Linearized Asymptotic Stability for Fractional Differential Equations

We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. As a consequence we extend Lyapunov's first method to fractional differential equations by proving that if the spectrum of the linearization is contained in the sector \{\lambda \in \C : |\arg \lambda| > \frac{\alpha \pi}{2}\} where $\alpha > 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable

Report of the ultraviolet and visible sensors panel

In order to meet the science objectives of the Astrotech 21 mission set the Ultraviolet (UV) and Visible Sensors Panel made a number of recommendations. In the UV wavelength range of 0.01 to 0.3 micro-m the focus is on the need for large format high quantum efficiency, radiation hard 'solar-blind' detectors. Options recommended for support include Si and non-Si charge coupled devices (CCDs) as well as photocathodes with improved microchannel plate readouts. For the 0.3 to 0.9 micro-m range, it was felt that Si CCDs offer the best option for high quantum efficiencies at these wavelengths. In the 0.9 to 2.5 micro-m the panel recommended support for the investigation of monolithic arrays. Finally, the panel noted that the implementation of very large arrays will require new data transmission, data recording, and data handling technologies

The ARGUS Vertex Trigger

A fast second level trigger has been developed for the ARGUS experiment which recognizes tracks originating from the interaction region. The processor compares the hits in the ARGUS Micro Vertex Drift Chamber to 245760 masks stored in random access memories. The masks which are fully defined in three dimensions are able to reject tracks originating in the wall of the narrow beampipe of 10.5\,mm radius.Comment: gzipped Postscript, 27 page

Interannual variability of the stratospheric wave driving during northern winter

The strength of the stratospheric wave driving during northern winter is often quantified by the January–February mean poleward eddy heat flux at 100 hPa, averaged over 40°–80° N (or a similar area and period). Despite the dynamical and chemical relevance of the wave driving, the causes for its variability are still not well understood. In this study, ERA-40 reanalysis data for the period 1979–2002 are used to examine several factors that significantly affect the interannual variability of the wave driving. The total poleward heat flux at 100 hPa is poorly correlated with that in the troposphere, suggesting a decoupling between 100 hPa and the troposphere. However, the individual zonal wave-1 and wave-2 contributions to the wave driving at 100 hPa do exhibit a significant coupling with the troposphere, predominantly their stationary components. The stationary wave-1 contribution to the total wave driving significantly depends on the latitude of the stationary wave-1 source in the troposphere. The results suggest that this dependence is associated with the varying ability of stationary wave-1 activity to enter the tropospheric waveguide at mid-latitudes. The wave driving anomalies are separated into three parts: one part due to anomalies in the zonal correlation coefficient between the eddy temperature and eddy meridional wind, another part due to anomalies in the zonal eddy temperature amplitude, and a third part due to anomalies in the zonal eddy meridional wind amplitude. It is found that year-to-year variability in the zonal correlation coefficient between the eddy temperature and the eddy meridional wind is the most dominant factor in explaining the year-to-year variability of the poleward eddy heat flux

Optimal sequential fingerprinting: Wald vs. Tardos

We study sequential collusion-resistant fingerprinting, where the fingerprinting code is generated in advance but accusations may be made between rounds, and show that in this setting both the dynamic Tardos scheme and schemes building upon Wald's sequential probability ratio test (SPRT) are asymptotically optimal. We further compare these two approaches to sequential fingerprinting, highlighting differences between the two schemes. Based on these differences, we argue that Wald's scheme should in general be preferred over the dynamic Tardos scheme, even though both schemes have their merits. As a side result, we derive an optimal sequential group testing method for the classical model, which can easily be generalized to different group testing models.Comment: 12 pages, 10 figure

