We show that the greedy spanner algorithm constructs a (1+ )-spanner of weight −O(d)w(MST) for a point set in metrics of doubling dimension d, resolving an open problem posed by Gottlieb [11]. Our result generalizes the result by Narasimhan and Smid [15] who showed that a point set in d-dimension Euclidean space has a (1+ )-spanner of weight at most −O(d)w(MST). Our proof only uses the packing ...

In this paper, we study the linear structure of sets A ⊂ Fn2 with doubling constant σ(A) < 2, where σ(A) := |A+A| |A| . In particular, we show that A is contained in a small affine subspace. We also show that A can be covered by at most four shifts of some subspace V with |V | ≤ |A|. Finally, we classify all binary sets with small doubling constant.

We study the properties of generalized solutions to the Monge– Ampère equation detD2u = ν, where the Borel measure ν satisfies a condition, introduced by Jerison, that is weaker than the doubling property. When ν = f dx, this condition, which we call D , admits the possibility of f vanishing or becoming infinite. Our analysis extends the regularity theory (due to Caffarelli) available when 0 < ...

Voluntary motor actions aim at and are thus governed by predictable action effects. Therefore, representations of an action's effects normally must become activated prior to the action itself. In 5 psychological refractory period experiments the authors investigated whether the activation of such effect representations coincides with the response selection stage of information-processing theori...

The Psychological Refractory Period (PRP) paradigm is a dual-task procedure that can be used to examine the resource demands of specific cognitive processes. Inferences about the underlying processes are typically based on performance in the second of two speeded tasks. If the effect of a factor manipulated in Task 2 decreases as the stimulus onset asynchrony (SOA) between tasks decreases (unde...

In this paper, we review two types of doubling algorithm and some techniques for analyzing them. We then use the techniques to study the doubling algorithm for three different nonlinear matrix equations in the critical case. We show that the convergence of the doubling algorithm is at least linear with rate 1/2. As compared to earlier work on this topic, the results we present here are more gen...

We consider perturbations of Dirac type operators on complete, connected metric spaces equipped with a doubling measure. Under a suitable set of assumptions, we prove quadratic estimates for such operators and hence deduce that these operators have a bounded functional calculus. In particular, we deduce a Kato square root type estimate.

A large literature on multitasking bottlenecks suggests that people cannot generally make decisions or select responses in two different tasks at the same time. However, these tasks have all involved retrieving preinstructed responses, rather than spontaneously choosing actions based on anticipated hedonic consequences. To assess whether the same bottlenecks encompasses voluntary choices, a gam...