Neural blackboard architectures of combinatorial structures in cognition

Human cognition is unique in the way in which it relies on combinatorial (or compositional) structures. Language provides ample evidence for the existence of combinatorial structures, but they can also be found in visual cognition. To understand the neural basis of human cognition, it is therefore essential to understand how combinatorial structures can be instantiated in neural terms. In his recent book on the foundations of language, Jackendoff described four fundamental problems for a neural instantiation of combinatorial structures: the massiveness of the binding problem, the problem of 2, the problem of variables and the transformation of combinatorial structures from working memory to long-term memory. This paper aims to show that these problems can be solved by means of neural ‘blackboard’ architectures. For this purpose, a neural blackboard architecture for sentence structure is presented. In this architecture, neural structures that encode for words are temporarily bound in a manner that preserves the structure of the sentence. It is shown that the architecture solves the four problems presented by Jackendoff. The ability of the architecture to instantiate sentence structures is illustrated with examples of sentence complexity observed in human language performance. Similarities exist between the architecture for sentence structure and blackboard architectures for combinatorial structures in visual cognition, derived from the structure of the visual cortex. These architectures are briefly discussed, together with an example of a combinatorial structure in which the blackboard architectures for language and vision are combined. In this way, the architecture for language is grounded in perception

Algorithms for recognizing knots and 3-manifolds

This is a survey paper on algorithms for solving problems in 3-dimensional topology. In particular, it discusses Haken's approach to the recognition of the unknot, and recent variations.Comment: 17 Pages, 7 figures, to appear in Chaos, Fractals and Soliton

Crossing the symbolic threshold: a critical review of Terrence Deacon's The Symbolic Species

Terrence Deacon's views about the origin of language are based on a particular notion of a symbol. While the notion is derived from Peirce's semiotics, it diverges from that source and needs to be investigated on its own terms in order to evaluate the idea that the human species has crossed the symbolic threshold. Deacon's view is defended from the view that symbols in the animal world are widespread and from the extreme connectionist view that they are not even to be found in humans. Deacon's treatment of symbols involves a form of holism, as a symbol needs to be part of a system of symbols. He also appears to take a realist view of symbols. That combination of holism and realism makes the threshold a sharp threshold, which makes it hard to explain how the threshold was crossed. This difficulty is overcome if we take a mild realist position towards symbols, in the style of Dennett. Mild realism allows intermediate stages in the crossing but does not undermine Deacon's claim that the threshold is difficult to cross or the claim that it needs to be crossed quickly

A Necessary and Sufficient Condition for Graph Matching to be equivalent to Clique Search

This paper formulates a necessary and sufficient condition for a generic graph matching problem to be equivalent to the maximum vertex and edge weight clique problem in a derived association graph. The consequences of this results are threefold: first, the condition is general enough to cover a broad range of practical graph matching problems; second, a proof to establish equivalence between graph matching and clique search reduces to showing that a given graph matching problem satisfies the proposed condition;\ud and third, the result sets the scene for generic continuous solutions for a broad range of graph matching problems. To illustrate the mathematical framework, we apply it to a number of graph matching problems, including the problem of determining the graph edit distance