Spiraling of approximations and spherical averages of Siegel transforms

We consider the question of how approximations satisfying Dirichlet's theorem spiral around vectors in $\mathbb{R}^d$. We give pointwise almost everywhere results (using only the Birkhoff ergodic theorem on the space of lattices). In addition, we show that for $\textit{every}$ unimodular lattice, on average, the directions of approximates spiral in a uniformly distributed fashion on the $d-1$ dimensional unit sphere. For this second result, we adapt a very recent proof of Marklof and Str\"ombergsson \cite{MS3} to show a spherical average result for Siegel transforms on $\operatorname{SL}_{d+1}(\mathbb{R})/\operatorname{SL}_{d+1}(\mathbb{Z})$. Our techniques are elementary. Results like this date back to the work of Eskin-Margulis-Mozes \cite{EMM} and Kleinbock-Margulis \cite{KM} and have wide-ranging applications. We also explicitly construct examples in which the directions are not uniformly distributed.Comment: 20 pages, 1 figure. Noteworthy changes from the previous version: New title. New result added (Theorem 1.1). Strengthening of Theorem 1.

A software architecture for autonomous spacecraft

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.Includes bibliographical references (leaf 47).by Jimmy S. Shih.M.Eng

Escapement of the Cape rock lobster (Jasus lalandii ) through the mesh and entrance of commercial traps

Metal-framed traps covered with polyethylene mesh used in the fishery for the South African Cape rock lobster (Jasus lalandii) incidentally capture large numbers of undersize (<75 mm CL) specimens. Air-exposure, handling, and release procedures affect captured rock lobsters and reduce the productivity of the stock, which is heavily fished. Optimally, traps should retain legalsize rock lobsters and allow sublegal animals to escape before traps are hauled. Escapement, based on lobster morphometric measurements, through meshes of 62 mm, 75 mm, and 100 mm was investigated theoretically under controlled conditions in an aquarium, and during field trials. SELECT models were used to model escapement, wherever appropriate. Size-selectivity curves based on the logistic model fitted the aquarium and field data better than asymmetrical Richards curves. The lobster length at 50% retention (L50) on the escapement curve for 100-mm mesh in the aquarium (75.5 mm CL) approximated the minimum legal size (75 mm CL); however estimates of L50 increased to 77.4 mm in field trials where trapentrances were sealed, and to 82.2 mm where trap-entrances were open. Therfore, rock lobsters that cannot escape through the mesh of sealed field traps do so through the trap entrance of open traps. By contrast, the wider selection range and lower L25 of field, compared to aquarium, trials (SR = 8.2 mm vs. 2.6 mm; L25 =73.4 mm vs. 74.1 mm), indicate that small lobsters that should be able to escape from 100-mm mesh traps do not always do so. Escapement from 62-mm mesh traps with open entrance funnels increased by 40−60% over sealed traps. The findings of this study with a known size distribution, are related to those of a recent indirect (comparative) study for the same species, and implications for trap surveys, commercial catch rates, and ghost fishing are discussed

On the electromagnetic form factors of the proton from generalized Skyrme models

We compare the prediction of Skyrme-like effective Lagrangians with data for electromagnetic form factors of proton and consider the possibility of fixing the parameters of these higher-order Lagrangians. Our results indicate that one or two-parameter models can lead to better agreement with the data but more accurate determination of the effective Lagragian faces theoretical uncertainties.Comment: 8 pages, 2 figures, revte

Trayectoria de los indicadores del Sistema Universitario Estatal y sus relaciones con el Modelo de los indicadores del Desempeño de la Educación Superior

