Parameter choices and ranges for continuous gravitational wave searches for steadily spinning neutron stars

We consider the issue of selecting parameters and their associated ranges for carrying out searches for continuous gravitational waves from steadily rotating neutron stars. We consider three different cases (i) the "classic" case of a star spinning about a principal axis; (ii) a biaxial star, not spinning about a principal axis; (iii) a triaxial star spinning steady, but not about a principal axis (as described in Jones, MNRAS vol 402, 2503 (2010)). The first of these emits only at one frequency; the other two at a pair of harmonically related frequencies. We show that in all three cases, when written in terms of the original "source parameters", there exist a number of discrete degeneracies, with different parameter values giving rise to the same gravitational wave signal. We show how these can be removed by suitably restricting the source parameter ranges. In the case of the model as written down by Jones, there is also a continuous degeneracy. We show how to remove this through a suitable rewriting in terms of "waveform parameters", chosen so as to make the specialisations to the other stellar models particularly simple. We briefly consider the (non-trivial) relation between the assignment of prior probabilities on one set of parameters verses the other. The results of this paper will be of use when designing strategies for carrying out searches for such multi-harmonic gravitational wave signals, and when performing parameter estimation in the event of a detection.Comment: Updated to match version accepted by MNRAS: One new equation (equation 82)); typo (sign-error) corrected in equation (88); one more paragraph inserted into Summary and Discussion sectio

Health-aware control of an octorotor UAV system based on actuator reliability

A major goal in modern flight control systems is the need of improving the reliability. This work presents a reliable control approach of an octorotor UAV that allows distributing the control effort among the actuators using health actuator information. The octorotor is an over-actuated system where the redundancy of the actuators allows the redistribution of the control effort among the existing actuators according to a given control strategy. The priority is given to each actuator according to the capabilities and reliability of this actuatorPeer ReviewedPostprint (author's final draft

Deterministic Global Attitude Estimation

A deterministic attitude estimation problem for a rigid body in an attitude dependent potential field with bounded measurement errors is studied. An attitude estimation scheme that does not use generalized coordinate representations of the attitude is presented here. Assuming that the initial attitude, angular velocity and measurement noise lie within given ellipsoidal bounds, an uncertainty ellipsoid that bounds the attitude and the angular velocity of the rigid body is obtained. The center of the uncertainty ellipsoid provides point estimates, and its size gives the accuracy of the estimates. The point estimates and the uncertainty ellipsoids are propagated using a Lie group variational integrator and its linearization, respectively. The estimation scheme is optimal in the sense that the attitude estimation error and the size of the uncertainty ellipsoid is minimized at each measurement instant, and it is global since the attitude is represented by a rotation matrix.Comment: IEEE Conference on Decision and Control, 2006. 6 pages, 6 figure

Profinite complexes of curves, their automorphisms and anabelian properties of moduli stacks of curves

Let ${\cal M}_{g,[n]}$, for $2g-2+n>0$, be the D-M moduli stack of smooth curves of genus $g$ labeled by $n$ unordered distinct points. The main result of the paper is that a finite, connected \'etale cover {\cal M}^\l of ${\cal M}_{g,[n]}$, defined over a sub-$p$-adic field $k$, is "almost" anabelian in the sense conjectured by Grothendieck for curves and their moduli spaces. The precise result is the following. Let \pi_1({\cal M}^\l_{\ol{k}}) be the geometric algebraic fundamental group of {\cal M}^\l and let {Out}^*(\pi_1({\cal M}^\l_{\ol{k}})) be the group of its exterior automorphisms which preserve the conjugacy classes of elements corresponding to simple loops around the Deligne-Mumford boundary of {\cal M}^\l (this is the "$\ast$-condition" motivating the "almost" above). Let us denote by {Out}^*_{G_k}(\pi_1({\cal M}^\l_{\ol{k}})) the subgroup consisting of elements which commute with the natural action of the absolute Galois group $G_k$ of $k$. Let us assume, moreover, that the generic point of the D-M stack {\cal M}^\l has a trivial automorphisms group. Then, there is a natural isomorphism: {Aut}_k({\cal M}^\l)\cong{Out}^*_{G_k}(\pi_1({\cal M}^\l_{\ol{k}})). This partially extends to moduli spaces of curves the anabelian properties proved by Mochizuki for hyperbolic curves over sub-$p$-adic fields.Comment: This paper has been withdrawn because of a flaw in the paper "Profinite Teichm\"uller theory" of the first author, on which this paper built o