Earth’s Rotation: A Challenging Problem in Mathematics and Physics

A suitable knowledge of the orientation and motion of the Earth in space is a common need in various fields. That knowledge has been ever necessary to carry out astronomical observations, but with the advent of the space age, it became essential for making observations of satellites and predicting and determining their orbits, and for observing the Earth from space as well. Given the relevant role it plays in Space Geodesy, Earth rotation is considered as one of the three pillars of Geodesy, the other two being geometry and gravity. Besides, research on Earth rotation has fostered advances in many fields, such as Mathematics, Astronomy and Geophysics, for centuries. One remarkable feature of the problem is in the extreme requirements of accuracy that must be fulfilled in the near future, about a millimetre on the tangent plane to the planet surface, roughly speaking. That challenges all of the theories that have been devised and used to-date; the paper makes a short review of some of the most relevant methods, which can be envisaged as milestones in Earth rotation research, emphasizing the Hamiltonian approach developed by the authors. Some contemporary problems are presented, as well as the main lines of future research prospected by the International Astronomical Union/International Association of Geodesy Joint Working Group on Theory of Earth Rotation, created in 2013.This work has been partially supported by the Spanish government under Grants AYA2010-22039-C02-01 and AYA2010-22039-C02-02 from Ministerio de Economía y Competitividad (MINECO), the University of Alicante under Grant GRE11-08 and the Generalitat Valenciana, Grant GV/2014/072

Vibrio cholerae accessory colonisation factor AcfC: a chemotactic protein with a role in hyperinfectivity.

Vibrio cholerae O1 El Tor is an aquatic Gram-negative bacterium responsible for the current seventh pandemic of the diarrheal disease, cholera. A previous whole-genome analysis on V. cholerae O1 El Tor strains from the 2010 epidemic in Pakistan showed that all strains contained the V. cholerae pathogenicity island-1 and the accessory colonisation gene acfC (VC_0841). Here we show that acfC possess an open reading frame of 770 bp encoding a protein with a predicted size of 28 kDa, which shares high amino acid similarity with two adhesion proteins found in other enteropathogens, including Paa in serotype O45 porcine enteropathogenic Escherichia coli and PEB3 in Campylobacter jejuni. Using a defined acfC deletion mutant, we studied the specific role of AcfC in V. cholerae O1 El Tor environmental survival, colonisation and virulence in two infection model systems (Galleria mellonella and infant rabbits). Our results indicate that AcfC might be a periplasmic sulfate-binding protein that affects chemotaxis towards mucin and bacterial infectivity in the infant rabbit model of cholera. Overall, our findings suggest that AcfC contributes to the chemotactic response of WT V. cholerae and plays an important role in defining the overall distribution of the organism within the intestine

Detection of Phase Jumps of Free Core Nutation of the Earth and their Concurrence with Geomagnetic Jerks

We detected phase jumps of the Free Core Nutation (FCN) of the Earth directly from the analysis of the Very Long Baseline Interferometer (VLBI) observation of the Earth rotation for the period 1984-2003 by applying the Weighted Wavelet Z-Transform (WWZ) method and the Short-time Periodogram with the Gabor function (SPG) method. During the period, the FCN had two significant phase jumps in 1992 and 1998. These epochs coincide with the reported occurrence of geomagnetic jerks.Comment: 8 pages, 4 figure

The theory of canonical perturbations applied to attitude dynamics and to the Earth rotation. Osculating and nonosculating Andoyer variables