Using DNA Methylation Patterns to Infer Tumor Ancestry

Background: Exactly how human tumors grow is uncertain because serial observations are impractical. One approach to reconstruct the histories of individual human cancers is to analyze the current genomic variation between its cells. The greater the variations, on average, the greater the time since the last clonal evolution cycle (‘‘a molecular clock hypothesis’’). Here we analyze passenger DNA methylation patterns from opposite sides of 12 primary human colorectal cancers (CRCs) to evaluate whether the variation (pairwise distances between epialleles) is consistent with a single clonal expansion after transformation. Methodology/Principal Findings: Data from 12 primary CRCs are compared to epigenomic data simulated under a single clonal expansion for a variety of possible growth scenarios. We find that for many different growth rates, a single clonal expansion can explain the population variation in 11 out of 12 CRCs. In eight CRCs, the cells from different glands are all equally distantly related, and cells sampled from the same tumor half appear no more closely related than cells sampled from opposite tumor halves. In these tumors, growth appears consistent with a single ‘‘symmetric’ ’ clonal expansion. In three CRCs, the variation in epigenetic distances was different between sides, but this asymmetry could be explained by a single clonal expansion with one region of a tumor having undergone more cell division than the other. The variation in one CRC was complex and inconsistent with a simple single clonal expansion

Hybrid Algorithms Based on Integer Programming for the Search of Prioritized Test Data in Software Product Lines

In Software Product Lines (SPLs) it is not possible, in general, to test all products of the family. The number of products denoted by a SPL is very high due to the combinatorial explosion of features. For this reason, some coverage criteria have been proposed which try to test at least all feature interactions without the necessity to test all products, e.g., all pairs of features (pairwise coverage). In addition, it is desirable to first test products composed by a set of priority features. This problem is known as the Prioritized Pairwise Test Data Generation Problem. In this work we propose two hybrid algorithms using Integer Programming (IP) to generate a prioritized test suite. The first one is based on an integer linear formulation and the second one is based on a integer quadratic (nonlinear) formulation. We compare these techniques with two state-of-the-art algorithms, the Parallel Prioritized Genetic Solver (PPGS) and a greedy algorithm called prioritized-ICPL. Our study reveals that our hybrid nonlinear approach is clearly the best in both, solution quality and computation time. Moreover, the nonlinear variant (the fastest one) is 27 and 42 times faster than PPGS in the two groups of instances analyzed in this work.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Partially funded by the Spanish Ministry of Economy and Competitiveness and FEDER under contract TIN2014-57341-R, the University of Málaga, Andalucía Tech and the Spanish Network TIN2015-71841-REDT (SEBASENet)

Alice: The Rosetta Ultraviolet Imaging Spectrograph

We describe the design, performance and scientific objectives of the NASA-funded ALICE instrument aboard the ESA Rosetta asteroid flyby/comet rendezvous mission. ALICE is a lightweight, low-power, and low-cost imaging spectrograph optimized for cometary far-ultraviolet (FUV) spectroscopy. It will be the first UV spectrograph to study a comet at close range. It is designed to obtain spatially-resolved spectra of Rosetta mission targets in the 700-2050 A spectral band with a spectral resolution between 8 A and 12 A for extended sources that fill its ~0.05 deg x 6.0 deg field-of-view. ALICE employs an off-axis telescope feeding a 0.15-m normal incidence Rowland circle spectrograph with a concave holographic reflection grating. The imaging microchannel plate detector utilizes dual solar-blind opaque photocathodes (KBr and CsI) and employs a 2 D delay-line readout array. The instrument is controlled by an internal microprocessor. During the prime Rosetta mission, ALICE will characterize comet 67P/Churyumov-Gerasimenko's coma, its nucleus, and the nucleus/coma coupling; during cruise to the comet, ALICE will make observations of the mission's two asteroid flyby targets and of Mars, its moons, and of Earth's moon. ALICE has already successfully completed the in-flight commissioning phase and is operating normally in flight. It has been characterized in flight with stellar flux calibrations, observations of the Moon during the first Earth fly-by, and observations of comet Linear T7 in 2004 and comet 9P/Tempel 1 during the 2005 Deep Impact comet-collision observing campaignComment: 11 pages, 7 figure