We present algorithms for constructing a hierarchy of increasingly coarse Morse complexes that decompose a piecewise linear 2-manifold. While Morse complexes are defined only in the smooth category, we extend the construction to the piecewise linear category by ensuring structural integrity and simulating differentiability. We then simplify Morse complexes by cancelling pairs of critical points in order of increasing persistence. Keywords Computational topology, PL manifolds, Morse theory, topological persistence, hierarchy, algorithms, implementation, terrains 1. INTRODUCTION In this paper, we define the Morse complex decomposing a piecewise linear 2-manifold and present algorithms for constructing and simplifying this complex. 1.1 Motivation Physical simulation problems often start with a space and measurements over this space. If the measurements are scalar values, we talk about a height function of that space. We use this name throughout the paper, although the functions can ...

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The objectives of the Consulting Assistance on Economic Reform (CAER II) project are to contribute to broad-based and sustainable economic growth and to improve the policy reform content of USAID assistance activities that aim to strengthen markets in recipient countries. Services are provided by the Harvard Institute for International Development (HIID) and its subcontractors. It is funded by the U.S. Agency for International Development, Bureau for

This paper addresses the complex relationship between geography and macroeconomic growth. It investigates the ways in which geography may matter directly for growth, controlling for economic policies and institutions, as well as the effects of geography on policy choices and institutions. It finds that location and climate have large effects on income levels and income growth through their effects on transport costs, disease burdens, and agricultural productivity, among other channels. Furthermore, geography seems to be a factor in the choice of economic policy itself. When geographical regions that are conducive to modern economic growth are identified, it is found that there is a disjunction between such regions and many areas of the world of high population density and rapid population increase. This is especially true of populations that are located far from coasts and navigable rivers and that thus face large transport