Structure Relations and Darboux Contractions for 2D 2nd Order Superintegrable Systems

Two-dimensional quadratic algebras are generalizations of Lie algebras that include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. Distinct superintegrable systems and their quadratic algebras can be related by geometric contractions, induced by In\"on\"u-Wigner type Lie algebra contractions. These geometric contractions have important physical and geometric meanings, such as obtaining classical phenomena as limits of quantum phenomena as ${\hbar}\to 0$ and nonrelativistic phenomena from special relativistic as $c\to \infty$, and the derivation of the Askey scheme for obtaining all hypergeometric orthogonal polynomials as limits of Racah/Wilson polynomials. In this paper we show how to simplify the structure relations for abstract nondegenerate and degenerate quadratic algebras and their contractions. In earlier papers we have classified contractions of 2nd order superintegrable systems on constant curvature spaces and have shown that all results are derivable from free quadratic algebras contained in the enveloping algebras of the Lie algebras $e(2,{\mathbb C})$ in flat space and $o(3,{\mathbb C})$ on nonzero constant curvature spaces. The quadratic algebra contractions are induced by generalizations of In\"on\"u-Wigner contractions of these Lie algebras. As a special case we obtained the Askey scheme for hypergeometric orthogonal polynomials. Here we complete this theoretical development for 2D superintegrable systems by showing that the Darboux superintegrable systems are also characterized by free quadratic algebras contained in the symmetry algebras of these spaces and that their contractions are also induced by In\"on\"u-Wigner contractions. We present tables of the contraction results

Optimal policies for Bayesian olfactory search in turbulent flows

In many practical scenarios, a flying insect must search for the source of an emitted cue which is advected by the atmospheric wind. On the macroscopic scales of interest, turbulence tends to mix the cue into patches of relatively high concentration over a background of very low concentration, so that the insect will only detect the cue intermittently and cannot rely on chemotactic strategies which simply climb the concentration gradient. In this work, we cast this search problem in the language of a partially observable Markov decision process (POMDP) and use the Perseus algorithm to compute strategies that are near-optimal with respect to the arrival time. We test the computed strategies on a large two-dimensional grid, present the resulting trajectories and arrival time statistics, and compare these to the corresponding results for several heuristic strategies, including (space-aware) infotaxis, Thompson sampling, and QMDP. We find that the near-optimal policy found by our implementation of Perseus outperforms all heuristics we test by several measures. We use the near-optimal policy to study how the search difficulty depends on the starting location. We discuss additionally the choice of initial belief and the robustness of the policies to changes in the environment. Finally, we present a detailed and pedagogical discussion about the implementation of the Perseus algorithm, including the benefits -- and pitfalls -- of employing a reward shaping function.Comment: 35 pages, 19 figure

Targeted exercise against osteoporosis: A systematic review and meta-analysis for optimising bone strength throughout life

Background. Exercise is widely recommended to reduce osteoporosis, falls and related fragility fractures, but its effect on whole bone strength has remained inconclusive. The primary purpose of this systematic review and meta-analysis was to evaluate the effects of long-term supervised exercise (≥6 months) on estimates of lower-extremity bone strength from childhood to older age. Methods. We searched four databases (PubMed, Sport Discus, Physical Education Index, and Embase) up to October 2009 and included 10 randomised controlled trials (RCTs) that assessed the effects of exercise training on whole bone strength. We analysed the results by age groups (childhood, adolescence, and young and older adulthood) and compared the changes to habitually active or sedentary controls. To calculate standardized mean differences (SMD; effect size), we used the follow-up values of bone strength measures adjusted for baseline bone values. An inverse variance-weighted random-effects model was used to pool the results across studies. Results. Our quality analysis revealed that exercise regimens were heterogeneous; some trials were short in duration and small in sample size, and the weekly training doses varied considerably between trials. We found a small and significant exercise effect among pre- and early pubertal boys [SMD, effect size, 0.17 (95% CI, 0.02-0.32)], but not among pubertal girls [-0.01 (-0.18 to 0.17)], adolescent boys [0.10 (-0.75 to 0.95)], adolescent girls [0.21 (-0.53 to 0.97)], premenopausal women [0.00 (-0.43 to 0.44)] or postmenopausal women [0.00 (-0.15 to 0.15)]. Evidence based on per-protocol analyses of individual trials in children and adolescents indicated that programmes incorporating regular weight-bearing exercise can result in 1% to8% improvements in bone strength at the loaded skeletal sites. In premenopausal women with high exercise compliance, improvements ranging from 0.5% to 2.5% have been reported. Conclusions. The findings from our meta-analysis of RCTs indicate that exercise can significantly enhance bone strength at loaded sites in children but not in adults. Since few RCTs were conducted to investigate exercise effects on bone strength, there is still a need for further well-designed, long-term RCTs with adequate sample sizes to quantify the effects of exercise on whole bone strength and its structural determinants throughout life.peerReviewe

