Let Yi, i ≥ 1, be i.i.d. random variables having values in an mdimensional manifold M ⊂ Rd and consider sums ∑ni=1 ξ(nYi, {n1/mYj }j=1), where ξ is a real valued function defined on pairs (y,Y), with y ∈Rd and Y ⊂Rd locally finite. Subject to ξ satisfying a weak spatial dependence and continuity condition, we show that such sums satisfy weak laws of large numbers, variance asymptotics and centr...

If you want to know what Waldo is like, why 20041, the effectiveness of introspection not just ask him? Such is the commonsense (Wilson, 2002), the degree of automaticity logic behind the self-report method of person(Mills & Hogan, 1978; Paulhus & Levitt, ality assessment. It remains the field's most 1986), and the meaning of nonresponding commonly used mode of assessment-by far (Tourangeau, 20...

If the finitely presented group G splits over the finitely presented subgroup C, then classes are constructed in H2 (∞) (G) which reflect the splitting and which serve as lower bounds for isoperimetric functions for G. It is proved that H2 (∞) (G) = 0 for all word hyperbolic groups G. A converse is obtained for the combination theorem for hyperbolic groups of Bestvina-Feighn. The Mayer-Vietoris...

We give conditions for the Mayer-Vietoris property to hold for the algebraic K-theory of blow-up squares of toric varieties and schemes, using the theory of monoid schemes. These conditions are used to relate algebraic K-theory to topological cyclic homology in characteristic p. To achieve our goals, we develop many notions for monoid schemes based on classical algebraic geometry, such as separ...

8. Introduction Critical points of distance functions Toponogov's theorem; first application:a Background on finiteness theorems Homotopy Finiteness Appendix. Some volume estimates Betti numbers and rank Appendix: The generalized Mayer-Vietoris estimate Rank, curvature and diameter Ricci curvature, volume and the Laplacian Appendix. The maximum principle Ricci curvature, diameter growth and fin...

A second Leray spectral sequence of relative hypercohomology is constructed. (This is skew in generality to an earlier one constructed by S. Lubkin [(1968) Ann. Math. 87, 105-255].) The Mayer-Vietoris sequence of relative hypercohomology [Lubkin, S. (1968) Ann. Math. 87, 105-255] is also generalized.

Results of Bunge and Funk and of Johnstone, providing constructively sound descriptions of the global points of the lower and upper powerlocales, are extended here to describe the generalized points and proved in a way that displays in a symmetric fashion two complementary treatments of frames: as suplattices and as preframes. We then also describe the points of the Vietoris powerlocale. In eac...

Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes constitutes an expensive task because of a combinatorial explosion in the complex size. For n points in R, we present a scheme to construct a 3 √ 2approximation of the multi-scale filtration of the L∞-Rips complex, which extends to a O(d0.25)approximation of the...

We introduce generalized Priestley quasi-orders and show that subalgebras of bounded distributive meet-semilattices are dually characterized by means of generalized Priestley quasi-orders. This generalizes the well-known characterization of subalgebras of bounded distributive lattices by means of Priestley quasiorders (Adams, Algebra Univers 3:216–228, 1973; Cignoli et al., Order 8(3):299– 315,...