Geometry of Control-Affine Systems

Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X - i.e., an affine distribution F together with a distinguished vector field contained in F. We compute local invariants for point-affine distributions of constant type when dim(X)=n, rank(F)=n-1, and when dim(X)=3, rank(F)=1. Unlike linear distributions, which are characterized by integer-valued invariants - namely, the rank and growth vector - when dim(X)<=4, we find local invariants depending on arbitrary functions even for rank 1 point-affine distributions on manifolds of dimension 2

Geometry of Optimal Control for Control-Affine Systems

Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for point-affine distributions of constant type with metric structures for systems with 2 states and 1 control and systems with 3 states and 1 control, and use Pontryagin's maximum principle to find geodesic trajectories for homogeneous examples. Even in these low dimensions, the behavior of these systems is surprisingly rich and varied

Production of non-Abelian tensor gauge bosons. Tree amplitudes in generalized Yang-Mills theory and BCFW recursion relation

The BCFW recursion relation allows to calculate tree-level scattering amplitudes in generalized Yang-Mills theory and, in particular, four-particle amplitudes for the production rate of non-Abelian tensor gauge bosons of arbitrary high spin in the fusion of two gluons. The consistency of the calculations in different kinematical channels is fulfilled when all dimensionless cubic coupling constants between vector bosons (gluons) and high spin non-Abelian tensor gauge bosons are equal to the Yang-Mills coupling constant. There are no high derivative cubic vertices in the generalized Yang-Mills theory. The amplitudes vanish as complex deformation parameter tends to infinity, so that there is no contribution from the contour at infinity. We derive a generalization of the Parke-Taylor formula in the case of production of two tensor gauge bosons of spin-s and N gluons (jets). The expression is holomorhic in the spinor variables of the scattered particles, exactly as the MHV gluon amplitude is, and reduces to the gluonic MHV amplitude when s=1. In generalized Yang-Mills theory the tree level n-particle scattering amplitudes with all positive helicities vanish, but tree amplitudes with one negative helicity particle are already nonzero.Comment: 19 pages, LaTex fil

Male Partners' Involvement Towards Prenatal Screening and Diagnostic Testing for Down Syndrome

Introduction: Now, male partners' involvement in prenatal screening and diagnostic testing for Down syndrome is becoming increasingly recognized as well to ensure that parents are well informed of the risks and benefits of screening. The aim of study was to understand the degree of male partners' involvement during pregnancy in Singapore population. Methods: A cross-sectional survey of male partners' attending prenatal counseling was performed. The instrument used to measure the level of involvement is a self-assessment questionnaire that identifies the role of male partners with a Likert scale. Descriptive statistics was used to analyze data gained. Result: A total of 107 participants completed the questionnaire. Sixty-seven percent of male partners were found to have a highlevel of involvement while 32.7% was found to have a medium level of involvement. Most of them stated that women can pursue prenatal testing without their permission. Male partners found it more important for them to accompany their spouse to amniocentesis or CVS than to the Down syndrome screening test. When participants were asked about how much information about Down syndrome they sought prior to the appointment, how much discussion they had with their spouse about Down syndrome testing, and about whether they or their spouse should be the first person to receive test results, most stated that they were undecided. Conclusion: These results revealed that male partners were very well involved in the Down syndrome testing during pregnancy and future studies should assess possible underlying factors that influence male partners' involvement

The Prevalence of Carbon-13 in Respiratory Carbon Dioxide As an Indicator of the Type of Endogenous Substrate. The change from lipid to carbohydrate during the respiratory rise in potato slices

Isotope discrimination is a common feature of biosynthesis in nature, with the result that different classes of carbon compounds frequently display different 13C/12C ratios. The 13C/12C ratio of lipid in potato tuber tissue is considerably lower than that for starch or protein. We have collected respiratory CO2 from potato discs in successive periods through 24 hr from the time of cutting—an interval in which the respiration rate rises 3–5-fold. The 13C/12C ratio of the evolved CO2 was determined for each period, and compared with the 13C/12C ratios of the major tissue metabolites. In the first hours the carbon isotope ratio of the CO2 matches that of lipid. With time, the ratio approaches that typical of starch or protein. An estimation has been made of the contribution of lipid and carbohydrate to the total respiration at each juncture. In connection with additional observations, it was deduced that the basal, or initial, respiration represents lipid metabolism —- possibly the alpha-oxidation of long chain fatty acids -— while the developed repiration represents conventional tricarboxylic acid cycle oxidation of the products of carbohydrate glycolysis. The true isotopic composition of the respiratory CO2 may be obscured by fractionation attending the refixation of CO2 during respiration, and by CO2 arising from dissolved CO2 and bicarbonate preexisting in the tuber. Means are described for coping with both pitfalls

Multichannel calculation of excited vector ϕ\phi resonances and the ϕ(2170)\phi(2170)

A multichannel calculation of excited $J^{PC}=1^{--}$ $\phi$ states is carried out within a generalization of the Resonance-Spectrum Expansion, which may shed light on the classification of the $\phi(2170)$ resonance, discovered by BABAR and originally denoted X(2175). In this framework, a complete spectrum of bare $s\bar{s}$ states is coupled to those OZI-allowed decay channels that should be most relevant for the considered energy range. The included $S$- and $P$-wave two-meson channels comprise the lowest pseudoscalar, vector, scalar, and axial-vector mesons, while in the $q\bar{q}$ sector both the $^{3}S_1$ and $^{3}D_1$ states are coupled. The only two free parameters are tuned so as to reproduce mass and width of the $\phi(1020)$, but come out reasonably close to previously used values. Among the model's $T$-matrix poles, there are good candidates for observed resonances, as well other ones that should exist according to the quark model. Besides the expected resonances as unitarized confinement states, a dynamical resonance pole is found at $(2186-i246)$ MeV. The huge width makes its interpretation as the $\phi(2170)$ somewhat dubious, but further improvements of the model may change this conclusion.Comment: 6 pages, 5 figures, RevTex4; v2: very recent experimental result, some extra discussion, and 2 references added; v3: 3 new figures, 2 new equations, and some rephrasing; version accepted for publication in Phys. Rev.

Developing a comprehensive information security framework for mHealth: a detailed analysis

It has been clearly shown that mHealth solutions, which is the use of mobile devices and other wireless technology to provide healthcare services, deliver more patient-focused healthcare, and improve the overall efficiency of healthcare systems. In addition, these solutions can potentially reduce the cost of providing healthcare in the context of the increasing demands of the aging populations in advanced economies. These solutions can also play an important part in intelligent environments, facilitating real-time data collection and input to enable various functionalities. However, there are several challenges regarding the development of mHealth solutions: the most important of these being privacy and data security. Furthermore, the use of cloud computing is becoming an option for the healthcare sector to store healthcare data; but storing data in the cloud raises serious concerns. This paper investigates how data are managed both on mHealth devices as well as in the cloud. Firstly, a detailed analysis of the entire mHealth domain is undertaken to determine domain-specific features and a taxonomy for mHealth, from which a set of security requirements are identified in order to develop a new information security framework. It then examines individual information security frameworks for mHealth devices and the cloud, noting similarities and differences. Furthermore, key mechanisms to implement the new framework are discussed and the new framework is then presented. Finally, the paper presents how the new framework could be implemented in order to develop an Advanced Digital Medical Platform