COATES GRAPH APPROACH FOR GENERATING SYMBOLIC NETWORK FUNCTION

In this paper, symbolic code matrix ,constant matrix and count matrix are defined .The first twomatrices are used to describe the elemental expression of augmented matrix and the nede admittance equa-tion is thus obtained. The third matrix is used to obtain the incoming degree matrix, and according to thematrix all the 1- factors of the Coates graph are given. By using the data code, the determinant is expandedand the same items in the expansion are merged. Thus the symbolic network function in which no term can-cellation occurs is generated.     

Matlab语言与线性电路的符号仿真

目前的电路仿真软件通常是在电路中所有元件值都是给定的情况下得到一些数值结果，而非解析结果。该文利用Matlab的符号运算功能编程，通过节点列表法，实现了任意线性电路的自动解析求解，为电路分析提供了一个有效的辅助工具。     

Software tools for micro-analysis of programs

The paper proposes and describes several tools enabling their user to estimate the efficiency of Pascal or C-like programs. The approach consists of generating symbolic formulas expressing the efficiency of the programs being analyzed. The formulas are applicable to a variety of compiler-machine configurations. The actual numeric values of the variables in the symbolic formula are determined using linear programming techniques. The proposed approach reduces considerably the amount of benchmarking needed to analyze programs. Several examples are presented showing the applicability of the tools. The effort necessary to implement them is considerably reduced by the combined usage of Prolog and a symbolic formula manipulation package (Maple).     

Debugging programs that use macro-oriented data abstractions

Enhanced C (EC) is a set-oriented, extensible, C-like language. EC uses data abstractions to define new types. These data abstractions, called clusters, are macro-like devices that perform substitution on the typed syntax tree. Debugging programs that use clusters raise problems that are not encountered in ordinary programming languages. At compile time there is a need to determine and report whether the macro expansion will result in a legal program before this expansion actually takes place. At run-time the problems are how to account for replaced statements and how to handle variables whose types have been established by the clusters, variables that disappear, or variables whose names have been changed. This article presents these problems and their solutions as implemented by the EC compiler and the EC symbolic debugger. Similar debugging problems appear in other languages: The need to handle variables at run time is common to all languages that support data abstraction even if the abstractions are procedure oriented; also, a mild form of the problem of the replaced statement appears in inline procedure substitution of Ada. The solutions developed for the EC debugger apply to these cases as well.     

Genetic algorithms for symbolic clustering

This paper introduces a novel methodology for clustering of symbolic objects by making use of Genetic Algorithms (GAs). GAs are a family of computational models inspired by evolution. These algorithms encode potential solutions to specific problems on simple chromosome-like data structures and apply recombination operators to these structures so as to preserve critical information. A new type of representation for chromosome structure is presented here along with a new method for mutation. The efficacy of the proposed method is examined by application to numeric data of known number of classes and also to assertion type of symbolic objects drawn from the domain of fat oil, microcomputers, microprocessors and botany. The validity of the clusters obtained is examined.     

Artificial intelligence and symbols

The introduction of massive parallelism and the renewed interest in neural networks gives a new need to evaluate the relationship of symbolic processing and artificial intelligence. The physical symbol hypothesis has encountered many difficulties coping with human concepts and common sense. Expert systems are showing more promise for the early stages of learning than for real expertise. There is a need to evaluate more fully the inherent limitations of symbol systems and the potential for programming compared with training. This can give more realistic goals for symbolic systems, particularly those based on logical foundations.     

The interprocedural analysis and automatic parallelization of Scheme programs

Lisp and its descendants are among the most important and widely used of programming languages. At the same time, parallelism in the architecture of computer systems is becoming commonplace. There is a pressing need to extend the technology of automatic parallelization that has become available to Fortran programmers of parallel machines, to the realm of Lisp programs and symbolic computing. In this paper we present a comprehensive approach to the compilation of Scheme programs for shared-memory multiprocessors. Our strategy has two principal components:interprocedural analysis andprogram restructuring. We introduceprocedure strings andstack configurations as a framework in which to reason about interprocedural side-effects and object lifetimes, and develop a system of interprocedural analysis, using abstract interpretation, that is used in the dependence analysis and memory management of Scheme programs. We introduce the transformations ofexit-loop translation andrecursion splitting to treat the control structures of iteration and recursion that arise commonly in Scheme programs. We propose an alternative representation for s-expressions that facilitates the parallel creation and access of lists. We have implemented these ideas in a parallelizing Scheme compiler and run-time system, and we complement the theory of our work with snapshots of programs during the restructuring process, and some preliminary performance results of the execution of object codes produced by the compiler.This work was supported in part by the National Science Foundation under Grant No. NSF MIP-8410110, the U.S. Department of Energy under Grant No. DE-FG02-85ER25001, the Office of Naval Research under Grant No. ONR N00014-88-K-0686, the U.S. Air Force Office of Scientific Research under Grant No. AFOSR-F49620-86-C-0136, and by a donation from the IBM Corportation.     

FracSym: Automated symbolic computation of Lie symmetries of fractional differential equations

In this paper, we present an algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs) using the method as described by Buckwar & Luchko (1998) and Gazizov, Kasatkin & Lukashchuk (2007, 2009, 2011). The method has been generalised here to allow for the determination of symmetries for FDEs with n$n$ independent variables and for systems of partial FDEs. The algorithm has been implemented in the new MAPLE package FracSym (Jefferson and Carminati 2013) which uses routines from the MAPLE symmetry packages DESOLVII (Vu, Jefferson and Carminati, 2012) and ASP (Jefferson and Carminati, 2013). We introduce FracSym by investigating the symmetries of a number of FDEs; specific forms of any arbitrary functions, which may extend the symmetry algebras, are also determined. For each of the FDEs discussed, selected invariant solutions are then presented.     

A weighted multivariate Fuzzy C-Means method in interval-valued scientific production data

Clustering is the process of organizing objects into groups whose members are similar in some way. Most of the clustering methods involve numeric data only. However, this representation may not be adequate to model complex information which may be: histogram, distributions, intervals. To deal with these types of data, Symbolic Data Analysis (SDA) was developed. In multivariate data analysis, it is common some variables be more or less relevant than others and less relevant variables can mask the cluster structure. This work proposes a clustering method based on fuzzy approach that produces weighted multivariate memberships for interval-valued data. These memberships can change at each iteration of the algorithm and they are different from one variable to another and from one cluster to another. Furthermore, there is a different relevance weight associated to each variable that may also be different from one cluster to another. The advantage of this method is that it is robust to ambiguous cluster membership assignment since weights represent how important the different variables are to the clusters. Experiments are performed with synthetic data sets to compare the performance of the proposed method against other methods already established by the clustering literature. Also, an application with interval-valued scientific production data is presented in this work. Clustering quality results have shown that the proposed method offers higher accuracy when variables have different variabilities.     

A decision support tool for the diagnosis of breast cancer based upon Fuzzy ARTMAP

This paper presents research into the application of the fuzzy ARTMAP neural network model to the diagnosis of cancer from fine-needle aspirates of the breast. Trained fuzzy ARTMAP networks are differently pruned so as to maximise accuracy, sensitivity and specificity. The differently pruned networks are then employed in a cascade of networks intended to separate cases into certain and suspicious classes. This mimics the predictive behaviour of a human pathologist. The fuzzy ARTMAP model also provides symbolic rule extraction facilities and the validity of the derived rules for this domain is discussed. Additionally, results are provided showing the effects upon network performance of different input features and different observers. The implications of the findings are discussed.