Invariant and polynomial identities for higher rank matrices

We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank. We define permutation tensors and in term of them we construct discriminants and the determinant as the discriminant of order $d$, where $d$ is the dimension of the matrix. The characteristic polynomials and the Cayley--Hamilton theorem for higher rank matrices are obtained there from

Universal field equations for metric-affine theories of gravity

We show that almost all metric--affine theories of gravity yield Einstein equations with a non--null cosmological constant $\Lambda$. Under certain circumstances and for any dimension, it is also possible to incorporate a Weyl vector field $W_\mu$ and therefore the presence of an anisotropy. The viability of these field equations is discussed in view of recent astrophysical observations.Comment: 13 pages. This is a copy of the published paper. We are posting it here because of the increasing interest in f(R) theories of gravit

S-matrix poles and the second virial coefficient

For cutoff potentials, a condition which is not a limitation for the calculation of physical systems, the S-matrix is meromorphic. We can express it in terms of its poles, and then calculate the quantum mechanical second virial coefficient of a neutral gas. Here, we take another look at this approach, and discuss the feasibility, attraction and problems of the method. Among concerns are the rate of convergence of the 'pole' expansion and the physical significance of the 'higher' poles.Comment: 20 pages, 8 tables, submitted to J. Mol. Phy

Mapping auroral activity with Twitter

Twitter is a popular, publicly-accessible, social media service that has proven useful in mapping large-scale events in real-time. In this study, for the first time, the use of Twitter as a measure of auroral activity is investigated. Peaks in the number of aurora-related tweets are found to frequently coincide with geomagnetic disturbances (detection rate of 91%). Additionally, the number of daily aurora-related tweets is found to strongly correlate with several auroral strength proxies (ravg ≈ 0.7). An examination is made of the bias for location and time of day within Twitter data, and a first order correction of these effects is presented. Overall, the results suggest that Twitter can provide both specific details about an individual aurora and accurate real-time indication of when, and even from where, an aurora is visible

Phase estimation for thermal Gaussian states

We give the optimal bounds on the phase-estimation precision for mixed Gaussian states in the single-copy and many-copy regimes. Specifically, we focus on displaced thermal and squeezed thermal states. We find that while for displaced thermal states an increase in temperature reduces the estimation fidelity, for squeezed thermal states a larger temperature can enhance the estimation fidelity. The many-copy optimal bounds are compared with the minimum variance achieved by three important single-shot measurement strategies. We show that the single-copy canonical phase measurement does not always attain the optimal bounds in the many-copy scenario. Adaptive homodyning schemes do attain the bounds for displaced thermal states, but for squeezed states they yield fidelities that are insensitive to temperature variations and are, therefore, sub-optimal. Finally, we find that heterodyne measurements perform very poorly for pure states but can attain the optimal bounds for sufficiently mixed states. We apply our results to investigate the influence of losses in an optical metrology experiment. In the presence of losses squeezed states cease to provide Heisenberg limited precision and their performance is close to that of coherent states with the same mean photon number.Comment: typos correcte

Secrecy content of two-qubit states

We analyze the set of two-qubit states from which a secret key can be extracted by single-copy measurements plus classical processing of the outcomes. We introduce a key distillation protocol and give the corresponding necessary and sufficient condition for positive key extraction. Our results imply that the critical error rate derived by Chau, Phys. Rev. A {\bf 66}, 060302 (2002), for a secure key distribution using the six-state scheme is tight. Remarkably, an optimal eavesdropping attack against this protocol does not require any coherent quantum operation.Comment: 5 pages, RevTe

