We introduce a novel family of geometrical transformations for the non-rigid registration of medical images, called polyrigid and polyaffine. These transformations have nice mathematical properties, including differentiability and invertibility (i.e diffeomorphism). They are parameterized by a small number of intuitive parameters which allow to recover locally rigid and locally affine deformati...

A Declarative Subtyping 6 A.1 Properties of Well-Formedness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1 Proposition (Weakening) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Proposition (Substitution) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 A.2 Reflexivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

We raise, and provide an (unsatisfactory) answer to, the title's question: why, unlike all other fields, does the gravitational " metric " variable not have zero vacuum? After formulating, without begging it, we exhibit additions to the conventional action that express existence of the inverse through a field equation. The metric variable's invertibility is (on a par with its dimensionality and...

Spectral Sparsification and Restricted Invertibility Nikhil Srivastava 2010 In this thesis we prove the following two basic statements in linear algebra. Let B be an arbitrary n×m matrix where m ≥ n and suppose 0 < ε < 1 is given. 1. Spectral Sparsification. There is a nonnegative diagonal matrix Sm×m with at most dn/ε2e nonzero entries for which (1− ε)2BBT BSBT (1 + ε)2BBT . Thus the spectral ...

We discuss the finite dimensional structure theory of L p ; in particular, the theory of restricted invertibility and classification of subspaces of ℓ n p .

We discuss the nite dimensional structure theory of L p ; in particular, the theory of restricted invertibility and classiication of subspaces of`n p .

Rational expectations solutions are usually derived by assuming that all state variables relevant to forward-looking behaviour are directly observable, or that they are "...an invertible function of observables" (Mehra and Prescott, 1980). Using a framework that nests linearised DSGE models, we give a number of results useful for the analysis of linear rational expectations models with restrict...