On the Effect of Aleatoric and Epistemic Errors on the Learnability and Quality of NN-based Potential Energy Surfaces

The effect of noise in the input data for learning potential energy surfaces (PESs) based on neural networks for chemical applications is assessed. Noise in energies and forces can result from aleatoric and epistemic errors in the quantum chemical reference calculations. Statistical (aleatoric) noise arises for example due to the need to set convergence thresholds in the self consistent field (SCF) iterations whereas systematic (epistemic) noise is due to, {\it inter alia}, particular choices of basis sets in the calculations. The two molecules considered here as proxies are H$_{2}$CO and HONO which are examples for single- and multi-reference problems, respectively, for geometries around the minimum energy structure. For H$_2$CO it is found that adding noise to energies with magnitudes representative of single-point calculations does not deteriorate the quality of the final PESs whereas increasing the noise level commensurate with electronic structure calculations for more complicated, e.g. metal-containing, systems is expected to have a more notable effect. However, the effect of noise on the forces is more noticeable. On the other hand, for HONO which requires a multi-reference treatment, a clear correlation between model quality and the degree of multi-reference character as measured by the $T_1$ amplitude is found. It is concluded that for chemically "simple" cases the effect of aleatoric and epistemic noise is manageable without evident deterioration of the trained model - although the quality of the forces is important. However, considerably more care needs to be exercised for situations in which multi-reference effects are present

No increase in pregnancy rate of mares after preovulatory deep uterine horn application of misoprostol.

A potential source of fertility loss in mares is oviductal dysfunction, potentially caused by masses or debris in the lumen, that may prevent either sperm from reaching the fertilization site or the embryo from reaching the uterus. Recently a novel therapeutic method leading to increased pregnancy results was described by infusing misoprostol, a synthetic prostaglandin E1, in the uterus of mares with unexplained fertility problems. In this study, we aimed, after examining the compatibility of misoprostol with semen, to evaluate the pregnancy rate after routine preovulatory deep uterine horn application of misoprostol in clinically normal oestrous mares, which were inseminated in the same cycle. In experiment 1, ejaculates of 10 stallions diluted with INRA 96™ were mixed with different concentrations of misoprostol (0.01 mg/mL, 0.001 mg/mL, 0.0001 mg/mL, and 0.00001 mg/mL) and total semen motility was evaluated immediately, 12, 24, 48, and 72 h later, and compared with a control sample (mixed with NaCl 0.9%). In experiments 2 and 3, 33 privately-owned clinically normal oestrous mares were each allocated to a treatment or control group. Ovulation was then induced with intramuscularly 2.25 mg deslorelin acetate. At the moment of ovulation induction (experiment 2) and 24 h earlier (experiment 3), 0.2 mg misoprostol diluted in 2 mL NaCl 0.9% were applied deep in the uterine horn (treatment groups) and pure 2 mL NaCl 0.9% in the mares of the control groups. Mares were then inseminated 24 h after deslorelin administration and prior to ovulation with commercial chilled-warmed or frozen-thawed semen, as well as immediately after ovulation detection (both types of semen) maximally 48 h after ovulation induction. In experiment 1, regardless of time and compared with the control groups, all solutions with different concentrations of misoprostol had a negative effect on total motility of semen, which was significant for the highest concentrations (0.01 mg/mL: 18.0% reduction, CI = 22-13%, p = < 0.01). We found no beneficial effect of preovulatory uterine treatment with misoprostol on pregnancy rate (OR = 0.45, CI = 0.15-1.31, p = 0.14): in experiment 2, 2/11 (18.2%) mares of the treatment group became pregnant vs. 12/22 (54.5%) mares in the control group (OR = 0.19, CI = 0.03-1.06, p = 0.07), in experiment 3, 5/14 (35.7%) mares in the treatment group vs. 7/19 (36.8%) mares in the control group (OR = 0.95, CI = 0.23-4.02, p = 0.95), respectively. In conclusion, pregnancy rate was not increased in reproductively normal mares with routine preovulatory deep uterine horn application of misoprostol

Determination of the scalar polarizabilities of the proton using beam asymmetry Σ3\Sigma_{3} in Compton scattering

The scalar dipole polarizabilities, $\alpha_{E1}$ and $\beta_{M1}$, are fundamental properties related to the internal dynamics of the nucleon. The currently accepted values of the proton polarizabilities were determined by fitting to unpolarized proton Compton scattering cross section data. The measurement of the beam asymmetry $\Sigma_{3}$ in a certain kinematical range provides an alternative approach to the extraction of the scalar polarizabilities. At the Mainz Microtron (MAMI) the beam asymmetry was measured for Compton scattering below pion photoproduction threshold for the first time. The results are compared with model calculations and the influence of the experimental data on the extraction of the scalar polarizabilities is determined.Comment: 6 pages, 5 figure

