Perturbation theory for spectral subspaces

In der vorliegenden Arbeit wird die Variation abgeschlossener Unterräume eines Hilbertraumes untersucht, die mit isolierten Komponenten der Spektren von selbstadjungierten Operatoren unter beschränkten additiven Störungen assoziiert sind. Von besonderem Interesse ist hierbei die am wenigsten restriktive Bedingung an die Norm der Störung, die sicherstellt, dass die Differenz der zugehörigen orthogonalen Projektionen eine strikte Normkontraktion darstellt. Es wird ein Überblick über die bisher erzielten Resultate gegeben. Basierend auf einem Iterationsansatz wird eine allgemeine Schranke an die Variation der Unterräume für Störungen erzielt, die glatt von einem reellen Parameter abhängen. Durch Einführung eines Kopplungsparameters wird das Ergebnis auf den Fall additiver Störungen angewendet. Auf diese Weise werden zuvor bekannte Ergebnisse verbessert. Im Falle von additiven Störungen werden die Schranken an die Variation der Unterräume durch ein Optimierungsverfahren für die Stützstellen im Iterationsansatz weiter verschärft. Die zugehörigen Ergebnisse sind die besten, die bis zum jetzigen Zeitpunkt erzielt wurden.

A new information fusion method for land-use classification using high resolution satellite imagery

Satellite image classification involves designing and developing efficient image classifiers. With satellite image data and image analysis methods multiplying rapidly, selecting the right mix of data sources and data analysis approaches has become critical to the generation of quality land-use maps. In this study, a new postprocessing information fusion algorithm for the extraction and representation of land-use information based on high-resolution satellite imagery is presented. This approach can produce land-use maps with sharp interregional boundaries and homogeneous regions. The proposed approach is conducted in five steps. First, a GIS layer - ATKIS data - was used to generate two coarse homogeneous regions, i.e. urban and rural areas. Second, a thematic (class) map was generated by use of a hybrid spectral classifier combining Gaussian Maximum Likelihood algorithm (GML) and ISODATA classifier. Third, a probabilistic relaxation algorithm was performed on the thematic map, resulting in a smoothed thematic map. Fourth, edge detection and edge thinning techniques were used to generate a contour map with pixel-width interclass boundaries. Fifth, the contour map was superimposed on the thematic map by use of a region-growing algorithm with the contour map and the smoothed thematic map as two constraints. For the operation of the proposed method, a software package is developed using programming language C. This software package comprises the GML algorithm, a probabilistic relaxation algorithm, TBL edge detector, an edge thresholding algorithm, a fast parallel thinning algorithm, and a region-growing information fusion algorithm. The county of Landau of the State Rheinland-Pfalz, Germany was selected as a test site. The high-resolution IRS-1C imagery was used as the principal input data.

Evaluation and quantification of spectral information in tissue by confocal microscopy

A confocal imaging and image processing scheme is introduced to visualize and evaluate the spatial distribution of spectral information in tissue. The image data are recorded using a confocal laser-scanning microscope equipped with a detection unit that provides high spectral resolution. The processing scheme is based on spectral data, is less error-prone than intensity-based visualization and evaluation methods, and provides quantitative information on the composition of the sample. The method is tested and validated in the context of the development of dermal drug delivery systems, introducing a quantitative uptake indicator to compare the performances of different delivery systems is introduced. A drug penetration study was performed in vitro. The results show that the method is able to detect, visualize and measure spectral information in tissue. In the penetration study, uptake efficiencies of different experiment setups could be discriminated and quantitatively described. The developed uptake indicator is a step towards a quantitative assessment and, in a more general view apart from pharmaceutical research, provides valuable information on tissue composition. It can potentially be used for clinical in vitro and in vivo applications.

Application of Discrete Fourier Inter-Coefficient Difference for Assessing Genetic Sequence Similarity

Digital signal processing (DSP) techniques for biological sequence analysis continue to grow in popularity due to the inherent digital nature of these sequences. DSP methods have demonstrated early success for detection of coding regions in a gene. Recently, these methods are being used to establish DNA gene similarity. We present the inter-coefficient difference (ICD) transformation, a novel extension of the discrete Fourier transformation, which can be applied to any DNA sequence. The ICD method is a mathematical, alignment-free DNA comparison method that generates a genetic signature for any DNA sequence that is used to generate relative measures of similarity among DNA sequences. We demonstrate our method on a set of insulin genes obtained from an evolutionarily wide range of species, and on a set of avian influenza viral sequences, which represents a set of highly similar sequences. We compare phylogenetic trees generated using our technique against trees generated using traditional alignment techniques for similarity and demonstrate that the ICD method produces a highly accurate tree without requiring an alignment prior to establishing sequence similarity.