Structure relations and darboux contractions for 2D 2nd order superintegrable systems

Two-dimensional quadratic algebras are generalizations of Lie algebras that include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. Distinct superintegrable systems and their quadratic algebras can be related by geometric contractions, induced by Inönü-Wigner type Lie algebra contractions. These geometric contractions have important physical and geometric meanings, such as obtaining classical phenomena as limits of quantum phenomena as h → 0 and nonrelativistic phenomena from special relativistic as c → ∞, and the derivation of the Askey scheme for obtaining all hypergeometric orthogonal polynomials as limits of Racah/Wilson polynomials. In this paper we show how to simplify the structure relations for abstract nondegenerate and degenerate quadratic algebras and their contractions. In earlier papers we have classif ied contractions of 2nd order superintegrable systems on constant curvature spaces and have shown that all results are derivable from free quadratic algebras contained in the enveloping algebras of the Lie algebras e(2, C) in flat space and o(3, C) on nonzero constant curvature spaces. The quadratic algebra contractions are induced by generalizations of Inönü-Wigner contractions of these Lie algebras. As a special case we obtained the Askey scheme for hypergeometric orthogonal polynomials. After constant curvature spaces, the 4 Darboux spaces are the 2D manifolds admitting the most 2nd order Killing tensors. Here we complete this theoretical development for 2D superintegrable systems by showing that the Darboux superintegrable systems are also characterized by free quadratic algebras contained in the symmetry algebras of these spaces and that their contractions are also induced by Inönü-Wigner contractions. We present tables of the contraction results

Differential effects of exercise on tibial shaft marrow density in young female athletes

Context:Increased mechanical loading can promote the preferential differentiation of bone marrow mesenchymal stem cells to osteoblastogenesis, but it is not known whether long-term bone strength-enhancing exercise in humans can reduce marrow adiposity.Objective:Our objective was to examine whether bone marrow density (MaD), as an estimate of marrow adiposity 1) differs between young female athletes with contrasting loading histories and bone strengths and 2) is an independent predictor of bone strength at the weight-bearing tibia.Design:Mid-tibial MaD, cortical area (CoA), total area, medullary area, strength strain index (SSI), and cortical volumetric bone mineral density (vBMD) (total, endocortical, midcortical, and pericortical) was assessed using peripheral quantitative computed tomography in 179 female athletes involved in both impact and nonimpact loading sports and 41 controls aged 17&ndash;40 years.Results:As we have previously reported CoA, total area, and SSI were 16% to 24% greater in the impact group compared with the controls (all P &lt; .001) and 12% to 18% greater than in the nonimpact group (all P &lt; .001). The impact group also had 0.5% higher MaD than the nonimpact and control groups (both P &lt; .05). Regression analysis further showed that midtibial MaD was significantly associated with SSI, CoA, endocortical vBMD, and pericortical vBMD (P &lt; .05) in all women combined, after adjusting for age, bone length, loading groups, medullary area, muscle cross-sectional area, and percent fat.Conclusion:In young female athletes, tibial bone MaD was associated with loading history and was an independent predictor of tibial bone strength. These findings suggest that an exercise-induced increase in bone strength may be mediated via reduced bone marrow adiposity and consequently increased osteoblastogenesis.<br /

Multiple common comorbidities produce left ventricular diastolic dysfunction associated with coronary microvascular dysfunction, oxidative stress, and myocardial stiffening

Aims More than 50% of patients with heart failure have preserved ejection fraction characterized by diastolic dysfunction. The prevalance of diastolic dysfunction is higher in females and associates with multiple comorbidities such as hypertension (HT), obesity, hypercholesterolemia (HC), and diabetes mellitus (DM). Although its pathophysiology remains incompletely understood, it has been proposed that these comorbidities induce systemic inflammation, coronary microvascular dysfunction, and oxidative stress, leading to myocardial fibrosis, myocyte stiffening and, ultimately, diastolic dysfunction. Here, we tested this hypothesis in a swine model chronically exposed to three common comorbidities. Methods and results DM (induced by streptozotocin), HC (produced by high fat diet), and HT (resulting from renal artery embolization), were produced in 10 female swine, which were followed for 6 months. Eight female healthy swine on normal pig-chow served as controls. The DM + HC + HT group showed hyperglycemia, HC, hypertriglyceridemia, renal dysfunction and HT, which were associated with systemic inflammation. Myocardial superoxide production was markedly increased, due to increased NOX activity and eNOS uncoupling, and associated with reduced NO production, and impaired coronary small artery endothelium-dependent vasodilation. These abnormalities were accompanied by increased myocardial collagen content, reduced capillary/fiber ratio, and elevated passive cardiomyocyte stiffness, resulting in an increased left ventricular end-diastolic stiffness (measured by pressure-volume catheter) and a trend towards a reduced E/A ratio (measured by cardiac MRI), while ejection fraction was maintained. Conclusions The combination of three common comorbidities leads to systemic inflammation, myocardial oxidative stress, and coronary microvascular dysfunction, which associate with myocardial stiffening and LV diastolic dysfunction with preserved ejection fraction