Photoproduction of π0\pi^0-pairs off protons and off neutrons

Total cross sections, angular distributions, and invariant-mass distributions have been measured for the photoproduction of $\pi^0\pi^0$ pairs off free protons and off nucleons bound in the deuteron. The experiments were performed at the MAMI accelerator facility in Mainz using the Glasgow photon tagging spectrometer and the Crystal Ball/TAPS detector. The accelerator delivered electron beams of 1508 and 1557~MeV, which produced bremsstrahlung in thin radiator foils. The tagged photon beam covered energies up to 1400~MeV. The data from the free proton target are in good agreement with previous measurements and were only used to test the analysis procedures. The results for differential cross sections (angular distributions and invariant-mass distributions) for free and quasi-free protons are almost identical in shape, but differ in absolute magnitude up to 15\%. Thus, moderate final-state interaction effects are present. The data for quasi-free neutrons are similar to the proton data in the second resonance region (final state invariant masses up to $\approx$1550~MeV), where both reactions are dominated by the $N(1520)3/2^-\rightarrow \Delta(1232)3/2^+\pi$ decay. At higher energies, angular and invariant-mass distributions are different. A simple analysis of the shapes of the invariant-mass distributions in the third resonance region is consistent with strong contributions of an $N^{\star}\rightarrow N\sigma$ decay for the proton, while the reaction is dominated by a sequential decay via a $\Delta\pi$ intermediate state for the neutron. The data are compared to predictions from the Two-Pion-MAID model and the Bonn-Gatchina coupled channel analysis.Comment: accepted for publication in Eur. Phys. J.

The isospin structure of photoproduction of pi-eta pairs from the nucleon in the threshold region

Photoproduction of $\pi\eta$-pairs from nucleons has been investigated from threshold up to incident photon energies of $\approx$~1.4~GeV. The quasi-free reactions $\gamma p\rightarrow p\pi^0\eta$, $\gamma n\rightarrow n\pi^0\eta$, $\gamma p\rightarrow n\pi^+\eta$, and $\gamma n\rightarrow p\pi^-\eta$ were for the first time measured from nucleons bound in the deuteron. The corresponding reactions from a free-proton target were also studied to investigate final-state interaction effects (for neutral pions the free-proton results could be compared to previous measurements; the $\gamma p\rightarrow n\pi^+\eta$ reaction was measured for the first time). For the $\pi^0\eta$ final state coherent production via the $\gamma d\rightarrow d\pi^0\eta$ reaction was also investigated. The experiments were performed at the tagged photon beam of the Mainz MAMI accelerator using an almost $4\pi$ coverage electromagnetic calorimeter composed of the Crystal Ball and TAPS detectors. The total cross sections for the four different final states obey the relation $\sigma(p\pi^0\eta)$ $\approx$ $\sigma(n\pi^0\eta)$ $\approx$ $2\sigma(p\pi^-\eta)$ $\approx$ $2\sigma(n\pi^+\eta)$ as expected for a dominant contribution from a $\Delta^{\star}\rightarrow\eta\Delta(1232)\rightarrow\pi\eta N$ reaction chain, which is also supported by the shapes of the invariant-mass distributions of nucleon-meson and $\pi$-$\eta$ pairs. The experimental results are compared to the predictions from an isobar reaction model.Comment: accepted for publication in Phys. Lett.

Photoproduction of π0-pairs off protons and off neutrons

Total cross sections, angular distributions, and invariant-mass distributions have been measured for the photoproduction of π0π0 pairs off free protons and off nucleons bound in the deuteron. The experiments were performed at the MAMI accelerator facility in Mainz using the Glasgow photon tagging spectrometer and the Crystal Ball/TAPS detector. The accelerator delivered electron beams of 1508 and 1557MeV, which produced bremsstrahlung in thin radiator foils. The tagged photon beam covered energies up to 1400MeV. The data from the free proton target are in good agreement with previous measurements and were only used to test the analysis procedures. The results for differential cross sections (angular distributions and invariant-mass distributions) for free and quasi-free protons are almost identical in shape, but differ in absolute magnitude up to 15%. Thus, moderate final-state interaction effects are present. The data for quasi-free neutrons are similar to the proton data in the second resonance region (final-state invariant masses up to ≈1550 MeV), where both reactions are dominated by the N(1520)3/2−→Δ(1232)3/2+π decay. At higher energies, angular and invariant-mass distributions are different. A simple analysis of the shapes of the invariant-mass distributions in the third resonance region is consistent with strong contributions of an N⋆→Nσ decay for the proton, while the reaction is dominated by a sequential decay via a Δπ intermediate state for the neutron. The data are compared to predictions from the Two-Pion-MAID model and the Bonn-Gatchina coupled-channel analysis

