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

Heavy rain effects on airplane performance

The objective is to determine if the aerodynamic characteristics of an airplane are altered while flying in the rain. Wind-tunnel tests conducted at the NASA Langley Research Center (LaRC) have shown losses in maximum lift, reduction in stall angle, and increases in drag when a wing is placed in a simulated rain spray. For these tests the water spray concentration used represented a very heavy rainfall. A lack of definition of the scaling laws for aerodynamic testing in a two-phase, two-component flow makes interpolation of the wind-tunnel test uncertain. Tests of a large-scale wing are to be conducted at the LaRC. The large-scale wing is mounted on top of the Aircraft Landing Dynamics Facility (ALDF) carriage. This carriage (which is 70-foot long, 30-foot wide, and 30-foot high) is propelled with the wing model attached down a 3000-foot long test track by a water jet at speeds of up to 170 knots. A simulated rain spray system has been installed along 500 feet of the test track and can simulate rain falls from 2 to 40 inches/hour. Operational checks are underway and the initial tests should be completed by the Fall of 1989

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

Water as a Factor in Energy Resources Development

Water, in many cases, is a key factor in the development of energy resources in the western states. The total water supply available in the arid west is fixed; yet potential water uses in the region are growing continually. In fact, in many areas quantities of water desired to be put to beneficial use has already surpassed the limit of local supplies as indicated by filings for water rights. The availability of water, in adequate quantities and of suitable quality, is one of the essentials to the economic viability of some economic sectors in the states in the Colorado River Basin. Many existing water uses are already under economic pressure which could shift water to users who can afford to pay higher prices. With the entire region undergoing an energy boom, Duchesne and Uintah Counties, which are agriculture oriented, for example, may see water bought from agriculture for energy development

Ancient Egypt 1921 Part 1

Part 1 of the 1921 Ancient Egypt books. Contents include the alphabet in the XIIth dynasty, the Lahun caskets, burial rites of West Africa, a Negro captive, and Queen Tetisheri.https://knowledge.e.southern.edu/kweeks_coll/1014/thumbnail.jp

Wolf 1130: A Nearby Triple System Containing a Cool, Ultramassive White Dwarf

Following the discovery of the T8 subdwarf WISEJ200520.38+542433.9 (Wolf 1130C), with common proper motion to a binary (Wolf 1130AB) consisting of an M subdwarf and a white dwarf, we set out to learn more about the old binary in the system. We find that the A and B components of Wolf 1130 are tidally locked, which is revealed by the coherence of more than a year of V band photometry phase folded to the derived orbital period of 0.4967 days. Forty new high-resolution, near-infrared spectra obtained with the Immersion Grating Infrared Spectrometer (IGRINS) provide radial velocities and a projected rotational velocity (v sin i) of 14.7 +/- 0.7 km/s for the M subdwarf. In tandem with a Gaia parallax-derived radius and verified tidal-locking, we calculate an inclination of i=29 +/- 2 degrees. From the single-lined orbital solution and the inclination we derive an absolute mass for the unseen primary (1.24+0.19-0.15 Msun). Its non-detection between 0.2 and 2.5 microns implies that it is an old (>3.7 Gyr) and cool (Teff<7000K) ONe white dwarf. This is the first ultramassive white dwarf within 25pc. The evolution of Wolf 1130AB into a cataclysmic variable is inevitable, making it a potential Type Ia supernova progenitor. The formation of a triple system with a primary mass >100 times the tertiary mass and the survival of the system through the common-envelope phase, where ~80% of the system mass was lost, is remarkable. Our analysis of Wolf 1130 allows us to infer its formation and evolutionary history, which has unique implications for understanding low-mass star and brown dwarf formation around intermediate mass stars.Comment: 37 pages, 9 Figures, 5 Table

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