Spectral properties of non-local uniformly-elliptic operators

In this paper we consider the spectral properties of a class of non-local uniformly elliptic operators, which arise from the study of non-local uniformly elliptic partial differential equations. Such equations arise naturally in the study of a variety of physical and biological systems with examples ranging from Ohmic heating to population dynamics. The operators studied here are bounded perturbations of linear (local) differential operators, and the non-local perturbation is in the form of an integral term. We study the eigenvalues, the multiplicities of these eigenvalues, and the existence of corresponding positive eigenfunctions. It is shown here that the spectral properties of these non-local operators can differ considerably from those of their local counterpart. However, we show that under suitable hypotheses, there still exists a principal eigenvalue of these operators

Comment on "How green is blue hydrogen?"

This paper is written in response to the paper “How green is blue hydrogen?” by R. W. Howarth and M. Z. Jacobson. It aims at highlighting and discussing the method and assumptions of that paper, and thereby providing a more balanced perspective on blue hydrogen, which is in line with current best available practices and future plant specifications aiming at low CO2 emissions. More specifically, in this paper, we show that: (i) the simplified method that Howarth and Jacobson used to compute the energy balance of blue hydrogen plants leads to significant overestimation of CO2 emissions and natural gas (NG) consumption and (ii) the assumed methane leakage rate is at the high end of the estimated emissions from current NG production in the United States and cannot be considered representative of all-NG and blue hydrogen value chains globally. By starting from the detailed and rigorously calculated mass and energy balances of two blue hydrogen plants in the literature, we show the impact that methane leakage rate has on the equivalent CO2 emissions of blue hydrogen. On the basis of our analysis, we show that it is possible for blue hydrogen to have significantly lower equivalent CO2 emissions than the direct use of NG, provided that hydrogen production processes and CO2 capture technologies are implemented that ensure a high CO2 capture rate, preferably above 90%, and a low-emission NG supply chain

Comment on “How green is blue hydrogen?”

This paper is written in response to the paper “How green is blue hydrogen?” by R. W. Howarth and M. Z. Jacobson. It aims at highlighting and discussing the method and assumptions of that paper, and thereby providing a more balanced perspective on blue hydrogen, which is in line with current best available practices and future plant specifications aiming at low CO2 emissions. More specifically, in this paper, we show that: (i) the simplified method that Howarth and Jacobson used to compute the energy balance of blue hydrogen plants leads to significant overestimation of CO2 emissions and natural gas (NG) consumption and (ii) the assumed methane leakage rate is at the high end of the estimated emissions from current NG production in the United States and cannot be considered representative of all-NG and blue hydrogen value chains globally. By starting from the detailed and rigorously calculated mass and energy balances of two blue hydrogen plants in the literature, we show the impact that methane leakage rate has on the equivalent CO2 emissions of blue hydrogen. On the basis of our analysis, we show that it is possible for blue hydrogen to have significantly lower equivalent CO2 emissions than the direct use of NG, provided that hydrogen production processes and CO2 capture technologies are implemented that ensure a high CO2 capture rate, preferably above 90%, and a low-emission NG supply chain

Rehabilitation versus surgical reconstruction for non-acute anterior cruciate ligament injury (ACL SNNAP): a pragmatic randomised controlled trial

BackgroundAnterior cruciate ligament (ACL) rupture is a common debilitating injury that can cause instability of the knee. We aimed to investigate the best management strategy between reconstructive surgery and non-surgical treatment for patients with a non-acute ACL injury and persistent symptoms of instability.MethodsWe did a pragmatic, multicentre, superiority, randomised controlled trial in 29 secondary care National Health Service orthopaedic units in the UK. Patients with symptomatic knee problems (instability) consistent with an ACL injury were eligible. We excluded patients with meniscal pathology with characteristics that indicate immediate surgery. Patients were randomly assigned (1:1) by computer to either surgery (reconstruction) or rehabilitation (physiotherapy but with subsequent reconstruction permitted if instability persisted after treatment), stratified by site and baseline Knee Injury and Osteoarthritis Outcome Score—4 domain version (KOOS4). This management design represented normal practice. The primary outcome was KOOS4 at 18 months after randomisation. The principal analyses were intention-to-treat based, with KOOS4 results analysed using linear regression. This trial is registered with ISRCTN, ISRCTN10110685, and ClinicalTrials.gov, NCT02980367.FindingsBetween Feb 1, 2017, and April 12, 2020, we recruited 316 patients. 156 (49%) participants were randomly assigned to the surgical reconstruction group and 160 (51%) to the rehabilitation group. Mean KOOS4 at 18 months was 73·0 (SD 18·3) in the surgical group and 64·6 (21·6) in the rehabilitation group. The adjusted mean difference was 7·9 (95% CI 2·5–13·2; p=0·0053) in favour of surgical management. 65 (41%) of 160 patients allocated to rehabilitation underwent subsequent surgery according to protocol within 18 months. 43 (28%) of 156 patients allocated to surgery did not receive their allocated treatment. We found no differences between groups in the proportion of intervention-related complications.InterpretationSurgical reconstruction as a management strategy for patients with non-acute ACL injury with persistent symptoms of instability was clinically superior and more cost-effective in comparison with rehabilitation management

Adding 6 months of androgen deprivation therapy to postoperative radiotherapy for prostate cancer: a comparison of short-course versus no androgen deprivation therapy in the RADICALS-HD randomised controlled trial

