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.
7488203
On the Parallelization of Characteristic-Set-Based Algorithms
This paper presents a parallelized version of algorithms for computing characteristic sets, characteristic series and irreducible characteristic series of sets of multivariate polynomials, decomposing algebraic varieties into irreducible components and proving theorems mechanically in elementary geometries. These algorithms have been implemented with up to 12 processors in MAPLE system by utilizing distributed workstations connected by a local network. The timing statistics on a set of test problems with remarks is given. The encountered problems of using parallelism for these algorithms are discussed.
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.
1420299
Server-Side Parallel Data Reduction and Analysis
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.
646293
An oscillatory correlation model of human motion perception
An oscillatory correlation model of human motion perception is proposed based on the integration of motion and luminance information. The model is composed of two parallel pathways that segment the input scene based on motion and luminance, respectively. Combining these segmentations, the model refines the motion estimates in the integration stage to obtain the final segmentation in the motion pathway. For segmentation, LEGION (locally excitatory globally inhibitory oscillator network) is employed whereby the phases of oscillators are used for region labeling. The model performance is demonstrated using a set of psychophysical data.
11770982
The strong Hall property and symmetric chain orders
Abstract Let G =( X , Y ; E ) be a bipartite graph with | X |⩾| Y |. For A ⊆ X , write φ ( A )=| A |−| N ( A )| and for a ⩽| X |, define φ(a)= max {φ(A) | A⊆X, |A|=a} . The graph G is said to have the strong Hall property if φ ( a )+ φ ( b )⩽| X |−| Y | for all nonnegative integers a and b with a + b ⩽| X |. We shall prove that any unimodal and self-dual poset with the strong Hall property is a symmetric chain order. This result will also be used to show that the inversion poset S 5 is a symmetric chain order.
16321846
Semantics modeling based image retrieval system using neural networks
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.
748050
Oriented statistical nonlinear smoothing filter
This paper presents a nonlinear smoothing method which is based on an orientation-sensitive probability measure. By incorporating geometrical constraints through the coupling structure, we obtain a robust nonlinear smoothing algorithm. Even when noise is substantial the proposed smoothing algorithm can still preserve salient boundaries. Compared with anisotropic diffusive approaches, the proposed nonlinear algorithm not only performs better in preserving boundaries but also has a non-uniform stable state, whereby reliable results are available within a fixed number of iterations independent of images. A system using the proposed method and LEGION network has been developed and applied in noisy image segmentation and hydrographic feature extraction from digital ortho-photo quadrangles. Experimental results using synthetic and real images are provided.