Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers

We elaborate on the recent idea of a direct decomposition of Feynman integrals onto a basis of master integrals on maximal cuts using intersection numbers. We begin by showing an application of the method to the derivation of contiguity relations for special functions, such as the Euler beta function, the Gauss ${}_2F_1$ hypergeometric function, and the Appell $F_1$ function. Then, we apply the new method to decompose Feynman integrals whose maximal cuts admit 1-form integral representations, including examples that have from two to an arbitrary number of loops, and/or from zero to an arbitrary number of legs. Direct constructions of differential equations and dimensional recurrence relations for Feynman integrals are also discussed. We present two novel approaches to decomposition-by-intersections in cases where the maximal cuts admit a 2-form integral representation, with a view towards the extension of the formalism to $n$-form representations. The decomposition formulae computed through the use of intersection numbers are directly verified to agree with the ones obtained using integration-by-parts identities.Comment: 115 pages, 29 figures; references added; additional examples added; matches published versio

Temporal Aspects of Endogenous Pain Modulation During a Noxious Stimulus Prolonged for 1 Day

Background This study investigated (a) if a prolonged noxious stimulus (24‐hr topical capsaicin) in healthy adults would impair central pain inhibitory and facilitatory systems measured as a reduction in conditioned pain modulation (CPM) and enhancement of temporal summation of pain (TSP) and (b) if acute pain relief or exacerbation (cooling and heating the capsaicin patch) during the prolonged noxious stimulus would affect central pain modulation. Methods Twenty‐eight participants (26.2 ± 1.0 years; 12 women) wore a transdermal 8% capsaicin patch on the forearm for 24 hr. Data were collected at baseline (Day 0), 1 hr, 3 hr, Day 1 (post‐capsaicin application) and Day 3/4 (post‐capsaicin removal) that included capsaicin‐evoked pain intensity, heat pain thresholds (HPTs), TSP (10 painful cuff pressure stimuli on leg) and CPM (cuff pressure pain threshold on the leg prior vs. during painful cuff pressure conditioning on contralateral leg). After 3 hr, cold (12°C) and heat (42°C) stimuli were applied to the capsaicin patch to transiently increase and decrease pain intensity. Results Participants reported moderate pain scores at 1 hr (2.5 ± 2.0), 3 hr (3.7 ± 2.4), and Day 1 (2.4 ± 1.8). CPM decreased 3‐hr post‐capsaicin (p = .001) compared to Day 0 and remained diminished while the capsaicin pain score was reduced (0.4 ± 0.7, p \u3c .001) and increased (6.6 ± 2.2, p \u3c .001) by patch cooling and heating. No significant differences occurred for CPM during patch cooling or heating compared to initial 3HR; however, CPM during patch heating was reduced compared with patch cooling (p = .01). TSP and HPT did not change. Conclusions This prolonged experimental pain model is useful to provide insight into subacute pain conditions and may provide insight into the transition from acute to chronic pain. Significance During the early hours of a prolonged noxious stimulus in healthy adults, CPM efficacy was reduced and did not recover by temporarily removing the ongoing pain indicating a less dynamic neuroplastic process

An Integrand Reconstruction Method for Three-Loop Amplitudes

We consider the maximal cut of a three-loop four point function with massless kinematics. By applying Groebner bases and primary decomposition we develop a method which extracts all ten propagator master integral coefficients for an arbitrary triple-box configuration via generalized unitarity cuts. As an example we present analytic results for the three loop triple-box contribution to gluon-gluon scattering in Yang-Mills with adjoint fermions and scalars in terms of three master integrals.Comment: 15 pages, 1 figur

Hepta-Cuts of Two-Loop Scattering Amplitudes

We present a method for the computation of hepta-cuts of two loop scattering amplitudes. Four dimensional unitarity cuts are used to factorise the integrand onto the product of six tree-level amplitudes evaluated at complex momentum values. Using Gram matrix constraints we derive a general parameterisation of the integrand which can be computed using polynomial fitting techniques. The resulting expression is further reduced to master integrals using conventional integration by parts methods. We consider both planar and non-planar topologies for 2 to 2 scattering processes and apply the method to compute hepta-cut contributions to gluon-gluon scattering in Yang-Mills theory with adjoint fermions and scalars.Comment: 37 pages, 6 figures. version 2 : minor updates, published versio

The Use of Decision–Analytic Models in Atopic Eczema: A Systematic Review and Critical Appraisal

