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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)
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)
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)
Causes of death varied systematically in the United States during the 20th century as the human environment came under control. Infections became less deadly, while heart disease grew dominant, followed by cancer. Logistic models of growth and multi-species competition in which the causes of death are the competitors describe precisely the evolutionary(More)
Renewables are not green. To reach the scale at which they would contribute importantly to meeting global energy demand, renewable sources of energy, such as wind, water and biomass, cause serious environmental harm. Measuring renewables in watts per square metre that each source could produce smashes these environmental idols. Nuclear energy is green.(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)
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)