Weighted Euclidean biplots

We construct a weighted Euclidean distance that approximates any distance or dissimilarity measure between individuals that is based on a rectangular cases-by-variables data matrix. In contrast to regular multidimensional scaling methods for dissimilarity data, the method leads to biplots of individuals and variables while preserving all the good properties of dimension-reduction methods that are based on the singular-value decomposition. The main benefits are the decomposition of variance into components along principal axes, which provide the numerical diagnostics known as contributions, and the estimation of nonnegative weights for each variable. The idea is inspired by the distance functions used in correspondence analysis and in principal component analysis of standardized data, where the normalizations inherent in the distances can be considered as differential weighting of the variables. In weighted Euclidean biplots we allow these weights to be unknown parameters, which are estimated from the data to maximize the fit to the chosen distances or dissimilarities. These weights are estimated using a majorization algorithm. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing the matrix and displaying its rows and columns in biplots.

Improved coronary artery definition with T2-weighted, free-breathing, three-dimensional coronary MRA.

BACKGROUND: Three-dimensional (3D) navigator-gated and prospectively corrected free-breathing coronary magnetic resonance angiography (MRA) allows for submillimeter image resolution but suffers from poor contrast between coronary blood and myocardium. Data collected over >100 ms/heart beat are also susceptible to bulk cardiac and respiratory motion. To address these problems, we examined the effect of a T2 preparation prepulse (T2prep) for myocardial suppression and a shortened acquisition window on coronary definition. METHODS AND RESULTS: Eight healthy adult subjects and 5 patients with confirmed coronary artery disease (CAD) underwent free-breathing 3D MRA with and without T2prep and with 120- and 60-ms data-acquisition windows. The T2prep resulted in a 123% (P<0. 001) increase in contrast-to-noise ratio (CNR). Coronary edge definition was improved by 33% (P<0.001). Acquisition window shortening from 120 to 60 ms resulted in better vessel definition (11%; P<0.001). Among patients with CAD, there was a good correspondence with disease. CONCLUSIONS: Free-breathing, T2prep, 3D coronary MRA with a shorter acquisition window resulted in improved CNR and better coronary artery definition, allowing the assessment of coronary disease. This approach offers the potential for free-breathing, noninvasive assessment of the major coronary arteries.

Diffusion-weighted spectroscopy: a novel approach to determine macromolecule resonances in short-echo time 1H-MRS.

Quantification of short-echo time proton magnetic resonance spectroscopy results in >18 metabolite concentrations (neurochemical profile). Their quantification accuracy depends on the assessment of the contribution of macromolecule (MM) resonances, previously experimentally achieved by exploiting the several fold difference in T(1). To minimize effects of heterogeneities in metabolites T(1), the aim of the study was to assess MM signal contributions by combining inversion recovery (IR) and diffusion-weighted proton spectroscopy at high-magnetic field (14.1 T) and short echo time (= 8 msec) in the rat brain. IR combined with diffusion weighting experiments (with δ/Δ = 1.5/200 msec and b-value = 11.8 msec/μm(2)) showed that the metabolite nulled spectrum (inversion time = 740 msec) was affected by residuals attributed to creatine, inositol, taurine, choline, N-acetylaspartate as well as glutamine and glutamate. While the metabolite residuals were significantly attenuated by 50%, the MM signals were almost not affected (< 8%). The combination of metabolite-nulled IR spectra with diffusion weighting allows a specific characterization of MM resonances with minimal metabolite signal contributions and is expected to lead to a more precise quantification of the neurochemical profile.

Whole-body 3D T1-weighted MR imaging in patients with prostate cancer: feasibility and evaluation in screening for metastatic disease.

