Noisy Monte Carlo: Convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution $\pi$ by simulating a Markov chain with transition kernel $P$ such that $\pi$ is invariant under $P$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $P$. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace $P$ by an approximation $\hat{P}$. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how 'close' the chain given by the transition kernel $\hat{P}$ is to the chain given by $P$. We apply these results to several examples from spatial statistics and network analysis.Comment: This version: results extended to non-uniformly ergodic Markov chain

Regularizing effect and local existence for non-cutoff Boltzmann equation

The Boltzmann equation without Grad's angular cutoff assumption is believed to have regularizing effect on the solution because of the non-integrable angular singularity of the cross-section. However, even though so far this has been justified satisfactorily for the spatially homogeneous Boltzmann equation, it is still basically unsolved for the spatially inhomogeneous Boltzmann equation. In this paper, by sharpening the coercivity and upper bound estimates for the collision operator, establishing the hypo-ellipticity of the Boltzmann operator based on a generalized version of the uncertainty principle, and analyzing the commutators between the collision operator and some weighted pseudo differential operators, we prove the regularizing effect in all (time, space and velocity) variables on solutions when some mild regularity is imposed on these solutions. For completeness, we also show that when the initial data has this mild regularity and Maxwellian type decay in velocity variable, there exists a unique local solution with the same regularity, so that this solution enjoys the $C^\infty$ regularity for positive time

Conformations of Proteins in Equilibrium

We introduce a simple theoretical approach for an equilibrium study of proteins with known native state structures. We test our approach with results on well-studied globular proteins, Chymotrypsin Inhibitor (2ci2), Barnase and the alpha spectrin SH3 domain and present evidence for a hierarchical onset of order on lowering the temperature with significant organization at the local level even at high temperatures. A further application to the folding process of HIV-1 protease shows that the model can be reliably used to identify key folding sites that are responsible for the development of drug resistance .Comment: 6 pages, 3 eps figure

Estimation of Dietary Iron Bioavailability from Food Iron Intake and Iron Status

Currently there are no satisfactory methods for estimating dietary iron absorption (bioavailability) at a population level, but this is essential for deriving dietary reference values using the factorial approach. The aim of this work was to develop a novel approach for estimating dietary iron absorption using a population sample from a sub-section of the UK National Diet and Nutrition Survey (NDNS). Data were analyzed in 873 subjects from the 2000–2001 adult cohort of the NDNS, for whom both dietary intake data and hematological measures (hemoglobin and serum ferritin (SF) concentrations) were available. There were 495 men aged 19–64 y (mean age 42.7±12.1 y) and 378 pre-menopausal women (mean age 35.7±8.2 y). Individual dietary iron requirements were estimated using the Institute of Medicine calculations. A full probability approach was then applied to estimate the prevalence of dietary intakes that were insufficient to meet the needs of the men and women separately, based on their estimated daily iron intake and a series of absorption values ranging from 1–40%. The prevalence of SF concentrations below selected cut-off values (indicating that absorption was not high enough to maintain iron stores) was derived from individual SF concentrations. An estimate of dietary iron absorption required to maintain specified SF values was then calculated by matching the observed prevalence of insufficiency with the prevalence predicted for the series of absorption estimates. Mean daily dietary iron intakes were 13.5 mg for men and 9.8 mg for women. Mean calculated dietary absorption was 8% in men (50th percentile for SF 85 µg/L) and 17% in women (50th percentile for SF 38 µg/L). At a ferritin level of 45 µg/L estimated absorption was similar in men (14%) and women (13%). This new method can be used to calculate dietary iron absorption at a population level using data describing total iron intake and SF concentration

Boundedness of Pseudodifferential Operators on Banach Function Spaces

We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$, then a pseudodifferential operator $\operatorname{Op}(a)$ is bounded on $X(\mathbb{R}^n)$ whenever the symbol $a$ belongs to the H\"ormander class $S_{\rho,\delta}^{n(\rho-1)}$ with $0<\rho\le 1$, $0\le\delta<1$ or to the the Miyachi class $S_{\rho,\delta}^{n(\rho-1)}(\varkappa,n)$ with $0\le\delta\le\rho\le 1$, $0\le\delta0$. This result is applied to the case of variable Lebesgue spaces $L^{p(\cdot)}(\mathbb{R}^n)$.Comment: To appear in a special volume of Operator Theory: Advances and Applications dedicated to Ant\'onio Ferreira dos Santo

Preventing child drowning in the Philippines: the need to address the determinants of health

