On the emergence of the correlation between life expectancy and the variance in the age at death.

Recent empirical studies have found various patterns in the correlations between lifespan inequality and life expectancy in modern human populations. However, it is unclear how general these regularities are. Here we establish three theorems that provide theoretical foundations for such regularities.

Quantizing Chaplygin Hamiltonizable nonholonomic systems.

In this article we develop a quantization procedure for Chaplygin Hamiltonizable nonholonomic systems-mechanical systems subject to non-integrable velocity constraints whose reduced mechanics is Hamiltonian after a suitable time reparametrization-using Poincaré transformations and geometric quantization. We illustrate the theory developed through examples and discuss potential applications to the study of the quantum mechanics of nanovehicles.

Life span inequality as a function of the moments of the deaths distribution: Connections and insights.

Recent work has unearthed many empirical regularities in mortality trends, including the inverse correlation between life expectancy and life span inequality, and the compression of mortality into older age ranges. These regularities have furnished important insights into the dynamics of mortality by describing, in demographic terms, how different attributes of the life table deaths distribution interrelate and change over time. However, though empirical evidence suggests that the demographically-meaningful metrics these regularities involve (e.

The Quantum Mechanics of a Rolling Molecular "Nanocar".

We formulate a mathematical model of a rolling "molecular wheelbarrow"-a two-wheeled nanoscale molecular machine-informed by experiments on molecular machines recently synthesized in labs. The model is a nonholonomic system (briefly, a system with non-integrable velocity constraints), for which no general quantization procedure exists. Nonetheless, we successfully embed the system in a Hamiltonian one and then quantize the result using geometric quantization and other tools; we extract from the result the quantum mechanics of the molecular wheelbarrow, and derive explicit formulae for the quantized energy spectrum.

The entropy of the life table: A reappraisal.

The life table entropy provides useful information for understanding improvements in mortality and survival in a population. In this paper we take a closer look at the life table entropy and use advanced mathematical methods to provide additional insights for understanding how it relates to changes in mortality and survival. By studying the entropy (H) as a functional, we show that changes in the entropy depend on both the relative change in life expectancy lost due to death (e(†)) and in life expectancy at birth (e0).