Optimal rates of decay for operator semigroups on Hilbert spaces

We investigate rates of decay for $C_0$-semigroups on Hilbert spaces under assumptions on the resolvent growth of the semigroup generator. Our main results show that one obtains the best possible estimate on the rate of decay, that is to say an upper bound which is also known to be a lower bound, under a comparatively mild assumption on the growth behaviour. This extends several statements obtained by Batty, Chill and Tomilov (J. Eur. Math. Soc., vol. 18(4), pp. 853-929, 2016). In fact, for a large class of semigroups our condition is not only sufficient but also necessary for this optimal estimate to hold. Even without this assumption we obtain a new quantified asymptotic result which in many cases of interest gives a sharper estimate for the rate of decay than was previously available, and for semigroups of normal operators we are able to describe the asymptotic behaviour exactly. We illustrate the strength of our theoretical results by using them to obtain sharp estimates on the rate of energy decay for a wave equation subject to viscoelastic damping at the boundary.Comment: 25 pages. To appear in Advances in Mathematic

House on a Sloping Building Site

Tato bakalářská práce se zabývá návrhem novostavby rodinného domu na svahu, který se nachází v katastrálním území obce Zbraslavice. Jedná se o dvoupodlažní, částečně podsklepený dům, který je navržený pro čtyřčlennou rodinu. Dům je samostatně stojící. Svislé nosné konstrukce přízemí jsou vyzděny z keramických bloků Porotherm, zateplené kontaktním zateplovacím systémem z expandovaných polystyrenových desek. Suterén je vyzděn ze ztraceného bednění Best a zateplen kontaktním zateplovacím systémem z extrudovaných polystyrenových desek. Objekt je zastřešen pultovou střechou o sklonu 5 stupňů s pohledovými krokvemi. Součástí domu je garáž pro dva osobní automobilyThis bachelor’s thesis deals with a design for a new detached house on a slope, which is situated in the cadester area of the Down of Zbraslavice. The building is a two-floor house with a partial basement, which is designed for a four-member family. The house is detached. The vertical load-bearing structures are walled with clay blocks Porotherm, insulated with a contact thermal insulation system from expanded polystyren slabs. The basement is walled with permanent formwork Best and insulated with contact thermal insulation system from extruded polystyrene slabs. The building is roofed with a mono-pitched roof with 5- degree slope and exposed rafters. A garage for two cars is a part of the house.

Communications Regulation in the Age of Digital Convergence : Legal and Economic Perspectives

This book brings together contributions of a distinguished panel of regulators as well as lawyers and economists from both academia and industry to present their insights on the digital convergence phenomenon in the telecommunications industry. The contributions cover a great deal of the relevant topics in communications regulation, such as technological and network neutrality, distribution of the digital dividend, and incentives for investment and innovation

Highly porous activated glassy carbon film sandwich structure for electrochemical energy storage in ultracapacitor applications: Study of the porous film structure and gradient

Glassy carbon plates were thermochemically gas phase oxidized to obtain monolithic sandwichlike electrode assemblies with high surface area porous films for electrochemical energy storage applications. Film thicknesses were varied by variation of oxidation parameters time, temperature, and oxygen concentration and measured with electron microscopy. The mass density of the porous carbon film material was estimated by fitting a geometrical model to experimental gravimetric data. Optical Raman spectroscopy line scans suggest that the porosity has a gradient between the surface and the film/bulk interface, which is supported by pore-size distribution data obtained from small-angle x-ray scattering (SAXS) on slightly oxidized and fully oxidized samples. Detailed inspection of the power law behavior of SAXS data suggests that the internal surface area of well-oxidized glassy carbon (GC) is compact and extends over the entire probed volume and thus has optimal pore connectivity. This effect goes along with pore enlargement and a relative decrease of internal surface area per volume. Slightly oxidized carbon has no pore space with a compact, high connectivity internal surface area. The corresponding SAXS power law and the x-ray density suggest that this high volumetric surface area must be interpreted as a result of surface roughness, rather than true geometric or volumetric surface area. In consequence, is this surface area of limited use for electrochemical energy storage

Metabolic reprogramming of murine cardiomyocytes during autophagy requires the extracellular nutrient sensor decorin.

