911 research outputs found
Computing Equilibria of Semi-algebraic Economies Using Triangular Decomposition and Real Solution Classification
In this paper, we are concerned with the problem of determining the existence
of multiple equilibria in economic models. We propose a general and complete
approach for identifying multiplicities of equilibria in semi-algebraic
economies, which may be expressed as semi-algebraic systems. The approach is
based on triangular decomposition and real solution classification, two
powerful tools of algebraic computation. Its effectiveness is illustrated by
two examples of application.Comment: 24 pages, 5 figure
Automated Generation of Geometric Theorems from Images of Diagrams
We propose an approach to generate geometric theorems from electronic images
of diagrams automatically. The approach makes use of techniques of Hough
transform to recognize geometric objects and their labels and of numeric
verification to mine basic geometric relations. Candidate propositions are
generated from the retrieved information by using six strategies and geometric
theorems are obtained from the candidates via algebraic computation.
Experiments with a preliminary implementation illustrate the effectiveness and
efficiency of the proposed approach for generating nontrivial theorems from
images of diagrams. This work demonstrates the feasibility of automated
discovery of profound geometric knowledge from simple image data and has
potential applications in geometric knowledge management and education.Comment: 31 pages. Submitted to Annals of Mathematics and Artificial
Intelligence (special issue on Geometric Reasoning
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