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A Theory of Holographic Topology and the Mathematical Model of Brain Thinking

     Part ( I ) : A Theory about the Topological Structure for Holographic Space

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   Part ( II ) : The Topologic Structure and its Specificity in Higher Hierarchy for Holographic Space
     Part ( III ) : The Application and Exploration for Holographic Topology and Thinking Model
Paper Set:

1.  Bi Jiaxiang, A Topological Structure for Space of Holographic Memorizer and Model for Artificial Intelligence (1) (Part 1: A Theory about the Topological Structure for Holographic Space), Science Exploration, (1985) 4, p73-83
  Abstract :
  In the paper, a topological structure of holographic space is introduced into and set up three axioms:
  a)  Entirety correlativity axiom for the information structure;
  b)  Equivalence potency axiom for the measureable subspace dismembered;
  c)  Definition domain invariance axiom for the linear combination.
  According to previous axioms, the paper combines the holographic space with topology, and discusses the problems about the basic structure and the ordered structure of an information system as well as the properties of  holographic space. And carries out a research about the entirety invariance and the definition domain invariance for the high-stratum structure of  holographic space under continuous transformation on local space. A new metheod for  information processing: exiension and combination on holographic information space are brought forward. Thereby, it is indicated that the concept for entirety structure of information and the problem about  the topological relation between informations have become a very important problem in the exploration of artificial intelligence now.  (In Chinese)

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2.  Bi Jiaxiang, AI Model and Intelligence System, Proceeding of 2001 National Conference on Artificial Intelligence, Progress of Artificial Intelligence In China 2001, p71-74
  Abstract: In the paper, to discuss some problems of the characters structures and functions for AI model on topological relation, to make the analysis and research on the problem of virtual machine of information intelligence system. And to point out that the intelligence system may be divided into three hierarchies: physical hierarchy, physiological hierarchy and psychical hierarchy, then, to describe and discuss the structures, characters and processing processes of informations on these hierarchies in more detail. (In Chinese)
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3. Jiaxiang Bi, Research about Holographic Relation and Topological Structure for Thinking Process on Brain and Artificial Intelligence System, Proceedings of the 9th International Conference on Neural Information Processing (ICONIP'02), Vol. 2, p857-861
   Abstract:   In the paper, we describe and discuss the coding method and self-organizing process of the informations in brain, advance a kind of the encoding system: the "natural encoding system" which is particular to nature itself. In the problem of machine imitation, further discuss the topological property equivalence problem of artificial and natural intelligence system on the basis of hierarchy structures of the virtual machine. And put up specifically the three large hierarchy structures of the intelligence system: the physical hierarchy, the physiological hierarchy and the psychological hierarchy. And describe the relations between the three large hierarchies and the some sub-stratums, the encoding method of informations, the holographic frame structure of the informations, the functions of the virtual machine system on different levels, etc. in more detail.
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  4. Jiaxiang Bi, A Research for Association Process in Neural Network, Neural Network and computational Intelligence, p115-119, Zhejiang University press, 2002
  Abstract:  This paper presents the association method for the information and the self-organizing process for bottom information in artificial neural network, and discusses that by means of association method how to constitute a primal conception system in artificial neural network: a kind of the basic construction system for thinking. (In Chinese)
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  5.  Bi Jiaxiang, The Parallel Structure for Artificial Neural Network Model, Proceeding of The 13th National Conference on Neural Networks, p274-279
  Abstract: This paper puts forward a kind of artificial neural network model that has large-scale parallel structure, points out that when the neuron number in neural network reaches or exceeds certain quantity, neural network system can produce a kind of new high-level information structure on hardware entity structure by the action of information that gets, and points out the important meaning that forms this kind of information structure in artificial neural network model. (In Chinese)
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  6. Bi Jiaxiang, Human Cognizance Course and the Information Expression Method in Machine, Proceeding of 2003 National Conference on Artificial Intelligence (CAAI-10), Progress of Artificial Intelligence In China 2003, p88-92
   Abstract: This paper analyses human cognizance course, put forward the concept of visualization symbol system and abstract symbol system, and put forward the viewpoint which the locating of informations in conception system is the cognizance and understanding, and constructs some ordinary examples about the informations expression method in machine. (In Chinese)
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