For decades, the sphere eversion has been a favorite subject for mathematical visualization. The 1998 video The Optiverse shows minimax eversions, computed automatically by minimizing elastic bending energy using Brakke’s Evolver. We contrast these geometrically optimal eversions with earlier ones, including those by Morin, Phillips,

For decades, the sphere eversion has been a classic subject for mathematical visualization. The 1998 video The Optiverse shows geometrically optimal eversions created by minimizing elastic bending energy. We contrast these minimax eversions with earlier ones, including those by Morin, Phillips, Max, and Thurston. The minimax eversions were automatically generated by flowing downhill in energy u...

The Phillips curve has generally been estimated in a linear framework which implies a constant relationship between inflation and unemployment. Lately there have been several studies which claim that the slope of the Phillips curve is a function of macroeconomic conditions and that the relationship is asymmetric. If this is true the assumption of linearity is too restrictive. In this paper line...

This paper studies optimal monetary policy in a model where inflation is persistent. Two types of price setters are assumed to exist. One acts rationally given Calvo-type constraints on price setting. The other type sets prices according to a rule-of-thumb. This results in a Phillips curve with both a forward-looking term and a backward-looking term. The Phillips curve nests a standard purely f...

In this paper we introduce a small Keynesian model of economic growth which is centered around two advanced types of Phillips curves, one for money wages and one for prices, both being augmented by perfect myopic foresight and supplemented by a measure of the medium-term inflationary climate updated in an adaptive fashion. The model contains two potentially destabilizing feedback chains, the so...