Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

Effiziente und robuste, feature-basierte Wiedererkennung langer Zeitreihen in großen Datenbanken

Die Materialverfolgung gewinnt in der Metallindustrie immer mehr an Bedeutung:rnEs ist notwendig, dass ein Metallband im Fertigungsprozess ein festgelegtes Programm durchläuft - erst dann ist die Qualität des Endprodukts garantiert. Die bisherige Praxis besteht darin, jedem Metallband eine Nummer zuzuordnen, mit der dieses Band beschriftet wird. Bei einer tagelangen Lagerung der Bänder zwischen zwei Produktionsschritten erweist sich diese Methode als fehleranfällig: Die Beschriftungen können z.B. verloren gehen, verwechselt, falsch ausgelesen oder unleserlich werden. 2007 meldete die iba AG das Patent zur Identifikation der Metallbänder anhand ihres Dickenprofils an (Anhaus [3]) - damit kann die Identität des Metallbandes zweifelsfrei nachgewiesen werden, eine zuverlässige Materialverfolgung wurde möglich.Es stellte sich jedoch heraus, dass die messfehlerbehafteten Dickenprofile, die als lange Zeitreihen aufgefasst werden können, mit Hilfe von bisherigen Verfahren (z.B. L2-Abstandsminimierung oder Dynamic Time Warping) nicht erfolgreich verglichen werden können.Diese Arbeit stellt einen effizienten feature-basierten Algorithmus zum Vergleichrnzweier Zeitreihen vor. Er ist sowohl robust gegenüber Rauschen und Messausfällen als auch invariant gegenüber solchen Koordinatentransformationen der Zeitreihen wie Skalierung und Translation. Des Weiteren sind auch Vergleiche mit Teilzeitreihen möglich. Unser Framework zeichnet sich sowohl durch seine hohe Genauigkeit als auch durch seine hohe Geschwindigkeit aus: Mehr als 99.5% der Anfragen an unsere aus realen Profilen bestehende Testdatenbank werden richtig beantwortet. Mit mehreren hundert Zeitreihen-Vergleichen pro Sekunde ist es etwa um den Faktor 10 schneller als die auf dem Gebiet der Zeitreihenanalyse etablierten Verfahren, die jedoch nicht im Stande sind, mehr als 90% der Anfragen korrekt zu verarbeiten. Der Algorithmus hat sich als industrietauglich erwiesen. Die iba AG setzt ihn in einem weltweit einzigartigen dickenprofilbasierten Überwachungssystemrnzur Materialverfolgung ein, das in ersten Stahl- und Aluminiumwalzwerkenrnbereits erfolgreich zum Einsatz kommt.

Tropopause level Rossby wave breaking in the Northern Hemisphere: a feature-based validation of the ECHAM5-HAM climate model

Breaking synoptic-scale Rossby waves (RWB) at the tropopause level are central to the daily weather evolution in the extratropics and the subtropics. RWB leads to pronounced meridional transport of heat, moisture, momentum, and chemical constituents. RWB events are manifest as elongated and narrow structures in the tropopause-level potential vorticity (PV) field. A feature-based validation approach is used to assess the representation of Northern Hemisphere RWB in present-day climate simulations carried out with the ECHAM5-HAM climate model at three different resolutions (T42L19, T63L31, and T106L31) against the ERA-40 reanalysis data set. An objective identification algorithm extracts RWB events from the isentropic PV field and allows quantifying the frequency of occurrence of RWB. The biases in the frequency of RWB are then compared to biases in the time mean tropopause-level jet wind speeds. The ECHAM5-HAM model captures the location of the RWB frequency maxima in the Northern Hemisphere at all three resolutions. However, at coarse resolution (T42L19) the overall frequency of RWB, i.e. the frequency averaged over all seasons and the entire hemisphere, is underestimated by 28%.The higher-resolution simulations capture the overall frequency of RWB much better, with a minor difference between T63L31 and T106L31 (frequency errors of −3.5 and 6%, respectively). The number of large-size RWB events is significantly underestimated by the T42L19 experiment and well represented in the T106L31 simulation. On the local scale, however, significant differences to ERA-40 are found in the higher-resolution simulations. These differences are regionally confined and vary with the season. The most striking difference between T106L31 and ERA-40 is that ECHAM5-HAM overestimates the frequency of RWB in the subtropical Atlantic in all seasons except for spring. This bias maximum is accompanied by an equatorward extension of the subtropical westerlies.

