Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension in W, the size of the set of leaves of the foliation that are mapped onto sets of higher dimension. We discuss key examples of such foliations, including foliations of the Heisenberg group by left and right cosets of horizontal subgroups.

Lunar energetic neutral atom (ENA) spectra measured by the interstellar boundary explorer (IBEX)

The solar wind continuously flows out from the Sun, filling interplanetary space and directly interacting with the surfaces of small planetary bodies and other objects throughout the solar system. A significant fraction of these ions backscatter from the surface as energetic neutral atoms (ENAs). The first observations of these ENA emissions from the Moon were recently reported from the Interstellar Boundary Explorer (IBEX). These observations yielded a lunar ENA albedo of ˜10% and showed that the Moon reflects ˜150 metric tons of neutral hydrogen per year. More recently, a survey of the first 2.5 years of IBEX observations of lunar ENAs was conducted for times when the Moon was in the solar wind. Here, we present the first IBEX ENA observations when the Moon is inside the terrestrial magnetosheath and compare them with observations when the Moon is in the solar wind. Our analysis shows that: (1) the ENA intensities are on average higher when the Moon is in the magnetosheath, (2) the energy spectra are similar above ~0.6* solar wind energy but below there are large differences of the order of a factor of 10, (3) the energy spectra resemble a power law with a "hump" at ˜0.6 * solar wind energy, and (4) this "hump" is broader when the Moon is in the magnetosheath. We explore potential scenarios to explain the differences, namely the effects of the topography of the lunar surface and the consequences of a very different Mach number in the solar wind versus in the magnetosheath.

What determines the impact of alien birds and mammals in Europe?

An often-cited reason for studying the process of invasion by alien species is that the understanding sought can be used to mitigate the impacts of the invaders. Here, we present an analysis of the correlates of local impacts of established alien bird and mammal species in Europe, using a recently described metric to quantify impact. Large-bodied, habitat generalist bird and mammal species that are widespread in their native range, have the greatest impacts in their alien European ranges, supporting our hypothesis that surrogates for the breadth and the amount of resources a species uses are good indicators of its impact. However, not all surrogates are equally suitable. Impacts are generally greater for mammal species giving birth to larger litters, but in contrast are greater for bird species laying smaller clutches. There is no effect of diet breadth on impacts in birds or mammals. On average, mammals have higher impacts than birds. However, the relationships between impact and several traits show common slopes for birds and mammals, and relationships between impact and body mass and latitude do not differ between birds and mammals. These results may help to anticipate which species would have large impacts if introduced, and so direct efforts to prevent such introductions.

A g-factor metric for k-t-GRAPPA- and PEAK-GRAPPA-based parallel imaging.

PURPOSE The aim of this work is to derive a theoretical framework for quantitative noise and temporal fidelity analysis of time-resolved k-space-based parallel imaging methods. THEORY An analytical formalism of noise distribution is derived extending the existing g-factor formulation for nontime-resolved generalized autocalibrating partially parallel acquisition (GRAPPA) to time-resolved k-space-based methods. The noise analysis considers temporal noise correlations and is further accompanied by a temporal filtering analysis. METHODS All methods are derived and presented for k-t-GRAPPA and PEAK-GRAPPA. A sliding window reconstruction and nontime-resolved GRAPPA are taken as a reference. Statistical validation is based on series of pseudoreplica images. The analysis is demonstrated on a short-axis cardiac CINE dataset. RESULTS The superior signal-to-noise performance of time-resolved over nontime-resolved parallel imaging methods at the expense of temporal frequency filtering is analytically confirmed. Further, different temporal frequency filter characteristics of k-t-GRAPPA, PEAK-GRAPPA, and sliding window are revealed. CONCLUSION The proposed analysis of noise behavior and temporal fidelity establishes a theoretical basis for a quantitative evaluation of time-resolved reconstruction methods. Therefore, the presented theory allows for comparison between time-resolved parallel imaging methods and also nontime-resolved methods. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc.

VIRTOPSY--scientific documentation, reconstruction and animation in forensic: individual and real 3D data based geo-metric approach including optical body/object surface and radiological CT/MRI scanning.

Until today, most of the documentation of forensic relevant medical findings is limited to traditional 2D photography, 2D conventional radiographs, sketches and verbal description. There are still some limitations of the classic documentation in forensic science especially if a 3D documentation is necessary. The goal of this paper is to demonstrate new 3D real data based geo-metric technology approaches. This paper present approaches to a 3D geo-metric documentation of injuries on the body surface and internal injuries in the living and deceased cases. Using modern imaging methods such as photogrammetry, optical surface and radiological CT/MRI scanning in combination it could be demonstrated that a real, full 3D data based individual documentation of the body surface and internal structures is possible in a non-invasive and non-destructive manner. Using the data merging/fusing and animation possibilities, it is possible to answer reconstructive questions of the dynamic development of patterned injuries (morphologic imprints) and to evaluate the possibility, that they are matchable or linkable to suspected injury-causing instruments. For the first time, to our knowledge, the method of optical and radiological 3D scanning was used to document the forensic relevant injuries of human body in combination with vehicle damages. By this complementary documentation approach, individual forensic real data based analysis and animation were possible linking body injuries to vehicle deformations or damages. These data allow conclusions to be drawn for automobile accident research, optimization of vehicle safety (pedestrian and passenger) and for further development of crash dummies. Real 3D data based documentation opens a new horizon for scientific reconstruction and animation by bringing added value and a real quality improvement in forensic science.

Cessation of facial growth in subjects with short, average, and long facial types - Implications for the timing of implant placement

Placement of a single-tooth implant should be performed when a patient's facial growth has ceased. In this retrospective observational study, we evaluated if there was a difference in the timing of cessation of craniofacial growth in short, average, and long facial types. Based on the value of the angle between cranial base and mandibular plane (SN/MP angle), three groups comprising 48 subjects with short facial type (SF; SN/MP ≤28°), 77 with average facial type (AF; SN/MP ≥31.5° and ≤34.5°), and 44 with long facial type (LF; SN/MP ≥38°) were selected. Facial growth was assessed on lateral cephalograms taken at 15.4 years of age, and 2, 5, and 10 years later. Variables were considered to be stable when the difference between two successive measurements was less than 1 mm or 1°. We found no difference between facial types in the timing of cessation of facial growth. Depending on the variable, the mean age when variables became stable ranged from 18.0 years (Is-Pal in LF group) to 22.0 years (SN/MP in LF group). However, facial growth continued at the last follow-up in approximately 20% subjects. This study demonstrates that facial type is not associated with the timing of cessation of facial growth.

Explora: A Visualisation Tool for Metric Analysis of Software Corpora

When analysing software metrics, users find that visualisation tools lack support for (1) the detection of patterns within metrics; and (2) enabling analysis of software corpora. In this paper we present Explora, a visualisation tool designed for the simultaneous analysis of multiple metrics of systems in software corpora. Explora incorporates a novel lightweight visualisation technique called PolyGrid that promotes the detection of graphical patterns. We present an example where we analyse the relation of subtype polymorphism with inheritance and invocation in corpora of Smalltalk and Java systems and find that (1) subtype polymorphism is more likely to be found in large hierarchies; (2) as class hierarchies grow horizontally, they also do so vertically; and (3) in polymorphic hierarchies the length of the name of the classes is orthogonal to the cardinality of the call sites.