Los indicadores de un Modelo de Gestión usado por el Ministerio de Educación para evaluar el desempeño y asignar recursos a las universidades públicas colombianas se encuentran publicadas para el periodo 2003 a 2012. Este modelo fue reemplazado en 2015 por el Modelo de Indicadores de Desempeño de Educación Superior (MIDE) que clasifica a las universidades públicas y privadas. Se analizan y describen las trayectorias de las universidades públicas en el periodo, a lo largo de tres factores latentes de evolución. Con estos se construyeron tres clases dinámicas, las cuales se distinguen entre sí porque las trayectorias de las universidades que las conforman son indicadores de su grado de desarrollo en el período. Después se construyen una tipologías o enfoques desarrollados por las universidades en el período, se reconstruyen empíricamente los enfoques del MIDE y se comparan y establecen cercanías entre estos. Los factores fueron construidos con Análisis de Componentes principales aplicados a una reestructura de la matriz de indicadores, cuyas coordenadas sobre los factores contienen información sobre las trayectorias y sobre las variables que la describen y facilita la representación gráfica de tales trayectorias. Los enfoques se reconstruyeron con un Análisis de Correspondencias sobre una tabla de Contingencias de Universidades por niveles de formació

Hard X-ray Emission from the M87 AGN Detected with NuSTAR

M87 hosts a 3-6 billion solar mass black hole with a remarkable relativistic jet that has been regularly monitored in radio to TeV bands. However, hard X-ray emission \gtrsim 10keV, which would be expected to primarily come from the jet or the accretion flow, had never been detected from its unresolved X-ray core. We report NuSTAR detection up to 40 keV from the the central regions of M87. Together with simultaneous Chandra observations, we have constrained the dominant hard X-ray emission to be from its unresolved X-ray core, presumably in its quiescent state. The core spectrum is well fitted by a power law with photon index Gamma=2.11 (+0.15 -0.11). The measured flux density at 40 keV is consistent with a jet origin, although emission from the advection-dominated accretion flow cannot be completely ruled out. The detected hard X-ray emission is significantly lower than that predicted by synchrotron self-Compton models introduced to explain emission above a GeV.Comment: 5 pages, 4 figures, updated to better match the published version in the Astrophysical Journal Letters. A minor typo in the published version (angular scale should be 1 arcsec = 78 pc instead, no result of the paper is affected) is fixed her

Bacterial Quality of Private Water Wells in Clark County, Arkansas

Most private water wells in Clark County appeared to be contaminated by bacteria, apparently entering the wells from surface water seepage. Eighteen to 24% of the wells investigated were positive for fecal contamination. Deeper wells were less often contaminated. More than one-half of the wells sampled exceeded recommended limits of inorganic chemicals for safe potable water. High concentrations of iron and manganese were most common, exceeding recommended limits in more than 40% of the well

Rethinking the Pipeline of Demosaicing, Denoising and Super-Resolution

Incomplete color sampling, noise degradation, and limited resolution are the three key problems that are unavoidable in modern camera systems. Demosaicing (DM), denoising (DN), and super-resolution (SR) are core components in a digital image processing pipeline to overcome the three problems above, respectively. Although each of these problems has been studied actively, the mixture problem of DM, DN, and SR, which is a higher practical value, lacks enough attention. Such a mixture problem is usually solved by a sequential solution (applying each method independently in a fixed order: DM $\to$ DN $\to$ SR), or is simply tackled by an end-to-end network without enough analysis into interactions among tasks, resulting in an undesired performance drop in the final image quality. In this paper, we rethink the mixture problem from a holistic perspective and propose a new image processing pipeline: DN $\to$ SR $\to$ DM. Extensive experiments show that simply modifying the usual sequential solution by leveraging our proposed pipeline could enhance the image quality by a large margin. We further adopt the proposed pipeline into an end-to-end network, and present Trinity Enhancement Network (TENet). Quantitative and qualitative experiments demonstrate the superiority of our TENet to the state-of-the-art. Besides, we notice the literature lacks a full color sampled dataset. To this end, we contribute a new high-quality full color sampled real-world dataset, namely PixelShift200. Our experiments show the benefit of the proposed PixelShift200 dataset for raw image processing.Comment: Code is available at: https://github.com/guochengqian/TENe