We derive a new representation of Lagrangian subspaces in the form ImΠT [ I X ] , where Π is a symplectic matrix which is the product of a permutation matrix and a real orthogonal diagonal matrix, and X satisfies |Xij | ≤ { 1 if i = j, √ 2 if i = j. This representation allows us to limit element growth in the context of doubling algorithms for the computation of Lagrangian subspaces and the sol...

By reparametrization, one may assume that γ is Lipschitz with constant equal to length(γ). We will also make use of the following simple (and well-known) criterion: a compact set Γ is the image of a rectifiable curve if and only if it is connected and H(Γ) < ∞. Indeed, one may choose γ so that length(γ) ≤ CH(Γ); see, for example, [1, 2]. Here and below, H denotes the one-dimensional Hausdorff m...

We introduce a new problem in the study of doubling spaces: Given a point set S and a target dimension d∗, remove from S the fewest number of points so that the remaining set has doubling dimension at most d∗. We present a bicriteria approximation for this problem, and extend this algorithm to solve a group of proximity problems.

We introduce a novel approach towards Harnack’s inequality in the context of spaces of homogeneous type. This approach, based on the socalled critical density property and doubling properties for weights, avoids the explicit use of covering lemmas and BMO.

The accuracy of time-to-contact (TTC) judgments for single approaching objects is well researched, however, close to nothing is known about our ability to make simultaneous TTC judgments for two or more objects. Such complex judgments are required in many everyday situations, for instance when crossing a multi-lane street or when engaged in multi-player ball games. We used a prediction-motion p...

The authors describe ACT-R/perceptual-motor (ACT-R/PM), an integrated theory of cognition, perception, and action that consists of the ACT-R production system and a set of perceptual-motor modules. Each module (including cognition) is essentially serial, but modules run in parallel with one another. ACT-R/PM can model simple dual tasks such as the psychological refractory period (PRP), includin...

We give new examples of discrete Schrδdinger operators with potentials taking finitely many values that have purely singular continuous spectrum. If the hull X of the potential is strictly ergodic, then the existence of just one potential x in X for which the operator has no eigenvalues implies that there is a generic set in X for which the operator has purely singular continuous spectrum. A su...