The accelerating expansion of the universe suggests that an unknown component with strongly negative pressure, called dark energy, currently dominates the dynamics of the universe. Such a component makes up ∼ 70% of the energy density of the universe yet has not been predicted by the standard model of particle physics. The best method for exploring the nature of this dark energy is to map the r...

We extract, from a quark model potential that reproduces the number and ordering of nonstrange baryonic resonances up to 2.3 GeV, the quantum numbers for the dominant configurations in the ground and first non-radial excited states. From the pattern of quantum numbers we identify, from data, spectral regularities that allow us to predict the expected high spin low-lying spectrum from 2.3 to 3.0...

The topological structure of scalar, vector, and second-order tensor fields provides an important mathematical basis for data analysis and visualization. In this paper, we extend this framework towards higher-order tensors. First, we establish formal uniqueness properties for a geometrically constrained tensor decomposition. This allows us to define and visualize topological structures in symme...

We compute the group of Morita self-equivalences (the Picard group) of a Poisson structure on an orientable surface, under the assumption that the degeneracies of the Poisson tensor are linear. The answer involves mapping class groups of surfaces, i.e., groups of isotopy classes of diffeomorphisms. We also show that the Picard group of these structures coincides with the group of outer Poisson ...

Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions for each type of controllability are discussed. The results are applied to determine the degree of controllability for various atomic systems with degenerate energy levels and transition frequencies. Degrees of controllability for quantum systems and application to...

It now appears phenomenologically that the third family may be essentially different from the first two. Particularly the high value of the top quark mass suggests a special role. In the standard model all three families are treated similarly [becoming exactly the same at asymptotically high energies] so I need to extend the model to accommodate the goal of a really different third family. In t...

We propose a new approach to calculate perturbatively the effects of a particular deformed Heisenberg algebra on energy spectrum. We use this method to calculate the harmonic oscillator spectrum and find that corrections are in agreement with a previous calculation. Then, we apply this approach to obtain the hydrogen atom spectrum and we find that splittings of degenerate energy levels appear. ...

We discuss the deletion of a single vertex in a Delaunay tetrahedralization (DT). While some theoretical solutions exist for this problem, the many degeneracies in three dimensions make them impossible to be implemented without the use of extra mechanisms. In this paper, we present an algorithm that uses a sequence of bistellar flips to delete a vertex in a DT, and we present two different mech...

We present a spectral study of the evolution matrix of the totally asymmetric exclusion process on a ring at half filling. The natural symmetries (translation, charge conjugation combined with reflection) predict only two fold degeneracies. However , we have found that degeneracies of higher order also exist and, as the system size increases, higher and higher orders appear. These degeneracies ...

In the geometric realization of a cubical complex without degeneracies, a 2-set, dipaths and dihomotopies may not be combinatorial, i.e., not geometric realizations of combinatorial dipaths and equivalences. When we want to use geometric/topological tools to classify dipaths on the 1-skeleton, combinatorial dipaths, up to dihomotopy, and in particular up to combinatorial dihomotopy, we need tha...