Determination of histopathological tumor grade in neuroepithelial brain tumors by using spectral pattern analysis of in vivo spectroscopic data

OBJECT: In this study, 1H magnetic resonance (MR) spectroscopy was prospectively tested as a reliable method for presurgical grading of neuroepithelial brain tumors. METHODS: Using a database of tumor spectra obtained in patients with histologically confirmed diagnoses, 94 consecutive untreated patients were studied using single-voxel 1H spectroscopy (point-resolved spectroscopy; TE 135 msec, TE 135 msec, TR 1500 msec). A total of 90 tumor spectra obtained in patients with diagnostic 1H MR spectroscopy examinations were analyzed using commercially available software (MRUI/VARPRO) and classified using linear discriminant analysis as World Health Organization (WHO) Grade I/II, WHO Grade III, or WHO Grade IV lesions. In all cases, the classification results were matched with histopathological diagnoses that were made according to the WHO classification criteria after serial stereotactic biopsy procedures or open surgery. Histopathological studies revealed 30 Grade I/II tumors, 29 Grade III tumors, and 31 Grade IV tumors. The reliability of the histological diagnoses was validated considering a minimum postsurgical follow-up period of 12 months (range 12-37 months). Classifications based on spectroscopic data yielded 31 tumors in Grade I/II, 32 in Grade III, and 27 in Grade IV. Incorrect classifications included two Grade II tumors, one of which was identified as Grade III and one as Grade IV; two Grade III tumors identified as Grade II; two Grade III lesions identified as Grade IV; and six Grade IV tumors identified as Grade III. Furthermore, one glioblastoma (WHO Grade IV) was classified as WHO Grade I/II. This represents an overall success rate of 86%, and a 95% success rate in differentiating low-grade from high-grade tumors. CONCLUSIONS: The authors conclude that in vivo 1H MR spectroscopy is a reliable technique for grading neuroepithelial brain tumors.

Spectral waveform analysis of intranodal arterial blood flow in abnormally large superficial lymph nodes in dogs

Objective-To evaluate pulsed-wave Doppler spectral parameters as a method for distinguishing between neoplastic and inflammatory peripheral lymphadenopathy in dogs. Sample Population-40 superficial lymph nodes from 33 dogs with peripheral lymphadenopathy. Procedures-3 Doppler spectral tracings were recorded from each node. Spectral Doppler analysis including assessment of the resistive index, peak systolic velocity-to-end diastolic velocity (S:D) ratio, diastolic notch velocity-to-peak systolic velocity (N:S) ratio, and end diastolic velocity-to-diastolic notch velocity ratio was performed for each tracing. Several calculation methods were used to determine the Doppler indices for each lymph node. After the ultrasonographic examination, fine needle aspirates or excisional biopsy specimens of the examined lymph nodes were obtained, and lymphadenopathy was classified as either inflammatory or neoplastic (lymphomatous or metastatic) via cytologic or histologic examination. Results of Doppler analysis were compared with cytologic or histopathologic findings. Results-The Doppler index with the highest diagnostic accuracy was the S:D ratio calculated from the first recorded tracing; a cutoff value of 3.22 yielded sensitivity of 91%, specificity of 100%, and negative predictive value of 89% for detection of neoplasia. Overall diagnostic accuracy was 95%. At a sensitivity of 100%, the most accurate index was the N:S ratio calculated from the first recorded tracing; a cutoff value of 0.45 yielded specificity of 67%, positive predictive value of 81%, and overall diagnostic accuracy of 86.5%. Conclusions and Clinical Relevance-Results suggested that noninvasive Doppler spectral analysis may be useful in the diagnosis of neoplastic versus inflammatory peripheral lymphadenopathy in dogs.

Similarities in the Subgingival Microbiota Assessed by a Curet Sampling Method at Sites With Chronic Periodontitis

Background: The goal of this study was to determine whether site-specific differences in the subgingival microbiota could be detected by the checkerboard method in subjects with periodontitis. Methods: Subjects with at least six periodontal pockets with a probing depth (PD) between 5 and 7 mm were enrolled in the study. Subgingival plaque samples were collected with sterile curets by a single-stroke procedure at six selected periodontal sites from 161 subjects (966 subgingival sites). Subgingival bacterial samples were assayed with the checkerboard DNA-DNA hybridization method identifying 37 species. Results: Probing depths of 5, 6, and 7 mm were found at 50% (n = 483), 34% (n = 328), and 16% (n = 155) of sites, respectively. Statistical analysis failed to demonstrate differences in the sum of bacterial counts by tooth type (P = 0.18) or specific location of the sample (P = 0.78). With the exceptions of Campylobacter gracilis (P <0.001) and Actinomyces naeslundii (P <0.001), analysis by general linear model multivariate regression failed to identify subject or sample location factors as explanatory to microbiologic results. A trend of difference in bacterial load by tooth type was found for Prevotella nigrescens (P <0.01). At a cutoff level of >/=1.0 x 10(5), Porphyromonas gingivalis and Tannerella forsythia (previously T. forsythensis) were present at 48.0% to 56.3% and 46.0% to 51.2% of sampled sites, respectively. Conclusions: Given the similarities in the clinical evidence of periodontitis, the presence and levels of 37 species commonly studied in periodontitis are similar, with no differences between molar, premolar, and incisor/cuspid subgingival sites. This may facilitate microbiologic sampling strategies in subjects during periodontal therapy.

