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A substitution ϕ is strong Pisot if its abelianization matrix is non-singular and all eigenvalues except the Perron-Frobenius eigenvalue have modulus less than one. For strong Pisot ϕ that satisfies a no cycle condition and for which the translation flow on the tiling space T ϕ has pure discrete spectrum, we describe the collection T P ϕ of pairs of(More)
If ϕ is a Pisot substitution of degree d, then the inflation and substitution homeomorphism Φ on the tiling space T Φ factors via geometric realization onto a d-dimensional solenoid. Under this realization, the collection of Φ-periodic asymptotic tilings corresponds to a finite set that projects onto the branch locus in a d-torus. We prove that if two such(More)
Anderson and Putnam showed that the cohomology of a substitution tiling space may be computed by collaring tiles to obtain a substitution which " forces its border. " One can then represent the tiling space as an inverse limit of an inflation and substitution map on a cellular complex formed from the collared tiles; the cohomology of the tiling space is(More)
There are few functionally meaningful clinical measures used to guide management of patients with ALS. Falls are common, can be debilitating, and result in increased health care costs. We assessed the performance and ability to predict falls of the Timed Up and Go (TUG) test, which quantifies walking ability, in a prospective longitudinal study. Thirty-one(More)
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