Asymptotic enumeration of correlation-immune boolean functions

A boolean function of $n$ boolean variables is {correlation-immune} of order $k$ if the function value is uncorrelated with the values of any $k$ of the arguments. Such functions are of considerable interest due to their cryptographic properties, and are also related to the orthogonal arrays of statistics and the balanced hypercube colourings of combinatorics. The {weight} of a boolean function is the number of argument values that produce a function value of 1. If this is exactly half the argument values, that is, $2^{n-1}$ values, a correlation-immune function is called {resilient}. An asymptotic estimate of the number $N(n,k)$ of $n$-variable correlation-immune boolean functions of order $k$ was obtained in 1992 by Denisov for constant $k$. Denisov repudiated that estimate in 2000, but we will show that the repudiation was a mistake. The main contribution of this paper is an asymptotic estimate of $N(n,k)$ which holds if $k$ increases with $n$ within generous limits and specialises to functions with a given weight, including the resilient functions. In the case of $k=1$, our estimates are valid for all weights.Comment: 18 page

Bedrock Geology of Bremer County, Iowa

https://ir.uiowa.edu/igs_ofm/1077/thumbnail.jp

Bedrock Geology of the Upper Iowa River Watershed Phase 4: Dorchester (Iowa) 7.5\u27 Quadrangle,

https://ir.uiowa.edu/igs_ofm/1058/thumbnail.jp

Extension of the sun-synchronous Orbit

Through careful consideration of the orbit perturbation force due to the oblate nature of the primary body a secular variation of the ascending node angle of a near-polar orbit can be induced without expulsion of propellant. Resultantly, the orbit perturbations can be used to maintain the orbit plane in, for example, a near-perpendicular (or at any other angle) alignment to the Sun-line throughout the full year of the primary body; such orbits are normally termed Sun-synchronous orbits [1, 2]. Sun-synchronous orbits about the Earth are typically near-circular Low-Earth Orbits (LEOs), with an altitude of less than 1500 km. It is normal to design a LEO such that the orbit period is synchronised with the rotation of the Earth‟s surface over a given period, such that a repeating ground-track is established. A repeating ground-track, together with the near-constant illumination conditions of the ground-track when observed from a Sun-synchronous orbit, enables repeat observations of a target over an extended period under similar illumination conditions [1, 2]. For this reason, Sun-synchronous orbits are extensively used by Earth Observation (EO) platforms, including currently the Environmental Satellite (ENVISAT), the second European Remote Sensing satellite (ERS-2) and many more. By definition, a given Sun-synchronous orbit is a finite resource similar to a geostationary orbit. A typical characterising parameter of a Sun-synchronous orbit is the Mean Local Solar Time (MLST) at descending node, with a value of 1030 hours typical. Note that ERS-1 and ERS-2 used a MLST at descending node of 1030 hours ± 5 minutes, while ENVISAT uses a 1000 hours ± 5 minutes MLST at descending node [3]. Following selection of the MLST at descending node and for a given desired repeat ground-track, the orbit period and hence the semi-major axis are fixed, thereafter assuming a circular orbit is desired it is found that only a single orbit inclination will enable a Sun-synchronous orbit [2]. As such, only a few spacecraft can populate a given repeat ground-track Sun-synchronous orbit without compromise, for example on the MLST at descending node. Indeed a notable feature of on-going studies by the ENVISAT Post launch Support Office is the desire to ensure sufficient propellant remains at end-of-mission for re-orbiting to a graveyard orbit to ensure the orbital slot is available for future missions [4]. An extension to the Sun-synchronous orbit is considered using an undefined, non-orientation constrained, low-thrust propulsion system. Initially the low-thrust propulsion system will be considered for the free selection of orbit inclination and altitude while maintaining the Sun-synchronous condition. Subsequently the maintenance of a given Sun-synchronous repeat-ground track will be considered, using the low-thrust propulsion system to enable the free selection of orbit altitude. An analytical expression will be developed to describe these extensions prior to then validating the analytical expressions within a numerical simulation of a spacecraft orbit. Finally, an analysis will be presented on transfer and injection trajectories to these orbits

Surficial Geology of the Upper Iowa River Watershed: Phase 4: Cresco Ne 7.5\u27 Quadrangle,

https://ir.uiowa.edu/igs_ofm/1055/thumbnail.jp

Bedrock Geology of the Upper Iowa River Watershed: Phase 4: Ridgeway 7.5\u27 Quadrangle,

https://ir.uiowa.edu/igs_ofm/1056/thumbnail.jp

Assessment of DNA extracted from FTA® cards for use on the Illumina iSelect BeadChip

<p>Abstract</p> <p>Background</p> <p>As FTA^®cards provide an ideal medium for the field collection of DNA we sought to assess the quality of genomic DNA extracted from this source for use on the Illumina BovineSNP50 iSelect BeadChip which requires unbound, relatively intact (fragment sizes ≥ 2 kb), and high-quality DNA. Bovine blood and nasal swab samples collected on FTA cards were extracted using the commercially available GenSolve kit with a minor modification. The call rate and concordance of genotypes from each sample were compared to those obtained from whole blood samples extracted by standard PCI extraction.</p> <p>Findings</p> <p>An ANOVA analysis indicated no significant difference (P > 0.72) in BovineSNP50 genotype call rate between DNA extracted from FTA cards by the GenSolve kit or extracted from whole blood by PCI. Two sample t-tests demonstrated that the DNA extracted from the FTA cards produced genotype call and concordance rates that were not different to those produced by assaying DNA samples extracted by PCI from whole blood.</p> <p>Conclusion</p> <p>We conclude that DNA extracted from FTA cards by the GenSolve kit is of sufficiently high quality to produce results comparable to those obtained from DNA extracted from whole blood when assayed by the Illumina iSelect technology. Additionally, we validate the use of nasal swabs as an alternative to venous blood or buccal samples from animal subjects for reliably producing high quality genotypes on this platform.</p

Bedrock Geology of the Davenport West 7.5\u27 Quadrangle, Scott County, Iowa

https://ir.uiowa.edu/igs_ofm/1064/thumbnail.jp

Surficial Geology of the Upper Iowa River Watershed Phase 4: Ridgeway 7.5\u27 Quadrangle,

https://ir.uiowa.edu/igs_ofm/1057/thumbnail.jp

Life on ice, Antarctica and Mars

The study of the origin of life and the prospects for human exploration of Mars are two themes developed in a new 57-minute film, Life on Ice, Antarctica, and Mars, produced by the InnerSpace Foundation and WHRO Television for broadcast by the Public Broadcasting System (PBS). A brief explanation of the film and how it relates to the future human exploration of space is presented