Dancing with the Junta Again

Distribution-free Junta Testing

We study the problem of testing whether an unknown n-variable Boolean function is a k-junta in the distribution-free property testing model, where the distance between functions is measured with respect to an arbitrary and unknown probability distribution over {0, 1}n. Our first main result is that distribution-free k-junta testing can be performed, with one-sided error, by an adaptive algorith...

Dancing with black holes

We describe efforts over the last six years to implement regularization methods suitable for studying one or more interacting black holes by direct N-body simulations. Three different methods have been adapted to large-N systems: (i) Time-Transformed Leapfrog, (ii) Wheel-Spoke, and (iii) Algorithmic Regularization. These methods have been tried out with some success on GRAPE-type computers. Spe...

Dancing with your ride

The technologies that make this possible are those of miniaturized electronics, digital communications, inexpensive distributed computation, and advanced control software. They enable us to get rid of most of the junk that currently encumbers automobiles – engines, power trains, dashboards, and steering wheels. They allow us to define a fundamentally new, radically restructured architecture for...

Dancing with Bees

Learning and Testing Junta Distributions

We consider the problem of learning distributions in the presence of irrelevant features. This problem is formalized by introducing a new notion of k-junta distributions. Informally, a distribution D over the domain X is a k-junta distribution with respect to another distribution U over the same domain if there is a set J ⊆ [n] of size |J | ≤ k that captures the difference between D and U . We ...