Two-dimensional models in quantum field theory: Reduction to the free-particle case.
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Journal Article↗
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Results for “Dimensionality Reduction”
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Many-body basis-set reduction applied to the two-dimensional t-Jz model.
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Journal Article↗
Theory of chaos in surface waves: The reduction from hydrodynamics to few-dimensional dynamics.
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Journal Article↗
Large-N reduction in the continuum three-dimensional Yang-Mills theory.
Numerical and theoretical evidence leads us to propose the following: Three-dimensional Euclidean Yang-Mills theory in the planar limit undergoes a phase transition on a torus of side l=l(c). For l>l(c) the planar limit is l independent, as expected of a noninteracting string theory. We expect the situation in four dimensions to be similar.
Journal Article↗
Propagation and reduction of error in three-dimensional structure determined from biplane views of unknown orientation.
We are developing a technique for determination of the three-dimensional (3-D) structure of vascular objects from two radiographic projection images acquired at arbitrary and unknown relative orientations. No separate calibration steps are required with this method, which exploits an inherent redundancy of biplane imaging to extract the imaging geometry as well as the 3-D locations of eight or more object points. The theoretical basis of this technique has been described previously. In this paper, we review the method from the perspective of linear algebra and describe an improvement, not heretofore reported, that reduces the method's sensitivity to experimental error. We then examine the feasibility and inherent accuracy of this approach by computer simulation of biplane imaging experiments. The precision with which 3-D object structure may be retrieved, together with the dependence of precision on the actual imaging geometry and errors in various measured quantities, is studied in detail. Our simulation studies show that the method is not only feasible but potentially accurate, typically determining object-point configurations with root-mean-square (RMS) error on the order of 1 to 2 mm. The method is also quite fast, requiring approximately one second of CPU time on a VAX 11/750 computer (0.6 MIPS).
Angiography↗
Three-dimensional surface displays of perfusion SPET in the evaluation of patients with pulmonary emphysema for thoracoscopic lung volume reduction surgery.
A modified, three-dimensional display was applied to 99Tcm-macroaggregated albumin (99Tcm-MAA) SPET to help assess the effect of thoracoscopic lung volume reduction surgery (LVRS) on regional lung perfusion. Surface-rendered three-dimensional images for 99Tcm-MAA and xenon-133 (133Xe) equilibrium (EQ) SPET were obtained in 11 patients with pulmonary emphysema before and after LVRS. A single three-dimensional fusion display of both images was then reconstructed, and the perfused lungs were transparently visible through the lung contours delineated by the three-dimensional 133Xe EQ image. The extent of preserved perfusion in the lung (the perfusion index) was estimated using the ratio (%) of the total pixel numbers of the segmented perfusion data to those of the 133Xe lung volume data. The three-dimensional fusion display provided an overview of the distribution of hypoperfusion in the lungs with geometric realism and enhanced the perception of anatomic size and configuration compared with multiple tomograms and three-dimensional perfusion images without superimposition of three-dimensional 133Xe image. Post-operatively, it displayed restored perfusion in the remaining lungs, and changes in the perfusion index correlated with %FEV1 (r = 0.731, P = 0.0001) more closely than the perfusion data alone (r = 0.593, P < 0.01). This method is useful for directing LVRS and assessing its effectiveness, as it provides precise tomographic information on regional perfusion.
Aged↗
Evaluation of left ventricular outflow tract area after septal reduction in obstructive hypertrophic cardiomyopathy: a real-time 3-dimensional echocardiographic study.
BACKGROUND: The comparative impact of percutaneous alcohol septal reduction (ASR) and surgical myectomy on the left ventricular outflow tract (LVOT) area in patients with obstructive hypertrophic cardiomyopathy (HC) is not well defined. Real-time 3-dimensional echocardiography (RT3DE) provides accurate information about the LVOT geometry and shape. We aimed to analyze the change in LVOT area after septal reduction interventions in patients with obstructive HC using RT3DE. METHODS: Thirty-one HC patients (mean age 53 +/- 17 years) undergoing ASR (n = 14) or myectomy (n = 17) were studied at baseline and during follow-up with RT3DE. LVOT area was measured after observing the LVOT in the 3D space as the smallest area during midsystole. LVOT pressure gradients were determined by conventional continuous wave Doppler. RESULTS: Overall, LVOT area increased from 0.86 +/- 0.20 to 2.50 +/- 0.88 cm2 (P < .01), and the resting LVOT pressure gradient decreased from 64 +/- 41 to 16 +/- 10 mm Hg (P < .01) after a median follow-up of 3 months after intervention (range 1-24 months). A similar significant decrease in LVOT pressure gradients was seen in myectomy and ASR groups (from 62 +/- 39 to 12 +/- 5 mm Hg and from 67 +/- 43 to 21 +/- 14 mm Hg, respectively, P < .01 in between each group, and P = NS between both groups). However, the increase in LVOT area was greater in myectomy than in ASR group (from 0.81 +/- 0.22 to 2.90 +/- 0.64 cm2 and 0.93 +/- to 0.16 to 2.02 +/- 0.92 cm2, respectively, P < .01 between both groups). CONCLUSION: RT3DE demonstrated an effective increase in LVOT area after both ASR and myectomy. This technique may be useful for assessing the results of septal reduction in patients with obstructive HC.
