Ascent sequences and upper triangular matrices containing non-negative integers

This paper presents a bijection between ascent sequences and upper triangular matrices whose non-negative entries are such that all rows and columns contain at least one non-zero entry. We show the equivalence of several natural statistics on these structures under this bijection and prove that some of these statistics are equidistributed. Several special classes of matrices are shown to have simple formulations in terms of ascent sequences. Binary matrices are shown to correspond to ascent sequences with no two adjacent entries the same. Bidiagonal matrices are shown to be related to order-consecutive set partitions and a simple condition on the ascent sequences generate this class.Comment: 13 page

Corruption and the Shadow Economy at the Regional Level

The links between corruption and the shadow economy have mostly been studied empirically at the country level. This paper contributes to this literature by examining the relationship at the sub-national level. Using World Bank Enterprise Survey data, we find that sub-national units in which more firms report that corruption is an obstacle to their operations also tend to have more firms that report informal competitors as an obstacle and vice versa. We also ask whether within country variation matters and find that regions with a bigger problem in one of these dimensions than their national average also tend to have a relatively bigger problem in the other dimension. Sub-Saharan Africa is different in that neither of these findings are evident in that sub-sample

Experts’ Perceptions versus Firms’ Experiences of Corruption and Foreign Direct Investment

This paper documents that standard measures of corruption based on the perceptions of experts and opinion surveys and measures based on the experiences of firms can in some cases lead to quite different conclusions as to how much of a problem corruption is in a country. We then show that while perceptions of corruption are significantly associated with the amount of foreign direct investment that a country attracts, the experience on the ground is not. This finding is robust to alternative perceptions and experience measures and the inclusion of standard empirical foreign direct investment model controls. When we look at establishment modes of foreign investors we find some evidence that direct investment that builds new operations from zero in a foreign country (greenfield investment) is significantly associated with the experience of corruption while mergers and acquisitions is driven by perceptions

Critical surfaces for general inhomogeneous bond percolation problems

We present a method of general applicability for finding exact or accurate approximations to bond percolation thresholds for a wide class of lattices. To every lattice we sytematically associate a polynomial, the root of which in $[0,1]$ is the conjectured critical point. The method makes the correct prediction for every exactly solved problem, and comparison with numerical results shows that it is very close, but not exact, for many others. We focus primarily on the Archimedean lattices, in which all vertices are equivalent, but this restriction is not crucial. Some results we find are kagome: $p_c=0.524430...$, $(3,12^2): p_c=0.740423...$, $(3^3,4^2): p_c=0.419615...$, $(3,4,6,4):p_c=0.524821...$, $(4,8^2):p_c=0.676835...$, $(3^2,4,3,4)$: $p_c=0.414120...$ . The results are generally within $10^{-5}$ of numerical estimates. For the inhomogeneous checkerboard and bowtie lattices, errors in the formulas (if they are not exact) are less than $10^{-6}$.Comment: Submitted to J. Stat. Mec

Bayesian Methods for Exoplanet Science

Exoplanet research is carried out at the limits of the capabilities of current telescopes and instruments. The studied signals are weak, and often embedded in complex systematics from instrumental, telluric, and astrophysical sources. Combining repeated observations of periodic events, simultaneous observations with multiple telescopes, different observation techniques, and existing information from theory and prior research can help to disentangle the systematics from the planetary signals, and offers synergistic advantages over analysing observations separately. Bayesian inference provides a self-consistent statistical framework that addresses both the necessity for complex systematics models, and the need to combine prior information and heterogeneous observations. This chapter offers a brief introduction to Bayesian inference in the context of exoplanet research, with focus on time series analysis, and finishes with an overview of a set of freely available programming libraries.Comment: Invited revie

The K2 M67 Study: A Curiously Young Star in an Eclipsing Binary in an Old Open Cluster

We present an analysis of a slightly eccentric ($e=0.05$), partially eclipsing long-period ($P = 69.73$ d) main sequence binary system (WOCS 12009, Sanders 1247) in the benchmark old open cluster M67. Using Kepler K2 and ground-based photometry along with a large set of new and reanalyzed spectra, we derived highly precise masses ($1.111\pm0.015$ and $0.748\pm0.005 M_\odot$) and radii ($1.071\pm0.008\pm0.003$ and $0.713\pm0.019\pm0.026 R_\odot$, with statistical and systematic error estimates) for the stars. The radius of the secondary star is in agreement with theory. The primary, however, is approximately $15\%$ smaller than reasonable isochrones for the cluster predict. Our best explanation is that the primary star was produced from the merger of two stars, as this can also account for the non-detection of photospheric lithium and its higher temperature relative to other cluster main sequence stars at the same $V$ magnitude. To understand the dynamical characteristics (low measured rotational line broadening of the primary star and the low eccentricity of the current binary orbit), we believe that the most probable (but not the only) explanation is the tidal evolution of a close binary within a primordial triple system (possibly after a period of Kozai-Lidov oscillations), leading to merger approximately 1Gyr ago. This star appears to be a future blue straggler that is being revealed as the cluster ages and the most massive main sequence stars die out.Comment: 33 pages, 11 figures, accepted to AJ, photometry files will be available with the electronic journal articl