On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

Regular exercise decreases liver tumors development in hepatocyte-specific PTEN-deficient mice independently of steatosis.

BACKGROUND & AIMS Unhealthy lifestyles predispose to non-alcoholic steatohepatitis (NASH), which may further result in the development of hepatocellular carcinoma (HCC). Although NASH patients benefit from physical activity, it is unknown whether regular exercise reduces the risk of developing HCC. Therefore, we studied the effect of regular exercise on the development of HCC in male hepatocyte-specific PTEN-deficient mice (AlbCrePten(flox/flox)), which develop steatohepatitis and HCC spontaneously. METHODS Mice were fed a standardized 10% fat diet and were randomly divided into exercise or sedentary groups. The exercise group ran on a motorized treadmill for 60 minutes/day, 5 days/week during 32 weeks. RESULTS After 32 weeks of regular exercise, 71% of exercised mice developed nodules larger than 15 mm(3) vs 100% of mice in the sedentary group. The mean number of tumors per liver was reduced by exercise, as well as the total tumoral volume per liver. Exercise did not affect steatosis and had no effect on the Non-alcoholic fatty liver disease (NAFLD) Activity Score (NAS). Exercise decreased tumor cell proliferation. Mechanistically, exercise stimulated the phosphorylation of AMPK and its substrate raptor, which decreased the kinase activity of mTOR. CONCLUSIONS These data show a benefit of regular exercise on the development of HCC in an experimental model of NASH and offer a rationale for encouraging predisposed patients to increase their physical activity for the prevention of HCC.

Pattern and process: competition causes regular spacing of individuals within plant populations

1 We used simulated and experimental plant populations to analyse mortality-driven pattern formation under size-dependent competition. Larger plants had an advantage under size-asymmetric but not under symmetric competition. Initial patterns were random or clumped. 2 The simulations were individual-based and spatially explicit. Size-dependent competition was modelled with different rules to partition overlapping zones of influence. 3 The experiment used genotypes of Arabidopsis thaliana with different morphological plasticity and hence size-dependent competition. Compared with wild types, transgenic individuals over-expressed phytochrome A and had decreased plasticity because of disabled phytochrome-mediated shade avoidance. Therefore, competition among transgenics was more asymmetric compared with wild-types. 4 Density-dependent mortality under symmetric competition did not substantially change the initial spatial pattern. Conversely, simulations under asymmetric competition and experimental patterns of transgenic over-expressors showed patterns of survivors that deviated substantially from random mortality independent of initial patterns. 5 Small-scale initial patterns of wild types were regular rather than random or clumped. We hypothesize that this small-scale regularity may be explained by early shade avoidance of seedlings in their cotyledon stage. 6 Our experimental results support predictions from an individual-based simulation model and support the conclusion that regular spatial patterns of surviving individuals should be interpreted as evidence for strong, asymmetric competitive interactions and subsequent density-dependent mortality.

Root system of singular perturbations of the harmonic oscillator type operators

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues μ k satisfying μ k+1 − μ k ≥ Δ > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.

How Entrepreneurs Become Skilled Cultural Operators

Cultural entrepreneurship and symbolic management perspectives portray entrepreneurs as skilled cultural operators and often assume them to be capable from the outset to purposefully use ‘cultural resources' in order to motivate resource-holding audiences to support their new ventures. We problematize this premise and develop a model of how entrepreneurs become skilful cultural operators and develop the cultural competences necessary for creating and growing their ventures. The model is grounded in a case study of an entrepreneur who set up shop and sought to acquire resources in a culturally unfamiliar setting. Our model proposes that two adaptive sensemaking processes - approval-driven sensemaking and autonomy-driven sensemaking - jointly facilitate the gradual development of cultural competences. These processes jointly enable entrepreneurs to gain cultural awareness and calibrate their symbolic enactments. Specifically, while approval-driven sensemaking facilitates recognizing cultural resources to symbolically couple a venture's identity claims more tightly with the cultural frames of targeted audiences and gain legitimate distinctiveness, autonomy-driven sensemaking enables recognizing cultural constraints and more effective symbolic decoupling to shield the venture from constraining cultural frames and defend the venture's autonomy and resources. We conclude the paper with a discussion of the theoretical implications of our study for cultural entrepreneurship and symbolic management research.

Sustained impact of a short small group course with systematic feedback in addition to regular clinical clerkship activities on musculoskeletal examination skills-a controlled study.