Adolescent↗
Current assessment of spinal degenerative disease with magnetic resonance imaging.
Radiography (plain roentgenography, myelography, computed tomography (CT), computed tomographic myelography) has been used to identify morphologic changes involving the various components of the diskovertebral unit. Added to this armamentarium of imaging techniques is magnetic resonance (MR) imaging, with its superior ability to define anatomy, its improved contrast sensitivity, and its potential to provide unique biochemical and physiologic information. The authors review the current use of MR imaging in defining degenerative changes in the spine including the various patterns of herniation, annular tears, canal stenosis, and the use of gadolinium-diethylenetriamine-pentaacetic acid for previously unoperated and operated patients. Prospective studies have compared surface-coil MR imaging, CT, and myelography in the evaluation of disk herniation and stenosis and found an 82.6% accuracy between MR imaging and surgical findings for the type and location of the disease. Recent experience with precontrast and postcontrast MR imaging in the postoperative lumbar spine indicated that it was 96% accurate in differentiating scar from disk in 44 patients at 50 reoperated levels. Three-dimensional imaging is, more and more, becoming an integral part of routine MR imaging. The theoretical and practical advantages of three-dimensional imaging are several and include a theoretical increase in the signal-to-noise ratio over two-dimensional imaging (by the square root of the number of partitions selected), the ability to obtain thin contiguous slices from the volume without the problem of cross-talk found in two-dimensional imaging, more accurate slice thickness than that achieved in two-dimensional imaging, and a reduction in susceptibility artifacts. Different three-dimensional techniques are capable of providing either high or low signal intensity cerebrospinal fluid (CSF), with excellent suppression of CSF pulsation artifacts. Certain sequences provide a high enough signal intensity that a computer algorithm may be used to display the CSF in a rotating three-dimensional manner, similar to a myelogram. This three-dimensional myelographic image has the potential of providing the clinician with a global assessment of the CSF spaces, an advantage previously lacking with other imaging techniques.
Contrast Media↗
Data reduction using a discrete wavelet transform in discriminant analysis of very high dimensionality data.
We present a method of data reduction using a wavelet transform in discriminant analysis when the number of variables is much greater than the number of observations. The method is illustrated with a prostate cancer study, where the sample size is 248, and the number of variables is 48,538 (generated using the ProteinChip technology). Using a discrete wavelet transform, the 48,538 data points are represented by 1271 wavelet coefficients. Information criteria identified 11 of the 1271 wavelet coefficients with the highest discriminatory power. The linear classifier with the 11 wavelet coefficients detected prostate cancer in a separate test set with a sensitivity of 97% and specificity of 100%.
Data Compression↗
Identification of an apoC-II variant (apoC-IIBethesda) in a kindred with apoC-II deficiency and type I hyperlipoproteinemia.
Apolipoprotein (apo) C-II deficiency is characterized by elevated plasma triglycerides, chylomicrons, and very low density lipoproteins, as well as reduced levels of low density and high density lipoproteins. A subject with apoC-II deficiency has been identified with an apoC-II plasma level of less than 0.05 mg/dl. The plasma apoC-II in the proband was immunochemically similar to apoC-II in normal subjects when analyzed by Ouchterlony immunodiffusion, however the apoC-II had an apparently lower molecular weight and higher pI when analyzed by two-dimensional gel electrophoresis. This apoC-II variant, designated apoC-IIBethesda, was not affected by neuraminidase treatment or reduction. Two-dimensional gel electrophoresis of the plasma of the mother of the proband revealed both normal apoC-II and apoC-IIBethesda, whereas analysis of the father and two siblings revealed apoC-II of normal electrophoretic mobility. These results were interpreted as indicating that the proband was a compound heterozygote with one allele for apoC-IIBethesda inherited from the mother and an allele coding for an abnormality which results in the virtual or complete absence of plasma apoC-II from the father. This proband represents the first example of a compound heterozygote for an apolipoprotein defect associated with a dyslipoproteinemia.
