Learning-assisted Theorem Proving with Millions of Lemmas

Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs. We show that in combination with learning-based relevance filtering, such methods significantly strengthen automated theorem proving of new conjectures over large formal mathematical libraries such as Flyspeck.Comment: journal version of arXiv:1310.2797 (which was submitted to LPAR conference

JWalk: a tool for lazy, systematic testing of java classes by design introspection and user interaction

Popular software testing tools, such as JUnit, allow frequent retesting of modified code; yet the manually created test scripts are often seriously incomplete. A unit-testing tool called JWalk has therefore been developed to address the need for systematic unit testing within the context of agile methods. The tool operates directly on the compiled code for Java classes and uses a new lazy method for inducing the changing design of a class on the fly. This is achieved partly through introspection, using Java’s reflection capability, and partly through interaction with the user, constructing and saving test oracles on the fly. Predictive rules reduce the number of oracle values that must be confirmed by the tester. Without human intervention, JWalk performs bounded exhaustive exploration of the class’s method protocols and may be directed to explore the space of algebraic constructions, or the intended design state-space of the tested class. With some human interaction, JWalk performs up to the equivalent of fully automated state-based testing, from a specification that was acquired incrementally

Automated protein structure modeling in CASP9 by I‐TASSER pipeline combined with QUARK‐based ab initio folding and FG‐MD‐based structure refinement

I‐TASSER is an automated pipeline for protein tertiary structure prediction using multiple threading alignments and iterative structure assembly simulations. In CASP9 experiments, two new algorithms, QUARK and fragment‐guided molecular dynamics (FG‐MD), were added to the I‐TASSER pipeline for improving the structural modeling accuracy. QUARK is a de novo structure prediction algorithm used for structure modeling of proteins that lack detectable template structures. For distantly homologous targets, QUARK models are found useful as a reference structure for selecting good threading alignments and guiding the I‐TASSER structure assembly simulations. FG‐MD is an atomic‐level structural refinement program that uses structural fragments collected from the PDB structures to guide molecular dynamics simulation and improve the local structure of predicted model, including hydrogen‐bonding networks, torsion angles, and steric clashes. Despite considerable progress in both the template‐based and template‐free structure modeling, significant improvements on protein target classification, domain parsing, model selection, and ab initio folding of β‐proteins are still needed to further improve the I‐TASSER pipeline. Proteins 2011; © 2011 Wiley‐Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/88077/1/23111_ftp.pd

Data generator for evaluating ETL process quality

Obtaining the right set of data for evaluating the fulfillment of different quality factors in the extract-transform-load (ETL) process design is rather challenging. First, the real data might be out of reach due to different privacy constraints, while manually providing a synthetic set of data is known as a labor-intensive task that needs to take various combinations of process parameters into account. More importantly, having a single dataset usually does not represent the evolution of data throughout the complete process lifespan, hence missing the plethora of possible test cases. To facilitate such demanding task, in this paper we propose an automatic data generator (i.e., Bijoux). Starting from a given ETL process model, Bijoux extracts the semantics of data transformations, analyzes the constraints they imply over input data, and automatically generates testing datasets. Bijoux is highly modular and configurable to enable end-users to generate datasets for a variety of interesting test scenarios (e.g., evaluating specific parts of an input ETL process design, with different input dataset sizes, different distributions of data, and different operation selectivities). We have developed a running prototype that implements the functionality of our data generation framework and here we report our experimental findings showing the effectiveness and scalability of our approach.Peer ReviewedPostprint (author's final draft

XMM-Newton observations of the supernova remnant IC443: I. soft X-ray emission from shocked interstellar medium

The shocked interstellar medium around IC443 produces strong X-ray emission in the soft energy band (E<1.5 keV). We present an analysis of such emission as observed with the EPIC MOS cameras on board the XMM-Newotn observatory, with the purpose to find clear signatures of the interactions with the interstellar medium (ISM) in the X-ray band, which may complement results obtained in other wavelenghts. We found that the giant molecular cloud mapped in CO emission is located in the foreground and gives an evident signature in the absorption of X-rays. This cloud may have a torus shape and the part of torus interacting with the IC443 shock gives rise to 2MASS-K emission in the southeast. The measured density of emitting X-ray shocked plasma increases toward the northeastern limb, where the remnant is interacting with an atomic cloud. We found an excellent correlation between emission in the 0.3-0.5 keV band and bright optical/radio filament on large spatial scales. The partial shell structure seen in this band therefore traces the encounter with the atomic cloud.Comment: 10 pages, 10 figures, accepted for publication in ApJ (20 September 2006, v649). For hi-res figures, see http://www.astropa.unipa.it/Library/OAPA_preprints/ic443ele1.ps.g

Effects of Dielectric Stoichiometry on the Photoluminescence Properties of Encapsulated WSe2 Monolayers

Two-dimensional transition-metal-dichalcogenide semiconductors have emerged as promising candidates for optoelectronic devices with unprecedented properties and ultra-compact performances. However atomically thin materials are highly sensitive to surrounding dielectric media, which imposes severe limitations to their practical applicability. Hence for their suitable integration into devices, the development of reliable encapsulation procedures that preserve their physical properties are required. Here, the excitonic photoluminescence of WSe2 monolayer flakes is assessed, at room temperature and 10 K, on mechanically exfoliated flakes encapsulated with SiOx and AlxOy layers employing chemical and physical deposition techniques. Conformal flakes coating on untreated - non-functionalized - flakes is successfully demonstrated by all the techniques except for atomic layer deposition, where a cluster-like oxide coating is observed. No significant compositional or strain state changes in the flakes are detected upon encapsulation by any of the techniques. Remarkably, our results evidence that the flakes' optical emission is strongly influenced by the quality of the encapsulating oxide - stoichiometry -. When the encapsulation is carried out with slightly sub-stoichiometric oxides two remarkable phenomena are observed. First, there is a clear electrical doping of the monolayers that is revealed through a dominant trion - charged exciton - room-temperature photoluminescence. Second, a strong decrease of the monolayers optical emission is measured attributed to non-radiative recombination processes and/or carriers transfer from the flake to the oxide. Power- and temperature-dependent photoluminescence measurements further confirm that stoichiometric oxides obtained by physical deposition lead to a successful encapsulation.Comment: 30 pages, 6 figure