A Formal Framework for Speedup Learning from Problems and Solutions

Speedup learning seeks to improve the computational efficiency of problem solving with experience. In this paper, we develop a formal framework for learning efficient problem solving from random problems and their solutions. We apply this framework to two different representations of learned knowledge, namely control rules and macro-operators, and prove theorems that identify sufficient conditions for learning in each representation. Our proofs are constructive in that they are accompanied with learning algorithms. Our framework captures both empirical and explanation-based speedup learning in a unified fashion. We illustrate our framework with implementations in two domains: symbolic integration and Eight Puzzle. This work integrates many strands of experimental and theoretical work in machine learning, including empirical learning of control rules, macro-operator learning, Explanation-Based Learning (EBL), and Probably Approximately Correct (PAC) Learning.Comment: See http://www.jair.org/ for any accompanying file

Observation of coherent population trapping in a V-type two-electron system

We observe coherent population trapping (CPT) in a two-electron atom---$^{174}$Yb---using the $\rm {^1S_0,F=0} \rightarrow {^3P_1,F'=1}$ transition. CPT is not possible for such a transition according to one-electron theory because the magnetic sublevels form a V-type system, but in a two-electron atom like Yb, the interaction of the electrons transforms the level structure into a $\Lambda$-type system, which allows the formation of a dark state and hence the observation of CPT. Since the two levels involved are degenerate, we use a magnetic field to lift the degeneracy. The single fluorescence dip then splits into five dips---the central unshifted one corresponds to coherent population oscillation, while the outer four are due to CPT. The linewidth of the CPT resonance is about 300 kHz and is limited by the natural linewidth of the excited state, which is to be expected because the excited state is involved in the formation of the dark state.Comment: 5 pages, 5 figures, 2 table

Observation of the nuclear magnetic octupole moment of 173^{173}Yb from precise measurements of hyperfine structure in the 3P2{^3P}_2 state

We measure hyperfine structure in the metastable ${^3P}_2$ state of $^{173}$Yb and extract the nuclear magnetic octupole moment. We populate the state using dipole-allowed transitions through the ${^3P}_1$ and ${^3S}_1$ states. We measure frequencies of hyperfine transitions of the ${^3P}_2 \rightarrow {^3S}_1$ line at 770 nm using a Rb-stabilized ring cavity resonator with a precision of 200 kHz. Second-order corrections due to perturbations from the nearby ${^3P}_1$ and ${^1P}_1$ states are below 30 kHz. We obtain the hyperfine coefficients as: $A=-742.11(2)$ MHz, $B=1339.2(2)$ MHz, which represent two orders-of-magnitude improvement in precision, and $C=0.54(2)$ MHz. From atomic structure calculations, we obtain the nuclear moments: quadrupole $Q=2.46(12)$ b and octupole $\Omega=-34.4(21)$ b\,$\times \mu_N$.Comment: 5 pages, 1 figur

Optical frequency metrology with a Rb-stabilized ring-cavity resonator -- Study of cavity-dispersion errors

We have developed a technique to measure the absolute frequencies of optical transitions by using an evacuated Rb-stabilized ring-cavity resonator as a transfer cavity. We study possible wavelength-dependent errors due to dispersion at the cavity mirrors by measuring the frequency of the same transition in the $D_2$ line of Cs at three cavity lengths. We find no discernable change in values within our error of 30 kHz. Our values are consistent with measurements using the frequency-comb technique and have similar accuracy.Comment: 3 pages, 2 figure

Atomic fountain of laser-cooled Yb atoms for precision measurements

We demonstrate launching of laser-cooled Yb atoms in a cold atomic fountain. Atoms in a collimated thermal beam are first cooled and captured in a magneto-optic trap (MOT) operating on the strongly-allowed ${^1S}_0 \rightarrow {^1P}_1$ transition at 399~nm (blue line). They are then transferred to a MOT on the weakly-allowed ${^1S}_0 \rightarrow {^3P}_1$ transition at 556~nm (green line). Cold atoms from the green MOT are launched against gravity at a velocity of around 2.5~m/s using a pair of green beams. We trap more than $10^7$ atoms in the blue MOT and transfer up to 70\% into the green MOT. The temperature for the odd isotope, $^{171}$Yb, is $\sim$1~mK in the blue MOT, and reduces by a factor of 40 in the green MOT.Comment: 6 pages, 7 figure

New observational Constraints on the Growth of the First Supermassive Black Holes

We constrain the total accreted mass density in supermassive black holes at z>6, inferred via the upper limit derived from the integrated X-ray emission from a sample of photometrically selected galaxy candidates. Studying galaxies obtained from the deepest Hubble Space Telescope images combined with the Chandra 4 Msec observations of the Chandra Deep Field South, we achieve the most restrictive constraints on total black hole growth in the early Universe. We estimate an accreted mass density <1000Mo Mpc^-3 at z~6, significantly lower than the previous predictions from some existing models of early black hole growth and earlier prior observations. These results place interesting constraints on early black growth and mass assembly by accretion and imply one or more of the following: (1) only a fraction of the luminous galaxies at this epoch contain active black holes; (2) most black hole growth at early epochs happens in dusty and/or less massive - as yet undetected - host galaxies; (3) there is a significant fraction of low-z interlopers in the galaxy sample; (4) early black hole growth is radiatively inefficient, heavily obscured and/or is due to black hole mergers as opposed to accretion or (5) the bulk of the black hole growth occurs at late times. All of these possibilities have important implications for our understanding of high redshift seed formation models.Comment: ApJ Accepted, 10 pages, 7 figures, 1 table, in emulateapj forma

Precise measurement of hyperfine structure in the 2P1/2{2P}_{1/2} state of 7^{7}Li using saturated-absorption spectroscopy

We report a precise measurement of the hyperfine interval in the ${2P}_{1/2}$ state of $^{7}$Li. The transition from the ground state ($D_1$ line) is accessed using a diode laser and the technique of saturated-absorption spectroscopy in hot Li vapor. The interval is measured by locking an acousto-optic modulator to the frequency difference between the two hyperfine peaks. The measured interval of 92.040(6)~MHz is consistent with an earlier measurement reported by us using an atomic-beam spectrometer [Das and Natarajan, J.\ Phys.\ B {\bf 41}, 035001 (2008)]. The interval yields the magnetic dipole constant in the $P_{1/2}$ state as $A=46.047(3)$, which is discrepant from theoretical calculations by $>80$~kHz.Comment: 5 pages, 3 figure