Private Electronic Money, Fiat Money and the Payments System

This paper provides insight on how a modern system of private electronic money would work and how the necessary network shall function. We present a model with two types of private electronic currencies with one being local, and the other being global. Both of them display transactional advantages and dominate fiat money in rate of return. However, in spite of these different returns, the two electronic currencies and fiat money circulate in equilibrium. We further observe that the local electronic currency can be sold with a premium or with a discount, depending on several factors including the probability of relocation faced by the agents in this economy. The higher the probability of relocation, the higher is this discount, and the lower the share of the local electronic currency in the young creditors’ portfolio.Private Money, Commodity Money, Network, Payments System, Competition

Stellar loci I. Metallicity dependence and intrinsic widths

Stellar loci are widely used for selection of interesting outliers, reddening determinations, and calibrations. However, hitherto the dependence of stellar loci on metallicity has not been fully explored and their intrinsic widths are unclear. In this paper, by combining the spectroscopic and re-calibrated imaging data of the SDSS Stripe 82, we have built a large, clean sample of dwarf stars with accurate colors and well determined metallicities to investigate the metallicity dependence and intrinsic widths of the SDSS stellar loci. Typically, one dex decrease in metallicity causes 0.20 and 0.02 mag decrease in colors u-g and g-r, and 0.02 and 0.02 mag increase in colors r-i and i-z, respectively. The variations are larger for metal-rich stars than for metal-poor ones, and for F/G/K stars than for A/M ones. Using the sample, we have performed two dimensional polynomial fitting to the u-g, g-r, r-i, and i-z colors as a function of color g-i and metallicity [Fe/H]. The residuals, at the level of 0.029, 0.008, 0.008 and 0.011 mag for the u-g, g-r, r-i, and i-z colors, respectively can be fully accounted for by the photometric errors and metallicity uncertainties, suggesting that the intrinsic widths of the loci are at maximum a few mmag. The residual distributions are asymmetric, revealing that a significant fraction of stars are binaries. In a companion paper, we will present an unbiased estimate of the binary fraction for field stars. Other potential applications of the metallicity dependent stellar loci are briefly discussed.Comment: 6 pages, 4 figures, 1 table, ApJ in pres

Stellar loci III: Photometric metallicities for half million FGK stars of Stripe 82

We develop a method to estimate photometric metallicities by simultaneously fitting the dereddened colors u-g, g-r, r-i and i-z from the SDSS with those predicted by the metallicity-dependent stellar loci. The method is tested with a spectroscopic sample of main-sequence stars in Stripe 82 selected from the SDSS DR9 and three open clusters. With 1 per cent photometry, the method is capable of delivering photometric metallicities precise to about 0.05, 0.12, and 0.18 dex at metallicities of 0.0, -1.0, and -2.0, respectively, comparable to the precision achievable with low-resolution spectroscopy at a signal-to-noise ratio of 10. We apply this method to the re-calibrated Stripe 82 catalog and derive metallicities for about 0.5 million stars of colors 0.3 < g-i < 1.6 mag and distances between 0.3 -- 18 kpc. Potential systematics in the metallicities thus derived, due to the contamination of giants and binaries, are investigated. Photometric distances are also calculated. About 91, 72, and 53 per cent of the sample stars are brighter than r = 20.5, 19.5, and 18.5 mag, respectively. The median metallicity errors are around 0.19, 0.16, 0.11, and 0.085 dex for the whole sample, and for stars brighter than r = 20.5, 19.5, and 18.5 mag, respectively. The median distance errors are 8.8, 8.4, 7.7, and 7.3 per cent for the aforementioned four groups of stars, respectively. The data are publicly available. Potential applications of the data in studies of the distribution, (sub)structure, and chemistry of the Galactic stellar populations, are briefly discussed. The results will be presented in future papers.Comment: 10 pages, 10 figures, ApJ accepte