Automatic algorithm for monitoring systolic pressure variation and difference in pulse pressure

BACKGROUND: Difference in pulse pressure (dPP) reliably predicts fluid responsiveness in patients. We have developed a respiratory variation (RV) monitoring device (RV monitor), which continuously records both airway pressure and arterial blood pressure (ABP). We compared the RV monitor measurements with manual dPP measurements. METHODS: ABP and airway pressure (PAW) from 24 patients were recorded. Data were fed to the RV monitor to calculate dPP and systolic pressure variation in two different ways: (a) considering both ABP and PAW (RV algorithm) and (b) ABP only (RV(slim) algorithm). Additionally, ABP and PAW were recorded intraoperatively in 10-min intervals for later calculation of dPP by manual assessment. Interobserver variability was determined. Manual dPP assessments were used for comparison with automated measurements. To estimate the importance of the PAW signal, RV(slim) measurements were compared with RV measurements. RESULTS: For the 24 patients, 174 measurements (6-10 per patient) were recorded. Six observers assessed dPP manually in the first 8 patients (10-min interval, 53 measurements); no interobserver variability occurred using a computer-assisted method. Bland-Altman analysis showed acceptable bias and limits of agreement of the 2 automated methods compared with the manual method (RV: -0.33% +/- 8.72% and RV(slim): -1.74% +/- 7.97%). The difference between RV measurements and RV(slim) measurements is small (bias -1.05%, limits of agreement 5.67%). CONCLUSIONS: Measurements of the automated device are comparable with measurements obtained by human observers, who use a computer-assisted method. The importance of the PAW signal is questionable.

Magic angle spinning magnetic resonance: a novel method opening up translational research into NAFLD?

NAFLD (non-alcoholic fatty liver disease) and NASH (non-alcoholic steatohepatitis) are of increasing importance, both in connection with insulin resistance and with the development of liver cirrhosis. Histological samples are still the 'gold standard' for diagnosis; however, because of the risks of a liver biopsy, non-invasive methods are needed. MAS (magic angle spinning) is a special type of NMR which allows characterization of intact excised tissue without need for additional extraction steps. Because clinical MRI (magnetic resonance imaging) and MRS (magnetic resonance spectroscopy) are based on the same physical principle as NMR, translational research is feasible from excised tissue to non-invasive examinations in humans. In the present issue of Clinical Science, Cobbold and co-workers report a study in three animal strains suffering from different degrees of NAFLD showing that MAS results are able to distinguish controls, fatty infiltration and steatohepatitis in cohorts. In vivo MRS methods in humans are not obtainable at the same spectral resolution; however, know-how from MAS studies may help to identify characteristic changes in crowded regions of the magnetic resonance spectrum.

Novel calculation method for chain conveyor systems

Sidexflexing plastic chains are used increasingly in material handling due to their highly flexible conveying design and layout options. These systems are often equipped with so called modular belts. Due to their specific force transmission, detailed calculation methods are not yet available. In the following, a generally valid calculation approach is derived and its difference to existing solutions shown by examples.

Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T2.33TC.

A case of distinct difference between the measured blood Ethanol concentration and the concentration estimated by Widmark's equation

In the last century, several mathematical models have been developed to calculate blood ethanol concentrations (BAC) from the amount of ingested ethanol and vice versa. The most common one in the field of forensic sciences is Widmark's equation. A drinking experiment with 10 voluntary test persons was performed with a target BAC of 1.2 g/kg estimated using Widmark's equation as well as Watson's factor. The ethanol concentrations in the blood were measured using headspace gas chromatography/flame ionization and additionally with an alcohol Dehydrogenase (ADH)-based method. In a healthy 75-year-old man a distinct discrepancy between the intended and the determined blood ethanol concentration was observed. A blood ethanol concentration of 1.83 g/kg was measured and the man showed signs of intoxication. A possible explanation for the discrepancy is a reduction of the total body water content in older people. The incident showed that caution is advised when using the different mathematical models in aged people. When estimating ethanol concentrations, caution is recommended with calculated results due to potential discrepancies between mathematical models and biological systems