Drowning is a public health issue in the Philippines, with children at significantly increased risk. Determinants of health (DoH) such as education, socio-economic status, ethnicity, and urbanization are factors that impact drowning risk. As drowning is a multisectoral issue, a national drowning prevention plan can drive collaboration with relevant stakeholders. This study reports trends in unintentional child (0–14 years) drowning in the Philippines (incidence, rates, and trends over time for fatal and non-fatal (years lived with a disability (YLDs) and disability adjusted life years (DALYs) from 2008–2017 and conducts an analysis of the Philippines’ Multisector Action Plan (MSAP) on Drowning Prevention. From 2008–2017, 27,928 (95%UI [Uncertainty Interval]: 22,794–33,828) children aged 0–14 years died from drowning (52.7% aged 5–14 years old). Rates of drowning have declined among both age groups, with greater reductions seen among 0–4 year olds (y = −0.3368x + 13.035; R2 = 0.9588). The MSAP has 12 child drowning-specific activities and 20 activities were identified where DoH will need to be considered during development and implementation. The MSAP activities, and work done to prevent drowning more generally, must consider DoH such as education, urbanization, water and sanitation health, and safe water transportation. A national drowning surveillance system and investment in research in the Philippines are recommended

Cost-effectiveness of alternative methods of surgical repair of inguinal hernia

Objectives: To assess the relative cost-effectiveness of laparoscopic methods of inguinal hernia repair compared with open flat mesh and open non-mesh repair. Methods: Data on the effectiveness of these alternatives came from three systematic reviews comparing: (i) laparoscopic methods with open flat mesh or non-mesh methods; (ii) open flat mesh with open non-mesh repair; and (iii) methods that used synthetic mesh to repair the hernia defect with those that did not. Data on costs were obtained from the authors of economic evaluations previously conducted alongside trials included in the reviews. A Markov model was used to model cost-effectiveness for a five-year period after the initial operation. The outcomes of the model were presented using a balance sheet approach and as cost per hernia recurrence avoided and cost per extra day at usual activities. Results: Open flat mesh was the most cost-effective method of preventing recurrences. Laparoscopic repair provided a shorter period of convalescence and less long-term pain compared with open flat mesh but was more costly. The mean incremental cost per additional day back at usual activities compared with open flat mesh was €38 and €80 for totally extraperitoneal and transabdominal preperitoneal repair, respectively. Conclusions: Laparoscopic repair is not cost-effective compared with open flat mesh repair in terms of cost per recurrence avoided. Decisions about the use of laparoscopic repair depend on whether the benefits (reduced pain and earlier return to usual activities) outweigh the extra costs and intraoperative risks. On the evidence presented here, these extra costs are unlikely to be offset by the short-term benefits of laparoscopic repair.Luke Vale, Adrian Grant, Kirsty McCormack, Neil W. Scott and the EU Hernia Trialists Collaboratio

Determining the Impact of Government Intervention on Firm Decisions for Sustainable Production

We use a game theoretic approach to assess how the government can influence firms’ corporate social responsibility (CSR) investment and production decisions to enhance social welfare, considering the negative externalities of unsustainable production and positive externalities from CSR investments. Using a Stackelberg duopoly as a base model and lump-sum tax as the government’s decision variable, we find that when the government chooses not to intervene, it results in greater environmental damage as firms will underinvest in CSR and overproduce in quantity to achieve profit maximization. As such, the model extends to the assumption that the government acts as a benevolent dictator to model how firms will act under a regulated environment to achieve the optimal outcome. Ultimately, we show that firms have to be placed under a regulated environment to prevent them from exploiting resources and damaging the environment, thereby negatively affecting societal welfare

Managing toxicities associated with immune checkpoint inhibitors: consensus recommendations from the Society for Immunotherapy of Cancer (SITC) Toxicity Management Working Group.

Cancer immunotherapy has transformed the treatment of cancer. However, increasing use of immune-based therapies, including the widely used class of agents known as immune checkpoint inhibitors, has exposed a discrete group of immune-related adverse events (irAEs). Many of these are driven by the same immunologic mechanisms responsible for the drugs\u27 therapeutic effects, namely blockade of inhibitory mechanisms that suppress the immune system and protect body tissues from an unconstrained acute or chronic immune response. Skin, gut, endocrine, lung and musculoskeletal irAEs are relatively common, whereas cardiovascular, hematologic, renal, neurologic and ophthalmologic irAEs occur much less frequently. The majority of irAEs are mild to moderate in severity; however, serious and occasionally life-threatening irAEs are reported in the literature, and treatment-related deaths occur in up to 2% of patients, varying by ICI. Immunotherapy-related irAEs typically have a delayed onset and prolonged duration compared to adverse events from chemotherapy, and effective management depends on early recognition and prompt intervention with immune suppression and/or immunomodulatory strategies. There is an urgent need for multidisciplinary guidance reflecting broad-based perspectives on how to recognize, report and manage organ-specific toxicities until evidence-based data are available to inform clinical decision-making. The Society for Immunotherapy of Cancer (SITC) established a multidisciplinary Toxicity Management Working Group, which met for a full-day workshop to develop recommendations to standardize management of irAEs. Here we present their consensus recommendations on managing toxicities associated with immune checkpoint inhibitor therapy