Mixture or mosaic? Genetic patterns in UK grey squirrels support a human-mediated ‘long-jump’ invasion mechanism

Aim Clarifying whether multiple introductions of a species remain relatively isolated or merge and interbreed is essential for understanding the dynamics of invasion processes. Multiple introductions from different sources can result in a mixture of genetically distinct populations, increasing the total genetic diversity. This mixing can resolve the ‘genetic paradox’, whereby in spite of the relatively small numbers of introduced individuals, the augmented diversity due to this mixing increases adaptability and the ability of the species to spread in new environments. Here, we aim to assess whether the expansion of a successful invader, the Eastern grey squirrel, was partly driven by the merger of multiple introductions and the effects of such a merger on diversity. Location UK, Ireland. Methods We analysed the genetic variation at 12 microsatellite loci of 381 individuals sampled from one historical and 14 modern populations of grey squirrels. Results Our data revealed that current UK population structure resembles a mosaic, with minimal interpopulation mixing and each element reflecting the genetic make-up of historic introductions. The genetic diversity of each examined population was lower than a US population or a historical UK population. Numbers of releases in a county did not correlate with county-level genetic diversity. Inbreeding coefficients remain high, and effective population sizes remain small. Main conclusions Our results support the conclusion that rapid and large-scale expansion in this species in the UK was not driven by a genetic mixing of multiple introduced populations with a single expansion front, but was promoted by repeated translocations of small propagules. Our results have implications for the management of grey squirrels and other invasive species and also demonstrate how invaders can overcome the genetic paradox, if spread is facilitated by human-mediated dispersal

Strongly-ordered infrared limits for subtraction counterterms from factorisation

After a brief introduction to the problem of subtraction of infrared divergences for high-order collider observables, we present a preliminary study of strongly-ordered soft and collinear multiple radiation from the point of view of factorisation. We show that the matrix elements of fields and Wilson lines that describe soft and collinear radiation in factorised scattering amplitudes can be re-factorised in strongly-ordered limits, providing a systematic method to compute them, to characterise their singularity structure, and to build local subtraction counterterms for strongly-ordered configurations. Our results provide tools for a detailed organisation of subtraction algorithms, in principle to all orders in perturbation theory

Strongly-ordered infrared limits for subtraction counterterms from factorisation

After a brief introduction to the problem of subtraction of infrared divergences for high-order collider observables, we present a preliminary study of strongly-ordered soft and collinear multiple radiation from the point of view of factorisation. We show that the matrix elements of fields and Wilson lines that describe soft and collinear radiation in factorised scattering amplitudes can be re-factorised in strongly-ordered limits, providing a systematic method to compute them, to characterise their singularity structure, and to build local subtraction counterterms for strongly-ordered configurations. Our results provide tools for a detailed organisation of subtraction algorithms, in principle to all orders in perturbation theory

Erratum to: Local analytic sector subtraction at NNLO

Eq. (3.55) should be replace

Towards the automation of the Local Analytic Sector subtraction

We present the state of the art of the Local Analytic Sector subtraction. The scheme is now complete at NLO in the massless case for the treatment of initial- and final-state radiations. Its flexibility has been improved by the introduction of damping factors, which can be tuned to reduce numerical instabilities, though preserving the simplicity of the algorithm. The same degree of universality has been reached at NNLO for final-state radiation, where we derived fully analytic and compact results for all integrated counterterms. This allows us to explicitly check the cancellation of the virtual infrared singularities in generic processes with massless final-state partons

Robustness tests for an optical time scale

Optical clocks have reached such an impressive accuracy and stability that the future redefinition of the second will be probably based on an optical transition. Consequently, building time scales based on optical clocks has become a key problem. Unfortunately, optical clocks are still laboratory prototypes and are not yet capable of long times of autonomous operation. It is hence critical to understand the impact of this limited optical clock availability on the generated time scale. In this work, after describing a simple and effective optical time scale algorithm, based on the steering of a flywheel oscillator towards the optical clock, we investigate in detail the impact of the limited availability of the optical clock on the performances of the steering algorithm and of the generated time scale through numerical simulations. In particular, we simulate a time scale generated by a hydrogen maser (with a flicker floor of 5.5 x 10(-16)) steered towards an optical clock, by considering six different scenarios for the availability of the latter, spanning from the ideal one, i.e. continuous operation of the optical clock, to the worst one, i.e. non-uniformly distributed frequency measurements with long unavailability periods. The results prove that the steering algorithm is robust and effective despite its very simple implementation, and it is capable of very good performances in all the considered scenarios, provided that the hydrogen maser behaves nominally. Specifically, they show that a time scale with an accuracy of a few hundreds of picoseconds can be easily realized in the ideal scenario, whereas in a more realistic scenario, with one measurement per week only, the time accuracy is nonetheless of a few nanoseconds, competing with the best time scales currently realized worldwide. The performances degradation due to a non-nominal maser behaviour is also discussed

