Computer Algebra and Neurodynamics
We review the capabilities of computer algebra and the characteristics of neurodynamics. Possible applications of computer algebra to the study of neurodynamics are then discussed. We have investigated some of the applications, in particular, to the computer aided analysis and derivation of neurodynamics by using and developing tools in computer algebra systems. Part of our own work in this direction is summarized.

title: GEOTHER: A Geometry Theorem Prover

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: 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: Integrating ecoinformatics resources on the semantic web
abstract: We describe ELVIS (the Ecosystem Location Visualization and Information System), a suite of tools for constructing food webs for a given location. We express both ELVIS input and output data 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. This is an end-to-end case study of the semantic web's utility for ecological and environmental research.

title: Protein Sequences Classification Using Modular RBF Neural Networks
abstract: A protein super-family consists of proteins which share amino acid sequence homology and which may therefore be functionally and structurally related. One of the benefits from this category grouping is that some hint of function may be deduced for individual members from information on other members of the family. Traditionally, two protein sequences are classified into the same class if they have high homology in terms of feature patterns extracted through sequence alignment algorithms. These algorithms compare an unseen protein sequence with all the identified protein sequences and returned the higher scored protein sequences. As the sizes of the protein sequence databases are very large, it is a very time consuming job to perform exhaustive comparison of existing protein sequence. Therefore, there is a need to build an improved classification system for effectively identifying protein sequences. This paper presents a modular neural classifier for protein sequences with improved classification criteria. The intelligent classification techniques described in this paper aims to enhance the performance of single neural classifiers based on a centralized information structure in terms of recognition rate, generalization and reliability. The architecture of the proposed model is a modular RBF neural network with a compensational combination at the transition output layer. The connection weights between the final output layer and the transition output layer are optimized by delta rule, which serve as an integrator of the local neural classifiers. To enhance the classification reliability, we present two heuristic rules to apply to decision-making. Two sets of protein sequences with ten classes of superfamilies downloaded from a public domain database, Protein Information Resources (PIR), are used in our simulation study. Experimental results with performance comparisons are carried out between single neural classifiers and the proposed modular neural classifier.

title: IMDS: intelligent malware detection system
abstract: The proliferation of malware has presented a serious threat to the security of computer systems. Traditional signature-based anti-virus systems fail to detect polymorphic and new, previously unseen malicious executables. In this paper, resting on the analysis of Windows API execution sequences called by PE files, we develop the Intelligent Malware Detection System (IMDS) using Objective-Oriented Association (OOA) mining based classification. IMDS is an integrated system consisting of three major modules: PE parser, OOA rule generator, and rule based classifier. An OOA_Fast_FP-Growth algorithm is adapted to efficiently generate OOA rules for classification. A comprehensive experimental study on a large collection of PE files obtained from the anti-virus laboratory of King-Soft Corporation is performed to compare various malware detection approaches. Promising experimental results demonstrate that the accuracy and efficiency of our IMDS system out perform popular anti-virus software such as Norton AntiVirus and McAfee VirusScan, as well as previous data mining based detection systems which employed Naive Bayes, Support Vector Machine (SVM) and Decision Tree techniques.

title: Gene Selection Through Sensitivity Analysis of Support Vector Machines
abstract: We present a novel approach to gene selection for microarry data through the sensitivity analysis of support vector machines (SVMs). A new measurement (sensitivity) is defined to quantify the saliencies of individual features (genes) by analyzing the discriminative function in SVMs. Our feature selection strategy is first to select the features with higher sensitivities but meanwhile keep the remaining ones, and then refine the selected subset by tentatively substituting some part with fragments of the previously rejected features. The accuracy of our method is validated experimentally on the benchmark microarray datasets.

title: A structure-based approach for multimedia information filtering
abstract: While multimedia documents are sequentially presented to users, an information filtering (IF) system is useful to achieve a good retrieval performance in terms of both quality and efficiency. Conventional approaches for designing an IF system are based on the user's evaluation on information relevance degree (IRD), but ignore other attributes in system design such as relative importance of the data in a collection of multimedia documents. In this paper, we aim at developing a framework of designing structure-based multimedia IF systems, which incorporates the characteristics of the importance and relevance of multimedia documents. A method of calculating the values of relative importance degree of multimedia documents is proposed. Furthermore, these values are combined into the IRD of multimedia documents to improve the representation of user profiles. An illustrative example is given to demonstrate the proposed techniques.