The Hamiltonian theory of Earth rotation, known as the Kinoshita-Souchay theory, operates with nonosculating Andoyer elements. This situation parallels a similar phenomenon that often happens (but seldom gets noticed) in orbital dynamics, when the standard Lagrange-type or Delaunay-type planetary equations unexpectedly render nonosculating orbital elements. In orbital mechanics, osculation loss happens when a velocity-dependent perturbation is plugged into the standard planetary equations. In attitude mechanics, osculation is lost when an angular-velocity-dependent disturbance is plugged in the standard dynamical equations for the Andoyer elements. We encounter exactly this situation in the theory of Earth rotation, because this theory contains an angular-velocity-dependent perturbation (the switch from an inertial frame to that associated with the precessing ecliptic of date). While the osculation loss does not influence the predictions for the figure axis of the planet, it considerably alters the predictions for the instantaneous spin-axis' orientation. We explore this issue in great detail

Tanzawaic acids, a chemically novel set of bacterial conjugation inhibitors

Bacterial conjugation is the main mechanism for the dissemination of multiple antibiotic resistance in human pathogens. This dissemination could be controlled by molecules that interfere with the conjugation process. A search for conjugation inhibitors among a collection of 1,632 natural compounds, identified tanzawaic acids A and B as best hits. They specially inhibited IncW and IncFII conjugative systems, including plasmids mobilized by them. Plasmids belonging to IncFI, IncI, IncL/M, IncX and IncH incompatibility groups were targeted to a lesser extent, whereas IncN and IncP plasmids were unaffected. Tanzawaic acids showed reduced toxicity in bacterial, fungal or human cells, when compared to synthetic conjugation inhibitors, opening the possibility of their deployment in complex environments, including natural settings relevant for antibiotic resistance dissemination.Work in the FDLC group was supported by grants BFU2014-55534-C2-1-P from the Spanish Ministry of Economy and Competitiveness (http://www.mineco.gob.es) and 612146/FP7-ICT-2013-10 and 282004/FP7-HEALTH-2011-2.3.1-2 from the European Seventh Framework Programme (https://ec.europa.eu/research/fp7). MG was supported by a PhD fellowship from the University of Cantabria (http://www.unican.es). JCG was supported by a postdoctoral fellowship ASTF 402-2010 from the European Molecular Biology Organization (http://www.embo.org). Biomar Microbial Technologies was supported by grant 282004/FP7-HEALTH-2011-2.3.1-2 from the European Seventh Framework Programme (https://ec.europa.eu/research/fp7).USD 1,495 APC fee funded by the EC FP7 Post-Grant Open Access PilotPeer reviewe

Methods for Compression of Feedback in Adaptive Multicarrier 4G Schemes

In this paper, several algorithms for compressing the feedback of channel quality information are presented and analyzed. These algorithms are developed for a proposed adaptive modulation scheme for future multi-carrier 4G mobile systems. These strategies compress the feedback data and, used together with opportunistic scheduling, drastically reduce the feedback data rate. Thus the adaptive modulation schemes become more suitable and efficient to be implemented in future mobile systems, increasing data throughput and overall system performance.This work has been partly funded by the Spanish government with projects MACAWI (TEC 2005-07477-c02-02), MAMBO2 (CCG06-UC3M-TIC-0698), and European COST Action 289 and is a result of work done within this European actio

Dynamical adjustments in IAU 2000A nutation series arising from IAU 2006 precession

The adoption of International Astronomical Union (IAU) 2006 precession model, IAU 2006 precession, requires IAU 2000A nutation to be adjusted to ensure compatibility between both theories. This consists of adding small terms to some nutation amplitudes relevant at the microarcsecond level. Those contributions were derived in previously published articles and are incorporated into current astronomical standards. They are due to the estimation process of nutation amplitudes by Very Long Baseline Interferometry (VLBI) and to the changes induced by the J2 rate present in the precession theory. We focus on the second kind of those adjustments, and develop a simple model of the Earth nutation capable of determining all the changes arising in the theoretical construction of the nutation series in a dynamical consistent way. This entails the consideration of three main classes of effects: the J2 rate, the orbital coefficients rate, and the variations induced by the update of some IAU 2006 precession quantities. With this aim, we construct a first order model for the nutations of the angular momentum axis of the non-rigid Earth. Our treatment is based on a Hamiltonian formalism and leads to analytical formulae for the nutation amplitudes in the form of in-phase, out-of-phase, and mixed secular terms. They allow numerical evaluation of the contributions of the former effects. We conclude that the accepted corrections associated with the J2 rate must be supplemented with new, hitherto unconsidered terms of the same order of magnitude, and that these should be incorporated into present standards

