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One of the most important sequences in enumerative combinatorics is OEIS sequence A85, the number of involutions of length n. In the Art of Computer Programming, vol. 3, Don Knuth derived the O(1/n) asymptotic formula for these numbers. In this modest tribute to our two heroes, Neil Sloane who just turned 85, and Don Knuth who was 85 a year ago, we go all the way to an $O(1/n^{85})$ asymptotic formula., Comment: 4 pages. In honor of Neil Sloane and Don Knuth

Electrometry based on electromagnetically induced transparency (EIT) in alkali Rydberg vapor cells may suffer reduced sensitivity due to spurious line broadening effects, caused by surface charges, contaminant gases, or other manufacturing defects. In order to draw conclusions about the deleterious effects of potential contaminant gases inside Rydberg electrometry vapor cells, we revisit collisional broadening and shifts of both the D$_2$ line and Rydberg levels of rubidium. Specifically, we measure the broadening and shifts of the $5{\rm S}_{1/2}\rightarrow 5{\rm P}_{3/2}$ (i.e., the D$_2$ line) and $5{\rm S}_{1/2}\rightarrow 5{\rm P}_{3/2}\rightarrow (25{\rm D},27{\rm S},30{\rm D},32{\rm S},35{\rm D},37{\rm S})$ transitions of $^{85}$Rb due to He, Ne, N$_2$ and Ar. By combining these measurements with observations of velocity changing collisions in the sub-Doppler spectrum of the D$_2$ line, we conclude the following: (1) that contaminant gases are most likely not the cause of irregular line shapes or shifts of Rydberg transitions due to the high pressures required, and (2) the sub-Doppler spectrum of the D$_2$ line, through its accompanying loss of contrast at high pressures, can validate that a vapor cell is sufficiently free of contaminant gas for EIT electrometry. We use the theory of Omont, J. Phys. France 38, 1343 (1977), to extend our results to a wide variety of possible contaminant gases and further derive scaling laws applicable to all gases., Comment: 10 pages, 6 figures, 3 tables

An experimental study on Rydberg electromagnetically induced transparency (EIT) in rubidium (Rb) vapor cells containing inert gases at pressures $\le 5$ Torr is reported. Using an inert-gas-free Rb vapor cell as a reference, we measure frequency shift and line broadening of the EIT spectra in Rb vapor cells with argon, neon or nitrogen gases at pressures ranging from a few mTorr to 5 Torr. The results qualitatively agree with a pseudo-potential model that includes $s$-wave scattering between the Rydberg electron and the inert-gas atoms, and the effect of polarization of the inert-gas atoms by the Rydberg atoms. Our results are important for establishing Rydberg-EIT as an all-optical and non-intrusive spectroscopic probe for field diagnostics in low-pressure radio-frequency discharges., Comment: 8 pages, 4 figures

The inherent polarization gradients in tight optical tweezers can be used to couple the atomic spins to the two-body motion under the action of a microwave spin-flip transition, so that such a spin-motion coupling offers an important control knob on the motional states of optically trapped two colliding atoms. Here, after preparing two elastically scattering $^{85}$Rb atoms in the three-dimensional ground-state in the optical tweezer, we employed this control in order to probe the colliding energies of elastic and inelastic channels. The combination of microwave spectra and corresponding s-wave pseudopotential model allows us to infer the effect of the state-dependent trapping potentials on the elastic colliding energies, as well as to reveal how the presence of inelastic interactions affects elastic part of the relative potential. Our work shows that the spin-motion coupling in a tight optical tweezer expand the experimental toolbox for fundamental studies of ultracold collisions in the two body systems with reactive collisions, and potentially for that of more complex interactions, such as optically trapped atom-molecule and molecule-molecule interactions., Comment: 8 pages, 5 figures

This Semiannual Report presents the activities and accomplishments of the U.S. Department of Education's Office of Inspector General (OIG) from April 1, 2022, through September 30, 2022. The report highlights the audits, investigations, and related work issued during this time frame. Sections include: (1) Pandemic Relief Oversight; (2) Disaster Recovery Oversight; (3) Federal Student Aid Programs and Operations; (4) Elementary and Secondary Education Programs; (5) Department Management and Operations; (6) Other OIG Efforts; (7) Required Reporting; and (8) Acronyms and Abbreviations. [For the previous report, "Semiannual Report to Congress, No. 84. October 1, 2021-March 31, 2022," see ED620763.]

Radio phoenices are complex and filamentary diffuse radio sources found in both merging and relaxed clusters. The formation of these sources was proposed to be due to adiabatic compression of old Active Galactic Nucleus (AGN) plasma in shock waves. Most of the previous spectral studies of these sources were limited to integrated spectral indices, which were found to be very steep as well as showing a curved spectrum. Here, we have performed a multi-frequency investigation of the radio phoenix in the Abell 85 cluster. Owing to the sensitive high-resolution observations, we found some of the finer filamentary structures that were previously undetected. We produced resolved spectral index maps of the radio phoenix between 323, 700, and 1280 MHz. The orientation of the filaments, as well as the gradient across the spectral index maps, suggest the possible direction of the shock motion from northeast to southwest. The integrated spectrum of the radio phoenix was found to be very steep and curved toward high-frequencies. Furthermore, the spectral index of the filaments was found to be less steep compared to the non-filamentary regions, implying greater energy injection in the filaments. The observed features in the radio phoenix in the Abell 85 cluster seem to be in support of the adiabatic shock compression mechanism., Comment: 20 pages, 12 figures, 4 tables, accepted for ApJ publication

