17,509 research outputs found

    Premise Selection for Mathematics by Corpus Analysis and Kernel Methods

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    Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of proofs. This work develops learning-based premise selection in two ways. First, a newly available minimal dependency analysis of existing high-level formal mathematical proofs is used to build a large knowledge base of proof dependencies, providing precise data for ATP-based re-verification and for training premise selection algorithms. Second, a new machine learning algorithm for premise selection based on kernel methods is proposed and implemented. To evaluate the impact of both techniques, a benchmark consisting of 2078 large-theory mathematical problems is constructed,extending the older MPTP Challenge benchmark. The combined effect of the techniques results in a 50% improvement on the benchmark over the Vampire/SInE state-of-the-art system for automated reasoning in large theories.Comment: 26 page

    Formation of antiwaves in gap-junction-coupled chains of neurons

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    Using network models consisting of gap junction coupled Wang-Buszaki neurons, we demonstrate that it is possible to obtain not only synchronous activity between neurons but also a variety of constant phase shifts between 0 and \pi. We call these phase shifts intermediate stable phaselocked states. These phase shifts can produce a large variety of wave-like activity patterns in one-dimensional chains and two-dimensional arrays of neurons, which can be studied by reducing the system of equations to a phase model. The 2\pi periodic coupling functions of these models are characterized by prominent higher order terms in their Fourier expansion, which can be varied by changing model parameters. We study how the relative contribution of the odd and even terms affect what solutions are possible, the basin of attraction of those solutions and their stability. These models may be applicable to the spinal central pattern generators of the dogfish and also to the developing neocortex of the neonatal rat

    Cosmology and Astrophysics from Relaxed Galaxy Clusters I: Sample Selection

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    This is the first in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. Here we present a new, automated method for identifying relaxed clusters based on their morphologies in X-ray imaging data. While broadly similar to others in the literature, the morphological quantities that we measure are specifically designed to provide a fair basis for comparison across a range of data quality and cluster redshifts, to be robust against missing data due to point-source masks and gaps between detectors, and to avoid strong assumptions about the cosmological background and cluster masses. Based on three morphological indicators - Symmetry, Peakiness and Alignment - we develop the SPA criterion for relaxation. This analysis was applied to a large sample of cluster observations from the Chandra and ROSAT archives. Of the 361 clusters which received the SPA treatment, 57 (16 per cent) were subsequently found to be relaxed according to our criterion. We compare our measurements to similar estimators in the literature, as well as projected ellipticity and other image measures, and comment on trends in the relaxed cluster fraction with redshift, temperature, and survey selection method. Code implementing our morphological analysis will be made available on the web.Comment: MNRAS, in press. 43 pages in total, of which 17 are tables (please think twice before printing). 18 figures, 4 tables. Machine-readable tables will be available from the journal and at the url below; code will be posted at http://www.slac.stanford.edu/~amantz/work/morph14

    Magnetic relaxation in metallic films: Single and multilayer structures

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    The intrinsic magnetic relaxations in metallic films will be discussed. It will be shown that the intrinsic damping mechanism in metals is caused by incoherent scattering of itinerant electron-hole pair excitations by phonons and magnons. Berger [L. Berger, Phys. Rev. B 54, 9353 (1996)] showed that the interaction between spin waves and itinerant electrons in multilayers can lead to interface Gilbert damping. Ferromagnetic resonance (FMR) studies were carried out using magnetic single and double layer films. The FMR linewidth of the Fe films in the double layer structures was found to always be larger than the FMR linewidth measured for the single Fe films having the same thickness. The increase in the FMR linewidth scaled inversely with the film thickness, and was found to be linearly dependent on the microwave frequency. These results are in agreement with Berger's predictions. (C) 2002 American Institute of Physics

    M2000 : an astrometric catalog in the Bordeaux Carte du Ciel zone +11 degrees < {delta} < +18 degrees

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    During four years, systematic observations have been conducted in drift scan mode with the Bordeaux automated meridian circle in the declination band [+11 ; +18]. The resulting astrometric catalog includes about 2 300 000 stars down to the magnitude limit V_M=16.3. Nearly all stars (96%) have been observed at least 6 times, the catalog being complete down to V_M=15.4. The median internal standard error in position is about 35 mas in the V_M magnitude range [11 ; 15], which degrades to about 50 mas when the faintest stars are considered. M2000 provides also one band photometry with a median internal standard error of 0.04 mag. Comparisons with the Hipparcos and bright part of Tycho-2 catalogs have enabled to estimate external errors in position to be lower than 40 mas. In this zone and at epoch 1998, the faint part of Tycho-2 is found to have an accuracy of 116 mas in alpha instead of 82 mas deduced from the model-based standard errors given in the catalog.Comment: The catalogue can be fetched directly from: ftp://cdsarc.u-strasbg.fr/cats/I/272 or queried from: http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=I/272 More information at : http://www.observ.u-bordeaux.fr/~soubiran/m2000.ht

    Fast Ground State Manipulation of Neutral Atoms in Microscopic Optical Traps

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    We demonstrate Rabi flopping at MHz rates between ground hyperfine states of neutral 87^{87}Rb atoms that are trapped in two micron sized optical traps. Using tightly focused laser beams we demonstrate high fidelity, site specific Rabi rotations with crosstalk on neighboring sites separated by 8μm8 \mu\rm m at the level of 10310^{-3}. Ramsey spectroscopy is used to measure a dephasing time of 870μs870 \mu\rm s which is \approx 5000 times longer than the time for a π/2\pi/2 pulse.Comment: 4 pages, 4 figure
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