Integrability of a Generalized Ito System: the Painleve Test

It is shown that a generalized Ito system of four coupled nonlinear evolution equations passes the Painleve test for integrability in five distinct cases, of which two were introduced recently by Tam, Hu and Wang. A conjecture is formulated on integrability of a vector generalization of the Ito system.Comment: LaTeX, 5 page

A system for synthetic vision and augmented reality in future flight decks

Rockwell Science Center is investigating novel human-computer interaction techniques for enhancing the situational awareness in future flight decks. One aspect is to provide intuitive displays that provide the vital information and the spatial awareness by augmenting the real world with an overlay of relevant information registered to the real world. Such Augmented Reality (AR) techniques can be employed during bad weather scenarios to permit flying in Visual Flight Rules (VFR) in conditions which would normally require Instrumental Flight Rules (IFR). These systems could easily be implemented on heads-up displays (HUD). The advantage of AR systems vs. purely synthetic vision (SV) systems is that the pilot can relate the information overlay to real objects in the world, whereas SV systems provide a constant virtual view, where inconsistencies can hardly be detected. The development of components for such a system led to a demonstrator implemented on a PC. A camera grabs video images which are overlaid with registered information. Orientation of the camera is obtained from an inclinometer and a magnetometer; position is acquired from GPS. In a possible implementation in an airplane, the on-board attitude information can be used for obtaining correct registration. If visibility is sufficient, computer vision modules can be used to fine-tune the registration by matching visual cues with database features. This technology would be especially useful for landing approaches. The current demonstrator provides a frame-rate of 15 fps, using a live video feed as background with an overlay of avionics symbology in the foreground. In addition, terrain rendering from a 1 arc sec. digital elevation model database can be overlaid to provide synthetic vision in case of limited visibility. For true outdoor testing (on ground level), the system has been implemented on a wearable computer

Global Behavior of the Douglas-Rachford Method for a Nonconvex Feasibility Problem

In recent times the Douglas-Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems

A feasibility approach for constructing combinatorial designs of circulant type

In this work, we propose an optimization approach for constructing various classes of circulant combinatorial designs that can be defined in terms of autocorrelations. The problem is formulated as a so-called feasibility problem having three sets, to which the Douglas-Rachford projection algorithm is applied. The approach is illustrated on three different classes of circulant combinatorial designs: circulant weighing matrices, D-optimal matrices, and Hadamard matrices with two circulant cores. Furthermore, we explicitly construct two new circulant weighing matrices, a $CW(126,64)$ and a $CW(198,100)$, whose existence was previously marked as unresolved in the most recent version of Strassler's table

Axion Dark Matter and Cosmological Parameters

We observe that photon cooling after big bang nucleosynthesis (BBN) but before recombination can remove the conflict between the observed and theoretically predicted value of the primordial abundance of $^7$Li. Such cooling is ordinarily difficult to achieve. However, the recent realization that dark matter axions form a Bose-Einstein condensate (BEC) provides a possible mechanism, because the much colder axions may reach thermal contact with the photons. This proposal predicts a high effective number of neutrinos as measured by the cosmic microwave anisotropy spectrum.Comment: 4 pages, one figure. Version to appear in Phys. Rev. Lett., incorporating useful comments by the referees and emphasizing that photon cooling by axion BEC is a possibility, not a certaint