Continental-scale temperature variability during the past two millennia

Past global climate changes had strong regional expression. To elucidate their spatio-temporal pattern, we reconstructed past temperatures for seven continental-scale regions during the past one to two millennia. The most coherent feature in nearly all of the regional temperature reconstructions is a long-term cooling trend, which ended late in the nineteenth century. At multi-decadal to centennial scales, temperature variability shows distinctly different regional patterns, with more similarity within each hemisphere than between them. There were no globally synchronous multi-decadal warm or cold intervals that define a worldwide Medieval Warm Period or Little Ice Age, but all reconstructions show generally cold conditions between ad 1580 and 1880, punctuated in some regions by warm decades during the eighteenth century. The transition to these colder conditions occurred earlier in the Arctic, Europe and Asia than in North America or the Southern Hemisphere regions. Recent warming reversed the long-term cooling; during the period ad 1971–2000, the area-weighted average reconstructed temperature was higher than any other time in nearly 1,400 years.

Field-scale water transport in unsaturated crystalline rock

Safe disposal of toxic wastes in geologic formations requires minimal water and gas movement in the vicinity of storage areas, Ventilation of repository tunnels or caverns built in solid rock can desaturate the near field up to a distance of meters from the rock surface, even when the surrounding geological formation is saturated and under hydrostatic pressures. A tunnel segment at the Grimsel test site located in the Aare granite of the Bernese Alps (central Switzerland) has been subjected to a resaturation and, subsequently, to a controlled desaturation, Using thermocouple psychrometers (TP) and time domain reflectometry (TDR), the water potentials psi and water contents theta were measured within the unsaturated granodiorite matrix near the tunnel wall at depths between 0 and 160 cm. During the resaturation the water potentials in the first 30 cm from the rock surface changed within weeks from values of less than -1.5 MPa to near saturation. They returned to the negative initial values during desaturation, The dynamics of this saturation-desaturation regime could be monitored very sensitively using the thermocouple psychrometers, The TDR measurements indicated that water contents changed dose to the surface, but at deeper installation depths the observed changes were within the experimental noise. The field-measured data of the desaturation cycle were used to test the predictive capabilities of the hydraulic parameter functions that were derived from the water retention characteristics psi(theta) determined in the laboratory. A depth-invariant saturated hydraulic conductivity k(s) = 3.0 x 10(-11) m s(-1) was estimated from the psi(t) data at all measurement depths, using the one-dimensional, unsaturated water flow and transport model HYDRUS Vogel er al., 1996, For individual measurement depths, the estimated k(s) varied between 9.8 x 10(-12) and 6.1 x 10(-11) The fitted k(s) values fell within the range of previously estimated k(s) for this location and led to a satisfactory description of the data, even though the model did not include transport of water vapor.

Large scale variation in Enterococcus faecalis illustrated by the genome analysis of strain OG1RF.

BACKGROUND: Enterococcus faecalis has emerged as a major hospital pathogen. To explore its diversity, we sequenced E. faecalis strain OG1RF, which is commonly used for molecular manipulation and virulence studies. RESULTS: The 2,739,625 base pair chromosome of OG1RF was found to contain approximately 232 kilobases unique to this strain compared to V583, the only publicly available sequenced strain. Almost no mobile genetic elements were found in OG1RF. The 64 areas of divergence were classified into three categories. First, OG1RF carries 39 unique regions, including 2 CRISPR loci and a new WxL locus. Second, we found nine replacements where a sequence specific to V583 was substituted by a sequence specific to OG1RF. For example, the iol operon of OG1RF replaces a possible prophage and the vanB transposon in V583. Finally, we found 16 regions that were present in V583 but missing from OG1RF, including the proposed pathogenicity island, several probable prophages, and the cpsCDEFGHIJK capsular polysaccharide operon. OG1RF was more rapidly but less frequently lethal than V583 in the mouse peritonitis model and considerably outcompeted V583 in a murine model of urinary tract infections. CONCLUSION: E. faecalis OG1RF carries a number of unique loci compared to V583, but the almost complete lack of mobile genetic elements demonstrates that this is not a defining feature of the species. Additionally, OG1RF's effects in experimental models suggest that mediators of virulence may be diverse between different E. faecalis strains and that virulence is not dependent on the presence of mobile genetic elements.