Objective: The objective of this systematic review was to identify and assess the quality of published economic decision–analytic models within atopic eczema against best practice guidelines, with the intention of informing future decision–analytic models within this condition. Methods: A systematic search of the following online databases was performed: MEDLINE, EMBASE, Cumulative Index to Nursing and Allied Health Literature (CINAHL), Cochrane Central Register of Controlled Trials, Database of Abstracts of Reviews of Effects, Cochrane Database of Systematic Reviews, NHS Economic Evaluation Database, EconLit, Scopus, Health Technology Assessment, Cost-Effectiveness Analysis Registry and Web of Science. Papers were eligible for inclusion if they described a decision–analytic model evaluating both the costs and benefits associated with an intervention or prevention for atopic eczema. Data were extracted using a standardised form by two independent reviewers, whilst quality was assessed using the model-specific Philips criteria. Results: Twenty-four models were identified, evaluating either preventions (n = 12) or interventions (n = 12): 14 reported using a Markov modelling approach, four utilised decision trees and one a discrete event simulation, whilst five did not specify the approach. The majority, 22 studies, reported that the intervention was dominant or cost effective, given the assumptions and analytical perspective taken. Notably, the models tended to be short-term (16 used a time horizon of ≤1 year), often providing little justification for the limited time horizon chosen. The methodological and reporting quality of the studies was generally weak, with only seven studies fulfilling more than 50% of their applicable Philips criteria. Conclusions: This is the first systematic review of decision models in eczema. Whilst the majority of models reported favourable outcomes in terms of the cost effectiveness of the new intervention, the usefulness of these findings for decision-making is questionable. In particular, there is considerable scope for increasing the range of interventions evaluated, for improving modelling structures and reporting quality

Global, regional, and national comparative risk assessment of 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks, 1990–2015: a systematic analysis for the Global Burden of Disease Study 2015

Background The Global Burden of Diseases, Injuries, and Risk Factors Study 2015 provides an up-to-date synthesis of the evidence for risk factor exposure and the attributable burden of disease. By providing national and subnational assessments spanning the past 25 years, this study can inform debates on the importance of addressing risks in context. Methods We used the comparative risk assessment framework developed for previous iterations of the Global Burden of Disease Study to estimate attributable deaths, disability-adjusted life-years (DALYs), and trends in exposure by age group, sex, year, and geography for 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks from 1990 to 2015. This study included 388 risk-outcome pairs that met World Cancer Research Fund-defi ned criteria for convincing or probable evidence. We extracted relative risk and exposure estimates from randomised controlled trials, cohorts, pooled cohorts, household surveys, census data, satellite data, and other sources. We used statistical models to pool data, adjust for bias, and incorporate covariates. We developed a metric that allows comparisons of exposure across risk factors—the summary exposure value. Using the counterfactual scenario of theoretical minimum risk level, we estimated the portion of deaths and DALYs that could be attributed to a given risk. We decomposed trends in attributable burden into contributions from population growth, population age structure, risk exposure, and risk-deleted cause-specifi c DALY rates. We characterised risk exposure in relation to a Socio-demographic Index (SDI).Background The Global Burden of Diseases, Injuries, and Risk Factors Study 2015 provides an up-to-date synthesis of the evidence for risk factor exposure and the attributable burden of disease. By providing national and subnational assessments spanning the past 25 years, this study can inform debates on the importance of addressing risks in context. Methods We used the comparative risk assessment framework developed for previous iterations of the Global Burden of Disease Study to estimate attributable deaths, disability-adjusted life-years (DALYs), and trends in exposure by age group, sex, year, and geography for 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks from 1990 to 2015. This study included 388 risk-outcome pairs that met World Cancer Research Fund-defi ned criteria for convincing or probable evidence. We extracted relative risk and exposure estimates from randomised controlled trials, cohorts, pooled cohorts, household surveys, census data, satellite data, and other sources. We used statistical models to pool data, adjust for bias, and incorporate covariates. We developed a metric that allows comparisons of exposure across risk factors—the summary exposure value. Using the counterfactual scenario of theoretical minimum risk level, we estimated the portion of deaths and DALYs that could be attributed to a given risk. We decomposed trends in attributable burden into contributions from population growth, population age structure, risk exposure, and risk-deleted cause-specifi c DALY rates. We characterised risk exposure in relation to a Socio-demographic Index (SDI)

Global, regional, and national incidence, prevalence, and years lived with disability for 328 diseases and injuries for 195 countries, 1990–2016: a systematic analysis for the Global Burden of Disease Study 2016

As mortality rates decline, life expectancy increases, and populations age, non-fatal outcomes of diseases and injuries are becoming a larger component of the global burden of disease. The Global Burden of Diseases, Injuries, and Risk Factors Study 2016 (GBD 2016) provides a comprehensive assessment of prevalence, incidence, and years lived with disability (YLDs) for 328 causes in 195 countries and territories from 1990 to 2016