Adolfo Zamora

Snyder noncommutative space-time from two-time physics

We show that the two-time physics model leads to a mechanical system with Dirac brackets consistent with the Snyder noncommutative space. A Euclidean version of this space is also obtained and it is shown that both spaces have a dual system describing a particle in a curved space.

Alternative proposal to modified Newtonian dynamics

From a study of conserved quantities of the so-called Modified Newtonian Dynamics (MOND) we propose an alternative to this theory. We show that this proposal is consistent with the Tully-Fisher law, has conserved quantities whose Newtonian limit are the energy and angular momentum, and can be useful to explain cosmic acceleration. The dynamics obtained suggests that, when acceleration is very small, time depends on acceleration. This result is analogous to that of special relativity where time depends on velocity. PACS numbers: 95.35.+d, 45.20.Dd Nowadays there are various observational results in astrophysics whose explanation represents a challenge for theoretical physics. One of those problems is to explain the rotation curves of the galaxies. Observations indicate a relationship V 4 ∝ M for the speed V of the distant stars in a galaxy of mass M. However, as the only force acting on those stars is gravity and their trajectories are circles, Newtonian dynamics indicates that the relationship to hold is V 2 = GM/r, where r is the distance from the star to the center of the galaxy. To account for the difference, some authors assume the existence of a sort of matter that does not radiate: the so-called dark matter. There are, however, other proposals which assume modifications to the gravitational field or to the laws of dynamics. By considering the behavior of the speed of the distant stars, M. Milgrom proposed a modification to Newton’s second law as [1] m� (z) d 2 x i dt 2 = F

SYSTEMATIC APPROXIMATIONS FOR GENETIC DYNAMICS

Although much progress has been made in recent years in describing the dynamics of genetic systems, both in population genetics and evolutionary computation, there is still a conspicuous lack of tools with which to derive systematic, approximate solutions to their dynamics. In this article, we propose and study perturbation theory and the renormalization group as potential tools to fill this gap. We concentrate mainly on selection–mutation systems, showing different implementations of the perturbative framework, developing, for example, perturbative expansions for the eigenvalues and eigenvectors of the transition matrix. The main focus, however, is on diagrammatic methods, taken from physics, where we show how approximations can be built up using a pictorial representation generated by a simple set of rules, and how the renormalization group can be used to systematically improve the perturbation theory.

Perturbation theory and the renormalization group in genetic dynamics

Although much progress has been made in recent years in the theory of GAs and GP, there is still a conspicuous lack of tools with which to derive systematic, approximate solutions to their dynamics. In this article we propose and study perturbation theory as a potential tool to fill this gap. We concentrate mainly on selection-mutation systems, showing different implementations of the perturbative framework, developing, for example, perturbative expansions for the eigenvalues and eigenvectors of the transition matrix. The main focus however, is on diagrammatic methods, taken from physics, where we show how approximations can be built up using a pictorial representation generated by a simple set of rules, and how the renormalization group can be used to systematically improve the perturbation theory.