The dementia cognitive fluctuation scale, a new psychometric test for clinicians to identify cognitive fluctuations in people with dementia.

OBJECTIVES Cognitive fluctuation (CF) is a common feature of dementia and a core diagnostic symptom for dementia with Lewy bodies (DLB). CF remains difficult to accurately and reliably detect clinically. This study aimed to develop a psychometric test that could be used by clinicians to facilitate the identification of CF and improve the recognition and diagnosis of DLB and Parkinson disease, and to improve differential diagnosis of other dementias. METHODS We compiled a 17-item psychometric test for identifying CF and applied this measure in a cross-sectional design. Participants were recruited from the North East of England, and assessments were made in individuals' homes. We recruited people with four subtypes of dementia and a healthy comparison group, and all subjects were administered this pilot scale together with other standard ratings. The psychometric properties of the scale were examined with exploratory factor analysis. We also examined the ability of individual items to identify CF to discriminate between dementia subtypes. The sensitivity and specificity of discriminating items were explored along with validity and reliability analyses. RESULTS Participants comprised 32 comparison subjects, 30 people with Alzheimer disease, 30 with vascular dementia, 29 with DLB, and 32 with dementia associated with Parkinson disease. Four items significantly discriminated between dementia groups and showed good levels of sensitivity (range: 78.6%-80.3%) and specificity (range: 73.9%-79.3%). The scale had very good levels of test-retest (Cronbach's alpha: 0.82) and interrater (0.81) reliabilities. The four items loaded onto three different factors. These items were: 1) marked differences in functioning during the daytime; 2) daytime somnolence; 3) daytime drowsiness; and 4) altered levels of consciousness during the day. CONCLUSIONS We identified four items that provide valid, sensitive, and specific questions for reliably identifying CF and distinguishing the Lewy body dementias from other major causes of dementia (Alzheimer disease and vascular dementia).

Affect and cognition measures in preference-based decisions: Validity testing of the Ottawa Decisional Conflict Scale and a decision-specific anxiety measure with men eligible for prostate cancer screening

Background. At present, prostate cancer screening (PCS) guidelines require a discussion of risks, benefits, alternatives, and personal values, making decision aids an important tool to help convey information and to help clarify values. Objective: The overall goal of this study is to provide evidence of the reliability and validity of a PCS anxiety measure and the Decisional Conflict Scale (DCS). Methods. Using data from a randomized, controlled PCS decision aid trial that measured PCS anxiety at baseline and DCS at baseline (T0) and at two-weeks (T2), four psychometric properties were assessed: (1) internal consistency reliability, indicated by factor analysis intraclass correlations and Cronbach's α; (2) construct validity, indicated by patterns of Pearson correlations among subscales; (3) discriminant validity, indicated by the measure's ability to discriminate between undecided men and those with a definite screening intention; and (4) factor validity and invariance using confirmatory factor analyses (CFA). Results. The PCS anxiety measure had adequate internal consistency reliability and good construct and discriminant validity. CFAs indicated that the 3-factor model did not have adequate fit. CFAs for a general PCS anxiety measure and a PSA anxiety measure indicated adequate fit. The general PCS anxiety measure was invariant across clinics. The DCS had adequate internal consistency reliability except for the support subscale and had adequate discriminate validity. Good construct validity was found at the private clinic, but was only found for the feeling informed subscale at the public clinic. The traditional DCS did not have adequate fit at T0 or at T2. The alternative DCS had adequate fit at T0 but was not identified at T2. Factor loadings indicated that two subscales, feeling informed and feeling clear about values, were not distinct factors. Conclusions. Our general PCS anxiety measure can be used in PCS decision aid studies. The alternative DCS may be appropriate for men eligible for PCS. Implications: More emphasis needs to be placed on the development of PCS anxiety items relating to testing procedures. We recommend that the two DCS versions be validated in other samples of men eligible for PCS and in other health care decisions that involve uncertainty. ^

