Public Debt and the Macroeconomic Stability of Japan

Recently, the outstanding debt of the Japanese government amounts to 695 trillion yen, which implies 139.5% of GDP. In this paper, we constructed three IS-LM type dynamic models and estimate the eigenvalues of their differential systems. Then we confirm whether or not the huge amount of public debt violates the stability conditions for the Japanese economy. Our estimation concludes the Japanese economy to be unstable with the existence of a saddle-point equilibrium. Our simulation also shows that severe tax reform would be required to restore the economic stability. Concretely, the government has to raise the consumption tax rate to 15% from 5%, and in addition, allowing the income elasticities of income taxes and inhabitant taxes to increase by 0.033 each, which is equivalent to tax hikes of about 8.3 trillion yen. We assert that structural reform for the government budget including a tax system is essential and emergent.public debt, Japan, macroeconomic stability, saddle-point equilibrium, structural reform

The pp-Center Problem in Tree Networks Revisited

We present two improved algorithms for weighted discrete $p$-center problem for tree networks with $n$ vertices. One of our proposed algorithms runs in $O(n \log n + p \log^2 n \log(n/p))$ time. For all values of $p$, our algorithm thus runs as fast as or faster than the most efficient $O(n\log^2 n)$ time algorithm obtained by applying Cole's speed-up technique [cole1987] to the algorithm due to Megiddo and Tamir [megiddo1983], which has remained unchallenged for nearly 30 years. Our other algorithm, which is more practical, runs in $O(n \log n + p^2 \log^2(n/p))$ time, and when $p=O(\sqrt{n})$ it is faster than Megiddo and Tamir's $O(n \log^2n \log\log n)$ time algorithm [megiddo1983]

Observability of hydrogen-rich exospheres in Earth-like exoplanets

(Abridged) The existence of an extended neutral hydrogen exosphere around small planets can be used as an evidence for the presence of water in their lower atmosphere but, to date, such feature has not been securely detected in rocky exoplanets. Planetary exospheres can be observed using transit spectroscopy of the Lyman-$\alpha$ line, which is limited mainly by interstellar medium absorption in the core of the line, and airglow contamination from the geocorona when using low-orbit space telescopes. Our objective is to assess the detectability of the neutral hydrogen exosphere of an Earth-like planet transiting a nearby M dwarf using Lyman-$\alpha$ spectroscopy and provide the necessary strategies to inform future observations. The spatial distribution in the upper atmosphere is provided by an empirical model of the geocorona, and we assume a velocity distribution based on radiative pressure as the main driver in shaping the exosphere. We compute the excess absorption in the stellar Lyman-$\alpha$ line while in transit, and use realistic estimates of the uncertainties involved in observations to determine the observability of the signal. We found that the signal in Lyman-$\alpha$ of the exosphere of an Earth-like exoplanet transiting M dwarfs with radii between 0.1 and 0.6 R$_\odot$ produces an excess absorption between 50 and 600 ppm. The Lyman-$\alpha$ flux of stars decays exponentially with distance because of interstellar medium absorption, which is the main observability limitation. Other limits are related to the stellar radial velocity and instrumental setup. The excess absorption in Lyman-$\alpha$ is observable using LUVOIR/LUMOS in M dwarfs up to a distance of $\sim$15 pc. The analysis of noise-injected data suggests that it would be possible to detect the exosphere of an Earth-like planet transiting TRAPPIST-1 within 20 transits.Comment: 12 pages, 13 figures, accepted for publication in Astronomy & Astrophysic