We also study the connectedness of Pisot dual tilings which play an important role in the study of β-expansion, substitution and symbolic dynamical system. It is shown that each tile generated by a Pisot unit of degree 3 is arcwise connected. This is naturally expected since the digit set consists of consecutive integers as above. However surprisingly, we found families of disconnected Pisot du...

Qa := ∫ Qa ⊗ P (xj|b,b ′,x, a,y) dxj [Symbolic Substitution] For all bi in Qa Qa := [ Qa ⊗ P (bi|b,x, a,y) ] |b′i=1 ⊕ [ Qa ⊗ P (bi|b,x, a,y) ] |b′i=0 [Case ⊕] Compute final Q-Value (discount and add reward): Qa := R(b,x, a,y)⊕ (γ ⊗Qa) Note that ∫ f (xj)⊗δ[xj−h(z)]dxj = f (xj){xj/h(z)}where the latter operation indicates that any occurrence of xj in f (x ′ j) is symbolically substituted with the...

This paper was was first drafted in 2001 as a formalization of the system described in U.S. patent U.S. 7,392,174. It describes a system for implementing a parser based on a kind of cross-product over vectors of contextually similar words. It is being published now in response to nascent interest in vector combination models of syntax and semantics. The method used aggressive substitution of co...

One-dimensional cut-and-project point sets obtained from the square lattice in the plane are considered from a unifying point of view and in the perspective of aperiodic wavelet constructions. We successively examine their geometrical aspects, combinato-rial properties from the point of view of the theory of languages, and self-similarity with algebraic scaling factor θ. We explain the relation...

This short paper describes four submissions to the Symbolic Melodic Similarity task of the MIREX 2010 edition. All four submissions rely on a local-alignment approach between sequences of n-grams, and they differ mainly on the substitution score between two n-grams. This score is based on a geometric representation that shapes musical pieces as curves in the pitch-time plane. One of the systems...

We show how fundamental ideas from signal processing, multiscale theory and wavelets may be applied to non-linear dynamics. The problems from dynamics include itereated function systems (IFS), dy-namical systems based on substitution such as the discrete systems built on rational functions of one complex variable and the corresponding Julia sets, and state spaces of subshifts in symbolic dynami...

In this paper, recent developments of the HFVE vision-substitution system are described; and the initial results of a trial of the “Silooet” software are reported. The system uses audiotactile methods to present features of visual images to blind people. Included are details of presenting objects found in prepared media and live images; object-related layouts and moving effects (including symbo...

We present a method to learn maximal generalized decision rules from databases by integrating discretization, generalization and rough set feature selection. Our method reduces the data horizontally and vertically. In the first phase, discretization and generalization are integrated and the numeric attributes are discretized into a few intervals. The primitive values of symbolic attributes are ...

We present SyNRAC, a symbolic computation package for solving real algebraic constraints. Algorithms in SyNRAC are implemented on the Maple software and they are expected to provide many users with symbolic methods of dealing with practical problems in engineering. SyNRAC is to be aimed to support symbolic, numerical, and symbolic-numeric computation. Until now we have emphasized on symbolic me...