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

OntoMathPROOntoMath^{PRO} Ontology: A Linked Data Hub for Mathematics

In this paper, we present an ontology of mathematical knowledge concepts that covers a wide range of the fields of mathematics and introduces a balanced representation between comprehensive and sensible models. We demonstrate the applications of this representation in information extraction, semantic search, and education. We argue that the ontology can be a core of future integration of math-aware data sets in the Web of Data and, therefore, provide mappings onto relevant datasets, such as DBpedia and ScienceWISE.Comment: 15 pages, 6 images, 1 table, Knowledge Engineering and the Semantic Web - 5th International Conferenc

A low noise, high thermal stability, 0.1 K test facility for the Planck HFI bolometers

We are developing a facility which will be used to characterize the bolometric detectors for Planck, an ESA mission to investigate the Cosmic Microwave Background. The bolometers operate at 0.1 K, employing neutron-transmutation doped (NTD) Ge thermistors with resistances of several megohms to achieve NEPs~1×10^(–17) W Hz^(–1/2). Characterization of the intrinsic noise of the bolometers at frequencies as low as 0.010 Hz dictates a test apparatus thermal stability of 40 nK Hz^(–1/2) to that frequency. This temperature stability is achieved via a multi-stage isolation and control geometry with high resolution thermometry implemented with NTD Ge thermistors, JFET source followers, and dedicated lock-in amplifiers. The test facility accommodates 24 channels of differential signal readout, for measurement of bolometer V(I) characteristics and intrinsic noise. The test facility also provides for modulated radiation in the submillimeter band incident on the bolometers, for measurement of the optical speed-of-response; this illumination can be reduced below detectable limits without interrupting cryogenic operation. A commercial Oxford Instruments dilution refrigerator provides the cryogenic environment for the test facility

Measuring Planck beams with planets

Aims. Accurate measurement of the cosmic microwave background (CMB) anisotropy requires precise knowledge of the instrument beam. We explore how well the Planck beams will be determined from observations of planets, developing techniques that are also appropriate for other experiments. Methods. We simulate planet observations with a Planck-like scanning strategy, telescope beams, noise, and detector properties. Then we employ both parametric and non-parametric techniques, reconstructing beams directly from the time-ordered data. With a faithful parameterization of the beam shape, we can constrain certain detector properties, such as the time constants of the detectors, to high precision. Alternatively, we decompose the beam using an orthogonal basis. For both techniques, we characterize the errors in the beam reconstruction with Monte Carlo realizations. For a simplified scanning strategy, we study the impact on estimation of the CMB power spectrum. Finally, we explore the consequences for measuring cosmological parameters, focusing on the spectral index of primordial scalar perturbations, n_s. Results. The quality of the power spectrum measurement will be significantly influenced by the optical modeling of the telescope. In our most conservative case, using no information about the optics except the measurement of planets, we find that a single transit of Jupiter across the focal plane will measure the beam window functions to better than 0.3% for the channels at 100–217 GHz that are the most sensitive to the CMB. Constraining the beam with optical modeling can lead to much higher quality reconstruction. Conclusions. Depending on the optical modeling, the beam errors may be a significant contribution to the measurement systematics for n_s

The adjoint problem in the presence of a deformed surface: the example of the Rosensweig instability on magnetic fluids

The Rosensweig instability is the phenomenon that above a certain threshold of a vertical magnetic field peaks appear on the free surface of a horizontal layer of magnetic fluid. In contrast to almost all classical hydrodynamical systems, the nonlinearities of the Rosensweig instability are entirely triggered by the properties of a deformed and a priori unknown surface. The resulting problems in defining an adjoint operator for such nonlinearities are illustrated. The implications concerning amplitude equations for pattern forming systems with a deformed surface are discussed.Comment: 11 pages, 1 figur

Markov Chain Beam Randomization: a study of the impact of PLANCK beam measurement errors on cosmological parameter estimation

We introduce a new method to propagate uncertainties in the beam shapes used to measure the cosmic microwave background to cosmological parameters determined from those measurements. The method, which we call Markov Chain Beam Randomization, MCBR, randomly samples from a set of templates or functions that describe the beam uncertainties. The method is much faster than direct numerical integration over systematic `nuisance' parameters, and is not restricted to simple, idealized cases as is analytic marginalization. It does not assume the data are normally distributed, and does not require Gaussian priors on the specific systematic uncertainties. We show that MCBR properly accounts for and provides the marginalized errors of the parameters. The method can be generalized and used to propagate any systematic uncertainties for which a set of templates is available. We apply the method to the Planck satellite, and consider future experiments. Beam measurement errors should have a small effect on cosmological parameters as long as the beam fitting is performed after removal of 1/f noise.Comment: 17 pages, 23 figures, revised version with improved explanation of the MCBR and overall wording. Accepted for publication in Astronomy and Astrophysics (to appear in the Planck pre-launch special issue

Initial test results on bolometers for the Planck high frequency instrument

We summarize the fabrication, flight qualification, and dark performance of bolometers completed at the Jet Propulsion Laboratory for the High Frequency Instrument (HFI) of the joint ESA/NASA Herschel/Planck mission to be launched in 2009. The HFI is a multicolor focal plane which consists of 52 bolometers operated at 100 mK. Each bolometer is mounted to a feedhorn-filter assembly which defines one of six frequency bands centered between 100-857 GHz. Four detectors in each of five bands from 143-857 GHz are coupled to both linear polarizations and thus measure the total intensity. In addition, eight detectors in each of four bands (100, 143, 217, and 353 GHz) couple only to a single linear polarization and thus provide measurements of the Stokes parameters, Q and U, as well as the total intensity. The measured noise equivalent power (NEP) of all detectors is at or below the background limit for the telescope and time constants are a few ms, short enough to resolve point sources as the 5 to 9 arc min beams move across the sky at 1 rpm

Nanopositioning of a diamond nanocrystal containing a single NV defect center

Precise control over the position of a single quantum object is important for many experiments in quantum science and nanotechnology. We report on a technique for high-accuracy positioning of individual diamond nanocrystals. The positioning is done with a home-built nanomanipulator under real-time scanning electron imaging, yielding an accuracy of a few nanometers. This technique is applied to pick up, move and position a single NV defect center contained in a diamond nanocrystal. We verify that the unique optical and spin properties of the NV center are conserved by the positioning process.Comment: 3 pages, 3 figures; high-resolution version available at http://www.ns.tudelft.nl/q

Via Hexagons to Squares in Ferrofluids: Experiments on Hysteretic Surface Transformations under Variation of the Normal Magnetic Field

We report on different surface patterns on magnetic liquids following the Rosensweig instability. We compare the bifurcation from the flat surface to a hexagonal array of spikes with the transition to squares at higher fields. From a radioscopic mapping of the surface topography we extract amplitudes and wavelengths. For the hexagon--square transition, which is complex because of coexisting domains, we tailor a set of order parameters like peak--to--peak distance, circularity, angular correlation function and pattern specific amplitudes from Fourier space. These measures enable us to quantify the smooth hysteretic transition. Voronoi diagrams indicate a pinning of the domains. Thus the smoothness of the transition is roughness on a small scale.Comment: 17 pages, 14 figure