University of Victoria

The Perceptron model was proposed as early as the 1950's as a toy model of a one-layer neural network. The basic model consists of a set of solutions (either the Hamming cube or the sphere of dimension n) and a set of constraints given by independent...

Random projections of high-dimensional probability measures have gained much attention in asymptotic convex geometry and high-dimensional statistics. While fluctuations at the level of the central limit theorem have been classically studied, only...

I will describe the large-scale behavior of a random growth model (Internal DLA) on random planar maps which approximate a random fractal surface embedded in the plane (Liouville quantum gravity, LQG). No prior knowledge of these objects will be...

If a tricky devil challenged you to complete a Sudoku puzzle of their design, what restrictions could you place on their design to guarantee it was impossible for them to thwart your attempts? More specifically, if you could dictate exactly how many...

An $(m,n)$-generalized bent function is a function from $\mathbb{Z}_2^n$ to $\mathbb{Z}_m$ so that its associated Fourier transformations have constant absolute value. It is known that an $(m,n)$-generalized bent function exists whenever one of the...

How many lines are spanned by a set of planar points?. If the points are collinear, then the answer is clearly "one". If they are not collinear, however, several different answers exist when sets are finite and "how many" is measured by cardinality...

Reproductive value is the relative expected number of off-springs produced by an individual in its remaining lifetime. It is also an invariant function for population processes with birth and death rates independent of the time except in cases when...

For a finite set X, a family F of subsets of X is said to be increasing if any set A that contains B in F is also in F. The p-biased product measure of F increases as p increases from 0 to 1, and often exhibits a drastic change around a specific...

A collection of families $(\F_{1}, \F_{2} , \cdots , \F_{k}) \in \mathcal{P}([n])^k$ is \emph{cross-Sperner} if there is no pair $i \not= j$ for which some $F_i \in \F_i$ is comparable to some $F_j \in \F_j$. Two natural measures of the `size' of...