Fisheye cameras are commonly used in applications like autonomous driving and surveillance to provide a large field of view (> 180 • ). However, they come at the cost of strong non-linear distortion which require more complex algorithms. In this paper, we explore Euclidean distance estimation on fisheye cameras for automotive scenes. Obtaining accurate and dense depth supervision is difficult in practice, but self-supervised learning approaches show promising results and could potentially overcome the problem. We present a novel self-supervised scale-aware framework for learning Euclidean distance and ego-motion from raw monocular fisheye videos without applying rectification. While it is possible to perform piece-wise linear approximation of fisheye projection surface and apply standard rectilinear models, it has its own set of issues like re-sampling distortion and discontinuities in transition regions. To encourage further research in this area, we will release this dataset as part of our WoodScape project [1]. We further evaluated the proposed algorithm on the KITTI dataset and obtained state-of-the-art results comparable to other self-supervised monocular methods. Qualitative results on an unseen fisheye video demonstrate impressive performance 1 .

Cancer research is not only a fast growing field involving many branches of science, but also an intricate and diversified field rife with anomalies. One such anomaly is the consistent reliance of cancer cells on glucose metabolism for energy production even in a normoxic environment. Glycolysis is an inefficient pathway for energy production and normally is used during hypoxic conditions. Since cancer cells have a high demand for energy (e.g. for proliferation) it is somehow paradoxical for them to rely on such a mechanism. An emerging conjecture aiming to explain this behavior is that cancer cells preserve this aerobic glycolytic phenotype for its use in invasion and metastasis. We follow this hypothesis and propose a new model for cancer invasion, depending on the dynamics of extra-and intracellular protons, by building upon the existing ones. We incorporate random perturbations in the intracellular proton dynamics to account for uncertainties affecting the cellular machinery. Finally, we address the well-posedness of our setting and use numerical simulations to illustrate the model predictions.

In this paper we propose a phenomenological model for the formation of an interstitial gap between the tumor and the stroma. The gap is mainly filled with acid produced by the progressing edge of the tumor front. Our setting extends existing models for acid-induced tumor invasion models to incorporate several features of local invasion like formation of gaps, spikes, buds, islands, and cavities. These behaviors are obtained mainly due to the random dynamics at the intracellular level, the go-or-grow-or-recede dynamics on the population scale, together with the nonlinear coupling between the microscopic (intracellular) and macroscopic (population) levels. The wellposedness of the model is proved using the semigroup technique and 1D and 2D numerical simulations are performed to illustrate model predictions and draw conclusions based on the observed behavior.

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We propose and analyze a multiscale model for acid-mediated tumor invasion accounting for stochastic effects on the subcellular level. The setting involves a PDE of reaction-diffusion-taxis type describing the evolution of the tumor cell density, the movement being directed towards pH gradients in the local microenvironment, which is coupled to a PDE-SDE system characterizing the dynamics of extracellular and intracellular proton concentrations, respectively. The global well-posedness of the model is shown and numerical simulations are performed in order to illustrate the solution behavior.2010 Mathematics Subject Classification. Primary: 34F05, 35R60, 92C17; Secondary: 35Q92, 60H10, 92C50.