Stellar Equilibrium vs. Gravitational Collapse

The idea of gravitational collapse can be traced back to the first solution of Einstein’s equations, but in these early stages, compelling evidence to support this idea was lacking. Furthermore, there were many theoretical gaps underlying the conviction that a star could not contract beyond its critical radius. The philosophical views of the early 20th century, especially those of Sir Arthur S. Eddington, imposed equilibrium as an almost unquestionable condition on theoretical models describing stars. This paper is a historical and epistemological account of the theoretical defiance of this equilibrium hypothesis, with a novel reassessment of J.R. Oppenheimer’s work on astrophysics

Heteroscedastic Gaussian processes for uncertainty modeling in large-scale crowdsourced traffic data

Accurately modeling traffic speeds is a fundamental part of efficient intelligent transportation systems. Nowadays, with the widespread deployment of GPS-enabled devices, it has become possible to crowdsource the collection of speed information to road users (e.g. through mobile applications or dedicated in-vehicle devices). Despite its rather wide spatial coverage, crowdsourced speed data also brings very important challenges, such as the highly variable measurement noise in the data due to a variety of driving behaviors and sample sizes. When not properly accounted for, this noise can severely compromise any application that relies on accurate traffic data. In this article, we propose the use of heteroscedastic Gaussian processes (HGP) to model the time-varying uncertainty in large-scale crowdsourced traffic data. Furthermore, we develop a HGP conditioned on sample size and traffic regime (SRC-HGP), which makes use of sample size information (probe vehicles per minute) as well as previous observed speeds, in order to more accurately model the uncertainty in observed speeds. Using 6 months of crowdsourced traffic data from Copenhagen, we empirically show that the proposed heteroscedastic models produce significantly better predictive distributions when compared to current state-of-the-art methods for both speed imputation and short-term forecasting tasks.Comment: 22 pages, Transportation Research Part C: Emerging Technologies (Elsevier

A family of rotation numbers for discrete random dynamics on the circle

We revisit the problem of well-defining rotation numbers for discrete random dynamical systems on the circle. We show that, contrasting with deterministic systems, the topological (i.e. based on Poincar\'{e} lifts) approach does depend on the choice of lifts (e.g. continuously for nonatomic randomness). Furthermore, the winding orbit rotation number does not agree with the topological rotation number. Existence and conversion formulae between these distinct numbers are presented. Finally, we prove a sampling in time theorem which recover the rotation number of continuous Stratonovich stochastic dynamical systems on $S^1$ out of its time discretisation of the flow.Comment: 15 page

A model for the Yield curve

The starting point is an interrogation about the non-broken character of the term structure of interest rates. Some arguments for that smooth character are presented here, all of which are based upon the assumption that market participants - arbitrageurs and speculators - always try to explore any misalignments discovered in the interest market. This led to the basic concept behind the model that the current short-term rate determines most of the value of the rate level for the subsequent period. A linear model describing that simple relationship is assumed and that constitutes the building block from where one can develop the mathematical equations necessary to work with different sets of market data. A number of different yield curves were modelled by adjustment to real market data using this basic model, all of them showing a very high quality of the fits when measured by the non-linear ratio R2. Nevertheless this fact still needs to be confirmed as the examples were drawn from non-independent markets and from a very short time window. The model can be improved by simple addition of a liquidity premium depend only upon the maturity of the rates. However, that improvement sophisticates tremendously the mathematical tractability of any real situation without any assurance that this added cost compensates for the increased quality of the fit. The model is designed around only 3 parameters that can all be interpreted in economic terms. Two of them, in particular, bring a significant improvement over the traditional views frequently extracted from the shape of the yield curve. Provided future tests confirm the high quality of the basic and the improved (with a liquidity premium) models, both are supportive of the expectation hypothesis (EH) and the liquidity premium hypothesis (LPH).

Disk and elliptical galaxies within renormalization group improved gravity

The paper is about possible effects of infrared quantum contributions to General Relativity on disk and elliptical galaxies. The Renormalization Group corrected General Relativity (RGGR model) is used to parametrize these quantum effects. The new RGGR results presented here concern the elliptical galaxy NGC 4374 and the dwarf disk galaxy DDO 47. Using the effective approach to Quantum Field Theory in curved background, one can argue that the proper RG energy scale, in the weak field limit, should be related to the Newtonian potential. In the context of galaxies, this led to a remarkably small variation of the gravitational coupling G, while also capable of generating galaxy rotation and dispersion curves of similar quality to the the best dark matter profiles (i.e., the profiles that have a core).Comment: 5 pages. This paper is based on a talk given by D.C. Rodrigues at the I CosmoSul meeting (Rio de Janeiro, RJ - Brazil. August, 01-05, 2011). To be published in AIP conference Proceeding