Apolipoprotein C-II↗
Systematic background selection with BasCoD enhances contrastive dimension reduction in single cell genomics.
In single-cell experiments spanning diverse conditions, distinguishing variation specific to one condition (e.g., treatment) from shared or background variation (e.g., control) is critical for uncovering treatment-specific molecular responses. However, these studies typically yield ultra-high-dimensional data, necessitating effective dimension reduction for reliable biological interpretation. Contrastive dimension reduction methods address this challenge by identifying low-dimensional features enriched in a target dataset relative to a background dataset that captures shared variation. Despite their growing utility, the success of such methods critically depends on the choice of background, yet no formal criterion exists for evaluating or selecting backgrounds. To address this gap, we introduce BasCoD, a statistical testing framework based on spectral subspace inclusion theory, that enables rigorous evaluation and systematic selection of background datasets. Applying BasCoD across a range of single-cell datasets, we show that it effectively identifies suitable backgrounds, substantially improving the contrast and interpretability of the resulting target representations. We further demonstrate how BasCoD can guide the design of contrastive analyses in large-scale single-cell experiments conducted under heterogeneous conditions and elucidate potential interaction effects in perturbation studies.
Single-Cell Analysis↗
Hypertensive heart disease: quantitative evaluation of response to therapy with cine MR imaging.
RATIONALE AND OBJECTIVES: To assess the ability of cine magnetic resonance (MR) imaging to help detect and quantity changes in left ventricular parameters in patients receiving antihypertensive therapy. MATERIALS AND METHODS: After undergoing baseline cine MR imaging of the heart, 16 (12 men, four women) hypertensive patients participating in a prospective drug trial began isradipine therapy. Follow-up serial cine MR imaging was performed at 3 months and 6 months. Myocardial mass, end-systolic volume, end-diastolic volume, stroke volume, and ejection fraction were measured. Results from transaxially acquired three-dimensional data sets and monoplanar imaging were compared. RESULTS: Three dimensional data showed reductions of 11% in end-systolic volume (P = .0051) and 17% in end-diastolic volume (P = .0023). These changes were not detected with monoplanar imaging. Changes in myocardial mass, stroke volume, and ejection fraction were not statistically significant. CONCLUSION: Three-dimensional cine MR imaging can depict small yet statistically significant reductions in left ventricular volumes in response to antihypertensive therapy.
Adult↗
Morphological classification of brains via high-dimensional shape transformations and machine learning methods.
A high-dimensional shape transformation posed in a mass-preserving framework is used as a morphological signature of a brain image. Population differences with complex spatial patterns are then determined by applying a nonlinear support vector machine (SVM) pattern classification method to the morphological signatures. Significant reduction of the dimensionality of the morphological signatures is achieved via wavelet decomposition and feature reduction methods. Applying the method to MR images with simulated atrophy shows that the method can correctly detect subtle and spatially complex atrophy, even when the simulated atrophy represents only a 5% variation from the original image. Applying this method to actual MR images shows that brains can be correctly determined to be male or female with a successful classification rate of 97%, using the leave-one-out method. This proposed method also shows a high classification rate for old adults' age classification, even under difficult test scenarios. The main characteristic of the proposed methodology is that, by applying multivariate pattern classification methods, it can detect subtle and spatially complex patterns of morphological group differences which are often not detectable by voxel-based morphometric methods, because these methods analyze morphological measurements voxel-by-voxel and do not consider the entirety of the data simultaneously.
Aged↗
Soft lithographic patterning of supported lipid bilayers onto a surface and inside microfluidic channels.
We present simple soft lithographic methods for patterning supported lipid bilayer (SLB) membranes onto a surface and inside microfluidic channels. Micropatterns of polyethylene glycol (PEG)-based polymers were fabricated on glass substrates by microcontact printing or capillary moulding. The patterned PEG surfaces have shown 97 +/- 0.5% reduction in lipid adsorption onto two dimensional surfaces and 95 +/- 1.2% reduction inside microfluidic channels in comparison to glass control. Atomic force microscopy measurements indicated that the deposition of lipid vesicles led to the formation of SLB membranes by vesicle fusion due to hydrophilic interactions with the exposed substrate. Furthermore, the functionality of the patterned SLBs was tested by measuring the binding interactions between biotin (ligand)-labeled lipid bilayer and streptavidin (receptor). SLB arrays were fabricated with spatial resolution down to approximately 500 nm on flat substrate and approximately 1 microm inside microfluidic channels, respectively.
