Premise Selection and External Provers for HOL4

Learning-assisted automated reasoning has recently gained popularity among the users of Isabelle/HOL, HOL Light, and Mizar. In this paper, we present an add-on to the HOL4 proof assistant and an adaptation of the HOLyHammer system that provides machine learning-based premise selection and automated reasoning also for HOL4. We efficiently record the HOL4 dependencies and extract features from the theorem statements, which form a basis for premise selection. HOLyHammer transforms the HOL4 statements in the various TPTP-ATP proof formats, which are then processed by the ATPs. We discuss the different evaluation settings: ATPs, accessible lemmas, and premise numbers. We measure the performance of HOLyHammer on the HOL4 standard library. The results are combined accordingly and compared with the HOL Light experiments, showing a comparably high quality of predictions. The system directly benefits HOL4 users by automatically finding proofs dependencies that can be reconstructed by Metis

The Influence of Prophylactic Ankle Strategies on Vertical Jump Performance

Nelson, C., Paulson, S. Shippensburg University, Shippensburg, PA Purpose: This study examined the effects of prophylactic ankle taping (PAT) and bracing (PAB) on lower extremity kinematics during vertical jump (VJ) performance. Methods: Eighteen volunteers (M±SD = age: 21.4±0.9, height 170.9±10.0 cm, mass 73.2±14.5 kg, body fat 17.3±6.7%) completed the VJ under three conditions: standard PAT, lace-up PAB, and no treatment (CON). Each testing session was separated by a min of 24 hrs in a randomized and counter-balanced order. Prior to testing, the prophylactic ankle condition was applied and six reflective markers were placed along the right side of the body. The subject completed a 5-min warm-up on a Monark 824E cycle ergometer (0.5 kp) in a range of 50-60 rev/min and then performed three VJ. Each VJ was filmed (60 Hz) from the sagittal plane and a Vertec was used to measure jump height. A one-way repeated-measure ANOVA was used to analyze the variables. A paired t-test was used to assess for statistically significant differences (p \u3c .05). Results: The ANOVA yielded statistically significant difference in VJ height (M: PAT = 49.7 cm; PAB = 49.6 cm; CON = 52.2 cm; p = .02). The average VJ height was higher during the CON by 4.85% and 4.22% as compared to the PAT and PAB, respectively. There was also a statistically significant difference in the ankle angle at takeoff (p = .04) as well as ankle (AROM; p \u3c .01) and knee range of motion (KROM; p \u3c .01). During the PAB, the ankle was more dorsiflexed then the CON. AROM was greatest in the CON and least in the PAB. KROM was greater during CON as compared to the PAT and PAB conditions. Conclusion: This study suggests that both PAT and PAB decreased AROM and KROM; which may have resulted in a lower VJ height. In addition, the PAB placed the ankle in a more dorsiflexed position as compared to the CON

Older women and everyday talk about the ageing body

This discourse analytic study shows how 10 older women, who exercise regularly or attend the University of the Third Age, adjust to the ageing body in their `everyday talk' through taking a dualist position. The part of the body which is discursively constructed as ageing becomes objectified through appealing to a wider cultural discourse of ageing as biological decline. This dualist position is embedded within a wider cultural discourse of personal agency. The individual's control of the ageing body is emphasized, the ability to monitor and manage `ageing body parts' through exerting the `active mind' and the `busy body' in activities, or simply focusing on `looking good'

Wind-tunnel investigation of the powered low-speed longitudinal aerodynamics of the Vectored-Engine-Over (VEO) wing fighter configuration

A wind-tunnel investigation incorporating both static and wind-on testing was conducted in the Langley 4- by 7-Meter Tunnel to determine the effects of vectored thrust along with spanwise blowing on the low-speed aerodynamics of an advanced fighter configuration. Data were obtained over a large range of thrust coefficients corresponding to takeoff and landing thrust settings for many nozzle configurations. The complete set of static thrust data and the complete set of longitudinal aerodynamic data obtained in the investigation are presented. These data are intended for reference purposes and, therefore, are presented without analysis or comment. The analysis of the thrust-induced effects found in the investigation are not discussed

A method to estimate trends in distributions of 1 min rain rates from numerical weather prediction data

It is known that the rain rate exceeded 0.01% of the time in the UK has experienced an increasing trend over the last 20 years. It is very likely that rain fade and outage experience a similar trend. This paper presents a globally applicable method to estimate these trends, based on the widely accepted Salonen-Poiares Baptista model. The input data are parameters easily extracted from numerical weather prediction reanalysis data. The method is verified using rain gauge data from the UK, and the predicted trend slopes of 0.01% exceeded rain rate are presented on a global grid

Algebraically Closed Fields in Isabelle/HOL

A fundamental theorem states that every field admits an algebraically closed extension. Despite its central importance, this theorem has never before been formalised in a proof assistant. We fill this gap by documenting its formalisation in Isabelle/HOL, describing the difficulties that impeded this development and their solutions.ERC Advanced Grant ALEXANDRIA (Project GA 742178

Searching for Planets in the Hyades V: Limits on Planet Detection in the Presence of Stellar Activity

We present the results of a radial velocity survey of a sample of Hyades stars, and discuss the effects of stellar activity on radial velocity measurements. The level of radial velocity scatter due to rotational modulation of stellar surface features for the Hyades is in agreement with the predictions of Saar & Donahue (1997)- the maximum radial velocity rms of up to ~50 m/s, with an average rms of ~16 m/s. In this sample of 94 stars, we find 1 new binary, 2 stars with linear trends indicative of binary companions, and no close-in giant planets. We discuss the limits on extrasolar planet detection in the Hyades and the constraints imposed on radial velocity surveys of young stars.Comment: To appear in the June 2004 issue of A

Introduction to the computational structural mechanics testbed

The Computational Structural Mechanics (CSM) testbed software system based on the SPAR finite element code and the NICE system is described. This software is denoted NICE/SPAR. NICE was developed at Lockheed Palo Alto Research Laboratory and contains data management utilities, a command language interpreter, and a command language definition for integrating engineering computational modules. SPAR is a system of programs used for finite element structural analysis developed for NASA by Lockheed and Engineering Information Systems, Inc. It includes many complementary structural analysis, thermal analysis, utility functions which communicate through a common database. The work on NICE/SPAR was motivated by requirements for a highly modular and flexible structural analysis system to use as a tool in carrying out research in computational methods and exploring computer hardware. Analysis examples are presented which demonstrate the benefits gained from a combination of the NICE command language with a SPAR computational modules

Formalising Mathematics in Simple Type Theory

Despite the considerable interest in new dependent type theories, simple type theory (which dates from 1940) is sufficient to formalise serious topics in mathematics. This point is seen by examining formal proofs of a theorem about stereographic projections. A formalisation using the HOL Light proof assistant is contrasted with one using Isabelle/HOL. Harrison's technique for formalising Euclidean spaces is contrasted with an approach using Isabelle/HOL's axiomatic type classes. However, every formal system can be outgrown, and mathematics should be formalised with a view that it will eventually migrate to a new formalism

The Psychological and Physiological Effects of Music on Athletic Performance

Please view abstract in the attached PDF file