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

Band Mapping in One-Step Photoemission Theory: Multi-Bloch-Wave Structure of Final States and Interference Effects

A novel Bloch-waves based one-step theory of photoemission is developed within the augmented plane wave formalism. Implications of multi-Bloch-wave structure of photoelectron final states for band mapping are established. Interference between Bloch components of initial and final states leads to prominent spectral features with characteristic frequency dispersion experimentally observed in VSe_2 and TiTe_2. Interference effects together with a non-free-electron nature of final states strongly limit the applicability of the common direct transitions band mapping approach, making the tool of one-step analysis indispensable.Comment: 4 jpg figure

Understanding Microbial Divisions of Labor

Divisions of labor are ubiquitous in nature and can be found at nearly every level of biological organization, from the individuals of a shared society to the cells of a single multicellular organism. Many different types of microbes have also evolved a division of labor among its colony members. Here we review several examples of microbial divisions of labor, including cases from both multicellular and unicellular microbes. We first discuss evolutionary arguments, derived from kin selection, that allow divisions of labor to be maintained in the face of non-cooperative cheater cells. Next we examine the widespread natural variation within species in their expression of divisions of labor and compare this to the idea of optimal caste ratios in social insects. We highlight gaps in our understanding of microbial caste ratios and argue for a shift in emphasis from understanding the maintenance of divisions of labor, generally, to instead focusing on its specific ecological benefits for microbial genotypes and colonies. Thus, in addition to the canonical divisions of labor between, e.g., reproductive and vegetative tasks, we may also anticipate divisions of labor to evolve to reduce the costly production of secondary metabolites or secreted enzymes, ideas we consider in the context of streptomycetes. The study of microbial divisions of labor offers opportunities for new experimental and molecular insights across both well-studied and novel model systems

Strictly One-Dimensional Electron System in Au Chains on Ge(001) Revealed By Photoelectron K-Space Mapping

Atomic nanowires formed by Au on Ge(001) are scrutinized for the band topology of the conduction electron system by k-resolved photoemission. Two metallic electron pockets are observed. Their Fermi surface sheets form straight lines without undulations perpendicular to the chains within experimental uncertainty. The electrons hence emerge as strictly confined to one dimension. Moreover, the system is stable against a Peierls distortion down to 10 K, lending itself for studies of the spectral function. Indications for unusually low spectral weight at the chemical potential are discussed.Comment: 4 pages, 4 figures - revised version with added Fig. 2e) and additional reference

Інвестиційне кредитування переробних підприємств АПК банківськими установами

Метою статті є аналіз динаміки інвестиційного кредитування банківськими установами переробних підприємств агропромислового комплексу. Під час проведення дослідження були використані аналітичний, статистико – економічний, графічний, порівняльний методи та метод системного аналізу

Your Proof Fails? Testing Helps to Find the Reason

Applying deductive verification to formally prove that a program respects its formal specification is a very complex and time-consuming task due in particular to the lack of feedback in case of proof failures. Along with a non-compliance between the code and its specification (due to an error in at least one of them), possible reasons of a proof failure include a missing or too weak specification for a called function or a loop, and lack of time or simply incapacity of the prover to finish a particular proof. This work proposes a new methodology where test generation helps to identify the reason of a proof failure and to exhibit a counter-example clearly illustrating the issue. We describe how to transform an annotated C program into C code suitable for testing and illustrate the benefits of the method on comprehensive examples. The method has been implemented in STADY, a plugin of the software analysis platform FRAMA-C. Initial experiments show that detecting non-compliances and contract weaknesses allows to precisely diagnose most proof failures.Comment: 11 pages, 10 figure

High-energy photoemission on Fe3O4: Small polaron physics and the Verwey transition

We have studied the electronic structure and charge ordering (Verwey) transition of magnetite (Fe3O4) by soft x-ray photoemission. Due to the enhanced probing depth and the use of different surface preparations we are able to distinguish surface and volume effects in the spectra. The pseudogap behavior of the intrinsic spectra and its temperature dependence give evidence for the existence of strongly bound small polarons consistent with both dc and optical conductivity. Together with other recent structural and theoretical results our findings support a picture in which the Verwey transition contains elements of a cooperative Jahn-Teller effect, stabilized by local Coulomb interaction

Unoccupied Band Structure of NbSe2 by Very-Low-Energy Electron Diffraction: Experiment and Theory

A combined experimental and theoretical study of very-low-energy electron diffraction at the (0001) surface of 2H-NbSe2 is presented. Electron transmission spectra have been measured for energies up to 50 eV above the Fermi level with k|| varying along the GammaK line of the Brillouin zone. Ab initio calculations of the spectra have been performed with the extended linear augmented plane wave k-p method. The experimental spectra are interpreted in terms of three-dimensional one-electron band structure. Special attention is paid to the quasi-particle lifetimes: by comparing the broadening of the spectral structures in the experimental and calculated spectra the energy dependence of the optical potential Vi is determined. A sharp increase of Vi at 20 eV is detected, which is associated with a plasmon peak in the Im(-1/epsilon) function. Furthermore, the electron energy loss spectrum and the reflectivity of NbSe2 are calculated ab initio and compared with optical experiments. The obtained information on the dispersions and lifetimes of the unoccupied states is important for photoemission studies of the 3D band structure of the valence band.Comment: 17 pages, 11 Postscript figures, submitted to Phys. Rev.