Computer Aided Analysis and Derivation for Artificial Neural Systems
The theoretical analysis and derivation of artificial neural systems, which consists essentially of manipulating symbolic mathematical objects according to certain mathematical and biological knowledge, can be done more efficiently with computer assistance by using and extending methods and systems of symbolic computation. After presenting the mathematical characteristics of neural systems and a brief review on Lyapunov stability theory, the authors present some features and capabilities of existing systems and the extension for manipulating objects occurring in the analysis of neural systems. Some strategies and a toolkit developed in MACSYMA for computer-aided analysis and derivation are described. A concrete example is given to demonstrate the derivation of a hybrid neural system, i.e. a system which in its learning rule combines elements of supervised and unsupervised learning. Future work and research directions are indicated.

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: 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: 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: 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: 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.

title: GLIF3: a representation format for sharable computer-interpretable clinical practice guidelines
abstract: The Guideline Interchange Format (GLIF) is a model for representation of sharable computer-interpretable guidelines. The current version of GLIF (GLIF3) is a substantial update and enhancement of the model since the previous version (GLIF2). GLIF3 enables encoding of a guideline at three levels: a conceptual flowchart, a computable specification that can be verified for logical consistency and completeness, and an implementable specification that is intended to be incorporated into particular institutional information systems. The representation has been tested on a wide variety of guidelines that are typical of the range of guidelines in clinical use. It builds upon GLIF2 by adding several constructs that enable interpretation of encoded guidelines in computer-based decision-support systems. GLIF3 leverages standards being developed in Health Level 7 in order to allow integration of guidelines with clinical information systems. The GLIF3 specification consists of an extensible object-oriented model and a structured syntax based on the resource description framework (RDF). Empirical validation of the ability to generate appropriate recommendations using GLIF3 has been tested by executing encoded guidelines against actual patient data. GLIF3 is accordingly ready for broader experimentation and prototype use by organizations that wish to evaluate its ability to capture the logic of clinical guidelines, to implement them in clinical systems, and thereby to provide integrated decision support to assist clinicians.

title: Primitive Auditory Segregation Based on Oscillatory Correlation
abstract: Auditory scene analysis is critical for complex auditory processing. We study ouditory segregation from the neurol network perspective, and develop o fromework for primitive ouditory scene analysis. The architecture is a laterally coupled two-dimensional network of relaxation oscillators with a global inhibitor. One dimension represents time and another one represents frequency. We show that this architecture, plus systematic delay lines, can in real time group auditory features into a stream by phase synchrony and segregate different streams by desynchronization. The network demonstrates a set of psychological phenomena regarding primitive auditory scene onalysis, including dependency on frequency proximity and the rate of presentation, sequential capturing, and competition among different perceptual organizations. We offer a neurocomputotional theory-shifting synchronization theory-for explaining how auditory segregation might be achieved in the brain, and the psychological phenomenon of streom segregation. Possible extensions of the model are discussed.

title: 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.

title: Enhancing the estimation of plant Jacobian for adaptive neural inverse control
abstract: To implement the specialized learning of the inverse dynamic neuro-controller for controlling nonlinear plants with noise, it is strongly desirable that an on-line trained neural plant emluator may provide a reasonably good estimation of the plant Jacobian under noise environments. This paper presents an approach for enhancing the estimation of the plant Jacobian which is on-line used in direct adaptive neural inverse control schemes. The estimated teaching signals are obtained by using the input–output data available at each time step, and then they are used to train the neural plant emluator by a new cost function introduced in this work for training the plant emluator. Convergence theorem for the adaptive back-propagation algorithm and stability of the closed-loop control system are established by using the Lyapunov theory. Simulations are conducted for demonstrating the effectiveness of the proposed strategy.