BACKGROUND The discrepancy between the extensive impact of musculoskeletal complaints and the common deficiencies in musculoskeletal examination skills lead to increased emphasis on structured teaching and assessment. However, studies of single interventions are scarce and little is known about the time-dependent effect of assisted learning in addition to a standard curriculum. We therefore evaluated the immediate and long-term impact of a small group course on musculoskeletal examination skills. METHODS All 48 Year 4 medical students of a 6 year curriculum, attending their 8 week clerkship of internal medicine at one University department in Berne, participated in this controlled study. Twenty-seven students were assigned to the intervention of a 6×1 h practical course (4-7 students, interactive hands-on examination of real patients; systematic, detailed feedback to each student by teacher, peers and patients). Twenty-one students took part in the regular clerkship activities only and served as controls. In all students clinical skills (CS, 9 items) were assessed in an Objective Structured Clinical Examination (OSCE) station, including specific musculoskeletal examination skills (MSES, 7 items) and interpersonal skills (IPS, 2 items). Two raters assessed the skills on a 4-point Likert scale at the beginning (T0), the end (T1) and 4-12 months after (T2) the clerkship. Statistical analyses included Friedman test, Wilcoxon rank sum test and Mann-Whitney U test. RESULTS At T0 there were no significant differences between the intervention and control group. At T1 and T2 the control group showed no significant changes of CS, MSES and IPS compared to T0. In contrast, the intervention group significantly improved CS, MSES and IPS at T1 (p < 0.001). This enhancement was sustained for CS and MSES (p < 0.05), but not for IPS at T2. CONCLUSIONS Year 4 medical students were incapable of improving their musculoskeletal examination skills during regular clinical clerkship activities. However, an additional small group, interactive clinical skills course with feedback from various sources, improved these essential examination skills immediately after the teaching and several months later. We conclude that supplementary specific teaching activities are needed. Even a single, short-lasting targeted module can have a long lasting effect and is worth the additional effort.

Alternative Formulations for Angular Momentum Operators, Cartesian and Spherical Polar Forms

The conversion between representations of angular momentum in spherical polar and cartesian form is discussed.

The heart challenge: The effect of regular aerobic exercise on body fat distribution in third and fourth grade school children: A randomized clinical trial

The pattern of body fat distribution known as "centralized", and characterized by a predominance of subcutaneous fat on the trunk and a "pot belly", has been associated with an increased risk of chronic disease. These patterns of fat distribution, as well as the lifestyle habit variables associated with adult fatness and chronic morbidity clearly begin to develop during childhood, indicating the need for intervention and primary prevention of obesity, particularly the centralized form, during childhood or adolescence. The purpose of this study was to determine whether regular aerobic exercise could beneficially alter the distribution of body fat in 8 and 9 year old children. One hundred and eighty-eight participants were randomized into either a regular aerobic exercise treatment group or a standard physical education program control group. A variety of aerobic activities was used for intervention 5 days per week during physical education class for a period of 12 weeks. Fat distribution was measured by a number of the most commonly used indices, including ratios of body circumferences and skinfolds and indices derived from a principal components analysis. Change over time in average pulse rate was used to determine if intervention actually occurred. Approximately 10% of the students were remeasured, allowing the calculation of intra- and interexaminer measurement reliability estimates for all indices.^ This study group was comparable to the U.S. population, though the study children were slightly larger for certain measures. No effect of the exercise intervention was found. The most likely explanation for this was inadequacy of the intervention, as indicated by the lack of any change in average pulse rate with treatment. The results of the measurement reliability analysis are reported and indicate that body circumference ratios are more precise than skinfold ratios, particularly when multiple observers are used. Reliability estimates for the principal component indices were also high.^ It remains unclear whether the distribution of body fat can be altered with exercise. It is likely that this issue will remain undecided until one highly reliable, valid, and sensitive measure of fat distribution can be found. ^

Impact of consciousness raising and social liberation on readiness to engage in regular physical activity among adults in Magnolia Park/Lawndale-Wayside, Houston, TX

According to the transtheoretical model, consciousness raising and social liberation are processes used to help individuals progress through the stages of change for a given behavior. This study assessed the impact of these two processes on readiness to engage in regular physical activity among a convenience sample of 35 adults in the Magnolia Park/Lawndale-Wayside area of Houston, TX. The duration of the study was approximately 4 weeks. All pre/post-test data were collected via self-administered surveys available in English or Spanish. Baseline data were used to determine the culturally relevant content of a one-dose intervention consisting of a presentation and dissemination of educational materials as well as a list of local physical activity opportunities. Although the intervention did not improve progression through the stages of change, significant increases were evident among 5 out of 6 processes of change. Based on these results and qualitative data, this study recommended that the Houston Parks and Recreation Department incorporate cultural competency into the design and publication of materials and revise the schedule of available programs (i.e.: increase the number of walking programs) in order to reflect the physical activity preferences of Magnolia Park/Lawndale-Wayside residents.^

