This paper studies concentration (i.e. inequality) aspects of the functions of Zipf and of Lotka. Since both functions are power laws (i.e. they are – mathematically the same) it suffices to develop one concentration theory for power laws and apply it twice for the different interpretations of the laws of Zipf and Lotka. After a brief repetition of the functional relationships between Zipf’s la...

In the present article some new aspects of word frequency distributions are presented, namely the h-point, the k-point, the m-point, the n-point, the Lorenz curve and Gini’s coefficient, all of which characterise some properties of texts. Their relationship to the measurement of vocabulary richness is scrutinized. It is an attempt at transferring some views from other domains of science to ling...

This paper offers a critical appraisal of the various methods employed to date to measure inequalities in health. It suggests that only two of these--the slope index of inequality and the concentration index--are likely to present an accurate picture of socioeconomic inequalities in health. The paper also presents several empirical examples to illustrate of the dangers of using other measures s...

We describe an unconventional method for treating initial value problems. The system of differential equations is discretized on a fixed interval, the initial value is left unspecified, and the underdetermined system is solved by a least squares minimization procedure. When applied to the celebrated Lorenz equations, it produces a simple smooth curve that terminates at a stationary point rather...

Implicit particle filters for data assimilation generate high-probability samples by representing each particle location as a separate function of a common reference variable. This representation requires that a certain underdetermined equation be solved for each particle and at each time an observation becomes available. We present a new implementation of implicit filters in which we find the ...

An attractor is a transitive set of a flow to which all positive orbit close to it converges. An attractor is singular-hyperbolic if it has singularities (all hyperbolic) and is partially hyperbolic with volume expanding central direction [16]. The geometric Lorenz attractor [6] is an example of a singular-hyperbolic attractor with topological dimension ≥ 2. We shall prove that all singular-hyp...