Two semi-Lagrangian fast methods for Hamilton-Jacobi-Bellman equations

In this paper we apply the Fast Iterative Method (FIM) for solving general Hamilton-Jacobi-Bellman (HJB) equations and we compare the results with an accelerated version of the Fast Sweeping Method (FSM). We find that FIM can be indeed used to solve HJB equations with no relevant modifications with respect to the original algorithm proposed for the eikonal equation, and that it overcomes FSM in many cases. Observing the evolution of the active list of nodes for FIM, we recover another numerical validation of the arguments recently discussed in [Cacace et al., SISC 36 (2014), A570-A587] about the impossibility of creating local single-pass methods for HJB equations

A level-set method for the evolution of cells and tissue during curvature-controlled growth

Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic, or cell behavioural in nature. The control of geometry on tissue growth has been evidenced in many in-vivo and in-vitro experiments, including bone remodelling, wound healing, and tissue engineering scaffolds. In this paper, we propose a generalisation of a mathematical model that captures the mechanistic influence of curvature on the joint evolution of cell density and tissue shape during tissue growth. This generalisation allows us to simulate abrupt topological changes such as tissue fragmentation and tissue fusion, as well as three dimensional cases, through a level-set-based method. The level-set method developed introduces another Eulerian field than the level-set function. This additional field represents the surface density of tissue synthesising cells, anticipated at future locations of the interface. Numerical tests performed with this level-set-based method show that numerical conservation of cells is a good indicator of simulation accuracy, particularly when cusps develop in the tissue's interface. We apply this new model to several situations of curvature-controlled tissue evolutions that include fragmentation and fusion.Comment: 15 pages, 10 figures, 3 supplementary figure

Deep Autoencoding Models for Unsupervised Anomaly Segmentation in Brain MR Images

Reliably modeling normality and differentiating abnormal appearances from normal cases is a very appealing approach for detecting pathologies in medical images. A plethora of such unsupervised anomaly detection approaches has been made in the medical domain, based on statistical methods, content-based retrieval, clustering and recently also deep learning. Previous approaches towards deep unsupervised anomaly detection model patches of normal anatomy with variants of Autoencoders or GANs, and detect anomalies either as outliers in the learned feature space or from large reconstruction errors. In contrast to these patch-based approaches, we show that deep spatial autoencoding models can be efficiently used to capture normal anatomical variability of entire 2D brain MR images. A variety of experiments on real MR data containing MS lesions corroborates our hypothesis that we can detect and even delineate anomalies in brain MR images by simply comparing input images to their reconstruction. Results show that constraints on the latent space and adversarial training can further improve the segmentation performance over standard deep representation learning

On the segmentation of astronomical images via level-set methods

Astronomical images are of crucial importance for astronomers since they contain a lot of information about celestial bodies that can not be directly accessible. Most of the information available for the analysis of these objects starts with sky explorations via telescopes and satellites. Unfortunately, the quality of astronomical images is usually very low with respect to other real images and this is due to technical and physical features related to their acquisition process. This increases the percentage of noise and makes more difficult to use directly standard segmentation methods on the original image. In this work we will describe how to process astronomical images in two steps: in the first step we improve the image quality by a rescaling of light intensity whereas in the second step we apply level-set methods to identify the objects. Several experiments will show the effectiveness of this procedure and the results obtained via various discretization techniques for level-set equations.Comment: 24 pages, 59 figures, paper submitte

Retroviral Integration Process in the Human Genome: Is It Really Non-Random? A New Statistical Approach

Retroviral vectors are widely used in gene therapy to introduce therapeutic genes into patients' cells, since, once delivered to the nucleus, the genes of interest are stably inserted (integrated) into the target cell genome. There is now compelling evidence that integration of retroviral vectors follows non-random patterns in mammalian genome, with a preference for active genes and regulatory regions. In particular, Moloney Leukemia Virus (MLV)–derived vectors show a tendency to integrate in the proximity of the transcription start site (TSS) of genes, occasionally resulting in the deregulation of gene expression and, where proto-oncogenes are targeted, in tumor initiation. This has drawn the attention of the scientific community to the molecular determinants of the retroviral integration process as well as to statistical methods to evaluate the genome-wide distribution of integration sites. In recent approaches, the observed distribution of MLV integration distances (IDs) from the TSS of the nearest gene is assumed to be non-random by empirical comparison with a random distribution generated by computational simulation procedures. To provide a statistical procedure to test the randomness of the retroviral insertion pattern, we propose a probability model (Beta distribution) based on IDs between two consecutive genes. We apply the procedure to a set of 595 unique MLV insertion sites retrieved from human hematopoietic stem/progenitor cells. The statistical goodness of fit test shows the suitability of this distribution to the observed data. Our statistical analysis confirms the preference of MLV-based vectors to integrate in promoter-proximal regions

Constant-angle surfaces in liquid crystals

We discuss some properties of surfaces in R3 whose unit normal has constant angle with an assigned direction field. The constant angle condition can be rewritten as an Hamilton-Jacobi equation correlating the surface and the direction field. We focus on examples motivated by the physics of interfaces in liquid crystals and of layered fluids, and discuss the properties of the constant-angle surfaces when the direction field is singular along a line (disclination) or at a point (hedgehog defect

A Semi-Lagrangian scheme for a modified version of the Hughes model for pedestrian flow

In this paper we present a Semi-Lagrangian scheme for a regularized version of the Hughes model for pedestrian flow. Hughes originally proposed a coupled nonlinear PDE system describing the evolution of a large pedestrian group trying to exit a domain as fast as possible. The original model corresponds to a system of a conservation law for the pedestrian density and an Eikonal equation to determine the weighted distance to the exit. We consider this model in presence of small diffusion and discuss the numerical analysis of the proposed Semi-Lagrangian scheme. Furthermore we illustrate the effect of small diffusion on the exit time with various numerical experiments

HandMap:Robust Hand Pose Estimation via Intermediate Dense Guidance Map Supervision

This work presents a novel hand pose estimation framework via intermediate dense guidance map supervision. By leveraging the advantage of predicting heat maps of hand joints in detection-based methods, we propose to use dense feature maps through intermediate supervision in a regression-based framework that is not limited to the resolution of the heat map. Our dense feature maps are delicately designed to encode the hand geometry and the spatial relation between local joint and global hand. The proposed framework significantly improves the state-of-the-art in both 2D and 3D on the recent benchmark datasets