Computing the first eigenpair of the p-Laplacian via inverse iteration of sublinear supersolutions

We introduce an iterative method for computing the first eigenpair $(\lambda_{p},e_{p})$ for the $p$-Laplacian operator with homogeneous Dirichlet data as the limit of $(\mu_{q,}u_{q})$ as $q\rightarrow p^{-}$, where $u_{q}$ is the positive solution of the sublinear Lane-Emden equation $-\Delta_{p}u_{q}=\mu_{q}u_{q}^{q-1}$ with same boundary data. The method is shown to work for any smooth, bounded domain. Solutions to the Lane-Emden problem are obtained through inverse iteration of a super-solution which is derived from the solution to the torsional creep problem. Convergence of $u_{q}$ to $e_{p}$ is in the $C^{1}$-norm and the rate of convergence of $\mu_{q}$ to $\lambda_{p}$ is at least $O(p-q)$. Numerical evidence is presented.Comment: Section 5 was rewritten. Jed Brown was added as autho

Seizures

Seizures are common in intensive care patients generally. Cardiac surgery or post-cardiac arrest patients are at particular risk of brain injury. Seizures are an important and potentially reversible cause of prolonged unconsciousness as well as being associated with poorer ICU outcome, although the latter may be multifactorial. Cerebral metabolic rate is greatly increased during seizure activity that may lead to energetic crisis and neuronal injury. Non-convulsive seizures are particularly common in ICU patients and are therefore under-recognised. Electroencephalography (EEG) is therefore an essential ICU investigation the diagnosis of seizures, epileptiform activity and for distinguishing these from other disorders of consciousness, which may have characteristic EEG signatures. Continuous EEG is particularly sensitive for clinically occult seizures and is also helpful for managing seizures refractory to simple treatment. However EEG requires specific expertise to perform and interpret which can be a barrier to its use

Tetra-methoxystilbene modulates ductal growth of the developing murine mammary gland

Extensive data suggest that estradiol contributes to the development of breast cancer by acting as a mitogen and exerting direct genotoxic effects after enzymatic conversion to 4-hydroxyestradiol (4-OHE2) via cytochrome P450 1B1 (CYP1B1). The mammary gland, ovary, and uterus all express CYP1B1. Overexpression of this enzyme has been associated with an increased risk of breast cancer and blockade might reduce this carcinogenic effect. For this reason, we conducted systematic in vitro and in vivo studies of a CYP1B1 inhibitor, TMS (2,3',4,5'-tetramethoxystilbene). We found that TMS blocked the enzymatic conversion of radiolabeled estradiol to both 2-hydroxyestradiol (2-OHE2) and 4-OHE2, but did not inhibit Cyp1b1 message formation. In vivo studies using mass spectrometry showed that TMS inhibited formation of 2-OHE2 and 4-OHE2 and the resulting estrogen-DNA adducts. To examine its biologic actions in vivo, we investigated whether TMS could block the hyperplastic changes that occur in the developing breast of aromatase-transfected mice. We found that TMS induced a significant reduction of ductal structures in mice less than 6 months in age. In older mice, no reduction in breast morphology occurred. These latter studies uncovered unexpected estrogen agonistic actions of TMS at high doses, including a paradoxical stimulation of breast ductal structures and the endometrium. These studies suggest that the enzyme inhibitory properties of TMS, as well as the effects on developing breast, could implicate a role for TMS in breast cancer prevention, but only in low doses and on developing breast

Concomitant CIS on TURBT does not impact oncological outcomes in patients treated with neoadjuvant or induction chemotherapy followed by radical cystectomy

© Springer-Verlag GmbH Germany, part of Springer Nature 2018Background: Cisplatin-based neoadjuvant chemotherapy (NAC) for muscle invasive bladder cancer improves all-cause and cancer specific survival. We aimed to evaluate whether the detection of carcinoma in situ (CIS) at the time of initial transurethral resection of bladder tumor (TURBT) has an oncological impact on the response to NAC prior to radical cystectomy. Patients and methods: Patients were identified retrospectively from 19 centers who received at least three cycles of NAC or induction chemotherapy for cT2-T4aN0-3M0 urothelial carcinoma of the bladder followed by radical cystectomy between 2000 and 2013. The primary and secondary outcomes were pathological response and overall survival, respectively. Multivariable analysis was performed to determine the independent predictive value of CIS on these outcomes. Results: Of 1213 patients included in the analysis, 21.8% had concomitant CIS. Baseline clinical and pathologic characteristics of the ‘CIS’ versus ‘no-CIS’ groups were similar. The pathological response did not differ between the two arms when response was defined as pT0N0 (17.9% with CIS vs 21.9% without CIS; p = 0.16) which may indicate that patients with CIS may be less sensitive to NAC or ≤ pT1N0 (42.8% with CIS vs 37.8% without CIS; p = 0.15). On Cox regression model for overall survival for the cN0 cohort, the presence of CIS was not associated with survival (HR 0.86 (95% CI 0.63–1.18; p = 0.35). The presence of LVI (HR 1.41, 95% CI 1.01–1.96; p = 0.04), hydronephrosis (HR 1.63, 95% CI 1.23–2.16; p = 0.001) and use of chemotherapy other than ddMVAC (HR 0.57, 95% CI 0.34–0.94; p = 0.03) were associated with shorter overall survival. For the whole cohort, the presence of CIS was also not associated with survival (HR 1.05 (95% CI 0.82–1.35; p = 0.70). Conclusion: In this multicenter, real-world cohort, CIS status at TURBT did not affect pathologic response to neoadjuvant or induction chemotherapy. This study is limited by its retrospective nature as well as variability in chemotherapy regimens and surveillance regimens.Peer reviewedFinal Accepted Versio

