Topology-Aware Surface Reconstruction for Point Clouds

We present an approach to inform the reconstruction of a surface from a point scan through topological priors. The reconstruction is based on basis functions which are optimized to provide a good fit to the point scan while satisfying predefined topological constraints. We optimize the parameters of a model to obtain likelihood function over the reconstruction domain. The topological constraints are captured by persistence diagrams which are incorporated in the optimization algorithm promote the correct topology. The result is a novel topology-aware technique which can: 1.) weed out topological noise from point scans, and 2.) capture certain nuanced properties of the underlying shape which could otherwise be lost while performing surface reconstruction. We showcase results reconstructing shapes with multiple potential topologies, compare to other classical surface construction techniques, and show the completion of real scan data

Cancer Induces Cardiomyocyte Remodeling and Hypoinnervation in the Left Ventricle of the Mouse Heart

Cancer is often associated with cachexia, cardiovascular symptoms and autonomic dysregulation. We tested whether extracardiac cancer directly affects the innervation of left ventricular myocardium. Mice injected with Lewis lung carcinoma cells (tumor group, TG) or PBS (control group, CG) were analyzed after 21 days. Cardiac function (echocardiography), serum levels of TNF-α and Il-6 (ELISA), structural alterations of cardiomyocytes and their innervation (design-based stereology) and levels of innervation-related mRNA (quantitative RT-PCR) were analysed. The groups did not differ in various functional parameters. Serum levels of TNF-α and Il-6 were elevated in TG. The total length of axons in the left ventricle was reduced. The number of dense core vesicles per axon profile was reduced. Decreased myofibrillar volume, increased sarcoplasmic volume and increased volume of lipid droplets were indicative of metabolic alterations of TG cardiomyocytes. In the heart, the mRNA level of nerve growth factor was reduced whereas that of β1-adrenergic receptor was unchanged in TG. In the stellate ganglion of TG, mRNA levels of nerve growth factor and neuropeptide Y were decreased and that of tyrosine hydroxylase was increased. In summary, cancer induces a systemic pro-inflammatory state, a significant reduction in myocardial innervation and a catabolic phenotype of cardiomyocytes in the mouse. Reduced expression of nerve growth factor may account for the reduced myocardial innervation

Voronoi Graph Traversal in High Dimensions with Applications to Topological Data Analysis and Piecewise Linear Interpolation

Voronoi diagrams and their dual, the Delaunay complex, are two fundamental geometric concepts that lie at the foundation of many machine learning algorithms and play a role in particular in classical piecewise linear interpolation and regression methods. More recently, they are also crucial for the construction of a common class of simplicial complexes such as Alpha and Delaunay-\vC ech complexes in topological data analysis. We propose a randomized approximation approach that mitigates the prohibitive cost of exact computation of Voronoi diagrams in high dimensions for machine learning applications. In experiments with data in up to 50 dimensions, we show that this allows us to significantly extend the use of Voronoi-based simplicial complexes in Topological Data Analysis (TDA) to higher dimensions. We confirm prior TDA results on image patches that previously had to rely on sub-sampled data with increased resolution and demonstrate the scalability of our approach by performing a TDA analysis on synthetic data as well as on filters of a ResNet neural network architecture. Secondly, we propose an application of our approach to piecewise linear interpolation of high dimensional data that avoids explicit complete computation of an associated Delaunay triangulation. QC 20201217Part of proceedings: ISBN 978-1-4503-7998-4</p

Septins are critical regulators of osteoclastic bone resorption

Abstract Septins are known to play key roles in supporting cytoskeletal stability, vesicular transport, endo-/exocytosis, stabilizing cellular membranes and forming diffusion barriers. Their function in mammalian cells is poorly investigated. The osteoclast offers an interesting tool to investigate septins because all cellular activities septins were reported to be involved in are critical for osteoclasts. However, the existence of septins in osteoclasts has not even been reported. Here we show that the SEPT9 gene and Septin 9 (SEPT9) protein are expressed and synthesized during differentiation of human osteoclasts. Pharmacological stabilization of septin filaments dose dependently inhibits bone resorption of human osteoclasts in vitro suggesting a role for septins in bone resorption. Attesting to this, conditional deletion of Sept9 in mice leads to elevated levels of trabecular bone and diminished femoral growth in vivo. Finally, systematic interrogation of the spatial organization of SEPT9 by confocal microscopy reveals that SEPT9 is closely associated to the structures known to be critical for osteoclast activity. We propose that septins in general and SEPT9 in particular play a previously unappreciated role in osteoclastic bone resorption