The extracellular matrix is a master regulator of tissue homeostasis in health and disease. Here we examined how the small, leucine-rich, extracellular matrix proteoglycan decorin regulates cardiomyocyte metabolism during fasting in vivo. First, we validated in Dcn-/- mice that decorin plays an essential role in autophagy induced by fasting. High-Throughput metabolomics analyses of cardiac tissue in Dcn-/- mice subjected to fasting revealed striking differences in the hexosamine biosynthetic pathway resulting in aberrant cardiac O-β-N-Acetylglycosylation as compared with WT mice. Functionally, Dcn-/- mice maintained cardiac function at a level comparable with nonfasted animals whereas fasted WT mice showed reduced ejection fraction. Collectively, our results suggest that reduced sensing of nutrient deprivation in the absence of decorin preempts functional adjustments of cardiac output associated with metabolic reprogramming. © 2018 Gubbiotti et al

Guidance in Radiology Report Summarization: An Empirical Evaluation and Error Analysis

Automatically summarizing radiology reports into a concise impression can reduce the manual burden of clinicians and improve the consistency of reporting. Previous work aimed to enhance content selection and factuality through guided abstractive summarization. However, two key issues persist. First, current methods heavily rely on domain-specific resources to extract the guidance signal, limiting their transferability to domains and languages where those resources are unavailable. Second, while automatic metrics like ROUGE show progress, we lack a good understanding of the errors and failure modes in this task. To bridge these gaps, we first propose a domain-agnostic guidance signal in form of variable-length extractive summaries. Our empirical results on two English benchmarks demonstrate that this guidance signal improves upon unguided summarization while being competitive with domain-specific methods. Additionally, we run an expert evaluation of four systems according to a taxonomy of 11 fine-grained errors. We find that the most pressing differences between automatic summaries and those of radiologists relate to content selection including omissions (up to 52%) and additions (up to 57%). We hypothesize that latent reporting factors and corpus-level inconsistencies may limit models to reliably learn content selection from the available data, presenting promising directions for future work.Comment: Accepted at INLG202

Influence of Drone Altitude, Image Overlap, and Optical Sensor Resolution on Multi-View Reconstruction of Forest Images

CITATION: Seifert, E., et al. 2019. Influence of drone altitude, image overlap, and optical sensor resolution on multi-view reconstruction of forest images. Remote Sensing, 11(10):1252, doi:10.3390/rs11101252.The original publication is available at http://www.mdpi.comPublication of this article was funded by the Stellenbosch University Open Access FundRecent technical advances in drones make them increasingly relevant and important toolsfor forest measurements. However, information on how to optimally set flight parameters and choosesensor resolution is lagging behind the technical developments. Our study aims to address this gap,exploring the effects of drone flight parameters (altitude, image overlap, and sensor resolution) onimage reconstruction and successful 3D point extraction. This study was conducted using video footageobtained from flights at several altitudes, sampled for images at varying frequencies to obtain forwardoverlap ratios ranging between 91 and 99%. Artificial reduction of image resolution was used to simulatesensor resolutions between 0.3 and 8.3 Megapixels (Mpx). The resulting data matrix was analysed usingcommercial multi-view reconstruction (MVG) software to understand the effects of drone variables on(1) reconstruction detail and precision, (2) flight times of the drone, and (3) reconstruction times duringdata processing. The correlations between variables were statistically analysed with a multivariategeneralised additive model (GAM), based on a tensor spline smoother to construct response surfaces.Flight time was linearly related to altitude, while processing time was mainly influenced by altitudeand forward overlap, which in turn changed the number of images processed. Low flight altitudesyielded the highest reconstruction details and best precision, particularly in combination with high imageoverlaps. Interestingly, this effect was nonlinear and not directly related to increased sensor resolution athigher altitudes. We suggest that image geometry and high image frequency enable the MVG algorithmto identify more points on the silhouettes of tree crowns. Our results are some of the first estimates ofreasonable value ranges for flight parameter selection for forestry applications.https://www.mdpi.com/2072-4292/11/10/1252Publisher's versio