Algorithmic Randomness for Infinite Time Register Machines

A concept of randomness for infinite time register machines (ITRMs), resembling Martin-L\"of-randomness, is defined and studied. In particular, we show that for this notion of randomness, computability from mutually random reals implies computability and that an analogue of van Lambalgen's theorem holds

Pytrec_eval: An Extremely Fast Python Interface to trec_eval

We introduce pytrec_eval, a Python interface to the tree_eval information retrieval evaluation toolkit. pytrec_eval exposes the reference implementations of trec_eval within Python as a native extension. We show that pytrec_eval is around one order of magnitude faster than invoking trec_eval as a sub process from within Python. Compared to a native Python implementation of NDCG, pytrec_eval is twice as fast for practically-sized rankings. Finally, we demonstrate its effectiveness in an application where pytrec_eval is combined with Pyndri and the OpenAI Gym where query expansion is learned using Q-learning.Comment: SIGIR '18. The 41st International ACM SIGIR Conference on Research & Development in Information Retrieva

Mechanism and kinetics of aging in Inconel 718

Age hardening in Inconel 718 is investigated using Brinell hardness measurements. Formation of a precipitate causes an increase in hardness

Transition of Consistency and Satisfiability under Language Extensions

This article is part of the first author’s Bachelor thesis under the supervision of the second author.This article is the first in a series of two Mizar articles constituting a formal proof of the Gödel Completeness theorem [17] for uncountably large languages. We follow the proof given in [18]. The present article contains the techniques required to expand formal languages. We prove that consistent or satisfiable theories retain these properties under changes to the language they are formulated in.Schlöder Julian J. - Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, D-53113 Bonn, GermanyKoepke Peter - Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, D-53113 Bonn, GermanyGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. König’s theorem. Formalized Mathematics, 1(3):589-593, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Patrick Braselmann and Peter Koepke. Coincidence lemma and substitution lemma. Formalized Mathematics, 13(1):17-26, 2005.Patrick Braselmann and Peter Koepke. Equivalences of inconsistency and Henkin models. Formalized Mathematics, 13(1):45-48, 2005.Patrick Braselmann and Peter Koepke. G¨odel’s completeness theorem. Formalized Mathematics, 13(1):49-53, 2005.Patrick Braselmann and Peter Koepke. A sequent calculus for first-order logic. Formalized Mathematics, 13(1):33-39, 2005.Patrick Braselmann and Peter Koepke. Substitution in first-order formulas: Elementary properties. Formalized Mathematics, 13(1):5-15, 2005.Patrick Braselmann and Peter Koepke. Substitution in first-order formulas. Part II. The construction of first-order formulas. Formalized Mathematics, 13(1):27-32, 2005.Czesław Bylinski. A classical first order language. Formalized Mathematics, 1(4):669-676, 1990.Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Agata Darmochwał. A first-order predicate calculus. Formalized Mathematics, 1(4):689-695, 1990.Kurt Gödel. Die Vollst¨andigkeit der Axiome des logischen Funktionenkalk¨uls. Monatshefte f¨ur Mathematik und Physik 37, 1930.W. Thomas H.-D. Ebbinghaus, J. Flum. Einf¨uhrung in die Mathematische Logik. Springer-Verlag, Berlin Heidelberg, 2007.Piotr Rudnicki and Andrzej Trybulec. A first order language. Formalized Mathematics, 1(2):303-311, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Interpretation and satisfiability in the first order logic. Formalized Mathematics, 1(4):739-743, 1990.Edmund Woronowicz. Many argument relations. Formalized Mathematics, 1(4):733-737, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990

Generalized Effective Reducibility

We introduce two notions of effective reducibility for set-theoretical statements, based on computability with Ordinal Turing Machines (OTMs), one of which resembles Turing reducibility while the other is modelled after Weihrauch reducibility. We give sample applications by showing that certain (algebraic) constructions are not effective in the OTM-sense and considerung the effective equivalence of various versions of the axiom of choice

Silicon on ceramic process. Silicon sheet growth development for the large-area silicon sheet task of the low-cost silicon solar array project

The technical and economic feasibility of producing solar-cell-quality sheet silicon was investigated. The sheets were made by coating one surface of carbonized ceramic substrates with a thin layer of large-grain polycrystalline silicon from the melt. Significant progress was made in all areas of the program

Dip-coating process: Silicon sheet growth development for the large-area silicon sheet task of the low-cost silicon solar array project

The objective of this research program is to investigate the technical and economic feasibility of producing solar-cell-quality sheet silicon by coating one surface of carbonized ceramic substrates with a thin layer of large-grain polycrystalline silicon from the melt. The past quarter demonstrated significant progress in several areas. Seeded growth of silicon-on-ceramic (SOC) with an EFG ribbon seed was demonstrated. Different types of mullite were successfully coated with silicon. A new method of deriving minority carrier diffusion length, L sub n from spectral response measurements was evaluated. ECOMOD cost projections were found to be in good agreement with the interim SAMIS method proposed by JPL. On the less positive side, there was a decrease in cell performance which we believe to be due to an unidentified source of impurities