arXiv subjects

Helge Rose

Publications and source records attributed to Helge Rose.

4 recordsLinked to original sources

arXiv2012

On the geometrization of matter by exotic smoothness

In this paper we discuss the question how matter may emerge from space. For that purpose we consider the smoothness structure of spacetime as underlying structure for a geometrical model of matter. For a large class of compact 4-manifolds, the elliptic surfaces, one is able to apply the knot surgery of Fintushel and Stern to change the smoothness structure. The influence of this surgery to the Einstein-Hilbert action is discussed. Using the Weierstrass representation, we are able to show that the knotted torus used in knot surgery is represented by a spinor fulfilling the Dirac equation and leading to a mass-less Dirac term in the Einstein-Hilbert action. For sufficient complicated links and knots, there are "connecting tubes" (graph manifolds, torus bundles) which introduce an action term of a gauge field. Both terms are genuinely geometrical and characterized by the mean curvature of the components. We also discuss the gauge group of the theory to be U(1)xSU(2)xSU(3).

gr-qc↗

arXiv2007

Dark energy and 3-manifold topology

We show that the differential-geometric description of matter by differential structures of spacetime leads to a unifying model of the three types of energy in the cosmos: matter, dark matter and dark energy. Using this model we are able to calculate the ratio of dark energy to the total energy of the cosmos.

gr-qc↗

arXiv1995

Smoothing representation of fitness landscapes - the genotype-phenotype map of evolution

We investigate an simple evolutionary game of sequences and demonstrate on this example the structure of fitness landscapes in discrete problems. We show the smoothing action of the genotype-phenotype mapping which still makes it feasible for evolution to work. Further we propose the density of sequence states as a classifying measure of fitness landscapes.

adap-org↗

arXiv1995

Guessing probability distributions from small samples

We propose a new method for the calculation of the statistical properties, as e.g. the entropy, of unknown generators of symbolic sequences. The probability distribution $p(k)$ of the elements $k$ of a population can be approximated by the frequencies $f(k)$ of a sample provided the sample is long enough so that each element $k$ occurs many times. Our method yields an approximation if this precondition does not hold. For a given $f(k)$ we recalculate the Zipf--ordered probability distribution by optimization of the parameters of a guessed distribution. We demonstrate that our method yields reliable results.

chao-dyn↗