Sigmoid functions have been applied in many areas to model self limited population growth. The most popular functions; General Logistic (GL), General von Bertalanffy (GV), and Gompertz (G), comprise a family of functions called Theta Logistic ( $$ \Uptheta $$ L ). Previously, we introduced a simple model of tumor cell population dynamics which provided a unifying foundation for these functions. In the model the total population ( N ) is divided into reproducing ( P ) and non-reproducing/quiescent ( Q (...) ) sub-populations. The modes of the rate of change of ratio P / N was shown to produce GL, GV or G growth. We now generalize the population dynamics model and extend the possible modes of the P / N rate of change. We produce a new family of sigmoid growth functions, Trans-General Logistic (TGL), Trans-General von Bertalanffy (TGV) and Trans-Gompertz (TG)), which as a group we have named Trans-Theta Logistic ( T $$ \Uptheta $$ L ) since they exist when the $$ \Uptheta $$ L are translated from a two parameter into a three parameter phase space. Additionally, the model produces a new trigonometric based sigmoid ( TS ). The $$ \Uptheta $$ L sigmoids have an inflection point size fixed by a single parameter and an inflection age fixed by both of the defining parameters. T $$ \Uptheta $$ L and TS sigmoids have an inflection point size defined by two parameters in bounding relationships and inflection point age defined by three parameters (two bounded). While the Theta Logistic sigmoids provided flexibility in defining the inflection point size, the Trans-Theta Logistic sigmoids provide flexibility in defining the inflection point size and age. By matching the slopes at the inflection points we compare the range of values of inflection point age for T $$ \Uptheta $$ L versus $$ \Uptheta $$ L for model growth curves. (shrink)
Auguste Comte (1798–1857) is the founder of positivism, a philosophical and political movement which enjoyed a very wide diffusion in the second half of the nineteenth century. It sank into an almost complete oblivion during the twentieth, when it was eclipsed by neopositivism. However, Comte's decision to develop successively a philosophy of mathematics, a philosophy of physics, a philosophy of chemistry and a philosophy of biology, makes him the first philosopher of science in the modern sense, and his constant attention (...) to the social dimension of science resonates in many respects with current points of view. His political philosophy, on the other hand, is even less known, because it differs substantially from the classical political philosophy we have inherited. Comte's most important works are (1) the Course on Positive Philosophy (1830-1842, six volumes, translated and condensed by Harriet Martineau as The Positive Philosophy of Auguste Comte); (2) the System of Positive Polity, or Treatise on Sociology, Instituting the Religion of Humanity, (1851-1854, four volumes); and (3) the Early Writings (1820-1829), where one can see the influence of Saint-Simon, for whom Comte served as secretary from 1817 to 1824. The Early Writings are still the best introduction to Comte's thought. In the Course, Comte said, science was transformed into philosophy; in the System, philosophy was transformed into religion. The second transformation met with strong opposition; as a result, it has become customary to distinguish, with Mill, between a “good Comte” (the author of the Course) and a “bad Comte” (the author of the System). Today's common conception of positivism corresponds mainly to what can be found in the Course. (shrink)
