We present novel wavelet-based inpainting algorithms. Applying ideas from anisotropic regularization and diffusion our models can better handle degraded pixels at edges. We interpret our algorithms within the framework of forward-backward splitting methods in convex analysis and prove that the conditions to ensure their convergence are fulfilled. Numerical examples illustrate the good performan...

The question of how to simultaneously promote growth and diffusion of ideas exhibits difficult yet pressing tradeoffs. To economists, it concerns the relationship between economic health and incentives for sharing information. When does the stimulus to innovation, founded on a profit motive, collide with access to information source material, which exhibits properties of a public good? To the l...

The equation describing the conduction of heat in solids has, over the past two centuries, proved to be a powerful tool for analyzing the dynamic motion of heat as well as for solving an enormous array of diffusion-type problems in physical sciences, biological sciences, earth sciences, and social sciences. This equation was formulated at the beginning of the nineteenth century by one of the mo...

Arguments about the spread of gender egalitarian values through a population highlight several sources of change. First, structural arguments point to increases in the proportion of women with high education, jobs with good pay, commitment to careers outside the family, and direct interests in gender equality. Second, value-shift arguments contend that gender norms change with economic affluenc...

Signals, systems, and control provide a powerful paradigm for intellectual thought in science and technology, yet these ideas have had virtually no penetration in K-12 education. In this paper we provide some suggestions for introducing these concepts into primary and secondary education, thus promoting their diffusion throughout the academic disciplines.

Viral products and ideas are intuitively understood to grow through a person-to-person diffusion process analogous to the spread of an infectious disease; however, until recently it has been prohibitively difficult to directly observe purportedly viral events, and thus to rigorously quantify or characterize their structural properties. Here we propose a formal measure of what we label “structur...