Combining Algebraic Computing and Term-Rewriting for Geometry Theorem Proving
This note reports some of our investigations on combining algebraic computing and term-rewriting techniques for automated geometry theorem proving. A general approach is proposed that requires both Clifford algebraic reduction and term-rewriting. Preliminary experiments for some concrete cases have been carried out by combining routines implemented in Maple V and Objective Caml. The experiments together with several examples illustrate the suitability and performance of our approach.

title: GEOTHER: A Geometry Theorem Prover

title: 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.

title: On Wu's Method for Proving Constructive Geometric Theorems
abstract: 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.

title: Automated Generation of Diagrams with Maple and Java
abstract: 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.

title: Reasoning about Surfaces Using Differential Zero and Ideal Decomposition
abstract: This paper presents methods for zero and ideal decomposition of partial differential polynomial systems and the application of these methods and their implementations to deal with problems from the local theory of surfaces. We show how to prove known geometric theorems and to derive unknown relations automatically. In particular, an algebraic relation between the first and the second fundamental coefficients in a very compact form has been derived, which is more general and has smaller degree than a relation discovered previously by Z. Li. Moreover, we provide symmetric expressions for Li's relation and clarify his statement. Some examples of theorem proving and computational difficulties encountered in our experiments are also discussed.

title: Lessons Learned from Managing a Petabyte
abstract: The amount of data collected and stored by the average business doubles each year. Many commercial databases are already approaching hundreds of terabytes, and at this rate, will soon be managing petabytes. More data enables new functionality and capability, but the larger scale reveals new problems and issues hidden in ''smaller'' terascale environments. This paper presents some of these new problems along with implemented solutions in the framework of a petabyte dataset for a large High Energy Physics experiment. Through experience with two persistence technologies, a commercial database and a file-based approach, we expose format-independent concepts and issues prevalent at this new scale of computing.

title: Wavelet transform-based frequency tuning ILC
abstract: A discrete wavelet transform-based cutoff frequency tuning method is proposed and experimental investigation is reported. In the method, discrete wavelet packet algorithm, as a time-frequency analysis tool, is employed to decompose the tracking error into different frequency regions so that the maximal error component can be identified at any time step. At each time step, the passband of the filter is from zero to the upper limit of frequency region where the maximal error component resides. Hence, the filter is a function of time as well as index of cycle. The experimental results show that this method can suppress higher frequency error components at proper time steps. While at the time steps where the major tracking error falls into lower frequency range, the cutoff frequency of the filter is set lower to reduce the influence of noises and uncertainties. This way, learning transient and long-term stability can be improved.

title: Server-Side Parallel Data Reduction and Analysis
abstract: Geoscience analysis is currently limited by cumbersome access and manipulation of large datasets from remote sources. Due to their data-heavy and compute-light nature, these analysis workloads represent a class of applications unsuited to a computational grid optimized for compute-intensive applications. We present the Script Workflow Analysis for MultiProcessing (SWAMP) system, which relocates data-intensive workflows from scientists' workstations to the hosting datacenters in order to reduce data transfer and exploit locality. Our colocation of computation and data leverages the typically reductive characteristics of these workflows, allowing SWAMP to complete workflows in a fraction of the time and with much less data transfer. We describe SWAMP's implementation and interface, which is designed to leverage scientists' existing script-based workflows. Tests with a production geoscience workflow show drastic improvements not only in overall execution time, but in computation time as well. SWAMP's workflow analysis capability allows it to detect dependencies, optimize I/O, and dynamically parallelize execution. Benchmarks quantify the drastic reduction in transfer time, computation time, and end-to-end execution time.

title: Hardware-software partitioning of real-time operating systems using Hopfield neural networks
abstract: The hardware–software automated partitioning of a real-time operating system in the system-on-a-chip (SoC-RTOS partitioning) is a NP-complete problem, and a crucial step in the hardware–software co-design of SoC. In this paper, a new model for SoC-RTOS partitioning is introduced, which can help in understanding the essence of the SoC-RTOS partitioning. A discrete Hopfield neural network approach for implementing the SoC-RTOS partitioning is proposed, where a novel energy function, operating equation and coefficients of the neural network are redefined. Simulations are carried out with comparison to other optimization techniques. Experimental results demonstrate the feasibility and effectiveness of the proposed method.

title: Semantics modeling based image retrieval system using neural networks
abstract: Semantics based image retrieval techniques show a promising direction to the development of CBIR systems. To design such systems, semantics modeling is one of the most difficult tasks. This paper aims to develop a semantics modeling approach using neural networks. In our work, a neural network is utilized to memorize the semantic patterns within the images. An intelligent image retrieval system is designed based on this model. User's relevance feedback is used for enhancing the retrieval performance. Experimental results from the prototype system demonstrate the effectiveness of the proposed approach.