Suppose that ? 1 and ? 2 are geometrically nite, convex co-compact, discrete groups of isometries of real hyperbolic space H 3 whose domains of discontinuity are diieomorphic. We show that if the respective scattering matrices S 1 (s) and S 2 (s) diier from each other by a trace-class perturbation on the unitary axis Re(s) = 1, then ? 1 and ? 2 are conjugate in PSL(2; C). This result reeects th...

In this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of the problem.

We consider the problem of inference on a regression function at a point when the entire function satisfies a sign or shape restriction under the null. We propose a test that achieves the optimal minimax rate adaptively over a range of Hölder classes, up to a log logn term, which we show to be necessary for adaptation. We apply the results to adaptive one-sided tests for the regression disconti...

The probability that an incumbent in the United States House of Representatives is reelected has risen dramatically over the last half-century; it now stands at more than 98%. A number of authors and commentators claim that this rise is due to an increase in bipartisan gerrymandering in favor of incumbents. Using a regression discontinuity approach, we …nd evidence of the opposite e¤ect. All el...

The longitudinal and transverse coupling impedances of a small discontinuity on the accelerator chamber wall can be expressed in terms of the electric and magnetic polarizabil-ities of the discontinuity. The polarizabilities are geometrical factors and can be found by solving a static (electric or magnetic) problem. However, they are known in the explicit analytical form only for a few simple-s...

We proposed a computational visual saliency modeling technique. The proposed technique makes use of a color co-occurrence histogram (CCH) that captures not only “how many” but also “where and how” image pixels are composed into a visually perceivable image. Hence the CCH encodes image saliency information that is usually perceived as the discontinuity between an image region or object and its s...