392 research outputs found
Zur Differentialgeometrie zweiparametriger Geradenmengen im KLEINschen Modell
In der vorliegenden Arbeit werden Geradenkongruenzen des projektiv abgeschlossenen dreidimensionalen euklidischen Raumes differentialgeometrisch untersucht. Nach J. PLÜCKER lassen sich Geraden in gleicher Weise als Grundelemente eines Geradenraumes auffassen wie die Punkte in einem Punktraum. Unter Beachtung dieser Überlegung scheint eine "natürliche" Behandlung der Geradenkongruenzen interessant und sinnvoll. Sie bildet den Gegenstand der vorliegenden Dissertation. Ein besonderes Augenmerk richtet sich dabei auf die Frage nach "kleinsten" Geradenkongruenzen ("Minimalkongruenzen") in der Geradenmenge des reellen projektiv abgeschlossenen dreidimensionalen euklidischen Raumes. Dahinter verbirgt sich eine gewisse Analogiebildung in der Liniengeometrie, die der klassischen Differentialgeometrie entstammt. Die Geradenkongruenzen bilden hierbei das liniengeometrische Analogon zu den Flächen des dreidimensionalen (Punkt-)Raumes. Das Wort "Kleinste" stellt im Geradenraum einen Bezug zu den Minimalflächen in der Differentialgeometrie her. Nun gestatten diese Fragestellungen in der Liniengeometrie eine anschauliche Interpretation, sobald man ein Punktmodell des Geradenraumes vorliegen hat. Einparametrige Geradenmannigfaltigkeiten (Regelflächen) lassen sich darin als Kurven und Geradenkongruenzen als zweidimensionale Flächen auffassen. Die vierparametrige Geradenmenge des reellen projektiven dreidimensionalen Raumes ist in diesem Modell eine Quadrik vom Index 2 in einem reellen projektiven fünfdimensionalen Raum, die so genannte KLEINsche Hyperquadrik. Der Modellwechsel wird durch die KLEINsche Abbildung vollzogen.In the available work line congruences of the projectively extended three-dimensional euclidean space will be analysed. Following to J. PLÜCKER lines can be seen as basic elements of an line space like in the same way points in a point-space. Taking this fact in consideration a "natural" handling with line congruences might be interesting and reasonable. A special detail in the thesis is the question to minimal congruences in the set of lines of the projectively extended euclidean three-space. It can also be seen as an analogous problem in the geometry of lines which can be find in the differential geometry of surfaces. In this case the line congruences are similar to the surfaces of the three-dimensional (point-)space. The phrase "minimal" means in the line space the connection to the minimal surfaces in the differential geometry. These questions offer in line geometry demonstrative interpretation possibilities if a point-model in the line space exists. One-parameter manifolds of lines (rule surfaces) can be seen in this ambiance as curves and line congruences as two dimensional surfaces. The four-parametric set of lines in the projectively extended three-dimensional euclidian space is in this model a quadric of the index 2 in a real projective five-dimensional space, the so called KLEIN-quadric. The changing of the model is managed by the KLEIN-mapping
On Axonometric Projection of the Contour of a Sphere
Ovaj se članak bavi pitanjem koje se javlja u nastavi nacrtne geometrije za studente preddiplomskog studija u području geodezije i kartografije: Ako se aksonometrijska slika konture kugle konstruira pomoću metode presjeka (L. Eckhart, 1937), tada parovi konturnih točaka, promatranih s obzirom na smjerove presjeka dviju nepridruženih pomoćnih projekcija, određuju općenito dva nekonjugirana promjera konturne elipse i njima konjugirane smjerove. Obratno, elipsa je općenito određena s dva zadana promjera i njima konjugiranim smjerovima. Promatra li se konstrukcija konturne elipse s ravninskog aspekta, iz ovog se načina konstrukcije može izvesti Pascalov teorem.The present article refers to a question that arose during the lecture of descriptive geometry for undergraduate students in the fields of geodesy and cartography: If the axonometric projection of the contour of a sphere is constructed with the help of the cutting method (L. Eckhart, 1937), the pairs of contour points with regard to the
cutting directions of two non-associated auxiliary projections determine two in general non conjugate diameters and
their conjugate directions of the ellipse of contour. Conversely an ellipse is in general overdetermined by two given diameters and their conjugate directions. The theorem of Pascal can be deduced from the figure of construction whereby the construction of the ellipse of contour is considered from a planar point of view
Are planetary nebulae derived from multiple evolutionary scenarios?
Our understanding of planetary nebulae has been significantly enhanced as a
result of several recent large surveys (Parker et al., these proceedings).
