A Divergence Critic for Inductive Proof

Inductive theorem provers often diverge. This paper describes a simple critic, a computer program which monitors the construction of inductive proofs attempting to identify diverging proof attempts. Divergence is recognized by means of a ``difference matching'' procedure. The critic then proposes lemmas and generalizations which ``ripple'' these differences away so that the proof can go through without divergence. The critic enables the theorem prover Spike to prove many theorems completely automatically from the definitions alone.Comment: See http://www.jair.org/ for any accompanying file

Electro-optic modulator for infrared laser using gallium arsenide crystal

Gallium arsenide electro-optic modulator used for infrared lasers has a mica quarter-wave plate and two calcite polarizers to amplitude or phase modulate an infrared laser light source in the wavelength range from 1 to 3 microns. The large single crystal has uniformly high resistivities, is strain free, and comparable in quality to good optical glass

Interferometric rotation sensor

Sensor generates interference fringes varying in number (horizontally and vertically) as a function of the total angular deviation relative to the line-of-sight axis. Device eliminates errors from zero or null shift due to lack of electrical circuitry stability

Development of a 10.6-micron laser modulator Final report, 18 Feb. - 18 Jul. 1966

Electro-optic modulation, crystal growth and properties, and design equations and performance for 10.6-micron laser modulator of gallium arsenid

Vibration damping system Patent

Vibration damping system operating in low vacuum environment for spacecraft mechanism

An Empirical Analysis of Search in GSAT

We describe an extensive study of search in GSAT, an approximation procedure for propositional satisfiability. GSAT performs greedy hill-climbing on the number of satisfied clauses in a truth assignment. Our experiments provide a more complete picture of GSAT's search than previous accounts. We describe in detail the two phases of search: rapid hill-climbing followed by a long plateau search. We demonstrate that when applied to randomly generated 3SAT problems, there is a very simple scaling with problem size for both the mean number of satisfied clauses and the mean branching rate. Our results allow us to make detailed numerical conjectures about the length of the hill-climbing phase, the average gradient of this phase, and to conjecture that both the average score and average branching rate decay exponentially during plateau search. We end by showing how these results can be used to direct future theoretical analysis. This work provides a case study of how computer experiments can be used to improve understanding of the theoretical properties of algorithms.Comment: See http://www.jair.org/ for any accompanying file

Building Abstractions

The use of abstraction has been largely informal. As a consequence, it has often been difficult to see how or why a particular abstraction works. This paper attempts to help correct this trend by presenting a formal theory of abstraction. We use this theory to characterise the different types of abstraction that can be built; the different classes of abstractions we identify capture the majority of abstractions of which we are aware. We end by proposing a method for automatically building one very common type of abstraction, that used in Abstrips; our proposal is motivated by consideration of the various formal properties that such a method should possess

HR: A System for Machine Discovery in Finite Algebras

We describe the HR concept formation program which invents mathematical definitions and conjectures in finite algebras such as group theory and ring theory. We give the methods behind and the reasons for the concept formation in HR, an evaluation of its performance in its training domain, group theory, and a look at HR in domains other than group theory

Development of a 10.6-micron laser modulator

Electro-optic coefficient of gallium arsenide measured at wavelengths from 2 to 12 microns by 10.6 micron laser modulato

Ecological and economic benefits of integrating sheep into viticulture production

The integration of crop and livestock systems has been recognized for its potential to reduce the environmental impacts associated with agriculture and improve farmer livelihoods. However, to date, most research has focused on the integration of cattle into crop and pasture systems. Here we examine the integration of sheep into vineyards and assess farmers’ perceived benefits and costs of the practice. Viticulture expansion has led to significant land use change in recent years and new environmental challenges, particularly with respect to herbicide use. Sheep integration into vineyards offers the potential to utilize the synergies of both systems to reduce external inputs, promote soil health, and increase farmer profit. Our study focuses in New Zealand, the world’s 15th largest wine producer, particularly in Marlborough, which produces 75% of the country’s wine. As a result, the case study is an excellent representation of New Zealand viticulture, while also providing unique insights into a novel practice. Using a semi-structured interview and survey, we interviewed fifteen farmers representing five percent of total New Zealand wine production to examine ecological and economic benefits of sheep integration in viticulture systems. We find that seasonal integration of sheep during vine dormancy is common, while integration during the growing season is rare. Overall, farmers perceive significantly more benefits than challenges with the integration of sheep into vineyards, particularly reduced mowing (100% of farmers) and herbicide use (66% of farmers). On average, farmers reported 1.3 fewer herbicide applications annually, saving US$$56 per hectare. As well, farmers indicated they were doing 2.2 fewer mows annually saving US$$64 per hectare. These results suggest that wide-scale adoption of seasonal integration of sheep and viticulture can provide large ecological benefits and higher profitability vis-à-vis conventional viticulture practices; however, further integration of the two systems may provide even greater benefits not currently realized