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The principal components transformation offers an effective methods for dimensionality reduction and for the assessment of the mutual dependence of observed variables in a data set. An iterative procedure, the so-called power method, for finding a multivariate distribution's eigenvectors and eigenvalues is demonstrated. The projection of feature vectors onto the principal components is shown.
Whether or not high accuracy classification methods can be scaled to large applications is crucial for the ultimate usefulness of such methods in text categorization. This paper applies two statistical learning algorithms, the Linear Least Squares Fit (LLSF) mapping and a Nearest Neighbor classifier named ExpNet, to a large collection of MEDLINE documents. With the use of suitable dimensionality reduction techniques and efficient algorithms, both LLSF and ExpNet successfully scaled to this very large problem with a result significantly outperforming word-matching and other automatic learning methods applied to the same corpus.
In tubular structures, spatial aspects of the dose distribution may be important in determining the normal tissue response. Conventional dose-volume-histograms (DVHs) and dose-surface-histograms (DSHs) lack spatial information and may not be adequate to represent the three-dimensional (3D) dose data. A new 3D dose distribution data reduction scheme which preserves its longitudinal and circumferential character is presented. Dose distributions were generated at each axial level for esophagus or rectum in 123 patients with lung cancer or prostate cancer. Dose distribution histograms at each axial level were independently analyzed along the esophageal or rectal circumference to generate dose-circumference-histogram (DCH) sheets. Two types of plots were then generated from the DCH sheet. The first considered the percentage of the circumference at each axial level receiving various doses. The second considered the minimum dose delivered to any percentage of the circumference at each axial level. The DCH as a treatment planning tool can be easily implemented in a 3D planing system and is potentially useful for the study of the relationship between the complication risk and the longitudinal and circumferential dose distributions.
For dynamic multileaf collimator-based intensity modulated radiotherapy in which small beam elements are used to generate continuous modulation, the sheer size of the dose calculation matrix could pose serious computational challenges. In order to circumvent this problem, the dose calculation matrix was reduced to a sparse matrix by truncating the weakly contributing entries below a certain cutoff to zero. Subsequently, the sparse matrix was compressed and matrix indexing vectors were generated to facilitate matrix-vector and matrix-matrix operations used in inverse planning. The application of sparsity permitted the reduction of overall memory requirement by an order of magnitude. In addition, the effect of disregarding the small scatter components on the quality of optimization was investigated by repeating the inverse planning using the dense dose calculation matrix. Comparison of dense and sparse matrix-based plans revealed an insignificant difference in optimization outcome, thus demonstrating the feasibility and usefulness of the sparse method in inverse planning. Furthermore, two additional methods of memory minimization are suggested, namely hexagonal dose sampling and limited normal tissue sampling.
This paper presents one-dimensional simulations of an experimental, amperometric sensor system designed to reduce fouling at the sensor surface. The effect exploited in this system depends on differences in the diffusion coefficients of the analytes and foulants. We describe this effect and present simulations of a typical analyte (H2O2) and foulant (bovine serum albumin). The simulations show effective reduction of foulants: the concentration at the sensor surface is more than five orders of magnitude smaller than in the sample, while concentration of analyte is only reduced by one order of magnitude, and so remains measurable. Thus in cases where the target species has a lower diffusivity than the foulant (for example ions in samples containing protein) this technique can be very effective in extending the maintenance interval or lifetime of a sensor and increasing its operational value. Using a calibration factor obtained from experiments to relate concentration to amperometric signal, we predict a signal strength from the simulations that is consistent with the experimental results. The peak signal is approximately 10(-7) Amps in both simulation and experiment, and the time taken to reach this peak value is within a factor of three.
A new method, MUNIN (Multi-dimensional NMR spectra interpretation), is introduced for the automated interpretation of three-dimensional NMR spectra. It is based on a mathematical concept referred to as three-way decomposition. An NMR spectrum is decomposed into a sum of components, with each component corresponding to one or a group of peaks. Each component is defined as the direct product of three one-dimensional shapes. A consequence is reduction in dimensionality of the spectral data used in further analysis. The decomposition may be applied to frequency-domain or time-domain data, or to a mixture of these. Features of MUNIN include good resolution in crowded regions and the absence of assumptions about line shapes. Uniform sampling of time-domain data, a prerequisite for discrete Fourier transform, is not required. This opens an avenue for the processing of NMR data that do not follow oscillating behaviour, e.g. from relaxation measurements. The application of MUNIN is illustrated for a 1H-15N-NOESY-HSQC, where each component is defined as the set of all NOE peaks formed by a given amide group. As a result, the extraction of structural information simply consists of one-dimensional peak picking of the shape along the NOE-axis obtained for each amide group.
