Von Fuzzy-Sets zu Computing-with-Words

Dieser Artikel bietet einen Überblick über die Entwicklung und Zusammenhänge der einzelnen Elemente der Fuzzy-Logik, wovon Fuzzy-Set-Theorie die Grundlage bildet. Die Grundproblematik besteht in der Handhabung von linguistischen Informationen, die häufig durch Ungenauigkeit gekennzeichnet sind. Die verschiedenen technischen Anwendungen von Fuzzy-Logik bieten eine Möglichkeit, intelligentere Computersysteme zu konstruieren, die mit unpräzisen Informationen umgehen können. Solche Systeme sind Indizien für die Entstehung einer neuen Ära des Cognitive-Computing, di in diesemArtikel ebenfalls zur Sprache kommt. Für das bessere Verständnis wird der Artikel mit einem Beispiel aus der Meteorologie (d. h. Schnee in Adelboden) begleitet.

A comprehensive discussion of HMBC pulse sequences. III. Solving the problem of missing and weakly observed long-range correlations

The intensity of long-range correlations observed with the classical HMBC pulse sequence using static optimization of the long-range coupling delay is directly related to the size of the coupling constant and is often set as a compromise. As such, some long-range correlations might appear with a reduced intensity or might even be completely absent from the spectra. After a short introduction, this third manuscript will give a detailed review of some selected HMBC variants dedicated to improve the detection of long-range correlations, such as the ACCORD-HMBC, CIGAR-HMBC, and Broadband HMBC experiments. Practical details about the accordion optimization, which affords a substantial improvement in both the number and intensity of the long-range correlations observed, but introduces a modulation in F1, will be discussed. The incorporation of the so-called constant time variable delay in the CIGAR-HMBC experiment, which can trigger or even completely suppress 1H–1H coupling modulation inherent to the utilization of the accordion principle, will be also discussed. The broadband HMBC scheme, which consists of recording a series of HMBC spectra with different delays set as a function of the long-range heteronuclear coupling constant ranges and transverse relaxation times T2, is also examined.

Gravitational wave background from Standard Model physics: qualitative features

Because of physical processes ranging from microscopic particle collisions to macroscopic hydrodynamic fluctuations, any plasma in thermal equilibrium emits gravitational waves. For the largest wavelengths the emission rate is proportional to the shear viscosity of the plasma. In the Standard Model at 0T > 16 GeV, the shear viscosity is dominated by the most weakly interacting particles, right-handed leptons, and is relatively large. We estimate the order of magnitude of the corresponding spectrum of gravitational waves. Even though at small frequencies (corresponding to the sub-Hz range relevant for planned observatories such as eLISA) this background is tiny compared with that from non-equilibrium sources, the total energy carried by the high-frequency part of the spectrum is non-negligible if the production continues for a long time. We suggest that this may constrain (weakly) the highest temperature of the radiation epoch. Observing the high-frequency part directly sets a very ambitious goal for future generations of GHz-range detectors.

Regularity conditions in the realisability problem in applications to point processes and random closed sets

We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive ex-tension for linear functionals accompanied by additional conditions that ensure the regularity of the extension needed for interpreting it as a probability measure. It is shown in which case the extens ion can be chosen to possess some invariance properties. The results are applied to the existence of point processes with given correlation measure and random closed sets with given two-point covering function or contact distribution function. It is shown that the regularity condition can be efficiently checked in many cases in order to ensure that the obtained point processes are indeed locally finite and random sets have closed realisations.

Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

3D documentation and visualization of external injury findings by integration of simple photography in CT/MRI data sets (IprojeCT).

This study evaluated the feasibility of documenting patterned injury using three dimensions and true colour photography without complex 3D surface documentation methods. This method is based on a generated 3D surface model using radiologic slice images (CT) while the colour information is derived from photographs taken with commercially available cameras. The external patterned injuries were documented in 16 cases using digital photography as well as highly precise photogrammetry-supported 3D structured light scanning. The internal findings of these deceased were recorded using CT and MRI. For registration of the internal with the external data, two different types of radiographic markers were used and compared. The 3D surface model generated from CT slice images was linked with the photographs, and thereby digital true-colour 3D models of the patterned injuries could be created (Image projection onto CT/IprojeCT). In addition, these external models were merged with the models of the somatic interior. We demonstrated that 3D documentation and visualization of external injury findings by integration of digital photography in CT/MRI data sets is suitable for the 3D documentation of individual patterned injuries to a body. Nevertheless, this documentation method is not a substitution for photogrammetry and surface scanning, especially when the entire bodily surface is to be recorded in three dimensions including all external findings, and when precise data is required for comparing highly detailed injury features with the injury-inflicting tool.

