35 research outputs found
Scaling in a continuous time model for biological aging
In this paper we consider a generalization to the asexual version of the
Penna model for biological aging, where we take a continuous time limit. The
genotype associated to each individual is an interval of real numbers over
which Dirac --functions are defined, representing genetically
programmed diseases to be switched on at defined ages of the individual life.
We discuss two different continuous limits for the evolution equation and two
different mutation protocols, to be implemented during reproduction. Exact
stationary solutions are obtained and scaling properties are discussed.Comment: 10 pages, 6 figure
On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles
In this paper we revisit the Bialynicki-Birula & Mycielski uncertainty
principle and its cases of equality. This Shannon entropic version of the
well-known Heisenberg uncertainty principle can be used when dealing with
variables that admit no variance. In this paper, we extend this uncertainty
principle to Renyi entropies. We recall that in both Shannon and Renyi cases,
and for a given dimension n, the only case of equality occurs for Gaussian
random vectors. We show that as n grows, however, the bound is also
asymptotically attained in the cases of n-dimensional Student-t and Student-r
distributions. A complete analytical study is performed in a special case of a
Student-t distribution. We also show numerically that this effect exists for
the particular case of a n-dimensional Cauchy variable, whatever the Renyi
entropy considered, extending the results of Abe and illustrating the
analytical asymptotic study of the student-t case. In the Student-r case, we
show numerically that the same behavior occurs for uniformly distributed
vectors. These particular cases and other ones investigated in this paper are
interesting since they show that this asymptotic behavior cannot be considered
as a "Gaussianization" of the vector when the dimension increases