Hipster: Integrating Theory Exploration in a Proof Assistant

This paper describes Hipster, a system integrating theory exploration with the proof assistant Isabelle/HOL. Theory exploration is a technique for automatically discovering new interesting lemmas in a given theory development. Hipster can be used in two main modes. The first is exploratory mode, used for automatically generating basic lemmas about a given set of datatypes and functions in a new theory development. The second is proof mode, used in a particular proof attempt, trying to discover the missing lemmas which would allow the current goal to be proved. Hipster's proof mode complements and boosts existing proof automation techniques that rely on automatically selecting existing lemmas, by inventing new lemmas that need induction to be proved. We show example uses of both modes

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

Transport in metallic multi-island Coulomb blockade systems: A systematic perturbative expansion in the junction transparency

We study electronic transport through metallic multi-island Coulomb-blockade systems. Based on a diagrammatic real-time approach, we develop a computer algorithm that generates and calculates all transport contributions up to second order in the tunnel-coupling strengths for arbitrary multi-island systems. This comprises sequential and cotunneling, as well as terms corresponding to a renormalization of charging energies and tunneling conductances. Multi-island cotunneling processes with energy transfer between different island are taken into account. To illustrate our approach we analyze the current through an island in Coulomb blockade, that is electrostatically coupled to a second island through which a large current is flowing. In this regime both cotunneling processes involving one island only as well as multi-island processes are important. The latter can be understood as photon-assisted sequential tunneling in the blockaded island, where the photons are provided by potential fluctuations due to sequential tunneling in the second island. We compare results of our approach to a P(E)-theory for photon-assisted tunneling in the weak coupling limit.Comment: 14 pages, 7 figures, published version; minor changes in Sec. IV

A quantitative central limit theorem for linear statistics of random matrix eigenvalues

It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate of convergence of order almost $1/n$ can be obtained using a quantitative multivariate CLT for traces of powers that was recently proven using Stein's method of exchangeable pairs.Comment: Title modified; main result stated under slightly weaker conditions; accepted for publication in the Journal of Theoretical Probabilit

Eta Carinae -- Physics of the Inner Ejecta

Eta Carinae's inner ejecta are dominated observationally by the bright Weigelt blobs and their famously rich spectra of nebular emission and absorption lines. They are dense (n_e ~ 10^7 to 10^8 cm^-3), warm (T_e ~ 6000 to 7000 K) and slow moving (~40 km/s) condensations of mostly neutral (H^0) gas. Located within 1000 AU of the central star, they contain heavily CNO-processed material that was ejected from the star about a century ago. Outside the blobs, the inner ejecta include absorption-line clouds with similar conditions, plus emission-line gas that has generally lower densities and a wider range of speeds (reaching a few hundred km/s) compared to the blobs. The blobs appear to contain a negligible amount of dust and have a nearly dust-free view of the central source, but our view across the inner ejecta is severely affected by uncertain amounts of dust having a patchy distribution in the foreground. Emission lines from the inner ejecta are powered by photoionization and fluorescent processes. The variable nature of this emission, occurring in a 5.54 yr event cycle, requires specific changes to the incident flux that hold important clues to the nature of the central object.Comment: This is Chapter 5 in a book entitled: Eta Carinae and the Supernova Impostors, Kris Davidson and Roberta M. Humphreys, editors Springe

First order valence transition in YbInCu_4 in the (B,T) - plane

The puzzling properties of the first order phase transition in YbInCu$_4$ and its alloys in the wide range of magnetic fields and temperatures are perfectly described in terms of a simple entropy transition for free Yb ions. In particular, it turns out that the transition line in the $(B,T)$-plane is very close to the elliptic shape, as it has been observed experimentally. Similar calculations are done, and the experiments are proposed for the $(\gamma{-}\alpha)$ phase transition in Ce in Megagauss fields. We speculate, that in case of YbInCu$_4$ the first order transition is a Mott transition between a higher temperature phase in which localized moments are stabilized by the entropy terms in the free energy, and a band-like non-magnetic ground state of the $f$-electrons.Comment: RevTeX, 5 pages, 2 figure

Cerebrospinal Fluid YKL-40 and Neurogranin in Familial Alzheimer's Disease: A Pilot Study

