In an Euclidean d-space, the container problem asks to pack n equally sized spheres into a minimal dilate of a fixed container. If the container is a smooth convex body and d ≥ 2 we show that solutions to the container problem can not have a “simple structure” for large n. By this we in particular find that there exist arbitrary small r > 0, such that packings in a smooth, 3-dimensional convex ...

Spray drying a mixture of silica and polystyrene latex (PSL) colloids above the decomposition temperature of PSL results in the formation of porous silica particles. By appropriate selection of the experimental conditions, such as the use of a tubular temperature, the weight fraction of colloids, and the flow rate of carrier gas, the resulting silica particles contain organized pores with a hex...

Do we expect periodic grid cells to emerge in bats, or perhaps dolphins, exploring a three-dimensional environment? How long will it take? Our self-organizing model, based on ring-rate adaptation, points at a complex answer. The mathematical analysis leads to asymptotic states resembling face centered cubic (FCC) and hexagonal close packed (HCP) crystal structures, which are calculated to be ve...

A recent Ontario arbitral award is reshaping the way employers and employees must approach the legal duty to accommodate employees with disabilities in the workplace. Entrenched in both federal and provincial human rights legislation, the duty to accommodate imposes a legal obligation on employers to accommodate employees with disabilities unless such accommodation would cause undue hardship on...

Two-dimensional (2-D) spatially varying convolutional filters for three-dimensional (3-D) depth extrapolation are efficiently designed and implemented by using McClellan transformations. Although efficient, McClellan transformations only approximate circularly symmetric depth extrapolation filters. The accuracy of the extrapolation filters can be increased only at an increase in the computation...

We analyze the distribution of ∑ m i=1 vixi where x1, . . . ,xm are fixed vectors from some lattice L ⊂ R (say Z) and v1, . . . , vm are chosen independently from a discrete Gaussian distribution over Z. We show that under a natural constraint on x1, . . . ,xm, if the vi are chosen from a wide enough Gaussian, the sum is statistically close to a discrete Gaussian over L. We also analyze the cas...

We propose a graphics processor unit (GPU)-accelerated method for real-time computing and rendering cellular automata (CA) that is applied to hexagonal grids. Based on our previous work [9] –which introduced first and second dimensional cases– this paper presents a model for hexagonal grid algorithms. Proposed method is novel and it encodes and transmits large CA key-codes to the graphics card ...