15,673 research outputs found
Portfolios and the market geometry
A geometric analysis of the time series of returns has been performed in the
past and it implied that the most of the systematic information of the market
is contained in a space of small dimension. Here we have explored subspaces of
this space to find out the relative performance of portfolios formed from the
companies that have the largest projections in each one of the subspaces. It
was found that the best performance portfolios are associated to some of the
small eigenvalue subspaces and not to the dominant directions in the distances
matrix. This occurs in such a systematic fashion over an extended period
(1990-2008) that it may not be a statistical accident.Comment: 13 pages 12 figure
A theorem regarding families of topologically non-trivial fermionic systems
We introduce a Hamiltonian for fermions on a lattice and prove a theorem
regarding its topological properties. We identify the topological criterion as
a topological invariant (the Pfaffian
polynomial). The topological invariant is not only the first Chern number, but
also the sign of the Pfaffian polynomial coming from a notion of duality. Such
Hamiltonian can describe non-trivial Chern insulators, single band
superconductors or multiorbital superconductors. The topological features of
these families are completely determined as a consequence of our theorem. Some
specific model examples are explicitly worked out, with the computation of
different possible topological invariants.Comment: 6 page
Finding a Spherically Symmetric Cosmology from Observations in Observational Coordinates -- Advantages and Challenges
One of the continuing challenges in cosmology has been to determine the
large-scale space-time metric from observations with a minimum of assumptions
-- without, for instance, assuming that the universe is almost
Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW). If we are lucky enough this
would be a way of demonstrating that our universe is FLRW, instead of
presupposing it or simply showing that the observations are consistent with
FLRW. Showing how to do this within the more general spherically symmetric,
inhomogeneous space-time framework takes us a long way towards fulfilling this
goal. In recent work researchers have shown how this can be done both in the
traditional Lema\^{i}tre-Tolman-Bondi (LTB) 3 + 1 coordinate framework, and in
the observational coordinate (OC) framework. In this paper we investigate the
stability of solutions, and the use of data in the OC field equations including
their time evolution and compare both approaches with respect to the
singularity problem at the maximum of the angular-diameter distance, the
stability of solutions, and the use of data in the field equations. This allows
a more detailed account and assessment of the OC integration procedure, and
enables a comparison of the relative advantages of the two equivalent solution
frameworks. Both formulations and integration procedures should, in principle,
lead to the same results. However, as we show in this paper, the OC procedure
manifests certain advantages, particularly in the avoidance of coordinate
singularities at the maximum of the angular-diameter distance, and in the
stability of the solutions obtained. This particular feature is what allows us
to do the best fitting of the data to smooth data functions and the possibility
of constructing analytic solutions to the field equations.Comment: 31 page
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