Rotational integral geometry of tensor valuations

We derive a new rotational Crofton formula for Minkowski tensors. In special cases, this formula gives (1) the rotational average of Minkowski tensors defined on linear subspaces and (2) the functional defined on linear subspaces with rotational average equal to a Minkowski tensor. Earlier results obtained for intrinsic volumes appear now as special cases.

Proton diffusion tensor spectroscopy of metabolites in human muscle in vivo

PURPOSE To study the apparent diffusivity and its directionality for metabolites of skeletal muscle in humans in vivo by (1) H magnetic resonance spectroscopy. METHODS The diffusion tensors were determined on a 3 Tesla MR system using optimized acquisition and processing methods including an adapted STEAM sequence with orientation-dependent diffusion weighting, pulse-triggering with individually adapted delays, eddy-current correction schemes, median filtering, and simultaneous prior-knowledge fitting of all related spectra. RESULTS The average apparent diffusivities, as well as the fractional anisotropies of taurine (ADCav  = 0.74 × 10(-3) s/mm(2) , FA = 0.46), creatine (ADCav  = 0.41 × 10(-3)  s/mm(2) , FA = 0.33), trimethylammonium compounds (ADCav  = 0.48 × 10(-3)  s/mm(2) , FA = 0.34), carnosine (ADCav  = 0.46 × 10(-3)  s/mm(2) , FA = 0.47), and water (ADCav  = 1.5 × 10(-3)  s/mm(2) , FA = 0.36) were estimated. The diffusivities of most metabolites and water were significantly different from each other. Diffusion was found to be anisotropic and the diffusion tensors showed tensor correlation coefficients close to 1 and were hence found to be essentially coaligned. The magnitudes of apparent metabolite diffusivities were largely ordered according to molecular weight, with taurine as the smallest molecule diffusing fastest, both along and across the fiber direction. CONCLUSION Diffusivities, directional dependence of diffusion and fractional anisotropies of (1) H MRS-visible muscle metabolites were presented. It was shown that metabolites share diffusion directionality with water and have similar fractional anisotropies, hinting at similar diffusion barriers. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc.

Preservation and representation of human bones and it's importance for anthropological Analysis - an introduction

This paper presents problems arising from the lack of standardized methods for recording skeletal remains. Using practical examples it is shown how preservation and representation of bones can distort observations and how this can be reduced by systematic data acquisition.

Proposal for an International Molybdenum Isotope Measurement Standard and Data Representation

Molybdenum isotopes are increasingly widely applied in Earth Sciences. They are primarily used to investigate the oxygenation of Earth's ocean and atmosphere. However, more and more fields of application are being developed, such as magmatic and hydrothermal processes, planetary sciences or the tracking of environmental pollution. Here, we present a proposal for a unifying presentation of Mo isotope ratios in the studies of mass-dependent isotope fractionation. We suggest that the δ98/95Mo of the NIST SRM 3134 be defined as +0.25‰. The rationale is that the vast majority of published data are presented relative to reference materials that are similar, but not identical, and that are all slightly lighter than NIST SRM 3134. Our proposed data presentation allows a direct first-order comparison of almost all old data with future work while referring to an international measurement standard. In particular, canonical δ98/95Mo values such as +2.3‰ for seawater and −0.7‰ for marine Fe–Mn precipitates can be kept for discussion. As recent publications show that the ocean molybdenum isotope signature is homogeneous, the IAPSO ocean water standard or any other open ocean water sample is suggested as a secondary measurement standard, with a defined δ98/95Mo value of +2.34 ± 0.10‰ (2s). Les isotopes du molybdène (Mo) sont de plus en plus largement utilisés dans les sciences de la Terre. Ils sont principalement utilisés pour étudier l'oxygénation de l'océan et de l'atmosphère de la Terre. Cependant, de plus en plus de domaines d'application sont en cours de développement, tels que ceux concernant les processus magmatiques et hydrothermaux, les sciences planétaires ou encore le suivi de la pollution environnementale. Ici, nous présentons une proposition de présentation unifiée des rapports isotopiques du Mo dans les études du fractionnement isotopique dépendant de la masse. Nous suggérons que le δ98/95Mo du NIST SRM 3134 soit définit comme étant égal à +0.25 ‰. La raison est que la grande majorité des données publiées sont présentés par rapport à des matériaux de référence qui sont similaires, mais pas identiques, et qui sont tous légèrement plus léger que le NIST SRM 3134. Notre proposition de présentation des données permet une comparaison directe au premier ordre de presque toutes les anciennes données avec les travaux futurs en se référant à un standard international. En particulier, les valeurs canoniques du δ98/95Mo comme celle de +2,3 ‰ pour l'eau de mer et de -0,7 ‰ pour les précipités de Fe-Mn marins peuvent être conservés pour la discussion. Comme les publications récentes montrent que la signature isotopique moyenne du molybdène de l'océan est homogène, le standard de l'eau océanique IAPSO ou tout autre échantillon d'eau provenant de l'océan ouvert sont proposé comme standards secondaires, avec une valeur définie du δ98/95 Mo de 2.34 ± 0.10 ‰ (2s).

