Error growth in the numerical integration of periodic orbits by multistep methods, with application to reversible systems

We study the growth with time of (the coefficients of the asymptoticexpansion of) the error in the numerical integration with linearmultistep methods of periodic solutions of systems of ordinarydifferential equations. Particular attention is devoted to reversiblesystems. It turns out that symmetric linear multistep methodscannot be recommended in spite of the fact that they mimic thereversibility of the true flow. For reversible second-ordersystems, linear multistep methods without parasitic double rootsare useful.     

Measuring the top quark mass in the eµ channel: A study

We describe a simple method to measure the top quark mass in the channel that may be useful in Run II of D? detector. The method is validated by applying it to the Run Ib eμ data.     

Level structures of 95,97Mo — A comparative study

High-spin states of ^95,97Mo (Z=42, N=53,55) nuclei have been investigated through ⁸²Se(¹⁸O, xn) reaction at Eb=60 MeV. The level scheme in ⁹⁵Mo has been observed upto ≏ 10 MeV in the present experiment. The level structure shows mainly single particle character. In ⁹⁷Mo, the ground state level sequence has been extended to ≏ 4.5 MeV while the previous information had been up to 2.4 MeV. A negative parity band built on 1437 keV (11/2⁻) excited state has been extended to 5.5 MeV. The structure seems to show a coexistence of single particle and collective modes of excitation. Properties of both the nuclei have been compared with shell model calculations using OXBASH.     

Development of a universal measure of quadrupedal forelimb-hindlimb coordination using digital motion capture and computerised analysis

Background  

Clinical spinal cord injury in domestic dogs provides a model population in which to test the efficacy of putative therapeutic interventions for human spinal cord injury. To achieve this potential a robust method of functional analysis is required so that statistical comparison of numerical data derived from treated and control animals can be achieved.     

Crisp and soft multivariate methods visualize individual cell nuclei in Raman images of liver tissue sections

Raman and infrared spectroscopy have been recognized to be promising tools in clinical diagnostics because they provide molecular contrast without external stains. Here, vertex component analysis (VCA) was applied to Raman and Fourier transform infrared (FTIR) images of liver tissue sections and the results were compared with K-means cluster analysis, fuzzy C-means cluster analysis and principal component analysis. The main components of VCA from three Raman images were assigned to the central vein, periportal vein, cell nuclei, liver parenchyma and bile duct. After resonant Mie scattering correction, VCA of FTIR images identified veins, liver parenchyma, cracks, but no cell nuclei. The advantages of VCA in the context of tissue characterization by vibrational spectroscopic imaging are that the tissue architecture is visualized and the spectral information is reconstructed. Composite images were constructed that revealed a high molecular contrast and that can be interpreted in a similar way like hematoxylin and eosin stained tissue sections.     

Hyperspectral unmixing of Raman micro-images for assessment of morphological and chemical parameters in non-dried brain tumor specimens

Hyperspectral unmixing is an unsupervised algorithm to calculate a bilinear model of spectral endmembers and abundances of components from Raman images. Thirty-nine Raman images were collected from six glioma brain tumor specimens. The tumor grades ranged from astrocytoma WHO II to glioblastoma multiforme WHO IV. The abundance plots of the cell nuclei were processed by an image segmentation procedure to determine the average nuclei size, the number of nuclei, and the fraction of nuclei area. The latter two morphological parameters correlated with the malignancy. A combination of spectral unmixing and non-negativity constrained linear least squares fitting is introduced to assess chemical parameters. First, endmembers of the most abundant and most dissimilar components were defined that represent all data sets. Second, the content of the obtained components’ proteins, nucleic acids, lipids, and lipid to protein ratios were determined in all Raman images. Except for the protein content, all chemical parameters correlated with the malignancy. We conclude that the morphological and chemical information offer new ways to develop Raman-based classification approaches that can complement diagnosis of brain tumors. The role of non-linear Raman modalities to speed-up image acquisition is discussed.

Spatial distribution of heme species in erythrocytes infected with Plasmodium falciparum by use of resonance Raman imaging and multivariate analysis

The multivariate algorithm hierarchical cluster analysis is applied to sets of resonance Raman spectra collected from human erythrocytes infected with the malaria parasite Plasmodium falciparum. The images obtained yield information about the distribution of hemoglobin and hemozoin (or malaria pigment) within the parasitized cells and about their molecular structure. This method has the advantage of conveying more information than other imaging approaches based on resonance Raman spectroscopy, and it is a promising tool to study the hemozoin formation process and its interaction with antimalarial drugs within unstained, well-preserved parasites.     

Delimitation of squamous cell cervical carcinoma using infrared microspectroscopic imaging

Infrared (IR) spectroscopic imaging coupled with microscopy has been used to investigate thin sections of cervix uteri encompassing normal tissue, precancerous structures, and squamous cell carcinoma. Methods for unsupervised distinction of tissue types based on IR spectroscopy were developed. One-hundred and twenty-two images of cervical tissue were recorded by an FTIR spectrometer with a 64×64 focal plane array detector. The 499,712 IR spectra obtained were grouped by an approach which used fuzzy C-means clustering followed by hierarchical cluster analysis. The resulting false color maps were correlated with the morphological characteristics of an adjacent section of hematoxylin and eosin-stained tissue. In the first step, cervical stroma, epithelium, inflammation, blood vessels, and mucus could be distinguished in IR images by analysis of the spectral fingerprint region (950–1480 cm⁻¹). In the second step, analysis in the spectral window 1420–1480 cm⁻¹ enables, for the first time, IR spectroscopic distinction between the basal layer, dysplastic lesions and squamous cell carcinoma within a particular sample. The joint application of IR microspectroscopic imaging and multivariate spectral processing combines diffraction-limited lateral optical resolution on the single cell level with highly specific and sensitive spectral classification on the molecular level. Compared with previous reports our approach constitutes a significant progress in the development of optical molecular spectroscopic techniques toward an additional diagnostic tool for the early histopathological characterization of cervical cancer.