Nonexponential decay of an unstable quantum system: Small-QQ-value s-wave decay

We study the decay process of an unstable quantum system, especially the deviation from the exponential decay law. We show that the exponential period no longer exists in the case of the s-wave decay with small $Q$ value, where the $Q$ value is the difference between the energy of the initially prepared state and the minimum energy of the continuous eigenstates in the system. We also derive the quantitative condition that this kind of decay process takes place and discuss what kind of system is suitable to observe the decay.Comment: 17 pages, 6 figure

Statistical Approaches for Estimating Sex-Specific Effects in Endocrine Disruptors Research

BACKGROUND: When a biologic mechanism of interest is anticipated to operate differentially according to sex, as is often the case in endocrine disruptors research, investigators routinely estimate sex-specific associations. Less attention has been given to potential sexual heterogeneity of confounder associations with outcomes. When relationships of covariates with outcomes differ according to sex, commonly applied statistical approaches for estimating sex-specific endocrine disruptor effects may produce divergent estimates. OBJECTIVES: We discuss underlying assumptions and evaluate the performance of two traditional approaches for estimating sex-specific effects, stratification and product terms, and introduce a simple modeling alternative: an augmented product term approach. METHODS: We describe the impact of assumptions regarding sexual heterogeneity of confounder relationships on estimates of sex-specific effects of the exposure of interest for three approaches: stratification, traditional product terms, and augmented product terms. Using simulated and applied examples, we demonstrate properties of each approach under a range of scenarios. RESULTS: In simulations, sex-specific exposure effects estimated using the traditional product term approach were biased when confounders had sex-dependent associations with the outcome. Sex-specific estimates from stratification and the augmented product term approach were unbiased but less precise. In the applied example, the three approaches yielded similar estimates, but resulted in some meaningful differences in conclusions based on statistical significance. CONCLUSIONS: Investigators should consider sexual heterogeneity of confounder associations when choosing an analytic approach to estimate sex-specific effects of endocrine disruptors on health. In the presence of sex-dependent confounding, our augmented product term approach may be advantageous over stratification when there is prior knowledge available to fit reduced models or when investigators seek an automated test for effect measure modification. https://doi.org/10.1289/EHP334

The various power decays of the survival probability at long times for free quantum particle

The long time behaviour of the survival probability of initial state and its dependence on the initial states are considered, for the one dimensional free quantum particle. We derive the asymptotic expansion of the time evolution operator at long times, in terms of the integral operators. This enables us to obtain the asymptotic formula for the survival probability of the initial state $\psi (x)$, which is assumed to decrease sufficiently rapidly at large $|x|$. We then show that the behaviour of the survival probability at long times is determined by that of the initial state $\psi$ at zero momentum $k=0$. Indeed, it is proved that the survival probability can exhibit the various power-decays like $t^{-2m-1}$ for an arbitrary non-negative integers $m$ as $t \to \infty$, corresponding to the initial states with the condition $\hat{\psi} (k) = O(k^m)$ as $k\to 0$.Comment: 15 pages, to appear in J. Phys.

Reducing bias through directed acyclic graphs

<p>Abstract</p> <p>Background</p> <p>The objective of most biomedical research is to determine an unbiased estimate of effect for an exposure on an outcome, i.e. to make causal inferences about the exposure. Recent developments in epidemiology have shown that traditional methods of identifying confounding and adjusting for confounding may be inadequate.</p> <p>Discussion</p> <p>The traditional methods of adjusting for "potential confounders" may introduce conditional associations and bias rather than minimize it. Although previous published articles have discussed the role of the causal directed acyclic graph approach (DAGs) with respect to confounding, many clinical problems require complicated DAGs and therefore investigators may continue to use traditional practices because they do not have the tools necessary to properly use the DAG approach. The purpose of this manuscript is to demonstrate a simple 6-step approach to the use of DAGs, and also to explain why the method works from a conceptual point of view.</p> <p>Summary</p> <p>Using the simple 6-step DAG approach to confounding and selection bias discussed is likely to reduce the degree of bias for the effect estimate in the chosen statistical model.</p

Untargeted metabolomic analysis investigating links between unprocessed red meat intake and markers of inflammation.