ROSINA/DFMS and IES observations of 67P: Ion-neutral chemistry in the coma of a weakly outgassing comet

Context. The Rosetta encounter with comet 67P/Churyumov-Gerasimenko provides a unique opportunity for an in situ, up-close investigation of ion-neutral chemistry in the coma of a weakly outgassing comet far from the Sun. Aims. Observations of primary and secondary ions and modeling are used to investigate the role of ion-neutral chemistry within the thin coma. Methods. Observations from late October through mid-December 2014 show the continuous presence of the solar wind 30 km from the comet nucleus. These and other observations indicate that there is no contact surface and the solar wind has direct access to the nucleus. On several occasions during this time period, the Rosetta/ROSINA/Double Focusing Mass Spectrometer measured the low-energy ion composition in the coma. Organic volatiles and water group ions and their breakup products (masses 14 through 19), CO2+ (masses 28 and 44) and other mass peaks (at masses 26, 27, and possibly 30) were observed. Secondary ions include H3O+ and HCO+ (masses 19 and 29). These secondary ions indicate ion-neutral chemistry in the thin coma of the comet. A relatively simple model is constructed to account for the low H3O+/H2O+ and HCO+/CO+ ratios observed in a water dominated coma. Results from this simple model are compared with results from models that include a more detailed chemical reaction network. Results. At low outgassing rates, predictions from the simple model agree with observations and with results from more complex models that include much more chemistry. At higher outgassing rates, the ion-neutral chemistry is still limited and high HCO+/CO+ ratios are predicted and observed. However, at higher outgassing rates, the model predicts high H3O+/H2O+ ratios and the observed ratios are often low. These low ratios may be the result of the highly heterogeneous nature of the coma, where CO and CO2 number densities can exceed that of water.

Automated 3D Lumbar Intervertebral Disc Segmentation from MRI Data Sets

This paper proposed an automated three-dimensional (3D) lumbar intervertebral disc (IVD) segmentation strategy from Magnetic Resonance Imaging (MRI) data. Starting from two user supplied landmarks, the geometrical parameters of all lumbar vertebral bodies and intervertebral discs are automatically extracted from a mid-sagittal slice using a graphical model based template matching approach. Based on the estimated two-dimensional (2D) geometrical parameters, a 3D variable-radius soft tube model of the lumbar spine column is built by model fitting to the 3D data volume. Taking the geometrical information from the 3D lumbar spine column as constraints and segmentation initialization, the disc segmentation is achieved by a multi-kernel diffeomorphic registration between a 3D template of the disc and the observed MRI data. Experiments on 15 patient data sets showed the robustness and the accuracy of the proposed algorithm.

Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.

Compact Singlet S Helium Wave functions(corrected)

This is a corrected version of the Phys. Rev. A 74,14501 (2006) article. The result is improved slightly from that in the original paper.

Fast Algorithms Using Minimal Data Structures for Common Topological Relationships in Large, Irregularly-spaced Topographic Data Sets

Digital terrain models (DTM) typically contain large numbers of postings, from hundreds of thousands to billions. Many algorithms that run on DTMs require topological knowledge of the postings, such as finding nearest neighbors, finding the posting closest to a chosen location, etc. If the postings are arranged irregu- larly, topological information is costly to compute and to store. This paper offers a practical approach to organizing and searching irregularly-space data sets by presenting a collection of efficient algorithms (O(N),O(lgN)) that compute important topological relationships with only a simple supporting data structure. These relationships include finding the postings within a window, locating the posting nearest a point of interest, finding the neighborhood of postings nearest a point of interest, and ordering the neighborhood counter-clockwise. These algorithms depend only on two sorted arrays of two-element tuples, holding a planimetric coordinate and an integer identification number indicating which posting the coordinate belongs to. There is one array for each planimetric coordinate (eastings and northings). These two arrays cost minimal overhead to create and store but permit the data to remain arranged irregularly.