These new discoveries suggest that the `PN phenomenon' is in fact more
heterogeneous than previously envisaged. Even after the careful elimination of
mimics from Galactic PN catalogues, there remains a surprising diversity in the
population of PNe and especially their central stars. Indeed, several
evolutionary scenarios are implicated in the formation of objects presently
catalogued as PNe. We provide a summary of these evolutionary pathways and give
examples of each. Eventually, a full census of local PNe can be used to
confront both stellar evolution theory and population synthesis models.Comment: 4 pages, 1 figure. To be published in Planetary Nebulae: an Eye to
the Future, Proceedings of IAU Symposium 283, held in Puerto de la Cruz,
Tenerife, Spain, July 25-29 201
Expression of the Inhibitory CD200 Receptor Is Associated with Alternative Macrophage Activation
Classical macrophage activation is inhibited by the CD200 receptor (CD200R). Here, we show that CD200R expression was specifically induced on human in vitro polarized macrophages of the alternatively activated M2a subtype, generated by incubation with IL-4 or IL-13. In mice, peritoneal M2 macrophages, elicited during infection with the parasites Taenia crassiceps or Tryponosoma brucei brucei, expressed increased CD200R levels compared to those derived from uninfected mice. However, in vitro stimulation of mouse peritoneal macrophages and T crassiceps infection in IL-4-/- and IL-4R-/- mice showed that, in contrast to humans, induction of CD200R in mice was not IL-4 or IL-13 dependent. Our data identify CD200R as a suitable marker for alternatively activated macrophages in humans and corroborate observations of distinct species- and/or site-specific mechanisms regulating macrophage polarization in mouse and man. Copyright (C) 2009 S. Karger AG, Base
Higgs-Dilaton cosmology: Are there extra relativistic species?
Recent analyses of cosmological data suggest the presence of an extra
relativistic component beyond the Standard Model content. The Higgs-Dilaton
cosmological model predicts the existence of a massless particle -the dilaton-
associated with the spontaneous symmetry breaking of scale invariance and
undetectable by any accelerator experiment. Its ultrarelativistic character
makes it a suitable candidate for contributing to the effective number of light
degrees of freedom in the Universe. In this Letter we analyze the dilaton
production at the (p)reheating stage right after inflation and conclude that no
extra relativistic degrees of freedom beyond those already present in the
Standard Model are expected within the simplest Higgs-Dilaton scenario. The
elusive dilaton remains thus essentially undetectable by any particle physics
experiment or cosmological observation.Comment: 7 pages, 1 figure, corrected typos; added reference
Comprehensive modelling of the planetary nebula LMC-SMP 61 and its [WC]-type central star
We present a comprehensive study of the Magellanic Cloud planetary nebula SMP
61 and of its nucleus, a Wolf-Rayet type star classified [WC 5-6]. We have
performed a detailed spectral analysis of the central star, using the Potsdam
code for expanding atmospheres in non-LTE. The fluxes from the model stellar
atmosphere were used to compute photoionization models of the nebula. All the
available observations, within their error bars, were used to constrain these
models. We find that the ionizing fluxes predicted by the stellar model are
basically consistent with the fluxes needed by the photoionization model to
reproduce the nebular emission, within the error margins. However, there are
indications that the stellar model overestimates the number and hardness of
Lyman continuum photons. The photoionization models imply a clumped density
structure of the nebular material. The observed CIII] 1909/CII 4267 line ratio
implies the existence of carbon-rich clumps in the nebula. Such clumps are
likely produced by stellar wind ejecta, possibly mixed with the nebular
material. We discuss our results with regard to the stellar and nebular
post-AGB evolution.Comment: 16 pages, 10 figures, Astronomy and Astrophysics in pres
Beschleunigte elektromagnetische Modellierung resonanter Hohlraumstrukuren durch effiziente Abspaltung des statischen Unterraums
[no abstract available
AI-based detection of contrast-enhancing MRI lesions in patients with multiple sclerosis.
BACKGROUND
Contrast-enhancing (CE) lesions are an important finding on brain magnetic resonance imaging (MRI) in patients with multiple sclerosis (MS) but can be missed easily. Automated solutions for reliable CE lesion detection are emerging; however, independent validation of artificial intelligence (AI) tools in the clinical routine is still rare.
METHODS
A three-dimensional convolutional neural network for CE lesion segmentation was trained externally on 1488 datasets of 934 MS patients from 81 scanners using concatenated information from FLAIR and T1-weighted post-contrast imaging. This externally trained model was tested on an independent dataset comprising 504 T1-weighted post-contrast and FLAIR image datasets of MS patients from clinical routine. Two neuroradiologists (R1, R2) labeled CE lesions for gold standard definition in the clinical test dataset. The algorithmic output was evaluated on both patient- and lesion-level.
RESULTS
On a patient-level, recall, specificity, precision, and accuracy of the AI tool to predict patients with CE lesions were 0.75, 0.99, 0.91, and 0.96. The agreement between the AI tool and both readers was within the range of inter-rater agreement (Cohen's kappa; AI vs. R1: 0.69; AI vs. R2: 0.76; R1 vs. R2: 0.76). On a lesion-level, false negative lesions were predominately found in infratentorial location, significantly smaller, and at lower contrast than true positive lesions (p < 0.05).
CONCLUSIONS
AI-based identification of CE lesions on brain MRI is feasible, approaching human reader performance in independent clinical data and might be of help as a second reader in the neuroradiological assessment of active inflammation in MS patients.
CRITICAL RELEVANCE STATEMENT
Al-based detection of contrast-enhancing multiple sclerosis lesions approaches human reader performance, but careful visual inspection is still needed, especially for infratentorial, small and low-contrast lesions
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