Non-spanning lattice 3-polytopes

We completely classify non-spanning $3$-polytopes, by which we mean lattice $3$-polytopes whose lattice points do not affinely span the lattice. We show that, except for six small polytopes (all having between five and eight lattice points), every non-spanning $3$-polytope $P$ has the following simple description: $P\cap \mathbb{Z}^3$ consists of either (1) two lattice segments lying in parallel and consecutive lattice planes or (2) a lattice segment together with three or four extra lattice points placed in a very specific manner. From this description we conclude that all the empty tetrahedra in a non-spanning $3$-polytope $P$ have the same volume and they form a triangulation of $P$, and we compute the $h^*$-vectors of all non-spanning $3$-polytopes. We also show that all spanning $3$-polytopes contain a unimodular tetrahedron, except for two particular $3$-polytopes with five lattice points.Comment: 20 pages. Changes from v2: small changes requested by journal referee; corrected typos in Thm 1.3; updated reference

Financial Aid and Higher Education Enrollment in Chile: A Government Policy Analysis

This paper evaluates the impact of the Chilean government's nancial aid on college and vocational education enrollment. We found that there is an endogenous process in the application for nancial aid. To solve this problem we use a two-step procedure with instrumental variables (IV) and found that nancial aid increases the probability of students going to college by over 30%. In the case of vocational education, we found that being pre-selected for college nancial aid decreases the enrollment. However, vocational nancial aid increases that probability of enrollment. Therefore, students choose college education over vocational education when they have nancial aid for both. Theoretical conclusion and public policy recommendations are provided.Financial aid; college enrollment; Chile; education; public policy.

A model-based methodology for managing technological risk

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Lattice 3-polytopes with few lattice points

We extend White's classification of empty tetrahedra to the complete classification of lattice $3$-polytopes with five lattice points, showing that, apart from infinitely many of width one, there are exactly nine equivalence classes of them with width two and none of larger width. We also prove that, for each $n\in \mathbb{N}$, there is only a finite number of (classes of) lattice $3$-polytopes with $n$ lattice points and of width larger than one. This implies that extending the present classification to larger sizes makes sense, which is the topic of subsequent papers of ours.Comment: 19 pages, 9 figure

Testing the Forecasting Performance of Ibex 35 Option-implied Risk-neutral Densities

Published also as: Documento de Trabajo Banco de España 0504/2005.risk-neutral densities, forecasting performance

Electronic excitation of furfural as probed by high-resolution vacuum ultraviolet spectroscopy, electron energy loss spectroscopy, and ab initio calculations

The electronic spectroscopy of isolated furfural (2-furaldehyde) in the gas phase has been investigated using high-resolution photoabsorption spectroscopy in the 3.5-10.8 eV energy-range, with absolute cross section measurements derived. Electron energy loss spectra are also measured over a range of kinematical conditions. Those energy loss spectra are used to derive differential cross sections and in turn generalised oscillator strengths. These experiments are supported by ab initio calculations in order to assign the excited states of the neutral molecule. The good agreement between the theoretical results and the measurements allows us to provide the first quantitative assignment of the electronic state spectroscopy of furfural over an extended energy range. (C) 2015 AIP Publishing LLC