Cardiac measures of heart period and high-frequency heart period variability are increasingly employed as dependent variables in studies of social and emotional development in infancy and childhood. This study describes significant developmental increases in these measures in a longitudinal sample assessed at 4, 9, 14, 24, and 48 months of age. In addition, developmental changes in the characte...

To get some intuition, we begin with the group of real numbers R under addition. A trivial upper bound for the size of a sum set is |A + A| ≤ |A| 2+|A| 2 (equality is obtained when every pair of elements of A have a distinct sum). If we build A by taking elements of R at random, then we expect |A+A| to be very close to this upper bound, since the probability of a1+a2 = a3+a4 is very small (wher...

The Clifford tori in S constitue a one-parameter family of flat, two-dimensional, constant mean curvature (CMC) submanifolds. This paper demonstrates that new, topologically non-trivial CMC surfaces resembling a pair of neighbouring Clifford tori connected at a sub-lattice consisting of at least two points by small catenoidal bridges can be constructed by perturbative PDE methods. That is, one ...

The retro-cue effect (RCE) describes superior working memory performance for validly cued stimulus locations long after encoding has ended. Importantly, this happens with delays beyond the range of iconic memory. In general, the RCE is a stable phenomenon that emerges under varied stimulus configurations and timing parameters. We investigated its susceptibility to dual-task interference to dete...

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.

Adolescence is a time of change and period personal social transition, which imposes degree risk taking with the goal achieving developmental benefits associated these changes [...]

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.