The Global mm-VLBI Array (GMVA) has demonstrated the ability to resolved what may be the general relativistic shadow of the supermassive black hole in M87 at 86 GHz, as well as delineate the inner jet to $\sim 1$~mas distance. We investigate the ability of the planned ngEHT, and the ngEHT + ngVLA at 85 GHz, to image such a nuclear 'ring', and the associated jet, using a constructed model based on the current estimate of the ring size, and a scaled version of the best VLBA image of the M87 jet at 43 GHz. While the resolution does not improve due to the limit set by the diameter of the Earth, the ngEHT alone should provide both a higher fidelity image of the ring on scales $\le 0.1$~mas, and a good image of a more extended jet to $\sim 1$~mas. Adding the ngVLA improves substantially the dynamic range (factor 3.5), as well as adds the ability to image structures on larger scales, in this case out to at least 5~mas, and potentially to much larger scales given the $\sim 10^5$ range in spatial scales covered by the ngVLA itself. Both arrays provide good image fidelity ($\le 0.1$), in the inner $\sim 1$~mas, but the ngEHT-only image does not reproduce the outer jet well, or at all, with fidelity values greater than unity. The combined array reproduces much of the outer jet with good fidelity ($\le 0.3$). Adding the ngVLA also decreases the susceptibility to antenna-based phase errors by a similar factor, and improves the ability for fringe fitting and subsequent phase and amplitude self-calibration. As for scales $< 100~\mu$as, ie. the ring itself, adding the ngVLA makes little change for very bright sources, where uniform weighting can be employed. But for faint sources, adding the ngVLA adds potentially an order-of magnitude sensitivity improvement (Issaoun et al. 2023)., Comment: 14 pages, 5 figures, ngVLA memo 118

Galaxy clusters are located at the nodes of cosmic filaments and therefore host a lot of hydrodynamical activity. However, cool core clusters are considered to be relatively relaxed systems without much merging activity. The Abell 85 cluster is a unique example where the cluster hosts both a cool core and multiple ongoing merging processes. In this work, we used 700 MHz uGMRT as well as MeerKAT L-band observations, carried out as part of the MGCLS, of the Abell 85. We reconfirm the presence of a minihalo in the cluster centre at 700MHz that was recently discovered in MGCLS. Furthermore, we discovered a radio bridge connecting the central minihalo and the peripheral radio phoenix. The mean surface brightness, size and flux density of the bridge at 700 MHz is found to be $\sim 0.14\ \mu$Jy/arcsec$^2$, $\sim 220$ kpc and $\sim 4.88$ mJy, respectively, with a spectral index of $\alpha_{700}^{1.28} = -0.92$. Although the origin of the seed relativistic electrons is still unknown, turbulent re-acceleration caused by both the spiralling sloshing gas in the intracluster medium (ICM) and the post-shock turbulence from the outgoing merging shock associated with the phoenix formation may be responsible for the bridge., Comment: 7 pages, 6 Figures, 2 Tables. Accepted for publication in MNRAS-L

This report describes how entrepreneurship competence is embedded in vocational education and training (VET) in Latvia. It complements existing knowledge with examples of methods, tools and approaches that can help policy-makers, VET providers and other stakeholders build better entrepreneurial learning ecosystems. The report is based on the pilot research of the Cedefop study "Entrepreneurship Competence in VET." It is part of a series of eight national case studies (Spain, France, Croatia, Italy, Latvia, Austria, Finland and Sweden) and a forthcoming final report.

We investigate Rydberg electromagnetically induced transparency (EIT) of $^{85}$Rb atomic vapor in a glass cell that contains a 5-Torr neon buffer gas. At low probe power, EIT lines exhibit a positive frequency shift of about 70~MHz and a broadening of about 120~MHz, with minimal dependence on the principal quantum number of the Rydberg states. The EIT line shift arises from s-wave scattering between the Rydberg electron and the Ne atoms, which induces a positive shift near 190~MHz, and from the polarization of the Ne atoms within the Rydberg atom, which adds a negative shift near -120~MHz. The line broadening is largely due to the Ne polarization. Our experimental results are in good qualitative agreement with our theoretical model, in which the shift is linear in buffer-gas density. Our results suggest that Rydberg-EIT can serve as a direct spectroscopic probe for buffer-gas density at low pressure, and that it is suitable for non-invasive measurement of electric fields in low-pressure noble-gas discharge plasmas and in dusty plasmas.

We report an experimental demonstration of anti-parity-time (anti-PT) symmetric optical four-wave mixing in thermal Rubidium vapor, where the propagation of two conjugate optical fields in a double-$\Lambda$ scheme is governed by a non-Hermitian Hamiltonian. We are particularly interested in studying quantum intensity correlations between the two conjugate fields near the exceptional point, taking into account loss and accompanied Langevin noise. Our experimental measurements of classical four-wave mixing gain and the associated two-mode relative-intensity squeezing are in reasonable agreement with the theoretical predictions.