Optimal Navigation Functions for Nonlinear Stochastic Systems

This paper presents a new methodology to craft navigation functions for nonlinear systems with stochastic uncertainty. The method relies on the transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear partial differential equation. This approach allows for optimality criteria to be incorporated into the navigation function, and generalizes several existing results in navigation functions. It is shown that the HJB and that existing navigation functions in the literature sit on ends of a spectrum of optimization problems, upon which tradeoffs may be made in problem complexity. In particular, it is shown that under certain criteria the optimal navigation function is related to Laplace's equation, previously used in the literature, through an exponential transform. Further, analytical solutions to the HJB are available in simplified domains, yielding guidance towards optimality for approximation schemes. Examples are used to illustrate the role that noise, and optimality can potentially play in navigation system design.Comment: Accepted to IROS 2014. 8 Page

Impact of spin-orbit currents on the electroweak skin of neutron-rich nuclei

Background: Measurements of neutron radii provide important constraints on the isovector sector of nuclear density functionals and offer vital guidance in areas as diverse as atomic parity violation, heavy-ion collisions, and neutron-star structure. Purpose: To assess the impact of spin-orbit currents on the electromagnetic- and weak-charge radii of a variety of nuclei. Special emphasis is placed on the experimentally accessible electroweak skin, defined as the difference between weak-charge and electromagnetic-charge radii. Methods: Two accurately calibrated relativistic mean field models are used to compute proton, neutron, charge, and weak-charge radii of a variety of nuclei. Results: We find that spin-orbit contributions to the electroweak skin of light neutron-rich nuclei, such as 22O and 48Ca, are significant and result in a substantial increase in the size of the electroweak skin relative to the neutron skin. Conclusions: Given that spin-orbit contributions to both the charge and weak-charge radii of nuclei are often as large as present or anticipated experimental error bars, future calculations must incorporate spin-orbit currents in the calculation of electroweak form factors.Comment: 17 pages, 2 figures, and 2 table

Thermoregulation in rats: Effects of varying duration of hypergravic fields

The effects of hypergravitational fields on the thermoregulatory system of the rat are examined. The question underlying the investigation was whether the response of the rat to the one hour cold exposure depends only upon the amplitude of the hypergravic field during the period of cold exposure or whether the response is also dependent on the amplitude and duration of the hypergravic field prior to cold exposure. One hour of cold exposure applied over the last hour of either a 1, 4, 7, 13, 19, 25, or 37 hr period of 3G evoked a decrease in core temperature (T sub c) of about 3 C. However, when rats were subjected concurrently to cold and acceleration following 8 days at 3G, they exhibited a smaller fall in T sub c, suggesting partial recovery of the acceleration induced impairment of temperature regulation. In another series of experiments, the gravitational field profile was changed in amplitude in 3 different ways. Despite the different gravitational field profiles used prior to cold, the magnitude of the fall in T sub c over the 1 hr period of cold exposure was the same in all cases. These results suggest that the thermoregulatory impairment has a rapid onset, is a manifestation of an ongoing effect of hypergravity, and is not dependent upon the prior G profile

Convex Relaxations of SE(2) and SE(3) for Visual Pose Estimation

This paper proposes a new method for rigid body pose estimation based on spectrahedral representations of the tautological orbitopes of $SE(2)$ and $SE(3)$. The approach can use dense point cloud data from stereo vision or an RGB-D sensor (such as the Microsoft Kinect), as well as visual appearance data. The method is a convex relaxation of the classical pose estimation problem, and is based on explicit linear matrix inequality (LMI) representations for the convex hulls of $SE(2)$ and $SE(3)$. Given these representations, the relaxed pose estimation problem can be framed as a robust least squares problem with the optimization variable constrained to these convex sets. Although this formulation is a relaxation of the original problem, numerical experiments indicate that it is indeed exact - i.e. its solution is a member of $SE(2)$ or $SE(3)$ - in many interesting settings. We additionally show that this method is guaranteed to be exact for a large class of pose estimation problems.Comment: ICRA 2014 Preprin

Effect of altered gravity on temperature regulation in mammals: Investigation of gravity effect on temperature regulation in mammals

Male, Long-Evans hooded rats were instrumented for monitoring core and hypothalamic temperatures as well as shivering and nonshivering thermogenesis in response to decreased ambient temperature in order to characterize the nature of the neural controller of temperature in rats at 1G and evaluate chronic implantation techniques for the monitoring of appropriate parameters at hypergravic fields. The thermoregulatory responses of cold-exposed rats at 2G were compared to those at 1G. A computer model was developed to simulate the thermoregulatory system in the rat. Observations at 1 and 2G were extended to acceleration fields of 1.5, 3.0 and 4.0G and the computer model was modified for application to altered gravity conditions. Changes in the acceleration field resulted in inadequate heat generation rather than increased heat loss. Acceleration appears to impair the ability of the neurocontroller to appropriately integrate input signals for body temperature maintenance

