Many important application problems in engineering can be formalized as nonlinear
optimization tasks. However, numerical methods for solving such problems
are brittle and do not scale well. For example, these methods depend critically
on choosing a good starting point from which to perform the optimization search.
In high-dimensional spaces, numerical...
This paper applies learning techniques to make engineering optimization more efficient and reliable. When the function to be optimized is highly non-linear, the search space generally forms several disjoint convex regions . Unless gradient-descent search is begun in the right region, the solution found will be suboptimal. This paper formalizes...
Many important application problems can be formalized as constrained non-linear optimization tasks. However, numerical methods for solving such problems are brittle and do not scale well. Furthermore, they do not provide much insight into the structure of the problem space. This paper describes a method for discovering efficient rules that...
Recently generalized Fibonacci numbers have received increasing attention. Some properties that are well known for traditional Fibonacci numbers do not generalize easily, some others do not generalize at all. In this paper we report some properties that we have generalized. Section 1 introduces the notation and a theorem due to...
We investigate several methods of computing Fibonacci numbers quickly and generalize some properties of the Fibonacci numbers to degree r Fibonacci (R-nacci) numbers. Sections 2 and 3 present several algorithms for computing the traditional, degree two, Fibonacci numbers quickly. Sections 4 and 5 investigate the structure of the binary representation...
Mud volcanoes (MVs) are considered as important methane (CH₄) sources for the
atmosphere; gas is not only released from macroseepage, i.e., from craters and visible gas bubbling
manifestations, but also from invisible and pervasive exhalation from the ground, named miniseepage.
CH₄ flux related to miniseepage was measured only in a...
AM is a computer program written by Doug Lenat that discovers elementary
mathematics starting from some initial knowledge of set theory. The success of this
program is not clearly understood.
This work is an attempt to explore the search space of AM in order to understand the success and eventual...
A specialized ATMS for efficiently computing equivalence relations in multiple contexts is introduced. This specialized ATMS overcomes the problems with existing solutions to reasoning with equivalence relations. The most direct implementation of an equivalence relation in the ATMS-encoding the reflexive, transitive, and symmetric rules in the consumer architecture-produces redundant equality...
The coverage of a learning algorithm is the number of concepts that can be learned by that algorithm from samples of a given size for given accuracy and confidence parameters. This thesis begins by asking whether good learning algorithms can be designed by maximizing their coverage. There are three questions...