This paper discusses a view to capture discovery as a translation from non-symbolic to symbolic representation. First, a relation between symbolic processing and non-symbolic processing is discussed. An intermediate form was introduced to represent both of them in the same framework and clarify the difference of these two. Characteristic of symbolic representation is to eliminate quantitative m...

Sensitivity to numerical magnitudes is thought to provide a foundation for higher-level mathematical skills such as calculation. It is still unclear how symbolic (e.g. Arabic digits) and nonsymbolic (e.g. Dots) magnitude systems develop and how the two formats relate to one another. Some theories propose that children learn the meaning of symbolic numbers by scaffolding them onto a pre-existing...

in this paper, the exp-function method, with the aid of a symbolic computation system such as maple, is applied to the (2+1) -dimensional calogero bogoyavlanskii schiff equation. exact and explicit generalized solitary solutions are obtained in more general forms. the free parameters can be determined by initial or boundary conditions. the method is straightforward and concise, and its applicat...

The debate over symbolic versus sub-symbolic representations of human cognition has been continuing for thirty years, with little indication of a resolution. The argument is this: Does the human cognitive system use symbols as a representation of knowledge, and does it process symbols and their respective constituents? Or does the human cognitive system use a distributed representation of knowl...

The debate over symbolic versus sub-symbolic representations of human cognition has been continuing for thirty years, with little indication of a resolution. The argument is this: Does the human cognitive system use symbols as a representation of knowledge, and does it process symbols and their respective constituents? Or does the human cognitive system use a distributed representation of knowl...

In this paper, a new technique called symbolic kernel Principal Component Analysis (KPCA) is explored to develop a model for face representation and recognition. The conventional kernel PCA method extracts single valued features from the original image space to represent face images. The proposed method reduces the dimensionality of original image space by representing the face images as symbol...

Despite reports of mathematical talent in autism spectrum disorders (ASD), little is known about basic number processing abilities in affected children. We investigated number sense, the ability to rapidly assess quantity information, in 36 children with ASD and 61 typically developing controls. Numerical acuity was assessed using symbolic (Arabic numerals) as well as non-symbolic (dot array) f...

This paper enables symbolic ternary simulation of systems with large embedded memories. Each memory array is replaced with a behavioral model, where the number of symbolic variables used to characterize the initial state of the memory is proportional to the number of distinct symbolic memory locations accessed. The behavioral model provides a conservative approximation of the replaced memory ar...