The limiting behavior of solutions to p-Laplacian problems with convection and exponential terms

We consider, for $a,l\geq1,$ $b,s,\alpha>0,$ and $p>q\geq1,$ the homogeneous Dirichlet problem for the equation $-\Delta_{p}u=\lambda u^{q-1}+\beta u^{a-1}\left\vert \nabla u\right\vert ^{b}+mt^{l-1}e^{\alpha t^{s}}$ in a smooth bounded domain $\Omega\subset\mathbb{R}^{N}.$ We prove that under certain setting of the parameters $\lambda,$ $\beta$ and $m$ the problem admits at least one positive solution. Using this result we prove that if $\lambda,\beta>0$ are arbitrarily fixed and $m$ is sufficiently small, then the problem has a positive solution $u_{p},$ for all $p$ sufficiently large. In addition, we show that $u_{p}$ converges uniformly to the distance function to the boundary of $\Omega,$ as $p\rightarrow\infty.$ This convergence result is new for nonlinearities involving a convection term.Comment: 18 page

Prehospital determinants of successful resuscitation after traumatic and non-traumatic out-of-hospital cardiac arrest.

BACKGROUND: Out-of-hospital cardiac arrest (OHCA) is prevalent in the UK. Reported survival is lower than in countries with comparable healthcare systems; a better understanding of outcome determinants may identify areas for improvement. METHODS: An analysis of 9109 OHCA attended in East of England between 1 January 2015 and 31 July 2017. Univariate descriptives and multivariable analysis were used to understand the determinants of survival for non-traumatic cardiac arrest (NTCA) and traumatic cardiac arrest (TCA). Two Utstein outcome variables were used: survival to hospital admission and hospital discharge. RESULTS: The incidence of OHCA was 55.1 per 100 000 population/year. The overall survival to hospital admission was 27.6% (95% CI 26.7% to 28.6%) and the overall survival to discharge was 7.9% (95% CI 7.3% to 8.5%). Survival to hospital admission and survival to hospital discharge were both greater in the NTCA group compared with the TCA group: 27.9% vs 19.3% p=0.001, and 8.0% vs 3.8% p=0.012 respectively.Determinants of NTCA and TCA survival were different, and varied according to the outcome examined. In NTCA, bystander cardiopulmonary resuscitation (CPR) was associated with survival at discharge but not at admission, and the likelihood of bystander CPR was dependent on geographical socioeconomic status. An air ambulance was associated with increased survival to both hospital admission and discharge in NTCA, but only with survival to admission in TCA. CONCLUSION: NTCA and TCA are clinically distinct entities with different predictors for outcome-future OHCA reports should aim to separate arrest aetiologies. Determinants of survival to hospital admission and discharge differ in a way that likely reflects the determinants of neurological injury. Bystander CPR public engagement may be best focused in more deprived areas

Depurinating estrogen‐DNA adducts, generators of cancer initiation: their minimization leads to cancer prevention

Estrogens can initiate cancer by reacting with DNA. Specific metabolites of endogenous estrogens, the catechol estrogen-3,4-quinones, react with DNA to form depurinating estrogen-DNA adducts. Loss of these adducts leaves apurinic sites in the DNA, generating mutations that can lead to the initiation of cancer. A variety of endogenous and exogenous factors can disrupt estrogen homeostasis, which is the normal balance between estrogen activating and protective enzymes. In fact, if estrogen metabolism becomes unbalanced and generates excessive catechol estrogen 3,4-quinones, formation of depurinating estrogen-DNA adducts increases and the risk of initiating cancer is greater. The levels of depurinating estrogen-DNA adducts are high in women diagnosed with breast cancer and those at high risk for the disease. High levels of depurinating estrogen-DNA adducts before the presence of breast cancer indicates that adduct formation is a critical factor in breast cancer initiation. Women with thyroid or ovarian cancer also have high levels of estrogen-DNA adducts, as do men with prostate cancer or non-Hodgkin lymphoma. Depurinating estrogen-DNA adducts are initiators of many prevalent types of human cancer. These findings and other discoveries led to the recognition that reducing the levels of estrogen-DNA adducts could prevent the initiation of human cancer. The dietary supplements N-acetylcysteine and resveratrol inhibit formation of estrogen-DNA adducts in cultured human breast cells and in women. These results suggest that the two supplements offer an approach to reducing the risk of developing various prevalent types of human cancer. [Figure: see text

Lay Consultations in Heart Failure Symptom Evaluation

Purpose: Lay consultations can facilitate or impede healthcare. However, little is known about how lay consultations for symptom evaluation affect treatment decision-making. The purpose of this study was to explore the role of lay consultations in symptom evaluation prior to hospitalization among patients with heart failure. Methods: Semi-structured interviews were conducted with 60 patients hospitalized for acute decompensated heart failure. Chi-square and Fisher\u27s exact tests, along with logistic regression were used to characterize lay consultations in this sample. Results: A large proportion of patients engaged in lay consultations for symptom evaluation and decision-making before hospitalization. Lay consultants provided attributions and advice and helped make the decision to seek medical care. Men consulted more often with their spouse than women, while women more often consulted with adult children. Conclusions: Findings have implications for optimizing heart failure self-management interventions, improving outcomes, and reducing hospital readmissions