Emerging research in computer graphics, inverse problems, and machine learning requires us to differentiate optimize parametric discontinuities. These discontinuities appear object boundaries, occlusion, contact, sudden change over time. In many domains, such as rendering physics simulation, we the parameters of models that are expressed integrals discontinuous functions. Ignoring during differ...

A recent econometric literature has critiqued the use of regression discontinuities where administrative borders serve as ‘cutoff’. Identification in this context is difficult since multiple treatments can change at cut-off and individuals easily sort on either side border. This note extends difference-in-discontinuities framework discussed Grembi et al. (2016) to a geographic setting. paper fo...

The interrelationships of the fundamental biological processes natural selection, mutation, and stochastic drift are quantified by the entropy rate of Moran processes with mutation, measuring the long-run variation of a Markov process. The entropy rate is shown to behave intuitively with respect to evolutionary parameters such as monotonicity with respect to mutation probability (for the neutra...

We present a fractal technique for addressing geometric analogy problems from the Raven's Standard Progressive Matrices test of general intelligence. In this method, an image is represented fractally, capturing its inherent selfsimilarity. We apply these fractal representations to problems from the Raven's test, and show how these representations afford a new method for solving complex geometri...