Fuzzy Web Knowledge Aggregation, Representation, and Reasoning for Online Privacy and Reputation Management

A social Semantic Web empowers its users to have access to collective Web knowledge in a simple manner, and for that reason, controlling online privacy and reputation becomes increasingly important, and must be taken seriously. This chapter presents Fuzzy Cognitive Maps (FCM) as a vehicle for Web knowledge aggregation, representation, and reasoning. With this in mind, a conceptual framework for Web knowledge aggregation, representation, and reasoning is introduced along with a use case, in which the importance of investigative searching for online privacy and reputation is highlighted. Thereby it is demonstrated how a user can establish a positive online presence.

Semantic Representation of Synaesthesia

Synaesthesia has multifaceted consequences for both subjective experience and cognitive performance. Here, I broach the issue of how synaesthesia is represented in semantic memory. I hypothesize that, for example, in grapheme colour synaesthesia, colour is represented as an additional feature in the semantic network that enables the formation of associations that are not present in non-synaesthetes. Thus, synaesthesia provokes richer memory representations which enable learning opportunities that are not present in non-synaesthetes, provides additional memory cues, and may trigger creative ideas.

Sparse representation based action and gesture recognition

In this paper we present a solution to the problem of action and gesture recognition using sparse representations. The dictionary is modelled as a simple concatenation of features computed for each action or gesture class from the training data, and test data is classified by finding sparse representation of the test video features over this dictionary. Our method does not impose any explicit training procedure on the dictionary. We experiment our model with two kinds of features, by projecting (i) Gait Energy Images (GEIs) and (ii) Motion-descriptors, to a lower dimension using Random projection. Experiments have shown 100% recognition rate on standard datasets and are compared to the results obtained with widely used SVM classifier.

Synchrotron x ray induced axonal transections in the brain of rats assessed by high-field diffusion tensor imaging tractography

Since approximately two thirds of epileptic patients are non-eligible for surgery, local axonal fiber transections might be of particular interest for them. Micrometer to millimeter wide synchrotron-generated X-ray beamlets produced by spatial fractionation of the main beam could generate such fiber disruptions non-invasively. The aim of this work was to optimize irradiation parameters for the induction of fiber transections in the rat brain white matter by exposure to such beamlets. For this purpose, we irradiated cortex and external capsule of normal rats in the antero-posterior direction with a 4 mm×4 mm array of 25 to 1000 µm wide beamlets and entrance doses of 150 Gy to 500 Gy. Axonal fiber responses were assessed with diffusion tensor imaging and fiber tractography; myelin fibers were examined histopathologically. Our study suggests that high radiation doses (500 Gy) are required to interrupt axons and myelin sheaths. However, a radiation dose of 500 Gy delivered by wide minibeams (1000 µm) induced macroscopic brain damage, depicted by a massive loss of matter in fiber tractography maps. With the same radiation dose, the damage induced by thinner microbeams (50 to 100 µm) was limited to their paths. No macroscopic necrosis was observed in the irradiated target while overt transections of myelin were detected histopathologically. Diffusivity values were found to be significantly reduced. A radiation dose ≤ 500 Gy associated with a beamlet size of < 50 µm did not cause visible transections, neither on diffusion maps nor on sections stained for myelin. We conclude that a peak dose of 500 Gy combined with a microbeam width of 100 µm optimally induced axonal transections in the white matter of the brain.

Representation via Probabilities: Models of Probabilistic Modeling

How do probabilistic models represent their targets and how do they allow us to learn about them? The answer to this question depends on a number of details, in particular on the meaning of the probabilities involved. To classify the options, a minimalist conception of representation (Su\'arez 2004) is adopted: Modelers devise substitutes (``sources'') of their targets and investigate them to infer something about the target. Probabilistic models allow us to infer probabilities about the target from probabilities about the source. This leads to a framework in which we can systematically distinguish between different models of probabilistic modeling. I develop a fully Bayesian view of probabilistic modeling, but I argue that, as an alternative, Bayesian degrees of belief about the target may be derived from ontic probabilities about the source. Remarkably, some accounts of ontic probabilities can avoid problems if they are supposed to apply to sources only.

Representation Matters: The Impact of Descriptive Women's Representation on the Political Involvement of Women

In a cross-country comparison of 33 European countries, we tested whether a high degree of female representation attenuates the assumed negative impact of gender on political involvement. Our multilevel analyses show positive interactive effects of female representation: the degree to which the representation of women in a given country's national parliament was descriptively adequate was positively related to women's ratings of the importance of politics and self-reported political interest. With respect to political participation, the findings are mixed.