Pilot Pouring in Superimposed Training for Channel Estimation in CB-FMT

Cyclic block filtered multi-tone (CB-FMT) is a waveform that can be efficiently synthesized through a filter-bank in the frequency domain. Although the main principles have been already established, channel estimation has not been addressed yet. This is because of assuming that the existing techniques based on pilot symbol assisted modulation (PSAM), implemented in OFDM-like schemes, can be reused. However, PSAM leads to an undesirable loss of data-rate. In this paper, an alternative method inspired by the superimposed training (ST) concept, namely pilot pouring ST (PPST), is proposed. In PPST, pilots are superimposed over data taking advantage of the particular spectral characteristics of CB-FMT. Exploiting the sub-channel spectrum, the pilot symbols are poured in those resources unused for data transmission. This spectral shaping of pilots is also exploited at the receiver to carry out channel estimation, by enhancing those channel estimates that exhibit a low data interference contribution. Furthermore, a frequency domain resource mapping strategy for the data and poured pilot symbols is proposed to enable an accurate estimation in strongly frequency-selective channels. The parameters of the proposed scheme are optimized to minimize the channel estimation mean squared error (MSE). Finally, several numerical results illustrate the performance advantages of the proposed technique as compared to other alternatives

Low-complexity power allocation in pilot-pouring superimposed training over CB-FMT

Pilot-pouring superimposed training (PPST) is a novel channel estimation technique specially designed for cyclic block filtered multi-tone (CB-FMT), where the pilot symbols are poured into the subcarriers taking advantage of the power left unused by the data symbols. Hence, since this technique is based on superimposed training (ST) principles, the data rate is not reduced, unlike the pilot symbol assisted modulation (PSAM). Besides, it exploits a weighted average at the receiver side that is capable of minimizing the mean squared error (MSE) of the channel estimation, and then enhancing the performance of the system. However, the existing proposal on PPST is limited to the minimization of the MSE to improve channel estimation for a given power allocation factor, without solving the joint optimization of channel estimation and data detection procedures. With this aim, this work addresses the whole problem to reach the best performance for both tasks, thus taking into account also the power allocation factor in the opt where the pilot symbols are poured into the subcarriers taking advantage of the power left unused by the data symbols. Hence, since this technique is based on superimposed training (ST) principles, the data rate is not reduced, unlike the pilot symbol assisted modulation (PSAM). Besides, it exploits a weighted average at the receiver side that is capable of minimizing the mean squared error (MSE) of the channel estimation, and then enhancing the performance of the system. However, the existing proposal on PPST is limited to the minimization of the MSE to improve channel estimation for a given power allocation factor, without solving the joint optimization of channel estimation and data detection procedures. With this aim, this work addresses the whole problem to reach the best performance for both tasks, thus taking into account also the power allocation factor in the optimization process, where the spectral efficiency must be maximized through the signal-to-interference plus noise ratio (SINR). Two optimization approaches are proposed, where the first one, referred as pilot-pouring optimization (PPO), is focused on performance at the expense of a high complexity, while the second one, denoted as low-complexity PPO (LPPO), is able to trade-off between performance and execution time. Numerical results are provided in order to show the validity of our proposal, where the different optimization problems are compared in terms of SINR and execution time.This work was supported by Spanish National Projects TERESA-ADA (TEC2017-90093-C3-2-R) (MINECO/AEI/FEDER, UE), and IRENE-EARTH (PID2020-115323RB-C33 / AEI / 10.13039/501100011033). The work of A. M. Tonello was supported by the Chair of Excellence Program of the Universidad Carlos III de Madrid