The diffusion of innovations according to Rogers. With successive groups of consumers adopting the new technology (shown in blue), its market share (yellow) will eventually reach the saturation level. In mathematics the S curve is known as the logistic function. Diffusion of Innovations is a theory that seeks to explain how, why, and at what rate new ideas and technology spread through cultures...

There is a long-standing controversy between two models of the Neolithic transition. The demic model assumes that the Neolithic range expansion was mainly due to the spread of populations, and the cultural model considers that it was essentially due to the spread of ideas. Here we integrate the demic and cultural models in a unified framework. We show that cultural diffusion explains ∼40% of th...

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machin...

The goal of quantitative photoacoustic tomography is to determine optical and acoustical material properties from initial pressure maps such as those obtained, for instance, from photoacoustic imaging. The most relevant parameters are absorption, diffusion, and Grüneisen coefficients, all of which can be heterogeneous. Recent work by Bal and Ren shows that, in general, unique reconstruction of ...

The Bicoid (Bcd) morphogen is essential for pattern formation in fruit flies. It forms an exponential concentration gradient along the embryo AP axis and turns on cascades of target genes in distinct anterior domains. The most commonly accepted model for gradient formation assumes that Bcd travels by simple diffusion and is uniformly degraded across syncytial embryos, yet several recent studies...

Consistently matching keypoints across images, and the related problem of finding clusters of nearby images, are critical components of various tasks in Computer Vision, including Structure from Motion (SfM). Unfortunately, occlusion and large repetitive structures tend to mislead most currently used matching algorithms, leading to characteristic pathologies in the final output. In this paper w...