Dynamics of Learning with Restricted Training Sets I: General Theory

We study the dynamics of supervised learning in layered neural networks, in the regime where the size $p$ of the training set is proportional to the number $N$ of inputs. Here the local fields are no longer described by Gaussian probability distributions and the learning dynamics is of a spin-glass nature, with the composition of the training set playing the role of quenched disorder. We show how dynamical replica theory can be used to predict the evolution of macroscopic observables, including the two relevant performance measures (training error and generalization error), incorporating the old formalism developed for complete training sets in the limit $\alpha=p/N\to\infty$ as a special case. For simplicity we restrict ourselves in this paper to single-layer networks and realizable tasks.Comment: 39 pages, LaTe

Chemical Abundances Of Open Clusters From High-Resolution Infrared Spectra. I. NGC 6940

We present near-infrared spectroscopic analysis of 12 red giant members of the Galactic open cluster NGC 6940. High-resolution (R$\simeq$45000) and high signal-to-noise ratio (S/N > 100) near-infrared H and K band spectra were gathered with the Immersion Grating Infrared Spectrograph (IGRINS) on the 2.7m Smith Telescope at McDonald Observatory. We obtained abundances of H-burning (C, N, O), ${\alpha}$ (Mg, Si, S, Ca), light odd-Z (Na, Al, P, K), Fe-group (Sc, Ti, Cr, Fe, Co, Ni) and neutron-capture (Ce, Nd, Yb) elements. We report the abundances of S, P, K, Ce, and Yb in NGC 6940 for the first time. Many OH and CN features in the H band were used to obtain O and N abundances. C abundances were measured from four different features: CO molecular lines in the K band, high excitation C I lines present in both near-infrared and optical, CH and $C_2$ bands in the optical region. We have also determined $^{12}C/^{13}C$ ratios from the R-branch band heads of first overtone (2-0) and (3-1) $^{12}CO$ (2-0) $^{13}CO$ lines near 23440 \overset{\lower.5em\circ}{\mathrm{A}} and (3-1) $^{13}CO$ lines at about 23730 \overset{\lower.5em\circ}{\mathrm{A}}. We have also investigated the HF feature at 23358.3 \overset{\lower.5em\circ}{\mathrm{A}}, finding solar fluorine abundances without ruling out a slight enhancement. For some elements (such as the ${\alpha}$ group), IGRINS data yield more internally self-consistent abundances. We also revisited the CMD of NGC 6940 by determining the most probable cluster members using Gaia DR2. Finally, we applied Victoria isochrones and MESA models in order to refine our estimates of the evolutionary stages of our targets.Comment: 16 pages, 10 figure

Magnetic moment non-conservation in magnetohydrodynamic turbulence models

The fundamental assumptions of the adiabatic theory do not apply in presence of sharp field gradients as well as in presence of well developed magnetohydrodynamic turbulence. For this reason in such conditions the magnetic moment $\mu$ is no longer expected to be constant. This can influence particle acceleration and have considerable implications in many astrophysical problems. Starting with the resonant interaction between ions and a single parallel propagating electromagnetic wave, we derive expressions for the magnetic moment trapping width $\Delta \mu$ (defined as the half peak-to-peak difference in the particle magnetic moment) and the bounce frequency $\omega_b$. We perform test-particle simulations to investigate magnetic moment behavior when resonances overlapping occurs and during the interaction of a ring-beam particle distribution with a broad-band slab spectrum. We find that magnetic moment dynamics is strictly related to pitch angle $\alpha$ for a low level of magnetic fluctuation, $\delta B/B_0 = (10^{-3}, \, 10^{-2})$, where $B_0$ is the constant and uniform background magnetic field. Stochasticity arises for intermediate fluctuation values and its effect on pitch angle is the isotropization of the distribution function $f(\alpha)$. This is a transient regime during which magnetic moment distribution $f(\mu)$ exhibits a characteristic one-sided long tail and starts to be influenced by the onset of spatial parallel diffusion, i.e., the variance $$ grows linearly in time as in normal diffusion. With strong fluctuations $f(\alpha)$ isotropizes completely, spatial diffusion sets in and $f(\mu)$ behavior is closely related to the sampling of the varying magnetic field associated with that spatial diffusion.Comment: 13 pages, 10 figures, submitted to PR

EPIC 220204960: A Quadruple Star System Containing Two Strongly Interacting Eclipsing Binaries

