD status available at baseline, 11% (n=1538) had COPD. Patients with COPD had a higher risk of MACE (6.02 vs 4.29 events/100 patient-years; p< 0.001) due to a significantly higher risk of myocardial infarction (MI) (3.55 vs 1.85 events/100 patient-years; p< 0.001) when compared with patients without COPD. These risks persisted after adjustment (MACE: adjusted hazard ratio (aHR) 1.30, 95% confidence interval [CI] 1.11– 1.52; p< 0.001; MI: aHR 1.45, 95% CI 1.18– 1.77; p< 0.001). However, patients with COPD did not have an increased risk of MALE or major bleeding. Patients with COPD were more frequently hospitalized for dyspnea and pneumonia (2.66 vs 0.9 events/100 patient-years; aHR 2.77, 95% CI 2.12– 3.63; p< 0.001) and more frequently discontinued study drug prematurely (19.36 vs 12.54 events/100 patient-years; p< 0.001; aHR 1.34, 95% CI 1.22– 1.47; p< 0.001). Conclusion: In patients with comorbid PAD and COPD, the risks of MACE, respiratory-related adverse events, and premature study drug discontinuation were higher when compared with patients without COPD. Registration: ClinicalTrials.gov: NCT01732822

Proinflammatory diet is associated with increased risk of squamous cell head and neck cancer

Diets high in fruits and vegetables and low in red meat intake have been associated with decreased risk of head and neck cancer. Additionally, chronic inflammation pathways and their association with cancer have been widely described. We hypothesized a proinflammatory diet, as measured by the dietary inflammatory index (DII®), is associated with increased risk of head and neck cancer. We used the Carolina Head and Neck Cancer (CHANCE) study, a population-based case–control study of head and neck squamous cell carcinoma. Cases were recruited from a 46-county region in central North Carolina. Controls, frequency-matched on age, race, and sex were identified through the North Carolina Department of Motor Vehicle records. The DII score, adjusted for energy using the density approach (E-DII), was calculated from a food frequency questionnaire and split into four quartiles based on the distribution among controls. Adjusted odds ratios (ORs) were estimated with unconditional logistic regression. Cases had higher E-DII scores (i.e., a more proinflammatory diet) compared with controls (mean: −0.14 vs. −1.50; p value &lt; 0.001). When compared with the lowest quartile, the OR for the highest quartile was 2.91 (95% confidence interval (CI): 2.16–3.95), followed by 1.93 (95% CI: 1.43–2.62) for the third quartile, and 1.37 (95% CI: 1.00–1.89) for the second quartile. Both alcohol and smoking had a significant additive interaction with E-DII (smoking relative excess risk due to interaction (RERI): 2.83; 95% CI: 1.36–4.30 and alcohol RERI: 1.75; 95% CI: 0.77–2.75). These results provide additional evidence for the association between proinflammatory diet and head and neck cancer