Solving and Certifying the Solution of a Linear System

The Reliable Computing journal has no more paper publication, only free, electronic publication.International audienceUsing floating-point arithmetic to solve a linear system yields a computed result, which is an approximation of the exact solution because of roundoff errors. In this paper, we present an approach to certify the computed solution. Here, "certify" means computing a guaranteed enclosure of the error. Our method is an iterative refinement method and thus it also improves the computed result. The method we present is inspired from the verifylss function of the IntLab library, with a first step, using floating-point arithmetic, to solve the linear system, followed by interval computations to get and refine an enclosure of the error. The specificity of our method is to relax the requirement of tightness of the error, in order to gain in performance. Indeed, only the order of magnitude of the error is needed. Experiments show a gain in accuracy and in performance, for various condition number of the matrix of the linear system

Quantitative Electroencephalography Analyzed by Statistical Pattern Recognition as a Diagnostic and Prognostic Tool in Mild Cognitive Impairment:Results from a Nordic Multicenter Cohort Study

Aim: To examine diagnostic and prognostic potential of quantitative electroencephalography (qEEG) analyzed by the statistical pattern recognition (SPR) method in patients with cognitive impairment. We compared the differential diagnostic ability of SPR to visual EEG analysis. Correlation between SPR findings and cerebrospinal fluid (CSF) Alzheimer disease (AD) biomarkers were evaluated. Methods: It is a multicenter cohort study involving 129 patients, (mild cognitive impairment [MCI], AD, and healthy controls). Standardized EEG was performed at baseline. Patients were continuously clinically evaluated. Results: Receiver Operating Characteristic curves showed a low discriminative ability of SPR and no ability to predict clinical progression in patients with MCI. Moderate correlation between SPR analysis and CSF AD biomarkers was found. Conclusion: The diagnostic and prognostic abilities of qEEG were low. The SPR method was superior to the visual EEG analysis. The qEEG method correlates well to CSF AD biomarkers, suggesting association with pathology in AD

Zemětřesné roje v různých tektonických prostředích: západní Čechy a jihozápadní Island

Ve své doktorské práci jsem se zabývala zemětřesnými roji, které se vysky- tují ve dvou tektonicky odlišných oblastech: v západních Čechách/Vogtlandu a na jihozápadním Islandu. Cílem mých výzkumů bylo hlubší pochopení samotné podstaty zemětřesných rojů, které vznikají v různých tektonických prostředích. Analyzovala jsem rojové aktivity ze západních Čech a jihozápadního Islandu z hlediska statistických charakteristik (magnitudo-četnostní rozložení, rozdělení mezijevových časů), uvolnění seismického momentu a časoprostorového rozložení ohnisek zemětřesení. Zjistila jsem, že rychlost, s jakou seismické jevy vznikají, a poměr výskytu slabých a silných seismických jevů jsou pro všechny analyzované zemětřesné aktivity ze západních Čech a jihozápadního Islandu stejné, zatímco rychlost uvolňování seismického momentu je v islandských rojích značně vyšší. Pro západočeské roje je charakteristické postupné uvolňování seismického mo- mentu, kdežto v islandských rojích se seismický moment uvolňuje v jedné krátké hlavní fázi. Všechny západočeské zemětřesné roje se odehrály v jedné ohniskové zóně Nový Kostel, která sestává z několika různě orientovaných zlomů/zlomových segmentů. Islandské roje jsou lokalizované ve větší oblasti podél Středoatlantského hřbetu až k jeho rozvětvení v oblasti vulkanického komplexu Hengill....In my doctoral thesis I have investigated earthquake swarms from two com- pletely different tectonic areas, West Bohemia/Vogtland and Southwest Iceland, with the aim of gaining a deeper insight into the nature of earthquake swarms in diverse tectonic environments. I analysed swarm-like activities from West Bo- hemia and Southwest Iceland from the perspective of statistical characteristics (magnitude-frequency distribution, interevent time distribution), seismic moment release, and space-time distribution of events. I found that the ratio of small to large events and the event rates are similar for all the activities in both areas, while the rate of the seismic moment release is significantly higher for the South- west Icelandic swarms. Seismic moment released step by step is characterised for the West Bohemia swarms, whereas seismic moment released in one dominant short-term phase is typical of Southwest Icelandic earthquake swarms. All the West Bohemian swarms took place in a bounded focal zone Nový Kostel that is fairly complex, consisting of several fault segments. The Southwest Icelandic swarms are distributed at much larger area along the Mid Atlantic Ridge up to its branching in the Hengill triple junction, the individual swarms clearly reflect a tectonic structure of respective focal areas. I have...Matematicko-fyzikální fakultaFaculty of Mathematics and Physic

A Geobotanical Analysis Of Circumpolar Arctic Vegetation, Climate, And Substrate

Thesis (Ph.D.) University of Alaska Fairbanks, 2009The objective of the research presented in this dissertation was to better understand the factors controlling the present and potential future distribution of arctic vegetation. The analysis compares the Circumpolar Arctic Vegetation Map (CAVM) with circumpolar data sets of environmental characteristics. Geographical information system (GIS) software was used to overlay the CAVM with a satellite index of vegetation (normalized difference vegetation index, NDVI) and environmental factors that are most important in controlling the distribution of arctic vegetation, including summer temperature, landscape age, precipitation, snow cover, substrate chemistry (pH and salinity), landscape type, elevation, permafrost characteristics, and distance to sea. Boosted regression tree analysis was used to determine the relative importance of different environmental characteristics for different vegetation types and for different regions. Results of this research include maps, charts and tables that summarize and display the spatial characteristics of arctic vegetation. The data for arctic land surface temperature and landscape age are especially important new resources for researchers. These results are available electronically, not only as summary data, but also as GIS data layers with a spatial context (www.arcticatlas.org). The results emphasize the value and reliability of NDVI for studying arctic vegetation. The relationship between NDVI and summer temperatures across the circumpolar arctic was similar to the correlated increases in NDVI and temperature seen over the time period of satellite records. Summaries of arctic biomass based on NDVI match those based on extrapolation from ground samples. The boosted regression tree analysis described ecological niches of arctic vegetation types, demonstrating the importance of summer temperatures and landscape age in controlling the distribution of arctic vegetation. As the world continues to focus on the Arctic as an area undergoing accelerated warming due to global climate change, results presented here from spatially explicit analysis of existing arctic vegetation and environmental characteristics can be used to better understand plant distribution patterns, evaluate change in the vegetation, and calibrate models of arctic vegetation and animal habitat