He Mokopirirākau: Cliff Curtis

Cliff hangers

The peregrine falcon holds a special place in the minds of environmentalists and conservation biologists. The crash in its population throughout the 1950s and 60s was linked to the rapidly increasing use of agricultural organochlorine pesticides which led to a thinning of the birds’ eggshells and dramatic breeding failure. Since the widespread ban on the use of these chemicals, populations have...

Cliff hanger

The asparagus season has recently ended for northern hemisphere crops. Tradition has it that, at the summer solstice, growers stop cutting spears to allow the plant to grow and produce enough resources to generate spears for the next spring’s crop. The plant is becoming increasingly fashionable and production is increasing to meet demand. But the cultivated asparagus has a wild relative that is...

CLiFF Notes

Stochastic Discrete Clenshaw-Curtis Quadrature

The partition function is fundamental for probabilistic graphical models—it is required for inference, parameter estimation, and model selection. Evaluating this function corresponds to discrete integration, namely a weighted sum over an exponentially large set. This task quickly becomes intractable as the dimensionality of the problem increases. We propose an approximation scheme that, for any...

The Finitary Andrews-Curtis Conjecture

The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent importance for computational group theory. It also resolves a question asked in [5] and shows that a computation in finite groups cannot lead to a counterexam...