Dynamic Chemical Shift Imaging for Image-Guided Thermal Therapy

Magnetic resonance temperature imaging (MRTI) is recognized as a noninvasive means to provide temperature imaging for guidance in thermal therapies. The most common method of estimating temperature changes in the body using MR is by measuring the water proton resonant frequency (PRF) shift. Calculation of the complex phase difference (CPD) is the method of choice for measuring the PRF indirectly since it facilitates temperature mapping with high spatiotemporal resolution. Chemical shift imaging (CSI) techniques can provide the PRF directly with high sensitivity to temperature changes while minimizing artifacts commonly seen in CPD techniques. However, CSI techniques are currently limited by poor spatiotemporal resolution. This research intends to develop and validate a CSI-based MRTI technique with intentional spectral undersampling which allows relaxed parameters to improve spatiotemporal resolution. An algorithm based on autoregressive moving average (ARMA) modeling is developed and validated to help overcome limitations of Fourier-based analysis allowing highly accurate and precise PRF estimates. From the determined acquisition parameters and ARMA modeling, robust maps of temperature using the k-means algorithm are generated and validated in laser treatments in ex vivo tissue. The use of non-PRF based measurements provided by the technique is also investigated to aid in the validation of thermal damage predicted by an Arrhenius rate dose model.

Generalized fuzzy clustering for segmentation of multi-spectral magnetic resonance images.

An integrated approach for multi-spectral segmentation of MR images is presented. This method is based on the fuzzy c-means (FCM) and includes bias field correction and contextual constraints over spatial intensity distribution and accounts for the non-spherical cluster's shape in the feature space. The bias field is modeled as a linear combination of smooth polynomial basis functions for fast computation in the clustering iterations. Regularization terms for the neighborhood continuity of intensity are added into the FCM cost functions. To reduce the computational complexity, the contextual regularizations are separated from the clustering iterations. Since the feature space is not isotropic, distance measure adopted in Gustafson-Kessel (G-K) algorithm is used instead of the Euclidean distance, to account for the non-spherical shape of the clusters in the feature space. These algorithms are quantitatively evaluated on MR brain images using the similarity measures.

Transconvolution and the virtual positron emission tomograph--a new method for cross calibration in quantitative PET∕CT imaging

PURPOSE Positron emission tomography (PET)∕computed tomography (CT) measurements on small lesions are impaired by the partial volume effect, which is intrinsically tied to the point spread function of the actual imaging system, including the reconstruction algorithms. The variability resulting from different point spread functions hinders the assessment of quantitative measurements in clinical routine and especially degrades comparability within multicenter trials. To improve quantitative comparability there is a need for methods to match different PET∕CT systems through elimination of this systemic variability. Consequently, a new method was developed and tested that transforms the image of an object as produced by one tomograph to another image of the same object as it would have been seen by a different tomograph. The proposed new method, termed Transconvolution, compensates for differing imaging properties of different tomographs and particularly aims at quantitative comparability of PET∕CT in the context of multicenter trials. METHODS To solve the problem of image normalization, the theory of Transconvolution was mathematically established together with new methods to handle point spread functions of different PET∕CT systems. Knowing the point spread functions of two different imaging systems allows determining a Transconvolution function to convert one image into the other. This function is calculated by convolving one point spread function with the inverse of the other point spread function which, when adhering to certain boundary conditions such as the use of linear acquisition and image reconstruction methods, is a numerically accessible operation. For reliable measurement of such point spread functions characterizing different PET∕CT systems, a dedicated solid-state phantom incorporating (68)Ge∕(68)Ga filled spheres was developed. To iteratively determine and represent such point spread functions, exponential density functions in combination with a Gaussian distribution were introduced. Furthermore, simulation of a virtual PET system provided a standard imaging system with clearly defined properties to which the real PET systems were to be matched. A Hann window served as the modulation transfer function for the virtual PET. The Hann's apodization properties suppressed high spatial frequencies above a certain critical frequency, thereby fulfilling the above-mentioned boundary conditions. The determined point spread functions were subsequently used by the novel Transconvolution algorithm to match different PET∕CT systems onto the virtual PET system. Finally, the theoretically elaborated Transconvolution method was validated transforming phantom images acquired on two different PET systems to nearly identical data sets, as they would be imaged by the virtual PET system. RESULTS The proposed Transconvolution method matched different PET∕CT-systems for an improved and reproducible determination of a normalized activity concentration. The highest difference in measured activity concentration between the two different PET systems of 18.2% was found in spheres of 2 ml volume. Transconvolution reduced this difference down to 1.6%. In addition to reestablishing comparability the new method with its parameterization of point spread functions allowed a full characterization of imaging properties of the examined tomographs. CONCLUSIONS By matching different tomographs to a virtual standardized imaging system, Transconvolution opens a new comprehensive method for cross calibration in quantitative PET imaging. The use of a virtual PET system restores comparability between data sets from different PET systems by exerting a common, reproducible, and defined partial volume effect.