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Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general. 1   Introduction 2   The Limits of Classical Probability Theory    2.1   Classical probability functions    2.2   Limitations    2.3   Infinitesimals to the rescue? 3   NAP Theory    3.1   First four axioms of NAP    3.2   Continuity and conditional probability    3.3   The final axiom of NAP    3.4   Infinite sums    3.5   Definition of NAP functions via infinite sums    3.6   Relation to numerosity theory 4   Objections and Replies    4.1   Cantor and the Archimedean property    4.2   Ticket missing from an infinite lottery    4.3   Williamson's infinite sequence of coin tosses    4.4   Point sets on a circle    4.5   Easwaran and Pruss 5   Dividends    5.1   Measure and utility    5.2   Regularity and uniformity    5.3   Credence and chance    5.4   Conditional probability 6   General Considerations    6.1   Non-uniqueness    6.2   Invariance Appendix  .

We define the complexity of DNA sequences as the information content per nucleotide, calculated by means of some Lempel-Ziv data compression algorithm. It is possible to use the statistics of the complexity values of the functional regions of different complete genomes to distinguish among genomes of different domains of life (Archaea, Bacteria and Eukarya). We shall focus on the distribution function of the complexity of non-coding regions. We show that the three domains may be plotted in separate regions within the two-dimensional space where the axes are the skewness coefficient and the curtosis coefficient of the aforementioned distribution. Preliminary results on 15 genomes are introduced.

Our aim is to present some ideas about the notion of scientific theory which includes the biological theories. We examine relationships among theories and examples of theoretical situations. In this context we propose definitions of emergent property and complexity. These definitions are exemplified by the development of some biological theories.

We study a Schrödinger-like equation with a nonlinear term. This nonlinearity has the effect of allowing the existence of highly concentrated stable solitary waves of a topological nature. Such solitary waves tend to move according to Bohmian mechanics. Therefore our model can be considered a nonsingular realization of de Broglie pilot wave theory.

In this paper we propose a mechanism which tries to explain the presence of periods of stability and instability which occur during the evolution of living forms. According to the Gaia hypothesis there are feedback mechanisms which stabilise the biosphere. Adding the presence of parameters which are out of control of the biosphere and of different time-scales, we propose a model which might explain the periods of instability., (Copyright 1998 Academic Press)