Linearly Solvable Stochastic Control Lyapunov Functions

This paper presents a new method for synthesizing stochastic control Lyapunov functions for a class of nonlinear stochastic control systems. The technique relies on a transformation of the classical nonlinear Hamilton-Jacobi-Bellman partial differential equation to a linear partial differential equation for a class of problems with a particular constraint on the stochastic forcing. This linear partial differential equation can then be relaxed to a linear differential inclusion, allowing for relaxed solutions to be generated using sum of squares programming. The resulting relaxed solutions are in fact viscosity super/subsolutions, and by the maximum principle are pointwise upper and lower bounds to the underlying value function, even for coarse polynomial approximations. Furthermore, the pointwise upper bound is shown to be a stochastic control Lyapunov function, yielding a method for generating nonlinear controllers with pointwise bounded distance from the optimal cost when using the optimal controller. These approximate solutions may be computed with non-increasing error via a hierarchy of semidefinite optimization problems. Finally, this paper develops a-priori bounds on trajectory suboptimality when using these approximate value functions, as well as demonstrates that these methods, and bounds, can be applied to a more general class of nonlinear systems not obeying the constraint on stochastic forcing. Simulated examples illustrate the methodology.Comment: Published in SIAM Journal of Control and Optimizatio

Analysis of flux-integrated cross sections for quasi-elastic neutrino charged-current scattering off 12^{12}C at MiniBooNE energies

Flux-averaged and flux-integrated cross sections for quasi-elastic neutrino charged-current scattering on nucleus are analyzed. It is shown that the flux-integrated differential cross sections are nuclear model-independent. We calculate these cross sections using the relativistic distorted-wave impulse approximation and relativistic Fermi gas model with the Booster Neutrino Beamline flux and compare results with the recent MiniBooNE experiment data. Within these models an axial mass $M_A$ is extracted from a fit of the measured $d\sigma/dQ^2$ cross section. The extracted value of $M_A$ is consistent with the MiniBooNE result. The measured and calculated double differential cross sections $d\sigma/dTd\cos\theta$ generally agree within the error of the experiment. But the Fermi gas model predictions are completely off of the data in the region of low muon energies and scattering angles.Comment: 23 pages, 8 figure

Why Higher Real Wages May Reduce Altruism for the Poor

The non-poor need to have information on the existence and the cause of the plight of the poor for redistribution to be a public good. Since gaining this information takes time, the full price of helping the poor includes both the money cost and the time involved in empathizing. Over the last century, the higher real incomes of the poor have reduced the manifestations of poverty. When poverty is less obvious, the non-poor are not as aware of poverty. This article also discusses when redistribution is most likely to be a public good.Altruism; Wage

Semidefinite Relaxations for Stochastic Optimal Control Policies

Recent results in the study of the Hamilton Jacobi Bellman (HJB) equation have led to the discovery of a formulation of the value function as a linear Partial Differential Equation (PDE) for stochastic nonlinear systems with a mild constraint on their disturbances. This has yielded promising directions for research in the planning and control of nonlinear systems. This work proposes a new method obtaining approximate solutions to these linear stochastic optimal control (SOC) problems. A candidate polynomial with variable coefficients is proposed as the solution to the SOC problem. A Sum of Squares (SOS) relaxation is then taken to the partial differential constraints, leading to a hierarchy of semidefinite relaxations with improving sub-optimality gap. The resulting approximate solutions are shown to be guaranteed over- and under-approximations for the optimal value function.Comment: Preprint. Accepted to American Controls Conference (ACC) 2014 in Portland, Oregon. 7 pages, colo

A variational principle for stationary, axisymmetric solutions of Einstein's equations

Stationary, axisymmetric, vacuum, solutions of Einstein's equations are obtained as critical points of the total mass among all axisymmetric and $(t,\phi)$ symmetric initial data with fixed angular momentum. In this variational principle the mass is written as a positive definite integral over a spacelike hypersurface. It is also proved that if absolute minimum exists then it is equal to the absolute minimum of the mass among all maximal, axisymmetric, vacuum, initial data with fixed angular momentum. Arguments are given to support the conjecture that this minimum exists and is the extreme Kerr initial data.Comment: 21 page