Ethnography of Language Planning and Policy

A decade ago, Hornberger & Johnson proposed that the ethnography of language planning and policy (ELPP) offers a useful way to understand how people create, interpret, and at times resist language policy and planning (LPP). They envisioned ethnographic investigation of layered LPP ideological and implementational spaces, taking up Hornberger\u27s plea five years earlier for language users, educators, and researchers to fill up and wedge open ideological and implementational spaces for multiple languages, literacies, identities, and practices to flourish and grow rather than dwindle and disappear. With roots going back to the 1980s and 1990s, ethnographic research in LPP had been gathering momentum since the turn of the millennium. This review encompasses selected ethnographic LPP research since 2000, exploring affordances and constraints of this research in yielding comparative and cumulative findings on how people interpret and engage with LPP initiatives. We highlight how common-sense wisdom about the perennial gap between policy and practice is given nuance through ethnographic research that identifies and explores intertwining dynamics of top-down and bottom-up LPP activities and processes, monoglossic and heteroglossic language ideologies and practices, potential equality and actual inequality of languages, and critical and transformative LPP research paradigms

On the geometry of four qubit invariants

The geometry of four-qubit entanglement is investigated. We replace some of the polynomial invariants for four-qubits introduced recently by new ones of direct geometrical meaning. It is shown that these invariants describe four points, six lines and four planes in complex projective space ${\bf CP}^3$. For the generic entanglement class of stochastic local operations and classical communication they take a very simple form related to the elementary symmetric polynomials in four complex variables. Moreover, their magnitudes are entanglement monotones that fit nicely into the geometric set of $n$-qubit ones related to Grassmannians of $l$-planes found recently. We also show that in terms of these invariants the hyperdeterminant of order 24 in the four-qubit amplitudes takes a more instructive form than the previously published expressions available in the literature. Finally in order to understand two, three and four-qubit entanglement in geometric terms we propose a unified setting based on ${\bf CP}^3$ furnished with a fixed quadric.Comment: 19 page

Aurorasaurus:a citizen science platform for viewing and reporting the aurora

A new, citizen science based, aurora observing and reporting platform has been developed with the primary aim of collecting auroral observations made by the general public to further improve the modeling of the aurora. In addition, the real-time ability of this platform facilitates the combination of citizen science observations with auroral oval models to improve auroral visibility nowcasting. Aurorasaurus provides easily understandable aurora information, basic gamification, and real-time location-based notification of verified aurora activity to engage citizen scientists. The Aurorasaurus project is one of only a handful of space weather citizen science projects and can provide useful results for the space weather and citizen science communities. Early results are promising with over 2,000 registered users submitting over 1,000 aurora observations and verifying over 1,700 aurora sightings posted on Twitter

Stellar Rotation in Young Clusters. II. Evolution of Stellar Rotation and Surface Helium Abundance

We derive the effective temperatures and gravities of 461 OB stars in 19 young clusters by fitting the H-gamma profile in their spectra. We use synthetic model profiles for rotating stars to develop a method to estimate the polar gravity for these stars, which we argue is a useful indicator of their evolutionary status. We combine these results with projected rotational velocity measurements obtained in a previous paper on these same open clusters. We find that the more massive B-stars experience a spin down as predicted by the theories for the evolution of rotating stars. Furthermore, we find that the members of binary stars also experience a marked spin down with advanced evolutionary state due to tidal interactions. We also derive non-LTE-corrected helium abundances for most of the sample by fitting the He I 4026, 4387, 4471 lines. A large number of helium peculiar stars are found among cooler stars with Teff < 23000 K. The analysis of the high mass stars (8.5 solar masses < M < 16 solar masses) shows that the helium enrichment process progresses through the main sequence (MS) phase and is greater among the faster rotators. This discovery supports the theoretical claim that rotationally induced internal mixing is the main cause of surface chemical anomalies that appear during the MS phase. The lower mass stars appear to have slower rotation rates among the low gravity objects, and they have a large proportion of helium peculiar stars. We suggest that both properties are due to their youth. The low gravity stars are probably pre-main sequence objects that will spin up as they contract. These young objects very likely host a remnant magnetic field from their natal cloud, and these strong fields sculpt out surface regions with unusual chemical abundances.Comment: 50 pages 18 figures, accepted by Ap