Background Previous evidence indicates that adjuvant, short-course androgen deprivation therapy (ADT) improves metastasis-free survival when given with primary radiotherapy for intermediate-risk and high-risk localised prostate cancer. However, the value of ADT with postoperative radiotherapy after radical prostatectomy is unclear. Methods RADICALS-HD was an international randomised controlled trial to test the efficacy of ADT used in combination with postoperative radiotherapy for prostate cancer. Key eligibility criteria were indication for radiotherapy after radical prostatectomy for prostate cancer, prostate-specific antigen less than 5 ng/mL, absence of metastatic disease, and written consent. Participants were randomly assigned (1:1) to radiotherapy alone (no ADT) or radiotherapy with 6 months of ADT (short-course ADT), using monthly subcutaneous gonadotropin-releasing hormone analogue injections, daily oral bicalutamide monotherapy 150 mg, or monthly subcutaneous degarelix. Randomisation was done centrally through minimisation with a random element, stratified by Gleason score, positive margins, radiotherapy timing, planned radiotherapy schedule, and planned type of ADT, in a computerised system. The allocated treatment was not masked. The primary outcome measure was metastasis-free survival, defined as distant metastasis arising from prostate cancer or death from any cause. Standard survival analysis methods were used, accounting for randomisation stratification factors. The trial had 80% power with two-sided α of 5% to detect an absolute increase in 10-year metastasis-free survival from 80% to 86% (hazard ratio [HR] 0·67). Analyses followed the intention-to-treat principle. The trial is registered with the ISRCTN registry, ISRCTN40814031, and ClinicalTrials.gov, NCT00541047. Findings Between Nov 22, 2007, and June 29, 2015, 1480 patients (median age 66 years [IQR 61–69]) were randomly assigned to receive no ADT (n=737) or short-course ADT (n=743) in addition to postoperative radiotherapy at 121 centres in Canada, Denmark, Ireland, and the UK. With a median follow-up of 9·0 years (IQR 7·1–10·1), metastasis-free survival events were reported for 268 participants (142 in the no ADT group and 126 in the short-course ADT group; HR 0·886 [95% CI 0·688–1·140], p=0·35). 10-year metastasis-free survival was 79·2% (95% CI 75·4–82·5) in the no ADT group and 80·4% (76·6–83·6) in the short-course ADT group. Toxicity of grade 3 or higher was reported for 121 (17%) of 737 participants in the no ADT group and 100 (14%) of 743 in the short-course ADT group (p=0·15), with no treatment-related deaths. Interpretation Metastatic disease is uncommon following postoperative bed radiotherapy after radical prostatectomy. Adding 6 months of ADT to this radiotherapy did not improve metastasis-free survival compared with no ADT. These findings do not support the use of short-course ADT with postoperative radiotherapy in this patient population

Duration of androgen deprivation therapy with postoperative radiotherapy for prostate cancer: a comparison of long-course versus short-course androgen deprivation therapy in the RADICALS-HD randomised trial

Background Previous evidence supports androgen deprivation therapy (ADT) with primary radiotherapy as initial treatment for intermediate-risk and high-risk localised prostate cancer. However, the use and optimal duration of ADT with postoperative radiotherapy after radical prostatectomy remains uncertain. Methods RADICALS-HD was a randomised controlled trial of ADT duration within the RADICALS protocol. Here, we report on the comparison of short-course versus long-course ADT. Key eligibility criteria were indication for radiotherapy after previous radical prostatectomy for prostate cancer, prostate-specific antigen less than 5 ng/mL, absence of metastatic disease, and written consent. Participants were randomly assigned (1:1) to add 6 months of ADT (short-course ADT) or 24 months of ADT (long-course ADT) to radiotherapy, using subcutaneous gonadotrophin-releasing hormone analogue (monthly in the short-course ADT group and 3-monthly in the long-course ADT group), daily oral bicalutamide monotherapy 150 mg, or monthly subcutaneous degarelix. Randomisation was done centrally through minimisation with a random element, stratified by Gleason score, positive margins, radiotherapy timing, planned radiotherapy schedule, and planned type of ADT, in a computerised system. The allocated treatment was not masked. The primary outcome measure was metastasis-free survival, defined as metastasis arising from prostate cancer or death from any cause. The comparison had more than 80% power with two-sided α of 5% to detect an absolute increase in 10-year metastasis-free survival from 75% to 81% (hazard ratio [HR] 0·72). Standard time-to-event analyses were used. Analyses followed intention-to-treat principle. The trial is registered with the ISRCTN registry, ISRCTN40814031, and ClinicalTrials.gov , NCT00541047 . Findings Between Jan 30, 2008, and July 7, 2015, 1523 patients (median age 65 years, IQR 60–69) were randomly assigned to receive short-course ADT (n=761) or long-course ADT (n=762) in addition to postoperative radiotherapy at 138 centres in Canada, Denmark, Ireland, and the UK. With a median follow-up of 8·9 years (7·0–10·0), 313 metastasis-free survival events were reported overall (174 in the short-course ADT group and 139 in the long-course ADT group; HR 0·773 [95% CI 0·612–0·975]; p=0·029). 10-year metastasis-free survival was 71·9% (95% CI 67·6–75·7) in the short-course ADT group and 78·1% (74·2–81·5) in the long-course ADT group. Toxicity of grade 3 or higher was reported for 105 (14%) of 753 participants in the short-course ADT group and 142 (19%) of 757 participants in the long-course ADT group (p=0·025), with no treatment-related deaths. Interpretation Compared with adding 6 months of ADT, adding 24 months of ADT improved metastasis-free survival in people receiving postoperative radiotherapy. For individuals who can accept the additional duration of adverse effects, long-course ADT should be offered with postoperative radiotherapy. Funding Cancer Research UK, UK Research and Innovation (formerly Medical Research Council), and Canadian Cancer Society