BAYESIAN STATISTICAL METHODS IN GENE-ENVIRONMENT AND GENE-GENE INTERACTION STUDIES

Complex diseases such as cancer result from multiple genetic changes and environmental exposures. Due to the rapid development of genotyping and sequencing technologies, we are now able to more accurately assess causal effects of many genetic and environmental factors. Genome-wide association studies have been able to localize many causal genetic variants predisposing to certain diseases. However, these studies only explain a small portion of variations in the heritability of diseases. More advanced statistical models are urgently needed to identify and characterize some additional genetic and environmental factors and their interactions, which will enable us to better understand the causes of complex diseases. In the past decade, thanks to the increasing computational capabilities and novel statistical developments, Bayesian methods have been widely applied in the genetics/genomics researches and demonstrating superiority over some regular approaches in certain research areas. Gene-environment and gene-gene interaction studies are among the areas where Bayesian methods may fully exert its functionalities and advantages. This dissertation focuses on developing new Bayesian statistical methods for data analysis with complex gene-environment and gene-gene interactions, as well as extending some existing methods for gene-environment interactions to other related areas. It includes three sections: (1) Deriving the Bayesian variable selection framework for the hierarchical gene-environment and gene-gene interactions; (2) Developing the Bayesian Natural and Orthogonal Interaction (NOIA) models for gene-environment interactions; and (3) extending the applications of two Bayesian statistical methods which were developed for gene-environment interaction studies, to other related types of studies such as adaptive borrowing historical data. We propose a Bayesian hierarchical mixture model framework that allows us to investigate the genetic and environmental effects, gene by gene interactions (epistasis) and gene by environment interactions in the same model. It is well known that, in many practical situations, there exists a natural hierarchical structure between the main effects and interactions in the linear model. Here we propose a model that incorporates this hierarchical structure into the Bayesian mixture model, such that the irrelevant interaction effects can be removed more efficiently, resulting in more robust, parsimonious and powerful models. We evaluate both of the 'strong hierarchical' and 'weak hierarchical' models, which specify that both or one of the main effects between interacting factors must be present for the interactions to be included in the model. The extensive simulation results show that the proposed strong and weak hierarchical mixture models control the proportion of false positive discoveries and yield a powerful approach to identify the predisposing main effects and interactions in the studies with complex gene-environment and gene-gene interactions. We also compare these two models with the 'independent' model that does not impose this hierarchical constraint and observe their superior performances in most of the considered situations. The proposed models are implemented in the real data analysis of gene and environment interactions in the cases of lung cancer and cutaneous melanoma case-control studies. The Bayesian statistical models enjoy the properties of being allowed to incorporate useful prior information in the modeling process. Moreover, the Bayesian mixture model outperforms the multivariate logistic model in terms of the performances on the parameter estimation and variable selection in most cases. Our proposed models hold the hierarchical constraints, that further improve the Bayesian mixture model by reducing the proportion of false positive findings among the identified interactions and successfully identifying the reported associations. This is practically appealing for the study of investigating the causal factors from a moderate number of candidate genetic and environmental factors along with a relatively large number of interactions. The natural and orthogonal interaction (NOIA) models of genetic effects have previously been developed to provide an analysis framework, by which the estimates of effects for a quantitative trait are statistically orthogonal regardless of the existence of Hardy-Weinberg Equilibrium (HWE) within loci. Ma et al. (2012) recently developed a NOIA model for the gene-environment interaction studies and have shown the advantages of using the model for detecting the true main effects and interactions, compared with the usual functional model. In this project, we propose a novel Bayesian statistical model that combines the Bayesian hierarchical mixture model with the NOIA statistical model and the usual functional model. The proposed Bayesian NOIA model demonstrates more power at detecting the non-null effects with higher marginal posterior probabilities. Also, we review two Bayesian statistical models (Bayesian empirical shrinkage-type estimator and Bayesian model averaging), which were developed for the gene-environment interaction studies. Inspired by these Bayesian models, we develop two novel statistical methods that are able to handle the related problems such as borrowing data from historical studies. The proposed methods are analogous to the methods for the gene-environment interactions on behalf of the success on balancing the statistical efficiency and bias in a unified model. By extensive simulation studies, we compare the operating characteristics of the proposed models with the existing models including the hierarchical meta-analysis model. The results show that the proposed approaches adaptively borrow the historical data in a data-driven way. These novel models may have a broad range of statistical applications in both of genetic/genomic and clinical studies.

Wave height (regular and irregular waves) reduction in 2m water depth over a 40-m-long salt marsh test section in a large scale laboratory flume

Coastal communities around the world face increasing risk from flooding as a result of rising sea level, increasing storminess, and land subsidence. Salt marshes can act as natural buffer zones, providing protection from waves during storms. However, the effectiveness of marshes in protecting the coastline during extreme events when water levels and waves are highest is poorly understood. Here, we experimentally assess wave dissipation under storm surge conditions in a 300-m-long wave flume that contains a transplanted section of natural salt marsh. We find that the presence of marsh vegetation causes considerable wave attenuation, even when water levels and waves are high. From a comparison with experiments without vegetation, we estimate that up to 60% of observed wave reduction is attributed to vegetation. We also find that although waves progressively flatten and break vegetation stems and thereby reduce dissipation, the marsh substrate remained remarkably stable and resistant to surface erosion under all conditions.The effectiveness of storm wave dissipation and the resilience of tidal marshes even at extreme conditions suggest that salt marsh ecosystems can be a valuable component of coastal protection schemes.