The width of 5-dimensional prismatoids

Santos' construction of counter-examples to the Hirsch Conjecture (2012) is based on the existence of prismatoids of dimension d of width greater than d. Santos, Stephen and Thomas (2012) have shown that this cannot occur in $d \le 4$. Motivated by this we here study the width of 5-dimensional prismatoids, obtaining the following results: - There are 5-prismatoids of width six with only 25 vertices, versus the 48 vertices in Santos' original construction. This leads to non-Hirsch polytopes of dimension 20, rather than the original dimension 43. - There are 5-prismatoids with $n$ vertices and width $\Omega(\sqrt{n})$ for arbitrarily large $n$. Hence, the width of 5-prismatoids is unbounded.Comment: 31 pages, 10 figures. Changes from v1: the introduction has been edited, and a minor correction made in the statement of Proposition 1.

A new species of Villiersicometes Santos-Silva, 2003 from French Guiana (Coleoptera, Disteniidae, Disteniinae)

Villiersicometes scellierae sp. nov. (Coleoptera, Disteniidae), is described from Saül, French Guiana. The species is illustrated and the key for species of Villiersicometes Santos-Silva, 2003 is modified

A new species of Villiersicometes Santos-Silva, 2003 (Coleoptera, Cerambycidae, Disteniinae)

Villiersicometes absalom sp. nov., a new species of Villiersicometes Santos-Silva, 2003 (Coleoptera, Cerambycidae, Disteniinae) is described from French Guiana. The species is illustrated and a key to the species of the genus is provided

The Euro Sovereign Debt Crisis, Determinants of Default Probabilities and Implied Ratings in the CDS Market: An Econometric Analysis

In this paper we take an innovative econometric look at the Euro Zone Sovereign Debt Crisis. We are particularly interested in understanding which determinants have led investors to ask for higher yields on sovereign debt from the Euro shatter belt. We dismiss the definition of speculation previously used in the literature, on the basis of the irrelevance of Granger Causality as an operational tool for this purpose. Instead, we suggest that speculative behavior would only exist if market assessment would be unrelated to economic fundamentals of such countries. Using a cross section of countries, we improve on the scarce literature on the Econometrics of Credit Default Swap Markets on sovereign debt. Firstly, we use an ordered probit model to determine whether economic fundamentals are driving the implied rating assessments. Secondly, we provide a pioneering application of quantile regression to this domain, to determine which variables matter at different conditional quantiles of the implied default probability distribution. Finally, Fisher’s Z statistic is used to relate bond markets to domestic saving rates. Overall, the different methodologies support the conclusion that the domestic savings rate is lenders’ main concern. Economies with worse saving habits are penalized both in the CDS market, and in the sovereign bonds markets. Notwithstanding, for countries on the top quantiles of the implied default probabilities, public debt and external debt also play a significant role, increasing the likelihood of higher insurance premium in the derivatives market. When looking at the Portuguese Case it seems clear that public policies that fail to take savings into proper account shall always be deemed to fail, as the country had the lowest net savings rate in the EU27 in 2008, followed closely by Greece.sovereign debt; Euro Area; Credit Default Swaps; Quantile Regression; Ordered Probit; savings rate