Shape-invariant multibeam backscatter data of the eastern slope of the Porcupine Seabight (50 m grid size)

In this study multibeam angular backscatter data acquired in the eastern slope of the Porcupine Seabight are analysed. Processing of the angular backscatter data using the 'NRGCOR' software was made for 29 locations comprising different geological provinces like: carbonate mounds, buried mounds, seafloor channels, and inter-channel areas. A detailed methodology is developed to produce a map of angle-invariant (normalized) backscatter data by correcting the local angular backscatter values. The present paper involves detailed processing steps and related technical aspects of the normalization approach. The presented angle-invariant backscatter map possesses 12 dB dynamic range in terms of grey scale. A clear distinction is seen between the mound dominated northern area (Belgica province) and the Gollum channel seafloor at the southern end of the site. Qualitative analyses of the calculated mean backscatter values i.e., grey scale levels, utilizing angle-invariant backscatter data generally indicate backscatter values are highest (lighter grey scale) in the mound areas followed by buried mounds. The backscatter values are lowest in the inter-channel areas (lowest grey scale level). Moderate backscatter values (medium grey level) are observed from the Gollum and Kings channel data, and significant variability within the channel seafloor provinces. The segmentation of the channel seafloor provinces are made based on the computed grey scale levels for further analyses based on the angular backscatter strength. Three major parameters are utilized to classify four different seafloor provinces of the Porcupine Seabight by employing a semi-empirical method to analyse multibeam angular backscatter data. The predicted backscatter response which has been computed at 20° is the highest for the mound areas. The coefficient of variation (CV) of the mean backscatter response is also the highest for the mound areas. Interestingly, the slope value of the buried mound areas are found to be the highest. However, the channel seafloor of moderate backscatter response presents the lowest slope and CV values. A critical examination of the inter-channel areas indicates less variability within the estimated three parameters.

Gravity mapping in the southern Weddell Sea region, Antarctica (Scale 1:2 000 000)

New maps of free-air and the Bouguer gravity anomalies on the Weddell Sea sector (70-81° S, 6-75° W) of Antarctica are presented. These maps are based on the first computer compilation of available gravity data collected by ''Sevmorgeologia'' in 1976-89 in the southern Weddell Sea and adjacent coasts of western Dronning Maud Land (WDML) and Coats Land. The accomplished gravity studies comprise airborne observations with a line spacing of about 20 km and conventional measurements at over-the-ice points, which were spaced at 10-30 km and supplemented by seismic soundings. Hence, anomalies on the maps represent mainly large-scale and deep crustal features. The dominant feature in free-air gravity map is a large dipolar gravity anomaly stretching along the continental margin. Following the major grain of seabed morphology this shelf-edge/slope anomaly (SESA) is clearly divided into three segments characterized by diverse anomaly amplitudes, wavelengths and trends. They are associated with continental margins of different geotectonic provinces of Antarctica surrounding the Weddell Sea. Apparent distinctions in the SESA signatures are interpreted as the gravity expression of tectonic, deep crustal structure segmentation of the continental margin. The prominent gravity highs (100-140 mGal) of the shelf edge anomaly mapped along WDML are assumed to represent high-density mantle injections intruded into the middle/lower crust during initial rifting of continental breakup. Enlarged wavelengths and diminished amplitudes of the gravity anomaly westwards, along the Weddell Sea embayment (WSE) margin, reflect a widening of the continental slope and a significant increase in thickness of underlying sediment strata. Low amplitude, negative free-air anomalies in the Filchner-Ronne Ice Shelves (FRIS) contrast sharply with the dominating positive anomalies offshore. This indicates a greater sedimentary thickness of the basin in this area. Crustal response to the enlarged sediment load is impressed in mostly positive features of the Bouguer gravity field observed here. Two pronounced positive Bouguer anomalies of 50-70 mGal and an average widths of 200 km dominate the Weddell Sea embayment margins towards the Antarctic Peninsula and the East Antarctic craton. They correlate well with very deep seabed troughs (> 1000 m below sea level). The gravity highs are most likely caused by a shallow upper mantle underneath graben-rift structures evolved at the margins of the WSE basin. A regional zone (> 100 km in width) of the prominent Bouguer and free-air negative anomalies (-40 to -60 mGal) adjacent Coats Land to the north of the ice shelf edge may indicate the presence of the thick old cratonic crust far offshore beneath the Weddell Sea Embayment.

