The main purpose of this paper is to prove that the jump discontinuity set of the solution of the total variation based denoising problem is contained in the jump set of the datum to be denoised. We also prove some extensions of this result for the total variation minimization ow, for anisotropic norms and for some more general convex functionals which include the minimal surface equation case ...

In a two-party legislature, districts represented by the majority may receive greater funds if majority-party legislators have greater proposal power or disproportionately form coalitions with each other. Funding types received by districts may depend on their legislators’ party identity when party preferences differ. Estimates from the United States, using fixedeffect and regression-discontinu...

Representations of space in the social sciences are remarkably dependent on images of break, rupture and disjunction. The distinctiveness of societies, nations, and cultures is predicated on a seemingly unproblematic division of space, on the fact that they occupy “naturally” discontinuous spaces. The premise of discontinuity forms the starting point from which to theorize contact, conflict and...

We characterize the class of strategy-proof social choice functions on the domain of symmetric single-peaked preferences. This class is strictly larger than the set of generalized median voter schemes (the class of strategy-proof and tops-only social choice functions on the domain of single-peaked preferences characterized by Moulin (1980)) since, under the domain of symmetric single-peaked pre...

We report a discovery of a new high redshift quasar at z = 5.96, observed with the FOCAS long-slit spectrograph on board the Subaru telescope. The spectrum shows strong and broad Lyα+NV emission lines with a sharp discontinuity to the blue side. A Lyβ+OVI emission line is also detected, providing a consistent redshift measurement with the Lyα+NV emission. The QSO has an absolute magnitude of MA...

Measures for the degree of non-projectivity of dependency grammar have received attention both on the formal and on the empirical side. The empirical characterization of discontinuity in constituent treebanks annotated with crossing branches has nevertheless been neglected so far. In this paper, we present two measures for the characterization of both the discontinuity of constituent structures...

Motivated by edge behaviour reported for biological organisms, we show that random walks with a bias at a boundary lead to a discontinuous probability density across the boundary. We continue by studying more general diffusion processes with such a discontinuity across an interior boundary. We show how hitting probabilities, occupancy times and conditional occupancy times may be solved from pro...

We focus on the problem of adaptive estimation of signal singularities from indirect and noisy observations. A typical example of such a singularity is a discontinuity (change–point) of the signal or of its derivative. We develop a change–point estimator which adapts to the unknown smoothness of a nuisance deterministic component and to an unknown jump amplitude. We show that the proposed estim...

U.S. cities are limited in their ability to set policy. Can these constraints mute the impact of mayors’ partisanship on policy outcomes? We hypothesize that mayoral partisanship will more strongly affect outcomes in policy areas where there is less shared authority between local, state, and federal governments. To test this hypothesis, we create a novel dataset combining U.S. mayoral election ...

On the basis of the integrable Kaup-Boussinesq version of the shallow water equations, an analytical theory of undular bores is constructed. The problem of the decay of an initial discontinuity is considered.