We use algebraic geometry to study matrix rigidity, and more generally, the complexity of computing a matrix-vector product, continuing a study initiated in [13, 11]. In particular, we (i) exhibit many non-obvious equations testing for (border) rigidity, (ii) compute degrees of varieties associated to rigidity, (iii) describe algebraic varieties associated to families of matrices that are expec...

Abstract It is often thought that some general terms or kind terms, in particular natural are rigid designators, and a properly extended notion of singular-term rigidity can help explain the behaviour such terms. In this article, I argue only legitimate general-term trivial one identify crucial asymmetries between posteriori necessary truths involving names If we pay attention to these asymmetr...

There has been increasing interest in understanding how firms undertake non-price adjustment activities, especially in situations where prices may be rigid despite changes in market conditions. Using scanner price data for over 4500 different food products from a large US supermarket chain, we document periods of rigidity in product additions and deletions: new products are less likely to be in...

M . Ratner's theorem on the rigidity of horocycle flows is extended to the rigidity of horospherical foliations on bundles over finite-volume locally-symmetric spaces of non-positive sectional curvature, and to other foliations of the same algebraic form.

Let P be a (non necessarily convex) embedded polyhedron in R, with its vertices on an ellipsoid. Suppose that the interior of P can be decomposed into convex polytopes without adding any vertex. Then P is infinitesimally rigid. More generally, let P be a polyhedron bounding a domain which is the union of polytopes C1, · · · , Cn with disjoint interiors, whose vertices are the vertices of P . Su...

We study the boundary and lens rigidity problems on domains without assuming convexity of boundary. show that such rigidities hold when domain is a simply connected compact Riemannian surface conjugate points. For more general class non-trapping surfaces with no points, we rigidity. also prove injectivity X-ray transform tensors in variety settings non-convex and, some situations, allowing non-...