Optimal Online Escape Path Against a Certificate

More than fifty years ago Bellman asked for the best escape path within a known forest but for an unknown starting position. This deterministic finite path is the shortest path that leads out of a given environment from any starting point. There are some worst case positions where the full path length is required. Up to now such a fixed ultimate optimal escape path for a known shape for any starting position is only known for some special convex shapes (i.e., circles, strips of a given width, fat convex bodies, some isosceles triangles). Therefore, we introduce a different, simple and intuitive escape path, the so-called certificate path which make use of some additional information w.r.t. the starting point s. This escape path depends on the starting position s and takes the distances from s to the outer boundary of the environment into account. Because of this, in the above convex examples the certificate path always (for any position s) leaves the environment earlier than the ultimate escape path. Next we assume that neither the precise shape of the environment nor the location of the starting point is not known, we have much less information. For a class of environments (convex shapes and shapes with kernel positions) we design an online strategy that always leaves the environment. We show that the path length for leaving the environment is always shorter than 3.318764 the length of the corresponding certificate path. We also give a lower bound of 3.313126 which shows that for the above class of environments the factor 3.318764 is (almost) tight

A Riemannian low-rank method for optimization over semidefinite matrices with block-diagonal constraints

We propose a new algorithm to solve optimization problems of the form $\min f(X)$ for a smooth function $f$ under the constraints that $X$ is positive semidefinite and the diagonal blocks of $X$ are small identity matrices. Such problems often arise as the result of relaxing a rank constraint (lifting). In particular, many estimation tasks involving phases, rotations, orthonormal bases or permutations fit in this framework, and so do certain relaxations of combinatorial problems such as Max-Cut. The proposed algorithm exploits the facts that (1) such formulations admit low-rank solutions, and (2) their rank-restricted versions are smooth optimization problems on a Riemannian manifold. Combining insights from both the Riemannian and the convex geometries of the problem, we characterize when second-order critical points of the smooth problem reveal KKT points of the semidefinite problem. We compare against state of the art, mature software and find that, on certain interesting problem instances, what we call the staircase method is orders of magnitude faster, is more accurate and scales better. Code is available.Comment: 37 pages, 3 figure

CFD multiphase modelling for evaluation of gas mixing in an anaerobic digester

Biogas production from municipal and industrial solid and liquid waste has captured the attention of engineers and managers both in the UK and globally due the substantial benefits for achieving environmental protection, energy generation and Green House Gas emission reductions. However, there are number of problems involved in scaling up experimental anaerobic digestion (AD) plants to field level plants. One such problem associated with AD is mixing, which is a vital component to segregate synthesized gas and biomass from digester liquid, to enhance homogeneity and to ensure adequate contact between bacteria and substrate in the AD. Such situations are well suited to Computational Fluid Dynamic (CFD) analysis, where models can be calibrated and validated using the pilot plant and can then be used to accurately simulate the performance of the large-scale reactors. The aim in this work has been to further understand and enhance the use of bubble mixing approaches to improve the performance of future bioreactors. A computational model has been developed to simulate the complex flows occurring in a digester. The paper discusses CFD simulations of a lab scale AD for evaluating mixing characteristics that provides understanding required for developing accurate simulations of mixing conditions in the large-scale systems with the reactor contents simulated for both Newtonian and non-Newtonian case

Image database system for glaucoma diagnosis support

Tato práce popisuje přehled standardních a pokročilých metod používaných k diagnose glaukomu v ranném stádiu. Na základě teoretických poznatků je implementován internetově orientovaný informační systém pro oční lékaře, který má tři hlavní cíle. Prvním cílem je možnost sdílení osobních dat konkrétního pacienta bez nutnosti posílat tato data internetem. Druhým cílem je vytvořit účet pacienta založený na kompletním očním vyšetření. Posledním cílem je aplikovat algoritmus pro registraci intenzitního a barevného fundus obrazu a na jeho základě vytvořit internetově orientovanou tři-dimenzionální vizualizaci optického disku. Tato práce je součásti DAAD spolupráce mezi Ústavem Biomedicínského Inženýrství, Vysokého Učení Technického v Brně, Oční klinikou v Erlangenu a Ústavem Informačních Technologií, Friedrich-Alexander University, Erlangen-Nurnberg.This master thesis describes a conception of standard and advanced eye examination methods used for glaucoma diagnosis in its early stage. According to the theoretical knowledge, a web based information system for ophthalmologists with three main aims is implemented. The first aim is the possibility to share medical data of a concrete patient without sending his personal data through the Internet. The second aim is to create a patient account based on a complete eye examination procedure. The last aim is to improve the HRT diagnostic method with an image registration algorithm for the fundus and intensity images and create an optic nerve head web based 3D visualization. This master thesis is a part of project based on DAAD co-operation between Department of Biomedical Engineering, Brno University of Technology, Eye Clinic in Erlangen and Department of Computer Science, Friedrich-Alexander University, Erlangen-Nurnberg.

Global Impacts Report 2017

Our fifth Global Impacts Report reflects on the progress of the MSC over the past 20 years, examines the sustainability performance of certified fisheries around the world and highlights areas of future interest