On right conjugacy closed loops of twice prime order

The right conjugacy closed loops of order 2p, where p is an odd prime, are classified up to isomorphism.Comment: Clarified definitions, added some remarks and a tabl

Average acceleration and intensity gradient of primary school children and associations with indicators of health and wellbeing

Average acceleration (AvAcc) and intensity gradient (IG) have been proposed as standardised metrics describing physical activity (PA) volume and intensity, respectively. We examined hypothesised between-group PA differences in AvAcc and IG, and their associations with health and wellbeing indicators in children. ActiGraph GT9X wrist accelerometers were worn for 24-h·d−1 over seven days by 145 children aged 9-10. Raw accelerations were averaged per 5-s epoch to represent AvAcc over 24-h. IG represented the relationship between log values for intensity and time. Moderate-to-vigorous PA (MVPA) was estimated using youth cutpoints. BMI z-scores, waist-to-height ratio (WHtR), peak oxygen uptake (VO2peak), Metabolic Syndrome risk (MetS score), and wellbeing were assessed cross-sectionally, and 8-weeks later. Hypothesised between-group differences were consistently observed for IG only (p<.001). AvAcc was strongly correlated with MVPA (r=0.96), while moderate correlations were observed between IG and MVPA (r=0.50) and AvAcc (r=0.54). IG was significantly associated with health indicators, independent of AvAcc (p<.001). AvAcc was associated with wellbeing, independent of IG (p<.05). IG was significantly associated with WHtR (p<.01) and MetS score (p<.05) at 8-weeks follow-up. IG is sensitive as a gauge of PA intensity that is independent of total PA volume, and which relates to important health indicators in children

ExoMol molecular line lists – XLIII. Rovibronic transitions corresponding to the close-lying X 2Π and A 2Σ+ states of NaO

The sodium monoxide radical (NaO) is observed in night-glow in the Earth’s mesosphere and likely has astronomical importance. This study concerns the optical transitions within the ground X 2Π state and to the very low-lying (Te ≈ 2000 cm−1) excited A 2Σ+ state. A line list consisting of rovibronic term values, allowed electric dipole transitions, Einstein coefficients, and partition functions for varying temperature are produced using a variational solution of the coupled-channel Schrödinger equations using the program duo. multi-reference configuration interaction (MRCI) ab initio calculations characterizing the potential energy curves of the two states, spin-orbit and L-uncoupling non-adiabatic matrix elements, as well as permanent and transition dipole moments were integral in the formation of the final deperturbation model. Ab initio potential energy curves are represented in the analytical Extended Morse Oscillator form and refined, along with the spin-orbit and L-uncoupling functions, by least-squares fitting to the available spectroscopic data. The input experimental data consisted of pure rotational transitions within the fine-structure components of the X 2Π state for v″ ∈ [0, 3] vibrational levels as well as the rovibronic A 2Σ+(v′ = 0) ← X 2Π(v″ = 0) transitions, both with limited coverage over rotational excitation. The lack of data detailing the vibrational structure of the X and A states points to the need for further experimental study of higher excited levels, which would provide a more robust spectroscopic model. The NaO NaOUCMe line list is available via www.exomol.com and the CDS data base

Coupling molecular spin states by photon-assisted tunneling

Artificial molecules containing just one or two electrons provide a powerful platform for studies of orbital and spin quantum dynamics in nanoscale devices. A well-known example of these dynamics is tunneling of electrons between two coupled quantum dots triggered by microwave irradiation. So far, these tunneling processes have been treated as electric dipole-allowed spin-conserving events. Here we report that microwaves can also excite tunneling transitions between states with different spin. In this work, the dominant mechanism responsible for violation of spin conservation is the spin-orbit interaction. These transitions make it possible to perform detailed microwave spectroscopy of the molecular spin states of an artificial hydrogen molecule and open up the possibility of realizing full quantum control of a two spin system via microwave excitation.Comment: 13 pages, 9 figure

Cut-point-free accelerometer metrics to assess children's physical activity: an example using the school day

The aims were to (i) investigate associations between a novel accelerometer metric: the minimum acceleration value above which the most active 30-minutes were accumulated during the school day (M30ACC), and health indicators, and (ii) demonstrate that applying an equivalent cut-point to the M30ACC metric gives comparable prevalence results as a moderate-to-vigorous physical activity (MVPA) cut-point approach. Two-hundred-and-ninety-six children (age 9-10-years) wore wrist-mounted accelerometers for 7-days. School day MVPA and M30ACC were calculated. Body mass index (BMI), waist-to-height ratio (WHtR), and cardiorespiratory fitness (CRF) were also measured. Mixed linear models investigated associations between M30ACC and health indicators. Agreement between ranked MVPA and M30ACC values was assessed using percent agreement, kappa, sensitivity, and specificity statistics. M30ACC thresholds associated with health indicators were 213 mg (BMI), 206 mg (WHtR), and 269 mg (CRF) for girls. The equivalent values for boys were 234mg (BMI), 230 mg (WHtR), and 327 mg (CRF). Less than half of girls and 75% of boys accumulated 30 minutes of school day MVPA. Just less than 50% of girls and >80% of boys had M30ACC values ≥200 mg, which is equivalent to brisk walking. Agreement between MVPA and M30ACC tertiles was high, reflected by the sensitivity and specificity values of > 90%. Results demonstrate the utility of M30ACC as a PA metric that is not heavily influenced by researcher decisions. M30ACC has potential as an accelerometer-specific metric for generating PA guidelines related to health indicators, and easily understood forms of activity such as brisk walking

Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization

One fundamental requirement for quantum computation is to perform universal manipulations of quantum bits at rates much faster than the qubit's rate of decoherence. Recently, fast gate operations have been demonstrated in logical spin qubits composed of two electron spins where the rapid exchange of the two electrons permits electrically controllable rotations around one axis of the qubit. However, universal control of the qubit requires arbitrary rotations around at least two axes. Here we show that by subjecting each electron spin to a magnetic field of different magnitude we achieve full quantum control of the two-electron logical spin qubit with nanosecond operation times. Using a single device, a magnetic field gradient of several hundred milliTesla is generated and sustained using dynamic nuclear polarization of the underlying Ga and As nuclei. Universal control of the two-electron qubit is then demonstrated using quantum state tomography. The presented technique provides the basis for single and potentially multiple qubit operations with gate times that approach the threshold required for quantum error correction.Comment: 11 pages, 4 figures. Supplementary Material included as ancillary fil

Elliptic Curves over Real Quadratic Fields are Modular

We prove that all elliptic curves defined over real quadratic fields are modular.Comment: 38 pages. Magma scripts available as ancillary files with this arXiv versio

Triplet-Singlet Spin Relaxation via Nuclei in a Double Quantum Dot

The spin of a confined electron, when oriented originally in some direction, will lose memory of that orientation after some time. Physical mechanisms leading to this relaxation of spin memory typically involve either coupling of the electron spin to its orbital motion or to nuclear spins. Relaxation of confined electron spin has been previously measured only for Zeeman or exchange split spin states, where spin-orbit effects dominate relaxation, while spin flips due to nuclei have been observed in optical spectroscopy studies. Using an isolated GaAs double quantum dot defined by electrostatic gates and direct time domain measurements, we investigate in detail spin relaxation for arbitrary splitting of spin states. Results demonstrate that electron spin flips are dominated by nuclear interactions and are slowed by several orders of magnitude when a magnetic field of a few millitesla is applied. These results have significant implications for spin-based information processing