Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

Geometry of the heart adapts to mechanical load, imposed by pressures and volumes of the cavities. We regarded preservation of cardiac geometry as a homeostatic control system. The control loop was simulated by a chain of models, starting with geometry of the cardiac walls, sequentially simulating circulation hemodynamics, myofiber stress and strain in the walls, transfer of mechano-sensed sign...

Short stemmed hip endoprostheses represent a relevant alternative to standard sized total hip stems. Especially in terms of bone stock preservation and minimal invasiveness the reduced length of such implants is beneficial. However, the smaller implant size is linked to a reduced surface geometry and thereby bone-implant-interface to provide implant stability. In order to evaluate the interfaci...

We obtain a global version of the Hamiltonian KAM theorem for invariant Lagrangean tori by glueing together local KAM conjugacies with help of a partition of unity. In this way we find a global Whitney smooth conjugacy between a nearly integrable system and an integrable one. This leads to preservation of geometry, which allows us to define all nontrivial geometric invariants of an integrable H...

Prevention is better than cure best applies here. As per many authors, posterior leaflet chordae preservation prevent Left ventricular rupture (LVR) and preserve LV geometry. We are presenting here 5 types of left ventricular rupture (LVR) post Mitral valve replacement (MVR) with different methods to repair with the advantages and disadvantages of each. The mortality rate is still very high des...

Ravinement surfaces are produced when the sea floor is eroded into a flat surface by the action of waves or tides during a marine transgression. They are preserved in the transgressive deposits as a sharp erosion surface. In a geological cross section across the ancient shoreline, primary ravinement surfaces appear as a subhorizontal line slightly dipping toward the sea. In a cross section, com...

The human amygdala preferentially responds to objects of potential value, such as hedonically valenced and novel stimuli. Many studies have documented age-related differences in amygdala responses to valenced stimuli, but relatively little is known about age-related changes in the amygdala's response to novelty. This study examines whether there are differences in amygdala novelty responses in ...

background: the aim of this study was to investigate vertebral geometry changes and determine cutoff value of vertebral height to predict fractures. methods: in a cross-sectional study, 280 postmenopausal women recruited .in all subjects bone mineral density and radiog raphy of the lumbar spine performed. lateral radiographs were evaluated for identification of vertebral fractures, using a vali...