Ozyesil: "3D Motion Estimation by Convex Programming"
3D structure recovery from a collection of 2D photos is a classical problem in computer vision that requires the estimation of the camera orientations and positions, i.e. the camera motion. For a large, irregular collection of images, high quality camera motion estimation turns out to be a complex, time consuming problem. In our work, we introduce a computationally efficient algorithm composed of iterative-global convex programming for camera orientation estimation and robust-distributed convex programming for camera location estimation. Our main contribution is a robust distributed convex program for camera position estimation, which is considered to be the most challenging part of the structure from motion problem. We introduce the concept of "global parallel-rigidity" to the camera location estimation problem, show how to extract maximally global parallel-rigid components of the available location information and formulate a stable semidefinite program (SDP) for high levels of pairwise direction information noise. For large sets of images, we also formulate fast convex programs to produce the global camera location solution from partial solutions. This is a joint work with Amit Singer (Princeton University) and Ronen Basri (Weizmann Institute of Science).
Bastian: "Invasion and metastasis in cancer: a theoretical-experimental approach"
The epithelial-mesenchymal transition (EMT) is a key process in carcinogenesis mediating invasion. In this work, we adopt a hybrid mathematical-experimental approach to study TGFβ-induced EMT. We employ random coefficients differential-equation-based and Ising-style mathematical models, and from mathematical analysis, generate a number of novel biological hypotheses for both in vitro and in vivo settings, which are then experimentally interrogated. I’ll give a brief overview of the mathematical model and key results and will present an array of experimental findings confirming the biological hypotheses. These findings illustrate that isolated, tiny, transient, molecular-level perturbations of key biological processes instantiate at the organ-level and persist, and these greatly affect macroscopic properties of the organism, such as metastatic efficiency. These findings suggest a notion of cellular commitment, and we hypothesize therapeutics for reducing metastatic efficiency in vivo.