39,396 research outputs found
Geometry of Control-Affine Systems
Motivated by control-affine systems in optimal control theory, we introduce
the notion of a point-affine distribution on a manifold X - i.e., an affine
distribution F together with a distinguished vector field contained in F. We
compute local invariants for point-affine distributions of constant type when
dim(X)=n, rank(F)=n-1, and when dim(X)=3, rank(F)=1. Unlike linear
distributions, which are characterized by integer-valued invariants - namely,
the rank and growth vector - when dim(X)<=4, we find local invariants depending
on arbitrary functions even for rank 1 point-affine distributions on manifolds
of dimension 2
A Kind of Affine Weighted Moment Invariants
A new kind of geometric invariants is proposed in this paper, which is called
affine weighted moment invariant (AWMI). By combination of local affine
differential invariants and a framework of global integral, they can more
effectively extract features of images and help to increase the number of
low-order invariants and to decrease the calculating cost. The experimental
results show that AWMIs have good stability and distinguishability and achieve
better results in image retrieval than traditional moment invariants. An
extension to 3D is straightforward
Affine Disjunctive Invariant Generation with Farkas' Lemma
Invariant generation is the classical problem that aims at automated
generation of assertions that over-approximates the set of reachable program
states in a program. We consider the problem of generating affine invariants
over affine while loops (i.e., loops with affine loop guards, conditional
branches and assignment statements), and explore the automated generation of
disjunctive affine invariants. Disjunctive invariants are an important class of
invariants that capture disjunctive features in programs such as multiple
phases, transitions between different modes, etc., and are typically more
precise than conjunctive invariants over programs with these features. To
generate tight affine invariants, existing constraint-solving approaches have
investigated the application of Farkas' Lemma to conjunctive affine invariant
generation, but none of them considers disjunctive affine invariants
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