We study statistics of tiles in random incommensurable Kakutani sequences partitions Rd. provide explicit formulas that illustrate the dependence on combinatorial structure, volumes participating and entropy underlying substitution system. These improve previous results for non-random multiscale tilings, imply a gap distribution formula Delone sets associated with tilings real line.

We have recently provided evidence for anticipatory grasp control mechanisms in the kinematic domain by showing that subjects modulate digit placement on an object based on its center of mass (CM) when it can be anticipated (Lukos et al., 2007). This behavior relied on sensorimotor memories about digit contact points and forces required for optimal manipulation. We found that accurate sensorimo...

introduction: children with attention deficit hyperactivity disorder have problem in sustain attention that is necessary for learning. the purpose of present study is comparing explicit and implicit memory in children with attention deficit disorder and typically developing children. material and methods: in present cross sectional study, fifteen children with attention deficit disorder compare...

In this report, the explicit probability density functions of the random Euclidean distances associated with regular hexagons are given, when the two endpoints of a link are randomly distributed in the same hexagon, and two adjacent hexagons sharing a side, respectively. Simulation results show the accuracy of the obtained closed-form distance distribution functions, which are important in a wi...

Let n be an integer and A0, . . . , Ak random subsets of {1, . . . , n} of fixed sizes a0, . . . , ak, respectively chosen independently and uniformly. We provide an explicit and easily computable total variation bound between the distance from the random variable W = | ∩j=0 A j|, the size of the intersection of the random sets, to a Poisson random variable Z with intensity λ = EW . In particul...

We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even when the dimension is large or infinite. Some applications to principal component analysis a...