On the signature of positive braids and adjacency for torus knots

The objects of study in this thesis are knots. More precisely, positive braid knots, which include algebraic knots and torus knots. In the first part of this thesis, we compare two classical knot invariants - the genus g and the signature σ - for positive braid knots. Our main result on positive braid knots establishes a linear lower bound for the signature in terms of the genus. In the second part of the thesis, a positive braid approach is applied to the study of the local behavior of polynomial functions from the complex affine plane to the complex numbers. After endowing polynomial function germs with a suitable topology, the adjacency problem arises: for a fixed germ f, what classes of germs g can be found arbitrarily close to f? We introduce two purely topological notions of adjacency for knots and discuss connections to algebraic notions of adjacency and the adjacency problem.

Probabilistic approach to cloud and snow detection on Advanced Very High Resolution Radiometer (AVHRR) imagery

Derivation of probability estimates complementary to geophysical data sets has gained special attention over the last years. Information about a confidence level of provided physical quantities is required to construct an error budget of higher-level products and to correctly interpret final results of a particular analysis. Regarding the generation of products based on satellite data a common input consists of a cloud mask which allows discrimination between surface and cloud signals. Further the surface information is divided between snow and snow-free components. At any step of this discrimination process a misclassification in a cloud/snow mask propagates to higher-level products and may alter their usability. Within this scope a novel probabilistic cloud mask (PCM) algorithm suited for the 1 km × 1 km Advanced Very High Resolution Radiometer (AVHRR) data is proposed which provides three types of probability estimates between: cloudy/clear-sky, cloudy/snow and clear-sky/snow conditions. As opposed to the majority of available techniques which are usually based on the decision-tree approach in the PCM algorithm all spectral, angular and ancillary information is used in a single step to retrieve probability estimates from the precomputed look-up tables (LUTs). Moreover, the issue of derivation of a single threshold value for a spectral test was overcome by the concept of multidimensional information space which is divided into small bins by an extensive set of intervals. The discrimination between snow and ice clouds and detection of broken, thin clouds was enhanced by means of the invariant coordinate system (ICS) transformation. The study area covers a wide range of environmental conditions spanning from Iceland through central Europe to northern parts of Africa which exhibit diverse difficulties for cloud/snow masking algorithms. The retrieved PCM cloud classification was compared to the Polar Platform System (PPS) version 2012 and Moderate Resolution Imaging Spectroradiometer (MODIS) collection 6 cloud masks, SYNOP (surface synoptic observations) weather reports, Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) vertical feature mask version 3 and to MODIS collection 5 snow mask. The outcomes of conducted analyses proved fine detection skills of the PCM method with results comparable to or better than the reference PPS algorithm.

Daytime Low Stratiform Cloud Detection on AVHRR Imagery

The near-real time retrieval of low stratiform cloud (LSC) coverage is of vital interest for such disciplines as meteorology, transport safety, economy and air quality. Within this scope, a novel methodology is proposed which provides the LSC occurrence probability estimates for a satellite scene. The algorithm is suited for the 1 × 1 km Advanced Very High Resolution Radiometer (AVHRR) data and was trained and validated against collocated SYNOP observations. Utilisation of these two combined data sources requires a formulation of constraints in order to discriminate cases where the LSC is overlaid by higher clouds. The LSC classification process is based on six features which are first converted to the integer form by step functions and combined by means of bitwise operations. Consequently, a set of values reflecting a unique combination of those features is derived which is further employed to extract the LSC occurrence probability estimates from the precomputed look-up vectors (LUV). Although the validation analyses confirmed good performance of the algorithm, some inevitable misclassification with other optically thick clouds were reported. Moreover, the comparison against Polar Platform System (PPS) cloud-type product revealed superior classification accuracy. From the temporal perspective, the acquired results reported a presence of diurnal and annual LSC probability cycles over Europe.

Effects of exposure to physical factors on homeopathic preparations as determined by ultraviolet light spectroscopy

Clinical trials have reported statistically significant and clinically relevant effects of homeopathic preparations. We applied ultraviolet (UV) spectroscopy to investigate the physical properties of homeopathic preparations and to contribute to an understanding of the not-yet-identified mode of action. In previous investigations, homeopathic preparations had significantly lower UV light transmissions than controls. The aim of this study was to explore the possible effects of external factors (UV light and temperature) on the homeopathic preparations. Homeopathic centesimal (c) dilutions, 1c to 30c, of copper sulfate (CuSO(4)), decimal dilutions of sulfur (S(8)), 1x to 30x, and controls (succussed potentization medium) were prepared, randomized, and blinded. UV transmission was measured at six different time points after preparation (from 4 to 256 days). In addition, one series of samples was exposed to UV light of a sterilization lamp for 12 h, one was incubated at 37 degrees Celsius for 24 h, and one was heated to 90 degrees Celsius for 15 min. UV light transmission values from 190 or 220 nm to 340 nm were measured several times and averaged. After each exposure, UV transmission of the homeopathic preparations of CuSO(4) was significantly reduced compared to the controls, particularly after heating to 37 degrees Celsius. Overall, the nonexposed CuSO(4) preparations did not show significantly lower UV transmission compared to controls; however, the pooled subgroup of measurements at days 26, 33, and 110 yielded significant differences. UV light transmission for S(8) preparations did not show any differences compared to controls. Our conclusion is that exposure to external factors, incubation at 37 degrees Celsius in particular, increases the difference in light transmission of homeopathic CuSO(4) preparations compared to controls.

Improved detection of pulmonary nodules on energy-subtracted chest radiographs with a commercial computer-aided diagnosis software: comparison with human observers

To retrospectively analyze the performance of a commercial computer-aided diagnosis (CAD) software in the detection of pulmonary nodules in original and energy-subtracted (ES) chest radiographs.

Effect of valsartan on the incidence of diabetes and cardiovascular events

It is not known whether drugs that block the renin-angiotensin system reduce the risk of diabetes and cardiovascular events in patients with impaired glucose tolerance.