Reduction and alkylation of protein disulfides prior to IEF, when performed directly in a centrifugal ultrafiltration device, provides an effective means of terminating the alkylation reaction, concentrating the proteins for analysis, and removing ionic impurities that interfere with IEF. When cells were lysed in "buffers" that support the activity of enzymes such as lysozyme and benzonase, the conductivity of the resulting lysate was an order of magnitude higher than when lysis was induced by chaotropic urea detergent solutions. Following reduction and alkylation, the conductivity of both lysates was lowered by ultrafiltration to the 0.1-0.2 mS/cm range in preparation for IEF. The detergent 3-(4-heptyl)phenyl 3-hydroxypropyl dimethylammonio propanesulfonate (C7BzO), which favors the solubilization of proteins, but which interferes with SDS equilibration and second dimension PAGE, was effectively removed by ultrafiltration and exchanged with CHAPS without measurable loss of protein. Disparate protein patterns of Rhodopseudomonas palustris lysates were revealed by two-dimensional gel electrophoresis depending on which reagent was used to induce cell lysis.
The authors have developed a method to reduce noise in three-dimensional (3D) phase-contrast magnetic resonance (MR) velocity measurements by exploiting the property that blood is incompressible and, therefore, the velocity field describing its flow must be divergence-free. The divergence-free condition is incorporated by a projection operation in Hilbert space. The velocity field obtained with 3D phase-contrast MR imaging is projected onto the space of divergence-free velocity fields. The reduction of noise is achieved because the projection operation eliminates the noise component that is not divergence-free. Signal-to-noise ratio (S/N) gains on the order of 15%-25% were observed. The immediate effect of this noise reduction manifests itself in higher-quality phase-contrast MR angiograms. Alternatively, the S/N gain can be traded for a reduction in imaging time and/or improved spatial resolution.
OBJECTIVES: We present the prenatal two-dimensional (2D-) and three-dimensional ultrasound (3D-US) diagnosis of limb reduction defects associated with homozygous alpha-thalassemia and a review of the literature. METHODS: At 17 weeks' gestation, amniocentesis was performed for cytogenetic and molecular studies, and 2D- and 3D-US examinations were made for evaluation of the fetal malformations. RESULTS: Amniocentesis revealed a 46,XY karyotype and molecular analysis of the amniocytes showed that the fetus was homozygous for the Southeast Asian deletion (--SEA/--SEA). 2D-US examination revealed bilateral ventriculomegaly, brachycephaly, pleural effusion, digital deficiency and hypoplasia of the right foot, and digital deficiency of the left foot. 3D-US confirmed the distal limb reduction defects. CONCLUSIONS: When the fetus is at risk for homozygous alpha-thalassemia, 2D- and 3D-US examinations are useful for prenatal detection of the associated limb reduction defects. Prenatal identification of the possible association with limb reduction defects is important for parental counseling and decision-making when intrauterine fetal therapy is an option.
PURPOSE: The aim of the study was to compare a conventional respiratory-gated 3D MR coronary angiographic technique (conventional MRCA) with a respiratory-gated 3D MR coronary angiographic technique that includes a slice interpolation technique (slice interpolation MRCA). Both MRCA techniques were compared based on the quality of visualization of the coronary arteries and the diagnostic accuracy in identifying hemodynamically significant coronary artery stenoses. METHOD: Forty patients with known proximal coronary artery stenosis after conventional CA were examined on a 1.5 T scanner, that is, 20 patients with each sequence. A 6 point grading system (0 = worst quality, 5 = best quality) was used to evaluate and compare the image quality. The length and proximal diameter of the depicted coronary arteries were measured. Detection of coronary artery stenoses was compared with that obtained by conventional CA by two blinded readers. RESULTS: With the slice interpolation technique, the average scan time of the entire heart was reduced by approximately 40%. With use of conventional MRCA, 69% of all proximal and middle coronary artery segments were visualized with a sufficient image quality; with the slice interpolation technique, 79% of these segments were depicted adequately. For the assessment of stenoses, sensitivity was 71% and specificity was 53% for conventional MRCA and 72 and 60% for slice interpolation MRCA, respectively. These differences in sensitivity and specificity were statistically not significant. CONCLUSION: The application of a slice interpolation technique reduces the scan time, maintains a comparable sensitivity and specificity for the assessment of coronary artery stenoses, and increases the number of completely identified coronary artery segments compared with the conventional technique.
A three-dimensional finite element model of a fractured human mandible treated with plating technique was developed to simulate and to study the biomechanical loads and the stress field distribution. Biomechanical properties of bone have been thoroughly investigated experimentally. In this work, using the finite element method, complete clinical conditions (after surgical reduction, post-operatory period, complete healing period) were simulated. The mandible fracture was located in the symphysis region and one or two titanium miniplates, fixed with monocortical screws, were evaluated. The behaviour of a reduced human mandible with screwed miniplates, as well as its complete healing, is investigated and described.
A new analytical strategy for biomarker recovery from directly coupled ultra-performance liquid chromatography time-of-flight mass spectrometry (UPLC Tof MS) data on biofluids is presented and exemplified using a study on hydrazine-induced liver toxicity. A key step in the strategy involves a novel procedure for reducing the spectroscopic search space by differential analysis of cohorts of normal and pathological samples using an orthogonal projection to latent structures discriminant analysis (O-PLS-DA). This efficiently sorts principal discriminators of toxicity from the background of thousands of metabolic features commonly observed in data sets generated by UPLC-MS analysis of biological fluids and is thus a powerful tool for biomarker discovery.
