A Parallel Approximation Algorithm for the Max Cut Problem on Cubic Graphs

We deal with the maximum cut problem on cubic graphs and we present a simple O(log n) time parallel algorithm, running on a CRCW PRAM with O(n) processors. The approximation ratio of our algorithm is 1. 3 and improves the best known parallel approximation ratio, i.e. 2, in the special case of cubic graphs

The first scattered light images of HD 112810, a faint debris disk in the Sco-Cen association

Context. Circumstellar debris disks provide insight into the formation and early evolution of planetary systems. Resolved belts in particular help to locate planetesimals in exosystems, and can hint at the presence of disk-sculpting exoplanets. Aims. We study the circumstellar environment of HD 112810 (HIP 63439), a mid-F-type star in the Sco-Cen association with a significant infrared excess indicating the presence of a circumstellar debris disk. Methods. We collected five high-contrast observations of HD 112810 with VLT/SPHERE. We identified a debris disk in scattered light, and found that the debris signature is robust over a number of epochs and a variety of reduction techniques. We modeled the disk, accounting for self-subtraction and assuming that it is optically thin. Results. We find a single-belt debris disk, with a radius of 118 ± 9 au and an inclination angle of 75.7-1.3+1.1. This is in good agreement with the constraints from spectral energy distribution modeling and from a partially resolved ALMA image of the system. No planets are detected, though planets below the detection limit (~2.6 MJ at a projected separation of 118 au) could be present and could have contributed to sculpting the ring of debris. Conclusions. HD 112810 adds to the growing inventory of debris disks imaged in scattered light. The disk is faint, but the radius and the inclination of the disk are promising for follow-up studies of the dust properties. © The Authors 2023.Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

A logistic growth theory of public expenditures: A study of five countries over 100 years

This paper offers a new theory and empirical testing of long-term trends of public expenditures for five countries. While Wagner’s Law would imply an exponential growth process of the ratio between public expenditures and national income (G/Y), the law should be rejected both on theoretical and empirical grounds, because it disregards the role of ever increasing distortionary taxation. However, under some conditions, the combination of Wagner’s Law and the Pigou’s conjecture that the excess burden of taxation constrains the growth of public expenditures can be captured by a non-linear first order differential equation. The equation is the Verhulst’s logistic, originally invented to model Malthusian predictions on population growth. The integration of a Verhulst equation generates an S-shaped curve. This analytical framework combines intuitions from a welfare economics and a public choice perspective, and potentially offers a new research strategy on the dynamics of government expenditures. We offer preliminary econometric estimates on long run trends (around 1870–1990) of G/Y in U.S., U.K., France, Germany, Italy. These estimates confirm a pattern of similar trajectories, in spite of different national parameters, and suggest that the logistic view of growth of government is consistent with observed data. Copyright Springer Science + Business Media, Inc. 2005