Dimethylpolysiloxanes↗
The effect of a new type of video glasses on the perceived intensity of pain and unpleasantness evoked by a cold pressor test.
The aim of the study was to evaluate whether distraction induced by a new generation of video glasses (I-Glasses, Virtual i-O, Seattle, WA) has an effect on the perceived intensity of pain and unpleasantness. The effects of three-dimensional video, two-dimensional video, and no video glasses (control) were compared in two groups of healthy volunteers (13 males and 11 females) in a randomized, controlled trial. A cold pressor stimulus (1-2 degrees C chilled water) was used to induce experimental pain, and the volunteers rated the intensity of pain and unpleasantness on 100-mm visual analogue scales. The ratings were statistically compared using the Wilcoxon signed-rank test. Between the groups (males and females), there was a significant difference (P < .01) in the rating of unpleasantness in the three-dimensional video condition, while there were no significant differences between the genders in the other conditions (two-dimensional, control). Three-dimensional video provided a significant reduction in both pain and unpleasantness (P < .01) compared with the control condition in the male group. However, in the female group, there was a significant reduction in unpleasantness with two-dimensional video compared with the control (P < .05). This suggests that the use of distraction by means of video glasses is able to reduce the perceived intensity of pain and unpleasantness.
Adult↗
Navigator-echo-based real-time respiratory gating and triggering for reduction of respiration effects in three-dimensional coronary MR angiography.
PURPOSE: To test the hypothesis that respiration effects in three-dimensional (3D) coronary magnetic resonance (MR) imaging can be reduced with navigator-echo-based gating or triggering according to the superior-inferior position of the diaphragm. MATERIALS AND METHODS: Real-time respiratory gating and respiratory triggering (breath hold with feedback) were implemented with navigator echoes in a magnetization-prepared, segmented, 3D coronary imaging sequence. The two techniques were first tested with a motion phantom. An imaging protocol that compared real-time respiratory-gated acquisition, real-time respiratory-triggered acquisition, and continuous acquisition was then evaluated in six healthy subjects. RESULTS: Real-time respiratory-gated and respiratory-triggered acquisition were superior to continuous acquisition with two signals averaged (P = .025). The performance of the gated acquisition was about the same as that of the triggered acquisition (P = .05). CONCLUSION: Navigator-echo-based, real-time respiratory-gating and respiratory-triggering techniques are practical methods for effective reduction of respiration effects in coronary MR imaging.
Adult↗
Working-memory load and dimensional complexity of the EEG.
This investigation shows that a working-memory load induced by a memory scanning task has an effect on nonlinear descriptors of the EEG dynamics. The effect was locally specific above the fronto-temporal (right) cortex and it may be described as a reduction in the dimensional complexity of cortical brain activity. The meaning of the effects seems to differ from that of EEG spectral power, which varied with time during the experiment and not with changes in the working-memory load conditions. Behaviorally controlled over- and underload led to increased variance of the dimensional complexity, thus indicating that dimensional complexity correlates more closely with actual performance than with more general descriptions of brain states. Habitual response speed had an effect at the parietal lead, thus indicating that fast responders reduced their dimensional complexity as the task demand increased. In contrast, the slower responders showed no such definite trend.
Adult↗
Fracture reduction and deformity correction with the hexapod Ilizarov fixator.
A configuration for the Ilizarov external fixator with six distractors and 12 ball joints in the form of a hexapod was developed. The system allows for six degrees of freedom bone fragment displacement by controlling the distractors. Using this assembly, universal three-dimensional corrections or reductions are possible without the need for complicated joint mechanisms. The device was used in 16 patients: five had displaced tibial fractures with severe soft tissue damage, 10 had deformities or pseudarthroses subsequent to treatment of tibial fractures, and one had an axis deviation in the course of tibial lengthening. Translational (to 40 mm) and rotational deformities (to 33 degrees) were corrected. Final radiographic examinations after the correction procedure was complete showed median residual deformities of 3.5 mm (range, 0-5 mm) and 1 degree (range, 0 degree-4 degrees) in the anteroposterior projection and of 1.5 mm (range, 0-6 mm) and less than 1 degree (range, 0 degree-9 degrees) in the lateral projection. The construction is a useful and important addition to the Ilizarov fixator system. As a bone fixation device it is unique in that its optimal use depends on the availability of computer software.
Adolescent↗