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...

Wiener-Hopf plus Hankel operators acting between Lebesgue spaces on the real line are studied in view of their invertibility, one sided-invertibility, Fredholm property, and the so-called n and d–normal properties. This is done in two different cases: (i) when the Fourier symbols of the operators are unitary functions, and (ii) when the Fourier symbols are related with sectorial elements appear...

We investigate a generalization of Hopf algebra slq (2) by weakening the invertibility of the generator K, i.e. exchanging its invertibility KK = 1 to the regularity KKK = K. This leads to a weak Hopf algebra wslq (2) and a J-weak Hopf algebra vslq (2) which are studied in detail. It is shown that the monoids of group-like elements of wslq (2) and vslq (2) are regular monoids, which supports th...

The solvability of the regulator equation for a general nonlinear system is discussed in this paper by using geometric method. The ‘feedback’ part of the regulator equation, that is, the feasible controllers for the regulator equation, is studied thoroughly. The concepts of minimal output zeroing control invariant submanifold and left invertibility are introduced to find all the possible contro...