Premise Selection for Mathematics by Corpus Analysis and Kernel Methods

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

Important Considerations in Plasmon-Enhanced Electrochemical Conversion at Voltage-Biased Electrodes.

In this perspective we compare plasmon-enhanced electrochemical conversion (PEEC) with photoelectrochemistry (PEC). PEEC is the oxidation or reduction of a reactant at the illuminated surface of a plasmonic metal (or other conductive material) while a potential bias is applied. PEC uses solar light to generate photoexcited electron-hole pairs to drive an electrochemical reaction at a biased or unbiased semiconductor photoelectrode. The mechanism of photoexcitation of charge carriers is different between PEEC and PEC. Here we explore how this difference affects the response of PEEC and PEC systems to changes in light, temperature, and surface morphology of the photoelectrode

Global behavior of cosmological dynamics with interacting Veneziano ghost

In this paper, we shall study the dynamical behavior of the universe accelerated by the so called Veneziano ghost dark energy component locally and globally by using the linearization and nullcline method developed in this paper. The energy density is generalized to be proportional to the Hawking temperature defined on the trapping horizon instead of Hubble horizon of the Friedmann-Robertson-Walker (FRW) universe. We also give a prediction of the fate of the universe and present the bifurcation phenomenon of the dynamical system of the universe. It seems that the universe could be dominated by dark energy at present in some region of the parameter space.Comment: 8 pages, 7 figures, accepted for publication in JHE

Accurate Transfer Maps for Realistic Beamline Elements: Part I, Straight Elements

The behavior of orbits in charged-particle beam transport systems, including both linear and circular accelerators as well as final focus sections and spectrometers, can depend sensitively on nonlinear fringe-field and high-order-multipole effects in the various beam-line elements. The inclusion of these effects requires a detailed and realistic model of the interior and fringe fields, including their high spatial derivatives. A collection of surface fitting methods has been developed for extracting this information accurately from 3-dimensional field data on a grid, as provided by various 3-dimensional finite-element field codes. Based on these realistic field models, Lie or other methods may be used to compute accurate design orbits and accurate transfer maps about these orbits. Part I of this work presents a treatment of straight-axis magnetic elements, while Part II will treat bending dipoles with large sagitta. An exactly-soluble but numerically challenging model field is used to provide a rigorous collection of performance benchmarks.Comment: Accepted to PRST-AB. Changes: minor figure modifications, reference added, typos corrected

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

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

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

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

Proof-Pattern Recognition and Lemma Discovery in ACL2

We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition to pre-processes data from libraries, and then suggests auxiliary lemmas in new proofs by analogy with already seen examples. This paper presents the implementation of ACL2(ml) alongside theoretical descriptions of the proof-pattern recognition and lemma discovery methods involved in it

First observation of medium-spin excitations in the 138Cs nucleus

Medium-spin, yrast excitations in the 138Cs nucleus, populated in the spontaneous fission of 248Cm, were observed for the first time. 138Cs was studied by means of prompt γ-ray spectroscopy using the EUROGAM2 array. The newly observed yrast cascade, built on the known 6- isomer at 80 keV, was successfully described by shell model calculations. Analogously to the 136I isotone, the 6- isomer in 138Cs has the \ensuremath{(\pi g_{7/2} ^4 d_{5/2} \nu f_{7/2})_{6^-}} dominating configuration and the 7- excitation, located 175 keV above, corresponds to the \ensuremath{(\pi g_{7/2} ^3 d_{5/2}^2 \nu f_{7/2})_{7^-}} as dominating configuration. Similarly as in 136I, changing the position of the d 5/2 proton orbital improves the reproduction of the data. However, in 138Cs the energy of this orbital should be increased compared to its energy in 133Sb, to get the best description, in contrast to 136I and 135Sb, where it had to be decreased. The best reproduction of excitation energies in 138Cs is obtained assuming that the πd 5/2 orbital in 138Cs is located about 100 keV higher than in 133Sb. These observations suggest that the lowering of the d 5/2 s.p. energy in 135Sb is not a physical effect due to the appearance of a neutron skin, as proposed by other authors, but rather an artifact due to some deficiency of the input data used in the shell model calculations in the region of the doubly magic 132Sn core

Gilbert Damping in Magnetic Multilayers

We study the enhancement of the ferromagnetic relaxation rate in thin films due to the adjacent normal metal layers. Using linear response theory, we derive the dissipative torque produced by the s-d exchange interaction at the ferromagnet-normal metal interface. For a slow precession, the enhancement of Gilbert damping constant is proportional to the square of the s-d exchange constant times the zero-frequency limit of the frequency derivative of the local dynamic spin susceptibility of the normal metal at the interface. Electron-electron interactions increase the relaxation rate by the Stoner factor squared. We attribute the large anisotropic enhancements of the relaxation rate observed recently in multilayers containing palladium to this mechanism. For free electrons, the present theory compares favorably with recent spin-pumping result of Tserkovnyak et al. [Phys. Rev. Lett. \textbf{88},117601 (2002)].Comment: 1 figure, 5page