The functor of toric varieties associated with Weyl chambers and Losev-Manin moduli spaces

A root system $R$ of rank $n$ defines an $n$-dimensional smooth projective toric variety $X(R)$ associated with its fan of Weyl chambers. We give a simple description of the functor of $X(R)$ in terms of the root system $R$ and apply this result in the case of root systems of type $A$ to give a new proof of the fact that the toric variety $X(A_n)$ is the fine moduli space $\bar{L}_{n+1}$ of stable $(n+1)$-pointed chains of projective lines investigated by Losev and Manin.Comment: 25 page

Numerical prediction and experimental analysis of ends-together yarn splicing

Pneumatic yarn splicing is a technical process for joining two yarn ends together. The process involves injecting compressed air into a splicing chamber. The inlet pressure and chamber slope determine the main parameters affecting this process. In this paper, large eddy simulation of the flow field in four selected splicing chambers is carried out. The chambers are used for splicing ends-together yarns. The results of these simulations are analyzed to investigate first the effects of the inlet pressure. Secondly, the effects of the geometry of the chambers on the flow field inside the splicing chambers are determined. These effects are studied and analyzed to interpret the experimental results, which have been obtained using the same splicing chambers. This provides further insight into the parameters that are important in order to obtain good splicing characteristics. It is demonstrated that the volume of the splicing chamber and the location of the air inlet channel play crucial roles in the splicing of the end-together yarns. The root mean square values of the velocity magnitude inside a splicing chamber have predictive values for the retained splice strength. The results provide solid evidence on the effectiveness of the computational fluid dynamics technology to study pneumatic splicing and optimize the geometry of an ends-together splicing chamber. </jats:p

Hormonal regulation of wheat growth during hydroponic culture

Hormonal control of root growth has been explored as one means to alleviate the crowding of plant root systems experienced in prototype hydroponic biomass production chambers being developed by the CELSS Breadboard Project. Four plant hormones, or their chemical analogs, which have been reported to selectively inhibit root growth, were tested by adding them to the nutrient solutions on day 10 of a 25 day growth test using spring wheat in hydroponic cultures. Growth and morphological changes is both shoot and root systems were evaluated. In no case was it possible to inhibit root growth without a comparable inhibition of shoot growth. It was concluded that this approach is unlikely to prove useful for wheat

Open subgroups of the automorphism group of a right-angled building

We study the group of type-preserving automorphisms of a right-angled building, in particular when the building is locally finite. Our aim is to characterize the proper open subgroups as the finite index closed subgroups of the stabilizers of proper residues. One of the main tools is the new notion of firm elements in a right-angled Coxeter group, which are those elements for which the final letter in each reduced representation is the same. We also introduce the related notions of firmness for arbitrary elements of such a Coxeter group and $n$-flexibility of chambers in a right-angled building. These notions and their properties are used to determine the set of chambers fixed by the fixator of a ball. Our main result is obtained by combining these facts with ideas by Pierre-Emmanuel Caprace and Timoth\'ee Marquis in the context of Kac-Moody groups over finite fields, where we had to replace the notion of root groups by a new notion of root wing groups.Comment: 29 page

Optimal Jackknife for Discrete Time and Continuous Time Unit Root Models

Maximum likelihood estimation of the persistence parameter in the discrete time unit root model is known for suffering from a downward bias. The bias is more pronounced in the continuous time unit root model. Recently Chambers and Kyriacou (2010) introduced a new jackknife method to remove the fi…rst order bias in the estimator of the persistence parameter in a discrete time unit root model. This paper proposes an improved jackknife estimator of the persistence parameter that works for both the discrete time unit root model and the continuous time unit root model. The proposed jackknife estimator is optimal in the sense that it minimizes the variance. Simulations highlight the performance of the proposed method in both contexts. They show that our optimal jackknife reduces the variance of the jackknife method of Chambers and Kyriacou by at least 10% in both cases.Bias reduction, Variance reduction, Vasicek model, Long-span Asymptotics, Autoregression

Improving Temporal Accuracy of Human Metabolic Chambers for Dynamic Metabolic Studies

Metabolic chambers are powerful tools for assessing human energy expenditure, providing flexibility and comfort for the subjects in a near free-living environment. However, the flexibility offered by the large living room size creates challenges in the assessment of dynamic human metabolic signals—such as those generated during high-intensity interval training and short-term involuntary physical activities—with sufficient temporal accuracy. Therefore, this paper presents methods to improve the temporal accuracy of metabolic chambers. The proposed methods include 1) adopting a shortest possible step size, here one minute, to compute the finite derivative terms for the metabolic rate calculation, and 2) applying a robust noise reduction method—total variation denoising—to minimize the large noise generated by the short derivative term whilst preserving the transient edges of the dynamic metabolic signals. Validated against 24-hour gas infusion tests, the proposed method reconstructs dynamic metabolic signals with the best temporal accuracy among state-of-the-art approaches, achieving a root mean square error of 0.27 kcal/min (18.8 J/s), while maintaining a low cumulative error in 24-hour total energy expenditure of less than 45 kcal/day (188280 J/day). When applied to a human exercise session, the proposed methods also show the best performance in terms of recovering the dynamics of exercise energy expenditure. Overall, the proposed methods improve the temporal resolution of the chamber system, enabling metabolic studies involving dynamic signals such as short interval exercises to carry out the metabolic chambers

Young diagrams and intersection numbers for toric manifolds associated with Weyl chambers

We study intersection numbers of invariant divisors in the toric manifold associated with the fan determined by the collection of Weyl chambers for each root system of classical type and of exceptional type $G_2$. We give a combinatorial formula for intersection numbers of certain subvarieties which are naturally indexed by elements of the Weyl group. These numbers describe the ring structure of the cohomology of the toric manifold.Comment: 20 page

Johnson Space Center's regenerative life support systems test bed

The Regenerative Life Support System (RLSS) Test Bed at NASA's Johnson Space Center is an atmospherically closed, controlled environment facility for the evaluation of regenerative life support systems using higher plants in conjunction with physicochemical life support systems. When completed, the facility will be comprised of two large scale plant growth chambers, each with approximately 10 m(exp 2) growing area. One of the two chambers, the Variable Pressure Growth Chamber (VPGC), will be capable of operating at lower atmospheric pressures to evaluate a range of environments that may be used in Lunar or Martian habitats; the other chamber, the Ambient Pressure Growth Chamber (APGC) will operate at ambient atmospheric pressure. The root zone in each chamber will be configurable for hydroponic or solid state media systems. Research will focus on: (1) in situ resource utilization for CELSS systems, in which simulated lunar soils will be used in selected crop growth studies; (2) integration of biological and physicochemical air and water revitalization systems; (3) effect of atmospheric pressure on system performance; and (4) monitoring and control strategies