Asymptotically efficient triangulations of the d-cube

Let $P$ and $Q$ be polytopes, the first of "low" dimension and the second of "high" dimension. We show how to triangulate the product $P \times Q$ efficiently (i.e., with few simplices) starting with a given triangulation of $Q$. Our method has a computational part, where we need to compute an efficient triangulation of $P \times \Delta^m$, for a (small) natural number $m$ of our choice. $\Delta^m$ denotes the $m$-simplex. Our procedure can be applied to obtain (asymptotically) efficient triangulations of the cube $I^n$: We decompose $I^n = I^k \times I^{n-k}$, for a small $k$. Then we recursively assume we have obtained an efficient triangulation of the second factor and use our method to triangulate the product. The outcome is that using $k=3$ and $m=2$, we can triangulate $I^n$ with $O(0.816^{n} n!)$ simplices, instead of the $O(0.840^{n} n!)$ achievable before.Comment: 19 pages, 6 figures. Only minor changes from previous versions, some suggested by anonymous referees. Paper accepted in "Discrete and Computational Geometry

The polytope of non-crossing graphs on a planar point set

For any finite set \A of $n$ points in $\R^2$, we define a $(3n-3)$-dimensional simple polyhedron whose face poset is isomorphic to the poset of ``non-crossing marked graphs'' with vertex set \A, where a marked graph is defined as a geometric graph together with a subset of its vertices. The poset of non-crossing graphs on \A appears as the complement of the star of a face in that polyhedron. The polyhedron has a unique maximal bounded face, of dimension $2n_i +n -3$ where $n_i$ is the number of points of \A in the interior of \conv(\A). The vertices of this polytope are all the pseudo-triangulations of \A, and the edges are flips of two types: the traditional diagonal flips (in pseudo-triangulations) and the removal or insertion of a single edge. As a by-product of our construction we prove that all pseudo-triangulations are infinitesimally rigid graphs.Comment: 28 pages, 16 figures. Main change from v1 and v2: Introduction has been reshape

Geographic Information Systems (GIS)-based spatially distributed model for runoff routing

A method is proposed for routing spatially distributed excess precipitation over a watershed to produce runoff at its outlet. The land surface is represented by a (raster) digital elevation model from which the stream network is derived. A routing response function is defined for each digital elevation model cell so that water movement from cell to cell can be convolved to give a response function along a flow path and responses from all cells can be summed to give the outlet hydrograph. An example application of analysis of runoff on Waller Creek in Austin, Texas, is presented.Waller Creek Working Grou

Electrical design of payload G-534: The Pool Boiling Experiment

Payload G-534, the Pool Boiling Experiment (PBE), is a Get Away Special that is scheduled to fly on the shuttle in 1992. This paper will give a brief overall description of the experiment with the main discussion being the electrical design with a detailed description of the power system and interface to the GAS electronics. The batteries used and their interface to the experiment Power Control Unit (PCU) and GAS electronics will be examined. The design philosophy for the PCU will be discussed in detail. The criteria for selection of fuses, relays, power semiconductors and other electrical components along with grounding and shielding policy for the entire experiment will be presented. The intent of this paper is to discuss the use of military tested parts and basic design guidelines to build a quality experiment for minimal additional cost

Battery selection for space experiments

This paper will delineate the criteria required for the selection of batteries as a power source for space experiments. Four basic types of batteries will be explored, lead acid, silver zinc, alkaline manganese and nickel cadmium. A detailed description of the lead acid and silver zinc cells while a brief exploration of the alkaline manganese and nickel cadmium will be given. The factors involved in battery selection such as packaging, energy density, discharge voltage regulation, and cost will be thoroughly examined. The pros and cons of each battery type will be explored. Actual laboratory test data acquired for the lead acid and silver zinc cell will be discussed. This data will include discharging under various temperature conditions, after three months of storage and with different types of loads. A description of the required maintenance for each type of battery will be investigated. The lifetime and number of charge/discharge cycles will be discussed

Battery selection for Space Shuttle experiments

This paper will delineate the criteria required for the selection of batteries as a power source for space experiments. Four basic types of batteries will be explored, lead acid, silver zinc, alkaline manganese, and nickel cadmium. A detailed description of the lead acid and silver zinc cells and a brief exploration of the alkaline manganese and nickel cadmium will be given. The factors involved in battery selection such as packaging, energy density, discharge voltage regulation, and cost will be thoroughly examined. The pros and cons of each battery type will be explored. Actual laboratory test data acquired for the lead acid and silver zinc cell will be discussed. This data will include discharging under various temperature conditions, after three months of storage, and with different types of loads. The lifetime and number of charge/discharge cycles will also be discussed. A description of the required maintenance for each type of battery will be investigated

Electrical design of Space Shuttle payload G-534: The pool boiling experiment

Payload G-534, the Pool Boiling Experiment (PBE), is a Get Away Special (GAS) payload that flew on the Space Shuttle Spacelab Mission J (STS 47) on September 19-21, 1992. This paper will give a brief overall description of the experiment with the main discussion being the electrical design with a detailed description of the power system and interface to the GAS electronics. The batteries used and their interface to the experiment Power Control Unit (PCU) and GAS electronics will be examined. The design philosophy for the PCU will be discussed in detail. The criteria for selection of fuses, relays, power semiconductors, and other electrical components along with grounding and shielding policy for the entire experiment are presented. The intent of this paper is to discuss the use of military tested parts and basic design guidelines to build a quality experiment for minimal additional cost

Do Quasi-Hyperbolic Preferences Explain Academic Procrastination? An Empirical Evaluation

Traditional neoclassical thought fails to explain questions such as problems of self-control. Behavioural economics have explained these matters on the basis of the intertemporal preferences of individuals and, specifically, the so-called (β, δ) model which emphasises present bias. This opens the way to the analysis of new situations in which people can adopt incorrect indecisions that make it necessary for the government to intervene. The literature which has developed the (β, δ) model and its implications has generated a categorisation of people that is widely used but which lacks a systematic empirical evaluation. It is important to value the need for this public action. In this article, we develop a method which makes it possible to verify the main implications that this model has to explain the procrastination of university students. Using an experimental time discount task with real monetary incentives, we estimate the students’ β and δ parameters and we analyse their correlation with their answers to a series of questions concerning how they plan to study for an exam. The results are ambiguous given that they back some of the model’s conclusions but reject others, including a number of the most basic ones, such as the relation between present biases and some of the categories of people, these being essential to predict their behaviour