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