One size doesn’t fit all: cross-sectional associations between neighborhood walkability, crime and physical activity depends on age and sex of residents

Abstract Background Low-income African American adults are disproportionately affected by obesity and are also least likely to engage in recommended levels of physical activity (Flegal et al. JAMA 303(3):235-41, 2010; Tucker et al. Am J Prev Med 40(4):454-61, 2011). Moderate-to-vigorous physical activity (MVPA) is an important factor for weight management and control, as well as for reducing disease risk (Andersen et al. Lancet 368(9532):299-304, 2006; Boreham and Riddoch J Sports Sci 19(12):915-29, 2001; Carson et al. PLoS One 8(8):e71417, 2013). While neighborhood greenspace and walkability have been associated with increased MVPA, evidence also suggests that living in areas with high rates of crime limits MVPA. Few studies have examined to what extent the confluence of neighborhood greenspace, walkability and crime might impact MVPA in low-income African American adults nor how associations may vary by age and sex. Methods In 2013 we collected self-reported data on demographics, functional limitations, objective measures of MVPA (accelerometry), neighborhood greenspace (geographic information system), and walkability (street audit) in 791 predominantly African-American adults (mean age 56 years) living in two United States (U.S.) low-income neighborhoods. We also acquired data from the City of Pittsburgh on all crime events within both neighborhoods. Exposure: To examine cross-sectional associations of neighborhood-related variables (i.e., neighborhood greenspace, walkability and crime) with MVPA, we used zero-inflated negative binomial regression models. Additionally, we examined potential interactions by age (over 65 years) and sex on relationships between neighborhood variables and MVPA. Results Overall, residents engaged in very little to no MVPA regardless of where they lived. However, for women, but not men, under the age of 65 years, living in more walkable neighborhoods was associated with more time engaged in MVPA in (β = 0.55, p = 0.007) as compared to their counterparts living in less walkable areas. Women and men age 65 years and over spent very little time participating in MVPA regardless of neighborhood walkability. Neither greenspace nor crime was associated with MVPA in age-sex subgroups. Conclusions Neighborhood walkability may play a stronger role on MVPA than accessible greenspace or crime in low-income urban communities. Walkability may differentially impact residents depending on their age and sex, which suggests tailoring public health policy design and implementation according to neighborhood demographics to improve activity for all.http://deepblue.lib.umich.edu/bitstream/2027.42/135725/1/12889_2016_Article_3959.pd

The Fragmented Mitochondrial Ribosomal RNAs of Plasmodium falciparum

The mitochondrial genome in the human malaria parasite Plasmodium falciparum is most unusual. Over half the genome is composed of the genes for three classic mitochondrial proteins: cytochrome oxidase subunits I and III and apocytochrome b. The remainder encodes numerous small RNAs, ranging in size from 23 to 190 nt. Previous analysis revealed that some of these transcripts have significant sequence identity with highly conserved regions of large and small subunit rRNAs, and can form the expected secondary structures. However, these rRNA fragments are not encoded in linear order; instead, they are intermixed with one another and the protein coding genes, and are coded on both strands of the genome. This unorthodox arrangement hindered the identification of transcripts corresponding to other regions of rRNA that are highly conserved and/or are known to participate directly in protein synthesis.The identification of 14 additional small mitochondrial transcripts from P. falciparum and the assignment of 27 small RNAs (12 SSU RNAs totaling 804 nt, 15 LSU RNAs totaling 1233 nt) to specific regions of rRNA are supported by multiple lines of evidence. The regions now represented are highly similar to those of the small but contiguous mitochondrial rRNAs of Caenorhabditis elegans. The P. falciparum rRNA fragments cluster on the interfaces of the two ribosomal subunits in the three-dimensional structure of the ribosome.All of the rRNA fragments are now presumed to have been identified with experimental methods, and nearly all of these have been mapped onto the SSU and LSU rRNAs. Conversely, all regions of the rRNAs that are known to be directly associated with protein synthesis have been identified in the P. falciparum mitochondrial genome and RNA transcripts. The fragmentation of the rRNA in the P. falciparum mitochondrion is the most extreme example of any rRNA fragmentation discovered