Dissolved organic matter molecular composition and concentrations from a large scale mesocosm study KOSMOS 2013 Kristineberg) on ocean acidification

Marine dissolved organic matter (DOM) represents one of the largest active carbon reservoirs on Earth. Changes in pool size or composition could have major impacts on the global carbon cycle. Ocean acidification is a potential driver for these changes because it influences marine primary production and heterotrophic respiration. Here we show that ocean acidification as expected for a 'business-as-usual' emission scenario in the year 2100 (900 µatm) does not affect the DOM pool with respect to its size and molecular composition. We applied ultrahigh-resolution mass spectrometry to monitor the production and turnover of 7,360 distinct molecular DOM features in an unprecedented long-term mesocosm study in a Swedish Fjord, covering a full cycle of marine production. DOM concentration and molecular composition did not differ significantly between present-day and year 2100 CO2 levels. Our findings are likely applicable to other coastal and productive marine ecosystems in general.

Mineraly of oceanic crust from the Kane Transform, Mid-Atlantic Ridge

Gabbroic cumulates drilled south of the Kane Transform Fault on the slow-spread Mid-Atlantic Ridge preserve up to three discrete magnetization components. Here we use absolute age constraints derived from the paleomagnetic data to develop a model for the magmatic construction of this section of the lower oceanic crust. By comparing the paleomagnetic data with mineral compositions, and based on thermal models of local reheating, we infer that magmas that began crystallizing in the upper mantle intruded into the lower oceanic crust and formed meter-scale sills. Some of these magmas were crystal-laden and the subsequent expulsion of interstitial liquid from them produced '"cumulus" sills. These small-scale magmatic injections took place over at least 210 000 years and at distances of ~3 km from the ridge axis and may have formed much of the lower crust. This model explains many of the complexities described in this area and can be used to help understand the general formation of oceanic crust at slow-spread ridges.

Quality assessment by region in spot images fused by means dual-tree complex wavelet transform

This work is motivated in providing and evaluating a fusion algorithm of remotely sensed images, i.e. the fusion of a high spatial resolution panchromatic image with a multi-spectral image (also known as pansharpening) using the dual-tree complex wavelet transform (DT-CWT), an effective approach for conducting an analytic and oversampled wavelet transform to reduce aliasing, and in turn reduce shift dependence of the wavelet transform. The proposed scheme includes the definition of a model to establish how information will be extracted from the PAN band and how that information will be injected into the MS bands with low spatial resolution. The approach was applied to Spot 5 images where there are bands falling outside PAN’s spectrum. We propose an optional step in the quality evaluation protocol, which is to study the quality of the merger by regions, where each region represents a specific feature of the image. The results show that DT-CWT based approach offers good spatial quality while retaining the spectral information of original images, case SPOT 5. The additional step facilitates the identification of the most affected regions by the fusion process.

Two Different Approaches of Feature Extraction for Classifying the EEG Signals

The electroencephalograph (EEG) signal is one of the most widely used signals in the biomedicine field due to its rich information about human tasks. This research study describes a new approach based on i) build reference models from a set of time series, based on the analysis of the events that they contain, is suitable for domains where the relevant information is concentrated in specific regions of the time series, known as events. In order to deal with events, each event is characterized by a set of attributes. ii) Discrete wavelet transform to the EEG data in order to extract temporal information in the form of changes in the frequency domain over time- that is they are able to extract non-stationary signals embedded in the noisy background of the human brain. The performance of the model was evaluated in terms of training performance and classification accuracies and the results confirmed that the proposed scheme has potential in classifying the EEG signals.