Publication search

Measuring Intelligence and Growth Rate: Variations on Hibbard’s Intelligence Measure

Published in Journal of Artificial General Intelligence

In 2011, Hibbard suggested an intelligence measure for agents who compete in an adversarial sequence prediction game. We argue that Hibbard’s idea should actually be considered as two separate ideas: first, that the intelligence of such agents can be measured based on the growth rates of the runtimes of the competitors that they defeat; and second,...

Picosecond cubic and quintic nonlinearity of lithium niobate at 532 nm

The nonlinear (NL) optical response of bulk lithium niobate (LiNbO$_3$) was investigated at 532 nm using the second harmonic of a Nd:YAG laser delivering pulses of 12 ps. The experiments were performed using the D4$\sigma$ method combined with the conventional Z-scan technique. Two- and three-photon absorption coefficients equal to 0.27 cm/GW and 2...

Equivalence of Hidden Markov Models with Continuous Observations

We consider Hidden Markov Models that emit sequences of observations that are drawn from continuous distributions. For example, such a model may emit a sequence of numbers, each of which is drawn from a uniform distribution, but the support of the uniform distribution depends on the state of the Hidden Markov Model. Such models generalise the more ...

Convergence of the weak K\"ahler-Ricci Flow on manifolds of general type

We study the K\"ahler-Ricci flow on compact K\"ahler manifolds whose canonical bundle is big. We show that the normalized K\"ahler-Ricci flow has long time existence in the viscosity sense, is continuous in a Zariski open set, and converges to the unique singular K\"ahler-Einstein metric in the canonical class. The key ingredient is a viscosity the...

A natural extension to the convex hull problem and a novel solution

We study a natural extension to the well-known convex hull problem by introducing multiplicity: if we are given a set of convex polygons, and we are allowed to partition the set into multiple components and take the convex hull of each individual component, what is the minimum total sum of the perimeters of the convex hulls? We show why this proble...