2,372 research outputs found
Perturbative Approach to Flat Chern Bands in the Hofstadter Model
We present a perturbative approach to the study of the Hofstadter model for
when the amount of flux per plaquette is close to a rational fraction. Within
this approximation certain eigenstates of the system are shown to be
multi-component wavefunctions that connect smoothly to the Landau levels of the
continuum. The perturbative corrections to these are higher Landau level
contributions that break rotational invariance and allow the perturbed states
to adopt the symmetry of the lattice. In the presence of interactions, this
approach allows for the calculation of generalised Haldane pseudopotentials,
and in turn, the many-body properties of the system. The method is sufficiently
general that it can apply to a wide variety of lattices, interactions and
magnetic field strengths.Comment: 40 pages, 15 figures; v2 includes minor changes, additional
references and an expanded background sectio
The Complexity of the Homotopy Method, Equilibrium Selection, and Lemke-Howson Solutions
We show that the widely used homotopy method for solving fixpoint problems,
as well as the Harsanyi-Selten equilibrium selection process for games, are
PSPACE-complete to implement. Extending our result for the Harsanyi-Selten
process, we show that several other homotopy-based algorithms for finding
equilibria of games are also PSPACE-complete to implement. A further
application of our techniques yields the result that it is PSPACE-complete to
compute any of the equilibria that could be found via the classical
Lemke-Howson algorithm, a complexity-theoretic strengthening of the result in
[Savani and von Stengel]. These results show that our techniques can be widely
applied and suggest that the PSPACE-completeness of implementing homotopy
methods is a general principle.Comment: 23 pages, 1 figure; to appear in FOCS 2011 conferenc
A trigonometric approach to quaternary code designs with application to one-eighth and one-sixteenth fractions
The study of good nonregular fractional factorial designs has received
significant attention over the last two decades. Recent research indicates that
designs constructed from quaternary codes (QC) are very promising in this
regard. The present paper shows how a trigonometric approach can facilitate a
systematic understanding of such QC designs and lead to new theoretical results
covering hitherto unexplored situations. We focus attention on one-eighth and
one-sixteenth fractions of two-level factorials and show that optimal QC
designs often have larger generalized resolution and projectivity than
comparable regular designs. Moreover, some of these designs are found to have
maximum projectivity among all designs.Comment: Published in at http://dx.doi.org/10.1214/10-AOS815 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Tests of Independence in Separable Econometric Models: Theory and Application
A common stochastic restriction in econometric models separable in the latent variables is the assumption of stochastic independence between the unobserved and observed exogenous variables. Both simple and composite tests of this assumption are derived from properties of independence empirical processes and the consistency of these tests is established. As an application, we simulate estimation of a random quasilinear utility function, where we apply our tests of independence.Cramerāvon Mises distance, Empirical independence processes, Random utility models, Semiparametric econometric models, Specification test of independence
Do European Stock Markets Affect Latin American Stock Markets?
In this study, we examine the response of Latin American stock markets to movements in European stock markets using VAR models. Our results vary depending on the openness of the country in terms of international trade. We find evidence that Latin American stock markets are responsive to changes in the stock market from Spain. Additionally, during the second and third subperiods, Spain has much stronger ties with Brazil, and this might explain why Brazil responds more to the shocks originating from Spain than from France. In conclusion, this study uncovers two important findings. First, Spain influences Latin American markets but these responses are not homogeneous across markets. Second, the influence of Spain has different magnitude in the three subperiods.Emerging Markets, Latin America, Stock Markets Interdependence, VAR
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