12,964 research outputs found
Modified newtonian dynamics and non-relativistic ChSAS gravity
In the context of the non-relativistic theories, a generalization of the
Chern--Weil-theorem allows us to show that extended Chern--Simons actions for
gravity in d=4 invariant under some specific non-relativistic groups lead to
modified Poisson equations. In some particular cases, these modified equations
have the form of the so-called MOND approach to gravity. The modifications
could be understood as due to the effects of dark matter. This result could
leads us to think that dark matter can be interpreted as a non-relativistic
limit of dark energy
Performance analysis and optimal selection of large mean-variance portfolios under estimation risk
We study the consistency of sample mean-variance portfolios of arbitrarily
high dimension that are based on Bayesian or shrinkage estimation of the input
parameters as well as weighted sampling. In an asymptotic setting where the
number of assets remains comparable in magnitude to the sample size, we provide
a characterization of the estimation risk by providing deterministic
equivalents of the portfolio out-of-sample performance in terms of the
underlying investment scenario. The previous estimates represent a means of
quantifying the amount of risk underestimation and return overestimation of
improved portfolio constructions beyond standard ones. Well-known for the
latter, if not corrected, these deviations lead to inaccurate and overly
optimistic Sharpe-based investment decisions. Our results are based on recent
contributions in the field of random matrix theory. Along with the asymptotic
analysis, the analytical framework allows us to find bias corrections improving
on the achieved out-of-sample performance of typical portfolio constructions.
Some numerical simulations validate our theoretical findings
On Nilcompactifications of Prime Spectra of Commutative Rings
Given a ring R and S one of its ideals, we obtain a compactification of the
prime spectrum of S through a mainly algebraic process. We name it the
R-nilcompactification of SpecS. We study some categorical properties of this
construction.Comment: 12 pages, 8 Tikz figure
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