Product R

The photoelectron momentum distributions with respect to the molecular axis shown in Fig. 2 were generated in the following way. Initially, the ions were assigned to the one of the two breakup channels, direct and indirect, by requiring the magnitude of the ion momentum to be within 3.5–17 a.u. and 37–46 a.u., respectively. This gating ensure that the ion comes from the breakup of the dimer along II(1/2)_g state (Fig. 1a). The ionization of atomic neon as well as dissociation over the other potential curves^{43 (link)} would result in the ion momentum smaller than 3 a.u. Subsequently, only ionization events have been considered, where ion and electron momentum vectors lie within slices along the polarization plane, defined by the conditions |p_x| < 0.55 a.u. for electrons as well as |p_x| < 3.5 a.u. and |p_x| < 12.0 a.u. for ions from the direct and indirect dissociation channels, respectively (the x-direction is the light propagation direction). These conditions ensure that the angle between a momentum vector and the polarization plane does not exceed 45° in the worst case. For the majority of events this angle is, however, smaller than 30°. Both, electron and ion momentum vectors were projected onto the polarization plane. The projection of the ion momentum defines the k_|| direction, whereas the two components, k_|| and k_⊥, of the electron projection are plotted in Fig. 2. This type of molecular frame transformation avoids nodes along the dimer axis. It does not conserve the product k·R, but the loss of contrast in the interference patterns is negligible. Another type of transformation, a natural one, where the ion momentum vector, not its projection, defines the k_|| direction is presented in the Supplementary Note 3 and Supplementary Fig. 4.

The data was analyzed using RStudio Version 2022.12.0 + 353⁵² . The analysis is split into two parts. In the first part we tested for differences between the means of the considered variables across the dosage levels. Model assumptions were checked using the Shapiro–Wilk test of normality and the Brown-Forsythe test of variance equality via the R functions shapiro.test and bf.test. If there was no evidence of non-normality and no evidence of variance inequality, the data were analyzed using a one-way analysis of variance (ANOVA, R function: aov). If there was no evidence of non-normality, but there was evidence of variance inequality, the data were analyzed using Welch’s ANOVA (R function: oneway.test). If there was evidence of non-normality, the data were analyzed with the Kruskal–Wallis test (R function kruskal.test). Post-hoc analyses were performed using either Dunnett’s test, the Games-Howell post hoc test, or Dunn’s test using the R functions dunnettTest, games_howell_test, or dunnTest, respectively. In the second part we studied the relationships between the variables of interest. The goals were to determine whether significant correlations exist and if one, or a combination, of these variables can be considered indicative of anxiety. To study the relationships between the variables we used Pearson’s product moment correlation coefficient via the R function cor.test⁵³ and a principal component analysis (PCA) via the R function prcomp⁵² . Following the PCA, we submitted the observations values on the principal components to a permutation testing scheme^{54 (link)}. The purpose of this permutation testing scheme was to test for statistical differences between each dosage level. We used the R functions aovp⁵⁵ and perm.test⁵⁶ to run these permutation tests. These functions implement modified versions of the standard one-way ANOVA and multiple comparison procedures used in part one of our analysis. For all permutation tests, we used a seed with value 2022. The 5% significance level was used for assessing statistical significance in all tests. Summary statistics are presented as represented as mean ± S.E.M.

Calves were randomly assigned to receive either RSB or a sham injection by means of a random number generator (www.randomizer.org). Calves in the RSB group received a rectus sheath injection with 0.3 ml/kg 0.25% bupivacaine HCl (Bupivacaina Recordati; Recordati S.p.A., Italy) containing dexmedetomidine HCl (1 μg/ml; Dexdomitor 0.5 mg/ml; Zoetis Inc., United States) as an adjuvant to prolong the effect of the local anesthetic, as previously described (28 (link), 29 (link)). Calves in the control group received a rectus sheath injection with an equivalent volume of sterile saline (0.9% NaCl). All injections were administered by the same operator (FM).
A 14-gauge catheter (Introcan Safety; BBraun Milano S.p.A., Italy) was aseptically placed in one of the jugular veins. Calves were allowed to rest in a quiet room for 120 min prior to induction of anesthesia. All procedures were performed in a dedicated clean area outside the barn. The area was protected from direct sun and well-ventilated. After premedication with an intravenous (IV) injection of 0.02–0.05 mg/kg xylazine (Nerfasin 100 mg/ml; Ati S.r.l., Italy) and 0.02 mg/kg butorphanol (Alvegesic 10 mg/ml; Dechra Veterinary Products S.r.l., Italy), anesthesia was induced with 2.5 mg/kg IV ketamine (Lobotor 100 mg/ml; ACME S.r.l., Italy). All calves were positioned in dorsal recumbency, raised from the ground, and laterally content by straw bales, with legs secured far from the surgical field and with the head elevated and the tip of the nose down to avoid aspiration. Intraoperative monitoring included heart rate (HR) determined by auscultation with a stethoscope, respiratory rate (f_R) calculated by direct observation of the thoracic excursions, arterial hemoglobin saturation of oxygen (SpO₂) measured with a portable pulse oximeter (CMS-50D1 Fingertip Pulse Oximeter; AccuMed, TX, United States), and rectal temperature. Data were continuously monitored and recorded every 5 min throughout the procedure. At baseline, skin incision, and at the end of surgery, a venous blood sample was collected in a heparinized syringe and analyzed immediately using an automated bench-top blood-gas analyzer (iSTAT 1 Analyser; VetScan, United States) for monitoring ventilation and electrolyte status.
If the calf responded to surgical stimulation with gross movement, spontaneous blinking, nystagmus, or increased jaw tone, additional boluses of IV ketamine (0.5 mg/kg) and/or xylazine (0.01 mg/kg) were administered. At the end of the surgical procedure, 1.1 mg/kg of flunixin meglumine (Alivios; Fatro S.p.A., Italy) was administered IV, and calves were positioned in sternal recumbency, with the neck extended forward for recovery. The time elapsed between the end of the surgery and the animal being able to hold sternal position without support (time-to-sternal) and the time from sternal recumbency to stand (time-to-stand) were recorded.

The statistical analyses were performed using SPSS (IBM Corp. Released 2020. IBM SPSS Statistics for Windows, Version 27.0. Armonk, NY: IBM Corp). For the non-parametric variables (RPE, RPD, sPDF and EES) the Friedman test was used to detect differences between the sessions. If differences were detected, the Wilcoxon signed rank test was used to identify where the differences lay. These results are presented as median ± interquartile range. For the parametric variables (Training volume, StO₂ and lactate) normality was checked and confirmed by visual inspection. Differences between the sessions were assessed with one-way repeated measures ANOVAs with Bonferroni post hoc tests. These results are presented as mean ± standard deviation (SD). Effect size for the parametric variables is presented as Cohen`s d effect size (d) and was calculated using the following equation: mean session 1–mean session 2 divided by the standard deviations of the difference. An effect size of 0.2–0.5 was considered small, 0.5–0.8 medium and > 0.8 large⁴³ . For the non-parametric variables effect size was calculated as product-movement r (r) using the following equation: r = z/√n, with z being the z-value of the Wilcoxon signed ranked test and n being the number of participants. A product-movement r of 0.1–0.29 was considered small, 0.3–0.49 medium and ≥ 0.5 large⁴³ . Statistical difference was accepted at p < 0.05.