Set Theory or Higher Order Logic to Represent Auction Concepts in Isabelle?

When faced with the question of how to represent properties in a formal proof system any user has to make design decisions. We have proved three of the theorems from Maskin's 2004 survey article on Auction Theory using the Isabelle/HOL system, and we have produced verified code for combinatorial Vickrey auctions. A fundamental question in this was how to represent some basic concepts: since set theory is available inside Isabelle/HOL, when introducing new definitions there is often the issue of balancing the amount of set-theoretical objects and of objects expressed using entities which are more typical of higher order logic such as functions or lists. Likewise, a user has often to answer the question whether to use a constructive or a non-constructive definition. Such decisions have consequences for the proof development and the usability of the formalization. For instance, sets are usually closer to the representation that economists would use and recognize, while the other objects are closer to the extraction of computational content. In this paper we give examples of the advantages and disadvantages for these approaches and their relationships. In addition, we present the corresponding Isabelle library of definitions and theorems, most prominently those dealing with relations and quotients.Comment: Preprint of a paper accepted for the forthcoming CICM 2014 conference (cicm-conference.org/2014): S.M. Watt et al. (Eds.): CICM 2014, LNAI 8543, Springer International Publishing Switzerland 2014. 16 pages, 1 figur

Split radius-form blocks for tube benders

Two-piece, radius-form block permits accurate forming and removing of parts with more than a 180 degree bend. Tube bender can shape flexible metal tubing in applications dealing with plumbing, heating, and pressure transmission lines

The development of a treadle pump: Lessons from the South African experience

Manual pumps / Design / South Africa

Planck pre-launch status: High Frequency Instrument polarization calibration

The High Frequency Instrument of Planck will map the entire sky in the millimeter and sub-millimeter domain from 100 to 857 GHz with unprecedented sensitivity to polarization (ΔP/T_(cmb) ~ 4 × 10^(-6) for P either Q or U and T_(cmb) ≃ 2.7 K) at 100, 143, 217 and 353 GHz. It will lead to major improvements in our understanding of the cosmic microwave background anisotropies and polarized foreground signals. Planck will make high resolution measurements of the E-mode spectrum (up to l ~ 1500) and will also play a prominent role in the search for the faint imprint of primordial gravitational waves on the CMB polarization. This paper addresses the effects of calibration of both temperature (gain) and polarization (polarization efficiency and detector orientation) on polarization measurements. The specific requirements on the polarization parameters of the instrument are set and we report on their pre-flight measurement on HFI bolometers. We present a semi-analytical method that exactly accounts for the scanning strategy of the instrument as well as the combination of different detectors. We use this method to propagate errors through to the CMB angular power spectra in the particular case of Planck-HFI, and to derive constraints on polarization parameters. We show that in order to limit the systematic error to 10% of the cosmic variance of the E-mode power spectrum, uncertainties in gain, polarization efficiency and detector orientation must be below 0.15%, 0.3% and 1° respectively. Pre-launch ground measurements reported in this paper already fulfill these requirements

The conduction pathway of potassium channels is water free under physiological conditions.

Ion conduction through potassium channels is a fundamental process of life. On the basis of crystallographic data, it was originally proposed that potassium ions and water molecules are transported through the selectivity filter in an alternating arrangement, suggesting a "water-mediated" knock-on mechanism. Later on, this view was challenged by results from molecular dynamics simulations that revealed a "direct" knock-on mechanism where ions are in direct contact. Using solid-state nuclear magnetic resonance techniques tailored to characterize the interaction between water molecules and the ion channel, we show here that the selectivity filter of a potassium channel is free of water under physiological conditions. Our results are fully consistent with the direct knock-on mechanism of ion conduction but contradict the previously proposed water-mediated knock-on mechanism