Quasifree photoproduction of η\eta mesons off protons and neutrons

Differential and total cross sections for the quasifree reactions $\gamma p\rightarrow\eta p$ and $\gamma n\rightarrow\eta n$ have been determined at the MAMI-C electron accelerator using a liquid deuterium target. Photons were produced via bremsstrahlung from the 1.5 GeV incident electron beam and energy-tagged with the Glasgow photon tagger. Decay photons of the neutral decay modes $\eta\rightarrow 2\gamma$ and $\eta\rightarrow 3\pi^0 \rightarrow 6\gamma$ and coincident recoil nucleons were detected in a combined setup of the Crystal Ball and the TAPS calorimeters. The $\eta$-production cross sections were measured in coincidence with recoil protons, recoil neutrons, and in an inclusive mode without a condition on recoil nucleons, which allowed a check of the internal consistency of the data. The effects from nuclear Fermi motion were removed by a kinematic reconstruction of the final-state invariant mass and possible nuclear effects on the quasifree cross section were investigated by a comparison of free and quasifree proton data. The results, which represent a significant improvement in statistical quality compared to previous measurements, agree with the known neutron-to-proton cross-section ratio in the peak of the $S_{11}(1535)$ resonance and confirm a peak in the neutron cross section, which is absent for the proton, at a center-of-mass energy $W = (1670\pm 5)$ MeV with an intrinsic width of $\Gamma\approx 30$ MeV

Measurement of the beam-helicity asymmetry I⊙I^{\odot} in the photoproduction of π0π±\pi^0\pi^{\pm}-pairs off protons and off neutrons

Beam-helicity asymmetries have been measured at the MAMI accelerator in Mainz for the photoproduction of mixed-charge pion pairs in the reactions $\boldsymbol{\gamma}p\rightarrow n\pi^0\pi^+$ off free protons and $\boldsymbol{\gamma}d\rightarrow (p)p\pi^0\pi^-$ and $\boldsymbol{\gamma}d\rightarrow (n)n\pi^0\pi^+$ off quasi-free nucleons bound in the deuteron for incident photon energies up to 1.4 GeV. Circularly polarized photons were produced from bremsstrahlung of longitudinally polarized electrons and tagged with the Glasgow-Mainz magnetic spectrometer. The charged pions, recoil protons, recoil neutrons, and decay photons from $\pi^0$ mesons were detected in the 4$\pi$ electromagnetic calorimeter composed of the Crystal Ball and TAPS detectors. Using a complete kinematic reconstruction of the final state, excellent agreement was found between the results for free and quasi-free protons, suggesting that the quasi-free neutron results are also a close approximation of the free-neutron asymmetries. A comparison of the results to the predictions of the Two-Pion-MAID reaction model shows that the reaction mechanisms are still not well understood, in particular at low incident photon energies in the second nucleon-resonance region.Comment: accepted for publication in Eur. phys. J.

Photoproduction of pi0-mesons off neutrons in the nucleon resonance region

Precise angular distributions have been measured for the first time for the photoproduction of $\pi^{0}$-mesons off neutrons bound in the deuteron. The effects from nuclear Fermi motion have been eliminated by a complete kinematic reconstruction of the final state. The influence of final-state-interaction effects has been estimated by a comparison of the reaction cross section for quasi-free protons bound in the deuteron to the results for free protons and then applied as a correction to the quasi-free neutron data. The experiment was performed at the tagged photon facility of the Mainz Microtron MAMI with the Crystal Ball and TAPS detector setup for incident photon energies between $0.45$~GeV and $1.4$~GeV. The results are compared to the predictions from reaction models and partial-wave analyses based on data from other isospin channels. The model predictions show large discrepancies among each other and the present data will provide much tighter constraints. This is demonstrated by the results of a new analysis in the framework of the Bonn-Gatchina coupled-channel analysis which included the present data.Comment: accepted for publication in Phys; Rev. Let

The N(1520) 3/2- helicity amplitudes from an energy-independent multipole analysis based on new polarization data on photoproduction of neutral pions

New data on the polarization observables T, P, and H for the reaction $\gamma p \to p\pi^0$ are reported. The results are extracted from azimuthal asymmetries when a transversely polarized butanol target and a linearly polarized photon beam are used. The data were taken at the Bonn electron stretcher accelerator ELSA using the CBELSA/TAPS detector. These and earlier data are used to perform a truncated energy-independent partial wave analysis in sliced-energy bins. This energy-independent analysis is compared to the results from energy-dependent partial wave analyses