Abs t r ac t . Image formation of a two-dimensional input image can be quantified by imposing an image induced connection and computing the associated torsion and curvature. The latter aspects of image formation are especially nonvanishing at sets of discontinuities and non-isolated singularities, such as ridges and ruts. Next dynamic scale-space theories for the input image are constructed on ...

Hebbian and competitive Hebbian algorithms are almost ubiquitous in modeling pattern formation in cortical development. We analyse in theoretical detail a particular model (adapted from Piepenbrock & Obermayer, 1999) for the development of Id stripe-like patterns, which places competitive and interactive cortical influences, and free and restricted initial arborisation onto a common footing.

Over 60 years have passed since Alan Turing first postulated a mechanism for biological pattern formation. Although Turing did not have the chance to extend his theories before his unfortunate death two years later, his work has not gone unnoticed. Indeed, many researchers have since taken up the gauntlet and extended his revolutionary and counter-intuitive ideas. Here, we reproduce the basics ...

We study a tissue interaction model on skin pattern formation proposed by Cruywagen and Murray [J. Nonlin. Sci., 2 (1992), 217–240]. We prove rigorously that the model has travelling wave solutions for all sufficiently large wave speeds, which were found numerically by Cruywagen, Maini, and Murray [J. Math. Biol., 33 (1994), 193– 210]. Our results also confirm the asymptotic expansions obtained...

This paper examines how cultural diversity in a population affects how farmers learn from one another during the process of technology adoption. The paper develops two models to study diversity in this context. It modifies an existing model from the literature to allow for cultural diversity. And it presents a game theoretic model in which technology adoption and network formation are determine...

We develop a new class of random-graph models for the statistical estimation of network formation that allow for substantial correlation in links. Various subgraphs (e.g., links, triangles, cliques, stars) are generated and their union results in a network. The challenge in estimating the frequencies with which subgraphs ‘truly’ form is that subgraphs can overlap and may also incidentally gener...

We introduce a game-theoretic model for network formation inspired by earlier stochastic models that mix localized and long-distance connectivity. In this model, players may purchase edges at distance d at a cost of d, and wish to minimize the sum of their edge purchases and their average distance to other players. In this model, we show there is a striking “small world” threshold phenomenon: i...

This paper describes how social factors can be incorporated into digital rights management. Specifically, we outline a design for a social distribution network that is built by agents that have incentive to discourage piracy. We pose the social distribution network formation as a game theoretic problem and identify the games played by the two types of agents.

We look at the concept of theory intersections inMmt, as a way to refactor theories in formal libraries, potentially yielding new interesting mathematical theories in the process. We argue, that theory intersections are a historically validated method to do so and present a concrete implementation in Mmt. Introduction An important driver of mathematical development is the discovery of new mathe...