We present a strongly interacting quadruple system associated with the K2 target EPIC 220204960. The K2 target itself is a Kp = 12.7 magnitude star at Teff ~ 6100 K which we designate as "B-N" (blue northerly image). The host of the quadruple system, however, is a Kp = 17 magnitude star with a composite M-star spectrum, which we designate as "R-S" (red southerly image). With a 3.2" separation and similar radial velocities and photometric distances, 'B-N' is likely physically associated with 'R-S', making this a quintuple system, but that is incidental to our main claim of a strongly interacting quadruple system in 'R-S'. The two binaries in 'R-S' have orbital periods of 13.27 d and 14.41 d, respectively, and each has an inclination angle of >89 degrees. From our analysis of radial velocity measurements, and of the photometric lightcurve, we conclude that all four stars are very similar with masses close to 0.4 Msun. Both of the binaries exhibit significant ETVs where those of the primary and secondary eclipses 'diverge' by 0.05 days over the course of the 80-day observations. Via a systematic set of numerical simulations of quadruple systems consisting of two interacting binaries, we conclude that the outer orbital period is very likely to be between 300 and 500 days. If sufficient time is devoted to RV studies of this faint target, the outer orbit should be measurable within a year.Comment: 20 pages, 18 figures, 7 tables; accepted for publication in MNRA

Detection of Coulomb Charging around an Antidot in the Quantum Hall Regime

We have detected oscillations of the charge around a potential hill (antidot) in a two-dimensional electron gas as a function of a large magnetic field B. The field confines electrons around the antidot in closed orbits, the areas of which are quantised through the Aharonov-Bohm effect. Increasing B reduces each state's area, pushing electrons closer to the centre, until enough charge builds up for an electron to tunnel out. This is a new form of the Coulomb blockade seen in electrostatically confined dots. Addition and excitation spectra in DC bias confirm the Coulomb blockade of tunnelling.Comment: 4 pages, 4 Postscript figure

Constraining Nucleosynthesis in Two CEMP Progenitors Using Fluorine

© 2020 The Author(s). The version of record [Aldo Mura-Guzmán, D Yong, C Abate, A Karakas, C Kobayashi, H Oh, S-H Chun, G Mace, Constraining nucleosynthesis in two CEMP progenitors using fluorine, Monthly Notices of the Royal Astronomical Society, Volume 498, Issue 3, November 2020, Pages 3549–3559] is available online at: https://doi.org/10.1093/mnras/staa2610.We present new fluorine abundance estimations in two carbon enhanced metal-poor (CEMP) stars, HE 1429-0551 and HE 1305+0007. HE 1429-0551 is also enriched in slow neutron-capture process (s-process) elements, a CEMP-s, and HE 1305+0007 is enhanced in both, slow and rapid neutron-capture process elements, a CEMP-s/r. The F abundances estimates are derived from the vibration-rotation transition of the HF molecule at 23358.6 Š using high-resolution infrared spectra obtained with the Immersion Grating Infrared Spectrometer (IGRINS) at the 4-m class Lowell Discovery Telescope. Our results include an F abundance measurement in HE 1429-0551 of A(F) = +3.93 ([F/Fe] = +1.90) at [Fe/H] = -2.53, and an F upper limit in HE 1305+0007 of A(F) < +3.28 ([F/Fe] < +1.00) at [Fe/H] = -2.28. Our new derived F abundance in HE 1429-0551 makes this object the most metal-poor star where F has been detected. We carefully compare these results with literature values and state-of-the-art CEMP-s model predictions including detailed asymptotic giant branch (AGB) nucleosynthesis and binary evolution. The modelled fluorine abundance for HE 1429-0551 is within reasonable agreement with our observed abundance, although is slightly higher than our observed value. For HE 1429-0551, our findings support the scenario via mass transfer by a primary companion during its thermally pulsing phase. Our estimated upper limit in HE 1305+0007, along with data from the literature, shows large discrepancies compared with AGB models. The discrepancy is principally due to the simultaneous s- and r-process element enhancements which the model struggles to reproduce.Peer reviewedFinal Published versio

Re-entrant resonant tunneling

We study the effect of electron-electron interactions on the resonant-tunneling spectroscopy of the localized states in a barrier. Using a simple model of three localized states, we show that, due to the Coulomb interactions, a single state can give rise to two resonant peaks in the conductance as a function of gate voltage, G(Vg). We also demonstrate that an additional higher-order resonance with Vg-position in between these two peaks becomes possibile when interactions are taken into account. The corresponding resonant-tunneling process involves two-electron transitions. We have observed both these effects in GaAs transistor microstructures by studying the time evolution of three adjacent G(Vg) peaks caused by fluctuating occupation of an isolated impurity (modulator). The heights of the two stronger peaks exibit in-phase fluctuations. The phase of fluctuations of the smaller middle peak is opposite. The two stronger peaks have their origin in the same localized state, and the third one corresponds to a co-tunneling process.Comment: 9 pages, REVTeX, 4 figure

Coulomb blockade of tunnelling through compressible rings formed around an antidot: an explanation for h/2eh/2e Aharonov-Bohm oscillations

We consider single-electron tunnelling through antidot states using a Coulomb-blockade model, and give an explanation for h/2e Aharonov-Bohm oscillations, which are observed experimentally when the two spins of the lowest Landau level form bound states. We show that the edge channels may contain compressible regions, and using simple electrostatics, that the resonance through the outer spin states should occur twice per h/e period. An antidot may be a powerful tool for investigating quantum Hall edge states in general, and the interplay of spin and charging effects that occurs in quantum dots.Comment: 5 pages, 4 Postscript figure