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This article describes the mathematics underlying the Loglet Lab software package for loglet analysis. " Loglet analysis " refers to the decomposition of growth and diffusion into S-shaped logistic components, roughly analogous to wavelet analysis, popular for signal processing and compression. The term " loglet " joins " logistic " and " wavelet. " Loglet(More)
expecting that more and richer people will demand more from the land, cultivating wider fields, logging more forests, and pressing nature, comes naturally. the past half-century of disciplined and dematerializing demand and more intense and efficient land use encourage a rational hope that humanity's pressure will not overwhelm nature. Beginning with the(More)
We introduce an extension to the widely-used logistic model of growth to a limit that in turn allows for a sigmoidally increasing carrying capacity, that is, the invention and diffusion of technologies which lift the limit. We study the effect of this dynamic carrying capacity on the trajectories of simple growth models, and we use the new model to(More)
Amid widespread reports of deforestation, some nations have nevertheless experienced transitions from deforestation to reforestation. In a causal relationship, the Forest Identity relates the carbon sequestered in forests to the changing variables of national or regional forest area, growing stock density per area, biomass per growing stock volume, and(More)
Learning actors' leverage for change along the journey to sustainability requires quantifying the component forces of environmental impact and integrating them. Population, income, consumers' behavior, and producers' efficiency jointly force impact. Here, we renovate the "IPAT Identity" to identify actors with the forces. Forcing impact I are P for(More)
"We revive the logistic model, which was tested and found wanting in early-20th-century studies of aggregate human populations, and apply it instead to life expectancy (death) and fertility (birth)....For death...the logistic portrays the situation crisply. Human life expectancy is reaching the culmination of a two-hundred year-process that forestalls death(More)
Like cities, forests grow by spreading out or by growing denser. Both inventories taken steadily by a single nation and other inventories gathered recently from many nations by the United Nations confirm the asynchronous effects of changing area and of density or volume per hectare. United States forests spread little after 1953, while growing density per(More)