Chow's theorem and universal holonomic quantum computation

A theorem from control theory relating the Lie algebra generated by vector fields on a manifold to the controllability of the dynamical system is shown to apply to Holonomic Quantum Computation. Conditions for deriving the holonomy algebra are presented by taking covariant derivatives of the curvature associated to a non-Abelian gauge connection. When applied to the Optical Holonomic Computer, these conditions determine that the holonomy group of the two-qubit interaction model contains $SU(2) \times SU(2)$. In particular, a universal two-qubit logic gate is attainable for this model.Comment: 13 page

Symmetry Reduction of Optimal Control Systems and Principal Connections

This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to obtain explicit expressions of the reduced system by exploiting the geometry. In particular, we show how to obtain a principal connection to be used in the reduction for various choices of symmetry groups, as opposed to assuming such a principal connection is given or choosing a particular symmetry group to simplify the setting. Our result synthesizes some previous works on symmetry reduction of nonlinear control and optimal control systems. Affine and kinematic optimal control systems are of particular interest: We explicitly work out the details for such systems and also show a few examples of symmetry reduction of kinematic optimal control problems.Comment: 23 pages, 2 figure

Reduction, Symmetry and Phases in Mechanics

Various holonomy phenomena are shown to be instances of the reconstruction procedure for mechanical systems with symmetry. We systematically exploit this point of view for fixed systems (for example with controls on the internal, or reduced, variables) and for slowly moving systems in an adiabatic context. For the latter, we obtain the phases as the holonomy for a connection which synthesizes the Cartan connection for moving mechanical systems with the Hannay-Berry connection for integrable systems. This synthesis allows one to treat in a natural way examples like the ball in the slowly rotating hoop and also non-integrable mechanical systems

Urban Poverty and Health in Developing Countries: Household and Neighborhood Effects

In the U.S. and other high-income countries, where most of the population lives in urban areas, there is intense scholarly and program interest in the effects of household and neighborhood living standards on health. Yet very few studies of developing-country cities have examined these issues. This paper investigates whether in these cities, the health of women and young children is influenced by both household and neighborhood standards of living. Using data from the urban samples of some 85 Demographic and Health surveys, and modelling living standards using factor-analytic MIMIC methods, we find, first, that the neighborhoods of poor households are more heterogeneous than is often asserted. To judge from our results, it appears that as a rule, poor urban households do not tend to live in uniformly poor communities; indeed, about 1 in 10 of a poor household's neighbors is relatively affluent, belonging to the upper quartile of the urban distribution of living standards. Do household and neighborhood living standards influence health? Applying multivariate models with controls for other socioeconomic variables, we discover that household living standards have a substantial influence on three measures of health: unmet need for modern contraception; birth attendance by doctors, nurses, or trained midwives; and children's height for age. Neighborhood living standards exert significant additional influence on health in many of the surveys we examine, especially in birth attendance. There is considerable evidence, then, indicating that both household and neighborhood living standards can make a substantively important difference to health.poverty, health, developing countries, urban, factor analysis, neighborhood

Optimal regulation in systems with stochastic time sampling

An optimal control theory that accounts for stochastic variable time sampling in a distributed microprocessor based flight control system is presented. The theory is developed by using a linear process model for the airplane dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved for the control law that minimizes the expected value of a quadratic cost function. The optimal cost obtained with a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained with a known and uniform information update interval

Space Shuttle separate-surface control-system study

A control system concept is presented that produces proportional control of yaw moment for the space shuttle from early entry to Mach 2 with only software modifications of the vehicle. It uses separate deflections of the inboard and outboard elevon surfaces and is evaluated, by determining the maximum static yawing moment available by considering the deflection limits of the elevon surfaces. A proportional moment slightly in excess of that produced by the most effective reaction control system (RCS) jet for yaw control can be obtained. In addition to the static moment study, a control law is designed which is intended to produce desired flying qualities

Ocean services user needs assessment. Volume 1: Survey results, conclusions and recommendations

An interpretation of environmental information needs of marine users, derived from a direct contact survey of eight important sectors of the marine user community is presented. Findings of the survey and results and recommendations are reported. The findings consist of specific and quantized measurement and derived product needs for each sector and comparisons of these needs with current and planned NOAA data and services. The following supportive and reference material are examined: direct contact interviews with industry members, analyses of current NOAA data gathering and derived product capabilities, evaluations of new and emerging domestic and foreign satellite data gathering capabilities, and a special commercial fishing survey conducted by the Jet Propulsion Laboratory (JPL)