20258295
Automated Generation of Diagrams with Maple and Java
This note shows how to draw diagrams automatically from the predicate specification of a given set of geometric relations among a set of points in the plane. It is done first in Maple by translating the geometric relations into polynomial equations, decomposing the obtained system of polynomials into irreducible representative triangular sets, and finding an adequate numerical solution from each triangular set. A Java class coding the solution and the polynomials in each triangular set is generated, compiled, and then executed with the main Java programs to draw a diagram. The whole process combining symbolic elimination in Maple with numerical computation, graphic drawing, and letter labeling in Java is fully automatic. The drawn diagrams may be animated and fine-tuned by mouse click and dragging and saved as PostScript files. We present the drawing method, discuss some techniques of implementation, and give several sample diagrams drawn by our program.
5752689
Stability analysis of biological systems with real solution classification
This paper presents a new and general approach for analyzing the stability of a large class of biological networks, modeled as autonomous systems of differential equations, using real solving and solution classification. The proposed approach, based on the classical technique of linearization from the qualitative theory of ordinary differential equations yet with exact symbolic computation, is applied to analyzing the local stability of the Cdc2-cyclin B/Wee1 system and the Mos/MEK/p42 MAPK cascade, two well-known models for cell and protein signaling that have been studied extensively in the literature. We provide rigorous proofs and generalizations for some of the previous results established experimentally and report our new findings.
35725775
A simple method for implicitizing rational curves and surfaces
Abstract This paper presents a simple method for converting rational parametric equations of curves and surfaces into implicit equations. The method proceeds via writing out the implicit polynomial F of estimated degree with indeterminate coefficients u i , substituting the rational expressions for the given parametric curve or surface into F to yield a rational expression g / h in the parameter s (or s and t ), equating the coefficients of g in terms of s (and t ) to 0 to generate a sparse, partially triangular system of linear equations in u i with constant coefficients, and finally solving the linear system for u i . If a nontrivial solution is found, then an implicit polynomial is obtained; otherwise, one repeats the same process, increasing the degree of F . Our experiments show that this simple method is efficient. It performs particularly well in the presence of base points and may detect the dependency of parameters incidentally.
10570969
Clifford Algebraic Calculus for Geometric Reasoning with Application to Computer Vision
In this paper we report on our recent study of Clifford algebra for geometric reasoning and its application to problems in computer vision. A general framework is presented for construction and representation of geometric objects with selected rewrite rules for simplification. It provides a mechanism suitable for devising methods and software tools for geometric reasoning and computation. The feasibility and efficiency of the approach are demonstrated by our preliminary experiments on automated theorem proving in plane Euclidean geometry. We also explain how non-commutative Grobner bases can be applied to geometric theorem proving. In addition to several well-known geometric theorems, two application examples from computer vision are given to illustrate the practical value of our approach.
10779017
On Wu's Method for Proving Constructive Geometric Theorems
In 1977 Wu Wen-tsiin discovered an efficient method for mechanical theorem proving. This method has been applied to prove and discover theorems in various kinds of geometries. Based on an extension of one of Wu's algorithmic procedures, the author implemented a prover CPS for proving so-called constructive geometric theorems, as well as a general theorem prover PS. Using this prover we proved more than one hundred non-trivial theorems and discovered also a number of interesting ones. This paper is a summarization of our early work, as a abbreviation of the chapter 2 from my Chinese doctoral dissertation.
34533255
Clifford Term Rewriting for Geometric Reasoning in 3D
Clifford algebra formalism has been used recently in combination with standard term-rewriting techniques for proving many non-trivial geometric theorems. The key issue in this approach consists in verifying whether two Clifford expressions are equal. This paper is concerned with the generalization of the work to 3D geometric problems. A rewriting system is proposed and its theoretical properties are investigated. Some examples and potential applications are also presented.
35246774
Identifying reasoning strategies in medical decision making: A methodological guide
Reasoning strategies are a key component in many medical tasks, including decision making, clinical problem solving, and understanding of medical texts. Identification of reasoning strategies used by clinicians may prove critical to the optimal design of decision support systems. This paper presents a formal method of cognitive-semantic analysis for the identification and characterization of reasoning strategies deployed in medical tasks and demonstrates its use through specific examples. Although semantic analysis was originally developed in the investigation of knowledge structures, it can also be applied to identify the reasoning and decision processes used by physicians and medical trainees in clinical tasks. Assumptions underlying the methods, as well as illustrations of their use in diagnostic explanation tasks, are presented. We discuss semantic analysis in the context of the current interests in developing medical ontologies and argue that a frame-based propositional analytic methodology can provide a systematic way of addressing the construction of such ontologies. Although the application of propositional analysis methods has some limitations, we show how such limitations are being addressed and present some examples of information tools that have been developed to ease, and make more systematic, the process of analysis.
499811
Laser Needle Guide for the Sonic Flashlight
We have extended the real-time tomographic reflection display of the Sonic Flashlight to a laser guidance system that aims to improve safety and accuracy of needle insertion, especially for deep procedures. This guidance system is fundamentally different from others currently available. Two low-intensity lasers are mounted on opposite sides of a needle aimed parallel to the needle. The needle is placed against a notch in the Sonic Flashlight mirror such that the laser beams reflect off the mirror to create bright red spots on the flat panel display. Due to diffuse reflection from these spots, the virtual image created by the flat panel display contains the spots, identifying the projected destination of the needle at its actual location in the tissue. We have implemented our design and validated its performance, identifying several areas for potential improvement.
8658919
Using Combinatorial Optimization Methods for Quantification Scheduling
Model checking is the process of verifying whether a model of a concurrent system satisfies a specified temporal property. Symbolic algorithms based on Binary Decision Diagrams (BDDs) have significantly increased the size of the models that can be verified. The main problem in symbolic model checking is the image computation problem, i.e., efficiently computing the successors or predecessors of a set of states. This paper is an in-depth study of the image computation problem. We analyze and evaluate several newheuristics, metrics, and algorithms for this problem. The algorithms use combinatorial optimization techniques such as hill climbing, simulated annealing, and ordering by recursive partitioning to obtain better results than was previously the case. Theoretical analysis and systematic experimentation are used to evaluate the algorithms.
571032
Nonlinear quantification scheduling in image computation
Computing the set of states reachable in one step from a given set of states, i.e. image computation, is a crucial step in several symbolic verification algorithms, including model checking and reachability analysis. So far, the best methods for quantification scheduling in image computation, with a conjunctively partitioned transition relation, have been restricted to a linear schedule. This results in a loss of flexibility during image computation. We view image computation as a problem of constructing an optimal parse tree for the image set. The optimality of a parse tree is defined by the largest BDD that is encountered during the computation of the tree. We present dynamic and static versions of a new algorithm, VarScore, which exploits the flexibility offered by the parse tree approach to the image computation. We show by extensive experimentation that our techniques outperform the best known techniques so far.
3857288
Using the Semantic Web to Integrate Ecoinformatics Resources
We demonstrate an end-to-end use case of the semantic web's utility for synthesizing ecological and environmental data. ELVIS (the Ecosystem Location Visualization and Information System) is a suite of tools for constructing food webs for a given location. ELVIS functionality is exposed as a collection of web services, and all input and output data is expressed in OWL, thereby enabling its integration with other semantic web resources. In particular, we describe using a Triple Shop application to answer SPARQL queries from a collection of semantic web documents.