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研究生:王玉梅
研究生(外文):Yu-Mei Wang
論文名稱:收縮臨界網路
論文名稱(外文):The Threshold Contraction Networks
指導教授:施茂祥
指導教授(外文):Mau-Hsiang Shih
學位類別:碩士
校院名稱:國立臺灣師範大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:英文
論文頁數:12
中文關鍵詞:全域穩定性臨界網路權重矩陣臨界向量收縮
外文關鍵詞:global asymptotic stabilitythreshold networksynaptic weight matrixthreshold vectorcontraction
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本篇論文主要解決臨界網路上一個全域穩定性問題.我們特徵化收縮臨界網路的權重矩陣與臨界向量,進而解決網路的全域穩定性問題.
A global asymptotic stability problem concerning the threshold network is settled. We describe
conditions on the synaptic weight matrix and the threshold vector such that the resulting threshold
network is a contraction.
1. Introduction ............................................ 1
2. The existence of the threshold contraction networks ..... 1
3. The characterization of the threshold contraction networks ................................................... 4
4. Concluding remarks ...................................... 10
References ................................................. 12
1. E. Goles, S. Martinez, Neural and Automata Networks : Dynamical Behavior and Applications, Kluwer Academic Publishers, Dordrecht, 1991.
2. F. Fogelman-Soulie, Y. Robert, M. Tchuente, Automata Networks in Computer Science : Theory and Applications, Nonlinear Science Series, Manchester Univ. Press, 1987.
3. F. Robert, Les Systemes Dynamiques Discrets, Mathematiques & Applications, Springer-Verlag, New York, 1995.
4. F. Robert, Discrete Iterations : A Metric Study, Springer Series in Computational Mathmatics, Springer-Verlag, 1986.
5. G. Weisbuch, S. Ryckebusch, Complex System Dynamics : An Introduction to Automata Networks, Santa Fe Institute, Studies in the Sciences of Complexity, Lecture Notes Vol II,
Addison-Wesley Publishing Company, New York, 1991.
6. J. Hertz, A. Krogh, R. G. Palmer, Introduction to The Theory of Neural Computation, Santa Fe Institute, Studies in the Sciences of Complexity, Lecture Notes Vol II, Addison-
Wesley Publishing Company, New York, 1991.
7. J. Gregg, Ones and Zeros : Understanding Boolean Algebra, Digital Circuits, and the Logic of Sets, IEEE press, 1998.
8. M.-H. Shih, J.-L. Ho, Solution of the boolean Markus-Yamabe problem, Advances in Appl. Math. 22, 60-102, 1999.
9. M.-H. Shih, J.-L. Dong, A combinatorial analogue of the Jacobian problem, preprint.
10. W. McCulloch and W. Pitts, A logical calculus of the ideas immanent in nervous activity, Bull. Math. Biophysics, 5 (1943), 115-133.
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