Deformations of calibrated subbundles of Euclidean spaces via twisting by special sections

We extend the "bundle constructions" of calibrated submanifolds, due to Harvey--Lawson in the special Lagrangian case, and to Ionel--Karigiannis--Min-Oo in the cases of exceptional calibrations, by "twisting" the bundles by a special (harmonic, holomorphic, parallel) section of a complementary bundle. The existence of such deformations shows that the moduli space of calibrated deformations of these "calibrated subbundles" includes deformations which destroy the linear structure of the fibre.Comment: 16 pages, no figures. Version 2: Only minor cosmetic and typographical revisions. To appear in "Annals of Global Analysis and Geometry.

Adventures in Invariant Theory

We provide an introduction to enumerating and constructing invariants of group representations via character methods. The problem is contextualised via two case studies arising from our recent work: entanglement measures, for characterising the structure of state spaces for composite quantum systems; and Markov invariants, a robust alternative to parameter-estimation intensive methods of statistical inference in molecular phylogenetics.Comment: 12 pp, includes supplementary discussion of example

Feasibility study of the solar scientific instruments for Spacelab/Orbiter

The feasibility and economics of mounting and operating a set of solar scientific instruments in the backup Skylab Apollo Telescope Mount (ATM) hardware was evaluated. The instruments used as the study test payload and integrated into the ATM were: the Solar EUV Telescope/Spectrometer; the Solar Active Region Observing Telescope; and the Lyman Alpha White Light Coronagraph. The backup ATM hardware consists of a central cruciform structure, called the "SPAR', a "Sun End Canister' and a "Multiple Docking Adapter End Canister'. Basically, the ATM hardware and software provides a structural interface for the instruments; a closely controlled thermal environment; and a very accurate attitude and pointing control capability. The hardware is an identical set to the hardware that flow on Skylab

Spectral and Spin Measurement of Two Small and Fast-Rotating Near-Earth Asteroids

In May 2012 two asteroids made near-miss "grazing" passes at distances of a few Earth-radii: 2012 KP24 passed at nine Earth-radii and 2012 KT42 at only three Earth-radii. The latter passed inside the orbital distance of geosynchronous satellites. From spectral and imaging measurements using NASA's 3-m Infrared Telescope Facility (IRTF), we deduce taxonomic, rotational, and physical properties. Their spectral characteristics are somewhat atypical among near-Earth asteroids: C-complex for 2012 KP24 and B-type for 2012 KT42, from which we interpret the albedos of both asteroids to be between 0.10 and 0.15 and effective diameters of 20+-2 and 6+-1 meters, respectively. Among B-type asteroids, the spectrum of 2012 KT42 is most similar to 3200 Phaethon and 4015 Wilson-Harrington. Not only are these among the smallest asteroids spectrally measured, we also find they are among the fastest-spinning: 2012 KP24 completes a rotation in 2.5008+-0.0006 minutes and 2012 KT42 rotates in 3.634+-0.001 minutes.Comment: 4 pages, 3 figures, accepted for publication in Icaru

The Ghosts of Bindings Past: Micro-Computed X-Ray Tomography for the Study of Bookbinding

This essay describes the results of a new application of micro-computed X-ray tomography (µCT) to conduct nondestructive investigations of the binding structures of premodern books. This application addresses a twofold challenge in the study of historic bindings and their construction. Few premodern books survive in their original bindings. Moreover, until recently, when books were rebound, the original structures were rarely documented, and the remains were usually discarded. Where original bindings do remain in situ, much of their structure is, by design, hidden. Particulars of construction may be surmised; but without destructive disbinding, little can be proven. µCT enables an exploratory, multilinear approach to codicological investigations that makes bindings accessible in the form of tractable volumetric data

Perturbative Solutions of the Extended Constraint Equations in General Relativity

The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface $Z$ in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-linear system of partial differential equations for the induced metric, the second fundamental form and two other tensorial quantities defined on $Z$, and are equivalent to the usual constraint equations that $Z$ satisfies as a spacelike hypersurface in a spacetime satisfying Einstein's vacuum equation. This article develops a method for finding perturbative, asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat solution on Euclidean space. This method is fundamentally different from the `classical' method of Lichnerowicz and York that is used to solve the usual constraint equations.Comment: This third and final version has been accepted for publication in Communications in Mathematical Physic

Preserving entanglement under decoherence and sandwiching all separable states

Every entangled state can be perturbed, for instance by decoherence, and stay entangled. For a large class of pure entangled states, we show how large the perturbation can be. Our class includes all pure bipartite and all maximally entangled states. For an entangled state, E, the constucted neighborhood of entangled states is the region outside two parallel hyperplanes, which sandwich the set of all separable states. The states for which these neighborhoods are largest are the maximally entangled ones. As the number of particles, or the dimensions of the Hilbert spaces for two of the particles increases, the distance between two of the hyperplanes which sandwich the separable states goes to zero. It is easy to decide if a state Q is in the neighborhood of entangled states we construct for an entangled state E. One merely has to check if the trace of EQ is greater than a constant which depends upon E and which we determine.Comment: Corrected first author's e-mail address. All the rest remains unchange

Nonlinear software sensor for monitoring genetic regulation processes with noise and modeling errors

Nonlinear control techniques by means of a software sensor that are commonly used in chemical engineering could be also applied to genetic regulation processes. We provide here a realistic formulation of this procedure by introducing an additive white Gaussian noise, which is usually found in experimental data. Besides, we include model errors, meaning that we assume we do not know the nonlinear regulation function of the process. In order to illustrate this procedure, we employ the Goodwin dynamics of the concentrations [B.C. Goodwin, Temporal Oscillations in Cells, (Academic Press, New York, 1963)] in the simple form recently applied to single gene systems and some operon cases [H. De Jong, J. Comp. Biol. 9, 67 (2002)], which involves the dynamics of the mRNA, given protein, and metabolite concentrations. Further, we present results for a three gene case in co-regulated sets of transcription units as they occur in prokaryotes. However, instead of considering their full dynamics, we use only the data of the metabolites and a designed software sensor. We also show, more generally, that it is possible to rebuild the complete set of nonmeasured concentrations despite the uncertainties in the regulation function or, even more, in the case of not knowing the mRNA dynamics. In addition, the rebuilding of concentrations is not affected by the perturbation due to the additive white Gaussian noise and also we managed to filter the noisy output of the biological systemComment: 21 pages, 7 figures; also selected in vjbio of August 2005; this version corrects a misorder in the last three references of the published versio

Rational Moral Ignorance

Philosophy and Phenomenological Research, EarlyView