BACKGROUND: Whether red meat consumption is associated with higher inflammation or confounded by increased adiposity remains unclear. Plasma metabolites capture the effects of diet after food is processed, digested, and absorbed, and correlate with markers of inflammation, so they can help clarify diet-health relationships. OBJECTIVE: To identify whether any metabolites associated with red meat intake are also associated with inflammation. METHODS: A cross-sectional analysis of observational data from older adults (52.84% women, mean age 63 ± 0.3 y) participating in the Multi-Ethnic Study of Atherosclerosis (MESA). Dietary intake was assessed by food-frequency questionnaire, alongside C-reactive protein (CRP), interleukin-2, interleukin-6, fibrinogen, homocysteine, and tumor necrosis factor alpha, and untargeted proton nuclear magnetic resonance (1H NMR) metabolomic features. Associations between these variables were examined using linear regression models, adjusted for demographic factors, lifestyle behaviors, and body mass index (BMI). RESULTS: In analyses that adjust for BMI, neither processed nor unprocessed forms of red meat were associated with any markers of inflammation (all P > 0.01). However, when adjusting for BMI, unprocessed red meat was inversely associated with spectral features representing the metabolite glutamine (sentinel hit: β = -0.09 ± 0.02, P = 2.0 × 10-5), an amino acid which was also inversely associated with CRP level (β = -0.11 ± 0.01, P = 3.3 × 10-10). CONCLUSIONS: Our analyses were unable to support a relationship between either processed or unprocessed red meat and inflammation, over and above any confounding by BMI. Glutamine, a plasma correlate of lower unprocessed red meat intake, was associated with lower CRP levels. The differences in diet-inflammation associations, compared with diet metabolite-inflammation associations, warrant further investigation to understand the extent that these arise from the following: 1) a reduction in measurement error with metabolite measures; 2) the extent that which factors other than unprocessed red meat intake contribute to glutamine levels; and 3) the ability of plasma metabolites to capture individual differences in how food intake is metabolized

The grinch who stole wisdom

Dr. Seuss is wise. How the Grinch Stole Christmas (Seuss, 1957) could serve as a parable for our time. It can also be seen as a roadmap for the development of contemplative wisdom. The abiding popularity of How the Grinch Stole Christmas additionally suggests that contemplative wisdom is more readily available to ordinary people, even children, than is normally thought. This matters because from the point of view of contemplatives in any of the world's philosophies or religions, people are confused about wisdom. The content of the nascent field of wisdom studies, they might say, is largely not wisdom at all but rather what it's like to live in a particular kind of prison cell, a well appointed cell perhaps, but not a place that makes possible either personal satisfaction or deep problem solving. I believe that what the contemplative traditions have to say is important; they offer a different orientation to what personal wisdom is, how to develop it, and how to use it in the world than is presently contained in either our popular culture or our sciences. In order to illustrate this I will examine, in some detail, one contemplative path within Buddhism. Buddhism is particularly useful in this respect because its practices are nontheistic and thus avoid many of the cultural landmines associated with the contemplative aspects of Western religions

Risk and protective factors for falls on one level in young children: multicentre case-control study

Background: Childhood falls are an important global public health problem, but there is a lack of evidence about their prevention. Falls on one level result in considerable morbidity and they are costly to health services. Objective: To estimate odds ratios for falls on one level in children aged 0-4 years for a range of safety behaviours, safety equipment use and home hazards. Design, setting and participants: Multicentre case-control study at hospitals, minor injury units and general practices in and around 4 UK study centres. Participants included 582 children less than 5 years of age with a medically attended fall injury occurring at home and 2460 controls matched on age, sex, calendar time and study centre. Main outcome measure: Fall on one level. Results: Cases’ most common injuries were bangs on the head (52%), cuts or grazes not needing stitches (29%) or cuts or grazes needing stitches (17%). Comparing cases to community controls in the adjusted analyses, significant findings were observed for only 2 exposures. Injured children were significantly less likely to live in a household without furniture corner covers (adjusted odds ratio (AOR) 0.72, 95%CI 0.55, 0.95), or without rugs and carpets firmly fixed to the floor (AOR 0.76, 95% CI 0.59, 0.98). Conclusions: We did not find any safety practices, use of safety equipment or home hazards associated with a reduced risk of fall on one level. Our findings do not provide evidence to support changes to current injury prevention practice

Variable selection: current practice in epidemiological studies

Selection of covariates is among the most controversial and difficult tasks in epidemiologic analysis. Correct variable selection addresses the problem of confounding in etiologic research and allows unbiased estimation of probabilities in prognostic studies. The aim of this commentary is to assess how often different variable selection techniques were applied in contemporary epidemiologic analysis. It was of particular interest to see whether modern methods such as shrinkage or penalized regression were used in recent publications. Stepwise selection methods remained the predominant method for variable selection in publications in epidemiological journals in 2008. Shrinkage methods were not used in any of the reviewed articles. Editors, reviewers and authors have insufficiently promoted the new, less controversial approaches of variable selection in the biomedical literature, whereas statisticians may not have adequately addressed the method’s feasibility