Let L be a countable language. We characterize, in terms of definable closure, those countable theories Σ of Lω1,ω(L) for which there exists an S∞-invariant probability measure on the collection of models of Σ with underlying set N. Restricting to Lω,ω(L), this answers an open question of Gaifman from 1964, via a translation between S∞-invariant measures and Gaifman’s symmetric measure-models w...

We propose a measure of clutter for real images that can be used to predict search times. This measure uses an efficient segmentation algorithm (P. Felzenszwalb & D. Huttenlocher, 2004) to count the number of regions in an image. This number is not uniquely defined, however, because it varies with the scale of segmentation. The relationship between the number of regions and the scale of segment...

For a subshift of nite type and a xed HH older continuous function, the zero measure invariant set of points where the Birkhoo averages do not exist is either empty or carries full Hausdorr dimension. Similar statements hold for conformal repellers and two-dimensional horseshoes, and the set of points where the pointwise dimensions, local entropies, Lyapunov exponents, and Birkhoo averages do n...

We provide an explicit representation of the nonequilibrium invariant measure for a chain of harmonic oscillators with conservative noise in the presence of stationary heat flow. By first determining the covariance matrix, we are able to express the measure as the product of Gaussian distributions aligned along some collective modes that are spatially localized with power-law tails. Numerical s...

Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only Borel me...