BACKGROUND: YKL-40 and neurogranin are promising additional cerebrospinal fluid (CSF) biomarkers for Alzheimer's disease (AD) which reflect different underlying disease mechanisms. OBJECTIVE: To compare the levels of CSF YKL-40 and neurogranin between asymptomatic carriers of familial AD (FAD) mutations (MC) and non-carriers (NC) from the same families. Another objective was to assess changes in YKL-40 and neurogranin, from the presymptomatic to clinical phase of FAD. METHODS: YKL-40 and neurogranin, as well as Aβ42, total tau-protein, and phospho-tau, were measured in the CSF of 14 individuals carrying one of three FAD mutations, APPswe (p.KM670/671NL), APParc (p.E693G), and PSEN1 (p.H163Y), as well as in 17 NC from the same families. Five of the MC developed mild cognitive impairment (MCI) during follow-up. RESULTS: In this pilot study, there was no difference in either CSF YKL-40 or neurogranin when comparing the presymptomatic MC to the NC. YKL-40 correlated positively with expected years to symptom onset and to age in both the MC and the NC, while neurogranin had no correlation to either variable in either of the groups. A subgroup of the participants underwent more than one CSF sampling in which half of the MC developed MCI during follow-up. The longitudinal data showed an increase in YKL-40 levels in the MC as the expected symptom onset approached. Neurogranin remained stable over time in both the MC and the NC. CONCLUSION: These findings support a positive correlation between progression from presymptomatic to symptomatic AD and levels of CSF YKL-40, but not neurogranin

The Cerium volume collapse: Results from the LDA+DMFT approach

The merger of density-functional theory in the local density approximation (LDA) and many-body dynamical mean field theory (DMFT) allows for an ab initio calculation of Ce including the inherent 4f electronic correlations. We solve the DMFT equations by the quantum Monte Carlo (QMC) technique and calculate the Ce energy, spectrum, and double occupancy as a function of volume. At low temperatures, the correlation energy exhibits an anomalous region of negative curvature which drives the system towards a thermodynamic instability, i.e., the $\gamma$-to-$\alpha$ volume collapse, consistent with experiment. The connection of the energetic with the spectral evolution shows that the physical origin of the energy anomaly and, thus, the volume collapse is the appearance of a quasiparticle resonance in the 4f-spectrum which is accompanied by a rapid growth in the double occupancy.Comment: 4 pages, 3 figure

A Reanalysis of theUltraviolet Extinction from Interstellar Dust in the Large Magellanic Cloud

We have reanalyzed the Large Magellanic Cloud's (LMC) ultraviolet (UV) extinction using data from the IUE final archive. Our new analysis takes advantage of the improved signal--to--noise of the IUE NEWSIPS reduction, the exclusion of stars with very low reddening, the careful selection of well matched comparison stars, and an analysis of the effects of Galactic foreground dust. Differences between the average extinction curves of the 30 Dor region and the rest of the LMC are reduced compared to previous studies. We find that there is a group of stars with very weak 2175 Ang. bumps that lie in or near the region occupied by the supergiant shell, LMC 2, on the southeast side of 30 Dor. The average extinction curves inside and outside LMC 2 show a very significant difference in 2175 Ang. bump strength, but their far--UV extinctions are similar. While it is unclear whether or not the extinction outside the LMC 2 region can be fit with the relation of Cardelli, Clayton and Mathis (CCM), sightlines near LMC 2 cannot be fit with CCM due to their weak 2175 Ang. bumps. While the extinction properties seen in the LMC lie within the range of properties seen in the Galaxy, the correlations of UV extinction properties with environment seen in the Galaxy do not appear to hold in the LMC.Comment: 29 pages, 10 figures, to be published in Ap

Ionoluminescence: A New Tool for Nuclear Microprobes in Geology

When an ion beam in the energy range of a few MeV/amu impacts on a mineral, visible light can often be observed. This light, induced by energetic ions, is termed ionoluminescence (IL). The intensity and wavelength of the ionoluminescent light provide information concerning the nature of luminescence centers, such as trace substituents and structural defects, found in the mineral. This makes IL a useful complement to other methods of ion beam analysis (IBA), such as particle induced X-ray emission (PIXE) and Rutherford backscattering (RBS), in characterizing geological samples. In the present study, a proton or alpha particle beam was used for the IL excitation and IBA with a nuclear microprobe. The results obtained with IL were compared with those of cathodoluminescence (CL) and photoluminescence (PL)