Self-Edjing Piling Platform Cantilevered from Damaged Quay Walls for Waterfront Piling

Piling of multiscale random models

This paper considers random balls in a D-dimensional Euclidean space whose centers are prescribed by a homogeneous Poisson point process and whose radii are forced to be in a finite interval with a power-law distribution. Random fields are constructed by counting the number of covering balls at each point. We are mainly interested in the simulation of these fields and in the empirical estimatio...

Piling Up Pillar[5]arenes To Self-Assemble Nanotubes.

New liquid-crystalline pillar[5]arene derivatives have been prepared by grafting first-generation Percec-type poly(benzylether) dendrons onto the macrocyclic scaffold. The molecules adopt a disc-shaped structure perfectly suited for self-organization into a columnar liquid-crystalline phase. In this way, the pillar[5]arene cores are piled up, thus forming a nanotubular wire encased within a she...

Piling Up, or Floating Away

Maximal Data Piling in Discrimination

In a binary discrimination problem, a linear classifier finds a linear hyperplane that separates two classes by partitioning the data space. Especially in a High Dimension Low Sample Size (HDLSS) setting, there are linear separating hyperplanes such that the projections of the training data points onto their normal direction vectors are identically zero, or some non-zero constant. Of interest i...

Piling-up Lemma for Markov Chains