The microtubule cytoskeleton is a dynamic structure in which the lengths of the microtubules are tightly regulated. One regulatory mechanism is the depolymerization of microtubules by motor proteins in the kinesin-13 family. These proteins are crucial for the control of microtubule length in cell division, neuronal development and interphase microtubule dynamics. The mechanism by which kinesin-13 proteins depolymerize microtubules is poorly understood. A central question is how these proteins target to microtubule ends at rates exceeding those of standard enzyme-substrate kinetics. To address this question we developed a single-molecule microscopy assay for MCAK, the founding member of the kinesin-13 family. Here we show that MCAK moves along the microtubule lattice in a one-dimensional (1D) random walk. MCAK-microtubule interactions were transient: the average MCAK molecule diffused for 0.83 s with a diffusion coefficient of 0.38 microm2 s(-1). Although the catalytic depolymerization by MCAK requires the hydrolysis of ATP, we found that the diffusion did not. The transient transition from three-dimensional diffusion to 1D diffusion corresponds to a "reduction in dimensionality" that has been proposed as the search strategy by which DNA enzymes find specific binding sites. We show that MCAK uses this strategy to target to both microtubule ends more rapidly than direct binding from solution.
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Four-dimensional (4D) CT is useful in many clinical situations, where detailed abdominal and thoracic imaging is needed over the course of the respiratory cycle. However, it usually delivers a larger radiation dose than the standard three-dimensional (3D) CT, since multiple scans at each couch position are required in order to provide the temporal information. Our purpose in this work is to develop a method to perform 4D CT scans at relatively low current, hence reducing the radiation exposure of the patients. To deal with the increased statistical noise caused by the low current, we proposed a novel 4D penalized weighted least square (4D-PWLS) smoothing method, which can incorporate both spatial and phase information. The 4D images at different phases were registered to the same phase via a deformable model, thereby, a regularization term combining temporal and spatial neighbors can be designed for the 4D-PWLS objective function. The proposed method was tested with phantom experiments and a patient study, and superior noise suppression and resolution preservation were observed. A quantitative evaluation of the benefit of the proposed method to 4D radiotherapy and 4D PET/CT imaging are under investigation.
High-dimensional data generated by a system with limited degrees of freedom are often constrained in low-dimensional manifolds in the original space. In this article, we investigate dimension-reduction methods for such intrinsically low-dimensional data through linear projections that preserve the manifold structure of the data. For intrinsically one dimensional data, this implies projecting to a curve on the plane with as few intersections as possible. We are proposing a supervised projection pursuit method that can be regarded as an extension of the single-index model for nonparametric regression. We show results from a toy and two robotic applications.
The full conformational space was explored for an achiral and two chiral beta-peptide models: namely For-beta-Ala-NH2, For-beta-Abu-NH2, and For-beta-Aib-NH2. Stability and conformational properties of all three model systems were computed at different levels of theory: RHF/3-21G, B3LYP/6-311++G(d,p)//RHF/3-21G, B3LYP/6-311++G(d,p), MP2//B3LYP/6-311++G(d,p), CCSD//B3LYP/6-311++G(d,p), and CCSD(T)//B3LYP/6-311++G(d,p). In addition, ab initio E = E(phi, micro, psi) potential energy hypersurfaces of all three models were determined, and their topologies were analyzed to determine the inherent flexibility properties of these beta-peptide models. Fewer points were found and assigned than expected on the basis of Multidimensional Conformational Analysis (MDCA). Furthermore, it has been demonstrated, that the four-dimensional surface, E = E(phi, mu, psi), can be reduced into a three-dimensional one: E = E[phi, f(phi), psi]. This reduction of dimensionality of freedom of motion suggests that beta-peptides are less flexible than one would have thought. This agrees with experimental data published on the conformational properties of peptides composed of beta-amino acid residues.
Several interventions have been shown to protect the ischemic myocardium from evolving to necrosis. However, three-dimensional evaluation of infarct size reduction using anatomical measurements is lacking. Therefore, Tc-99m labeled albumin microspheres were injected into the left atrium of 16 dogs, 1 min after coronary artery occlusion, to assess the hypoperfused zone. After 15 min, 8 dogs received, intravenously, gallopamil (Procorum) (Ga: 0.08 mg/k as a bolus + 0.2 mg/k/h for 6 h) and the remaining 8 dogs served as controls. At sacrifice (6 h), the left ventricle was cut into 3 mm slices, stained with triphenyltetrazolium chloride to delineate the size of infarction and autoradiographed to delineate the hypoperfused zone. Lateral reduction was calculated by the difference distance between hypoperfused zone and infarct size on the endocardium, mid-myocardium and epicardium; radial reduction was calculated by the difference of the transmural distance taken at mid-infarction and mid-hypoperfusion and the longitudinal reduction was calculated by the distance of the hypoperfused slices that did not infarct. With this technique it could be demonstrated that gallopamil reduced the size of infarction in all three dimensions.