Mathematics

To analyse the evolutionary emergence of structural complexity in physical processes, we introduce a general, but tractable, model of objects that interact to produce new objects. Since the objects— ϵ-machines —have well-defined structural properties, we demonstrate that complexity in the resulting population dynamical system emerges on several distinct organizational scales during evolution—from individuals to nested levels of mutually self-sustaining interaction. The evolution to increased organization is dominated by the spontaneous creation of structural hierarchies and this, in turn, is facilitated by the innovation and maintenance of relatively low-complexity, but general individuals.

Current analyses of genomes from numerous species show that the diversity of their functional and behavioral characters is not proportional to the number of genes that encode the organism. We investigate the hypothesis that the diversity of organismal character is due to hierarchical organization. We do this with the recently introduced model of the finitary process soup, which allows for a detailed mathematical and quantitative analysis of the population dynamics of structural complexity. Here we show that global complexity in the finitary process soup is due to the emergence of successively higher levels of organization, that the hierarchical structure appears spontaneously, and that the process of structural innovation is facilitated by the discovery and maintenance of relatively noncomplex, but general, individuals in a population.

The unit-Rayleigh distribution is a one-parameter distribution with support on the unit interval. It is defined as the so-called unit-Weibull distribution with a shape parameter equal to two. As a particular case among others, it seems that it has not been given special attention. This paper shows that the unit-Rayleigh distribution is much more interesting than it might at first glance, revealing closed-form expressions of important functions, and new desirable properties for application purposes. More precisely, on the theoretical level, we contribute to the following aspects: (i) we bring new characteristics on the form analysis of its main probabilistic and reliability functions, and show that the possible mode has a simple analytical expression, (ii) we prove new stochastic ordering results, (iii) we expose closed-form expressions of the incomplete and probability weighted moments at the basis of various probability functions and measures, (iv) we investigate distributional pro...

The experiment was conducted on the seedlings of Vance Delicious apple nursery taking two levels of chemical fertilizers, two organic manures and dual inoculation of Azotobacter and PSB in different combinations. The results reveal that the organic manures and ...

The velocity field in the neighborhood of axisymmetric constrictions in rigid tubes was investigated using laser Doppler anemometry and flow visualization. Upstream flow conditions were steady; and Reynolds numbers were in the range 500–2000, values which are ...

In this contribution, we consider the problem of finding the minimal Euclidean distance between a given converging decreasing one-dimensional array X in (R+)∞ and arrays of the form A a = ( a , a , … , a ︸ ,   0 , 0 ,   … a   t i m e s ) , with a being a natural number. We find a complete, if not always unique, solution. Our contribution illustrates how a formalism derived in the context of research evaluation and informetrics can be used to solve a purely mathematical problem.

Relative concentration theory studies the degree of inequality between two vectors (a 1,..., a N) and (α 1,..., α N). It extends concentration theory in the sense that, in the latter theory, one of the above vectors is (1/N,..., 1/N)(N coordinates). When studying relative ...