Time-frequency analysis of the Galileo satellite clocks: looking for the J2 relativistic effect and other periodic variations

When observed from the ground, the frequency of the atomic clocks flying on the satellites of a Global Navigation Satellite System is referred to as apparent frequency, because it is observed through the on-board signal generation chain, the propagation path, the relativistic effects, the measurement system, and the clock estimation algorithm. As a consequence, the apparent clock frequency is affected by periodic variations of different origins such as, for example, the periodic component of the J2 relativistic effect, due to the oblateness of the earth, and the clock estimation errors induced by the orbital estimation errors. We present a detailed characterization of the periodic variations affecting the apparent frequency of the Galileo clocks, obtained by applying time-frequency analysis and other signal processing techniques on space clock data provided by the European Space Agency. In particular, we analyze one year of data from three Galileo Passive Hydrogen Masers, flying on two different orbital planes. Time-frequency analysis reveals how the spectral components of the apparent frequency change with time. For example, it confirms that the amplitude of the periodic signal due to the orbital estimation errors depends on the angle between the sun and the orbital plane. Moreover, it allows to find a more precise estimate of the amplitude of the J2 effect, in agreement with the prediction of the general theory of relativity, and it shows that such amplitude suddenly decreases when the corresponding relativistic correction is applied to the data, thus validating the analytical formula used for the correction

Time–frequency analysis of the Galileo satellite clocks: looking for the J2 relativistic effect and other periodic variations

When observed from the ground, the frequency of the atomic clocks flying on the satellites of a Global Navigation Satellite System is referred to as apparent frequency, because it is observed through the on-board signal generation chain, the propagation path, the relativistic effects, the measurement system, and the clock estimation algorithm. As a consequence, the apparent clock frequency is affected by periodic variations of different origins such as, for example, the periodic component of the J2 relativistic effect, due to the oblateness of the earth, and the clock estimation errors induced by the orbital estimation errors. We present a detailed characterization of the periodic variations affecting the apparent frequency of the Galileo clocks, obtained by applying time–frequency analysis and other signal processing techniques on space clock data provided by the European Space Agency. In particular, we analyze one year of data from three Galileo Passive Hydrogen Masers, flying on two different orbital planes. Time–frequency analysis reveals how the spectral components of the apparent frequency change with time. For example, it confirms that the amplitude of the periodic signal due to the orbital estimation errors depends on the angle between the sun and the orbital plane. Moreover, it allows to find a more precise estimate of the amplitude of the J2 effect, in agreement with the prediction of the general theory of relativity, and it shows that such amplitude suddenly decreases when the corresponding relativistic correction is applied to the data, thus validating the analytical formula used for the correction

Robustness tests for an optical time scale

Optical clocks have reached such an impressive accuracy and stability that the future redefinition of the second will be probably based on an optical transition. Consequently, building time scales based on optical clocks has become a key problem. Unfortunately, optical clocks are still laboratory prototypes and are not yet capable of long times of autonomous operation. It is hence critical to understand the impact of this limited optical clock availability on the generated time scale. In this work, after describing a simple and effective optical time scale algorithm, based on the steering of a flywheel oscillator towards the optical clock, we investigate in detail the impact of the limited availability of the optical clock on the performances of the steering algorithm and of the generated time scale through numerical simulations. In particular, we simulate a time scale generated by a hydrogen maser (with a flicker floor of 5.5 × 10−16) steered towards an optical clock, by considering six different scenarios for the availability of the latter, spanning from the ideal one, i.e. continuous operation of the optical clock, to the worst one, i.e. non-uniformly distributed frequency measurements with long unavailability periods. The results prove that the steering algorithm is robust and effective despite its very simple implementation, and it is capable of very good performances in all the considered scenarios, provided that the hydrogen maser behaves nominally. Specifically, they show that a time scale with an accuracy of a few hundreds of picoseconds can be easily realized in the ideal scenario, whereas in a more realistic scenario, with one measurement per week only, the time accuracy is nonetheless of a few nanoseconds, competing with the best time scales currently realized worldwide. The performances degradation due to a non-nominal maser behaviour is also discussed