Trigonometry of 'complex Hermitian' type homogeneous symmetric spaces

This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and hyperbolic CH^N spaces, their analogues with indefinite Hermitian metric and some non-compact symmetric spaces associated to SL(N+1,R) are the generic members in this family. The method encapsulates trigonometry for this whole family of spaces into a single "basic trigonometric group equation", and has 'universality' and '(self)-duality' as its distinctive traits. All previously known results on the trigonometry of CP^N and CH^N follow as particular cases of our general equations. The physical Quantum Space of States of any quantum system belongs, as the complex Hermitian space member, to this parametrised family; hence its trigonometry appears as a rather particular case of the equations we obtain.Comment: 46 pages, LaTe

Massless particles in three-dimensional Lorentzian warped products

The model of a massless relativistic particle with curvature-dependent Lagrangian is well known in (d+1)-dimensional Minkowski space. For other gravitational fields less rigid than those with constant (zero) curvature only a few results are known. In this paper, we give a geometric approach in order to solve the field equations associated with that Lagrangian in the setting of an interesting three-dimensional background, namely, a three-dimensional warped product with Lorentzian fibers. When some rigidity conditions are imposed to the fiber (constant Gauss curvature), the trajectories can be totally described. Several examples help us clarify this.Ministerio de Educación y CienciaFondo Europeo de Desarrollo RegionalJunta de Andalucí

Pointwise estimates for the Bergman kernel of the weighted Fock space

We prove upper pointwise estimates for the Bergman kernel of the weighted Fock space of entire functions in $L^2(e^{-2\phi})$ where $\phi$ is a subharmonic function with $\Delta \phi$ a doubling measure. We derive estimates for the canonical solution operator to the inhomogeneous Cauchy-Riemann equation and we characterize the compactness of this operator in terms of $\Delta \phi$

Using Topological Statistics to Detect Determinism in Time Series

Statistical differentiability of the measure along the reconstructed trajectory is a good candidate to quantify determinism in time series. The procedure is based upon a formula that explicitly shows the sensitivity of the measure to stochasticity. Numerical results for partially surrogated time series and series derived from several stochastic models, illustrate the usefulness of the method proposed here. The method is shown to work also for high--dimensional systems and experimental time seriesComment: 23 RevTeX pages, 14 eps figures. To appear in Physical Review

Comparing estimates of physical activity in children across different cut-points and the associations with weight status

This study aimed to compare sedentary time (SED) and intensity-specific physical activity (PA) estimates and the associations of SED and PA with body mass index (BMI) and waist circumference (WC) using three different sets of cut-points in preschool-aged children. A total of 751 children (4.7 +/- 0.9 years, boys 52.7%) wore an ActiGraph GT3X+BT accelerometer on their hip for 7 days (24 h). Euclidean norm -1 G with negative values rounded to zero (ENMO) and activity counts from vertical axis (VACounts) and vector magnitude (VMCounts) were derived. Estimates of SED and light, moderate, vigorous, and moderate-to-vigorous PA (MVPA) were calculated for commonly used cut-points by Hildebrand et al., Butte et al., and Evenson et al. Furthermore, the prevalence of meeting the PA recommendation, 180 min/day of which at least 60 min/day being MVPA, were assessed for the cut-points. Multilevel mixed analysis was used to examine associations of SED and PA with BMI and WC. In accordance with the results, SED and PA intensity estimates differed largely across cut-points (i.e., SED = 22-341 min/day; light PA = 52-257 min/day; moderate PA = 5-18 min/day; vigorous PA = 7-17 min/day; MVPA = 13-35 min/day), and the prevalence of children meeting the PA recommendation varied from 4% to 70%. Associations of SED and PA with BMI or WC varied between the cut-points. Our results indicate that SED and PA estimates in preschool-aged children between studies using these cut-points are poorly comparable. Methods facilitating accelerometer-derived PA estimate comparison between studies are highly warranted.Peer reviewe

Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry

A new method to obtain trigonometry for the real spaces of constant curvature and metric of any (even degenerate) signature is presented. The method encapsulates trigonometry for all these spaces into a single basic trigonometric group equation. This brings to its logical end the idea of an absolute trigonometry, and provides equations which hold true for the nine two-dimensional spaces of constant curvature and any signature. This family of spaces includes both relativistic and non-relativistic homogeneous spacetimes; therefore a complete discussion of trigonometry in the six de Sitter, minkowskian, Newton--Hooke and galilean spacetimes follow as particular instances of the general approach. Any equation previously known for the three classical riemannian spaces also has a version for the remaining six spacetimes; in most cases these equations are new. Distinctive traits of the method are universality and self-duality: every equation is meaningful for the nine spaces at once, and displays explicitly invariance under a duality transformation relating the nine spaces. The derivation of the single basic trigonometric equation at group level, its translation to a set of equations (cosine, sine and dual cosine laws) and the natural apparition of angular and lateral excesses, area and coarea are explicitly discussed in detail. The exposition also aims to introduce the main ideas of this direct group theoretical way to trigonometry, and may well provide a path to systematically study trigonometry for any homogeneous symmetric space.Comment: 51 pages, LaTe

Prescribed Fire and Cattle Grazing to Manage Invasive Grasses for Cattle and Wildlife

Invasive grasses are in most cases introduced species able to outcompete native species. Buffelgrass (Cenchrus ciliaris), Guineagrass (Urochloa minima), and Old World bluestems (Dichanthium spp.) are typical examples of invasive species in southeastern United States. However, native grasses such as tanglehead (Heteropogon contortus) can become invasive and dominant in absence of cattle grazing just like any invasive species. Tanglehead and Kleberg bluestem (Dichanthium ischaemum) increased (p \u3c 0.05) from 1.4 and 1.8% in 1999 to 2.7 and 3.6% in 2002 and then to 8.1 and 9.4% in 2009, respectively. Monocultures of invasive species have very little value for wildlife, and in the case of mature tanglehead its palatability for cattle is very low. Prescribed fire may be used to improve palatability of tanglehead for cattle, and cattle grazing may be used to improve plant species richness for wildlife. To evaluate the effects of prescribed fire and cattle grazing on cattle preference and the botanical composition of a plant community dominated by tanglehead, we burned 3 patches of approximately 0.5 ha in a pasture of 107 ha in October 2016. Two months before the prescribed burning was executed, 10 mother cows were placed in the pasture to graze continually. We fitted GPS collars on 8 cows and location readings were collected every 10 minutes. GPS recordings indicate that cattle used burned patches 4.5 times more after burning compared to before burning. Percent forage utilization of tanglehead was 52% in the burned patches compared to 6% in the control areas. Plant species richness increased from 2.53 to 8.33 plant species per 0.25 m2, before and after burning, respectively, an increase of 330%. Prescribed fire and cattle grazing are valuable tools to increase tanglehead palatability and utilization by cattle and plant species richness for wildlife

The role of heart rate on the associations between body composition and heart rate variability in children with overweight/obesity : the ActiveBrains project

Background: Heart rate variability (HRV) is negatively associated with body mass index and adiposity in several populations. However, less information is available about this association in children with overweight and obesity, especially severe/morbid obesity, taking into consideration the dependence of HRV on heart rate (HR). Objectives: (1) to examine associations between body composition measures and HRV, (2) to study differences in HRV between children with overweight and severe/morbid obesity; and (3) to test whether relationships and differences tested in objectives 1 and 2, respectively are explained by the dependency of HRV on HR. Methods: A total of 107 children with overweight/obesity (58% boys, 10.03 +/- 1.13 years) participated in this study. Body composition measures were evaluated by Dual-energy X-ray absorptiometry (DXA). HRV parameters were measured with Polar RS800CXR (R). Results: Body composition measures were negatively associated with HRV indicators of parasympathetic activity (beta values ranging from -0.207 to -0.307, all p 0.05). Conclusion: All associations between adiposity/obesity and HRV could be explained by HR, suggesting a key confounding role of HR in HRV studies in children with weight disturbances