The tilting method ranks each observation in terms of its influence on a general statistic, which can be mean, covariance, etc. This approach is based on ‘tilting’ or re-weighting each data value to achieve a given small change of the statistic, while minimizing the total amount of tilt. Then the influence ranking for each data corresponds to the rank of the tilted data weights. The tilting met...

We show how the tilting tensor product theorem for algebraic groups implies a reduction formula for decomposition numbers of the symmetric group. We use this to prove generalisations of various theorems of Erdmann and of James and Williams. Let G be a semisimple, connected, simply-connected algebraic group over an algebraically closed field k of characteristic p > 0. The simple modules L(λ) are...

Up to now, the standardised motion sickness index has been mainly developed for shipping and only takes into account the vertical motion experienced by passengers. This index did not correlate with motion sickness incidence during two field tests realised in tilting trains conducted during 1998 and 2000. Therefore, a railway motion sickness index is required to predict the lack of comfort likel...

We give a complete picture of the interaction between Koszul and Ringel dualities for graded standardly stratified algebras (in the sense of Cline, Parshall and Scott) admitting linear tilting (co)resolutions of standard and proper costandard modules. We single out a certain class of graded standardly stratified algebras imposing the condition that standard filtrations of projective modules are...

We begin the study of a tilting theory in certain truncated categories of modules G(Γ) for the current Lie algebra associated to a finite-dimensional complex simple Lie algebra, where Γ = P × J , J is an interval in Z, and P is the set of dominant integral weights of the simple Lie algebra. We use this to put a tilting theory on the category G(Γ′) where Γ′ = P ′×J , where P ′ ⊆ P is saturated. ...

Let Uq denote the quantum group associated with a finite dimensional semisimple Lie algebra. Assume that q is a complex root of unity of odd order and that Uq is obtained via Lusztig’s q-divided powers construction. We prove that all regular projective (tilting) modules for Uq are rigid, i.e., have identical radical and socle filtrations. Moreover, we obtain the same for a large class of Weyl m...

Bootstrap tilting con dence intervals could be the method of choice in many applications for reasons of both speed and accuracy With the right implementa tion tilting intervals are times as fast as bootstrap BC a limits in terms of the number of bootstrap sam ples needed for comparable simulation accuracy Thus bootstrap samples might su ce instead of Tilting limits have other desirable properti...

A tilting phase transition is predicted for systems comprising rod like molecules which are irreversibly grafted to a flat surface, so that the non interacting rods are perpendicularly oriented. The transition is controlled by the grafting density ρ. It occurs as ρ increases as a result of the interplay between two energies. Tilt is favoured by the van-der-Waals attraction between the rods. It ...

Let T be a tilting object in a triangulated category which is equivalent to the bounded derived category of a finite-dimensional hereditary algebra. The text investigages the strong global dimension, in the sense of Ringel, of the opposite algebra A of the endomorphism algebra of T . This invariant is expressed in terms of the lengths of the sequences T0, . . . , Tl of tilting objects such that...