PURPOSE: To develop and assess the diagnostic performance of a three-dimensional (3D) whole-body T1-weighted magnetic resonance (MR) imaging pulse sequence at 3.0 T for bone and node staging in patients with prostate cancer. MATERIALS AND METHODS This prospective study was approved by the institutional ethics committee; informed consent was obtained from all patients. Thirty patients with prostate cancer at high risk for metastases underwent whole-body 3D T1-weighted imaging in addition to the routine MR imaging protocol for node and/or bone metastasis screening, which included coronal two-dimensional (2D) whole-body T1-weighted MR imaging, sagittal proton-density fat-saturated (PDFS) imaging of the spine, and whole-body diffusion-weighted MR imaging. Two observers read the 2D and 3D images separately in a blinded manner for bone and node screening. Images were read in random order. The consensus review of MR images and the findings at prospective clinical and MR imaging follow-up at 6 months were used as the standard of reference. The interobserver agreement and diagnostic performance of each sequence were assessed on per-patient and per-lesion bases. RESULTS: The signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) were significantly higher with whole-body 3D T1-weighted imaging than with whole-body 2D T1-weighted imaging regardless of the reference region (bone or fat) and lesion location (bone or node) (P < .003 for all). For node metastasis, diagnostic performance (area under the receiver operating characteristic curve) was higher for whole-body 3D T1-weighted imaging (per-patient analysis; observer 1: P < .001 for 2D T1-weighted imaging vs 3D T1-weighted imaging, P = .006 for 2D T1-weighted imaging + PDFS imaging vs 3D T1-weighted imaging; observer 2: P = .006 for 2D T1-weighted imaging vs 3D T1-weighted imaging, P = .006 for 2D T1-weighted imaging + PDFS imaging vs 3D T1-weighted imaging), as was sensitivity (per-lesion analysis; observer 1: P < .001 for 2D T1-weighted imaging vs 3D T1-weighted imaging, P < .001 for 2D T1-weighted imaging + PDFS imaging vs 3D T1-weighted imaging; observer 2: P < .001 for 2D T1-weighted imaging vs 3D T1-weighted imaging, P < .001 for 2D T1-weighted imaging + PDFS imaging vs 3D T1-weighted imaging). CONCLUSION: Whole-body MR imaging is feasible with a 3D T1-weighted sequence and provides better SNR and CNR compared with 2D sequences, with a diagnostic performance that is as good or better for the detection of bone metastases and better for the detection of lymph node metastases.

Accurate calculations of intermolecular interaction energies using explicitly correlated coupled cluster wave functions and a dispersion-weighted MP2 method.

Explicitly correlated coupled-cluster calculations of intermolecular interaction energies for the S22 benchmark set of Jurecka, Sponer, Cerny, and Hobza (Chem. Phys. Phys. Chem. 2006, 8, 1985) are presented. Results obtained with the recently proposed CCSD(T)-F12a method and augmented double-zeta basis sets are found to be in very close agreement with basis set extrapolated conventional CCSD(T) results. Furthermore, we propose a dispersion-weighted MP2 (DW-MP2) approximation that combines the good accuracy of MP2 for complexes with predominately electrostatic bonding and SCS-MP2 for dispersion-dominated ones. The MP2-F12 and SCS-MP2-F12 correlation energies are weighted by a switching function that depends on the relative HF and correlation contributions to the interaction energy. For the S22 set, this yields a mean absolute deviation of 0.2 kcal/mol from the CCSD(T)-F12a results. The method, which allows obtaining accurate results at low cost, is also tested for a number of dimers that are not in the training set.

High b-value diffusion-weighted imaging: A sensitive method to reveal white matter differences in schizophrenia.

Over the last 10 years, diffusion-weighted imaging (DWI) has become an important tool to investigate white matter (WM) anomalies in schizophrenia. Despite technological improvement and the exponential use of this technique, discrepancies remain and little is known about optimal parameters to apply for diffusion weighting during image acquisition. Specifically, high b-value diffusion-weighted imaging known to be more sensitive to slow diffusion is not widely used, even though subtle myelin alterations as thought to happen in schizophrenia are likely to affect slow-diffusing protons. Schizophrenia patients and healthy controls were scanned with a high b-value (4000s/mm(2)) protocol. Apparent diffusion coefficient (ADC) measures turned out to be very sensitive in detecting differences between schizophrenia patients and healthy volunteers even in a relatively small sample. We speculate that this is related to the sensitivity of high b-value imaging to the slow-diffusing compartment believed to reflect mainly the intra-axonal and myelin bound water pool. We also compared these results to a low b-value imaging experiment performed on the same population in the same scanning session. Even though the acquisition protocols are not strictly comparable, we noticed important differences in sensitivities in the favor of high b-value imaging, warranting further exploration.

Testing Spatial Autocorrelation in Weighted Networks : the Modes Permutation Test

In a weighted spatial network, as specified by an exchange matrix, the variances of the spatial values are inversely proportional to the size of the regions. Spatial values are no more exchangeable under independence, thus weakening the rationale for ordinary permutation and bootstrap tests of spatial autocorrelation. We propose an alternative permutation test for spatial autocorrelation, based upon exchangeable spatial modes, constructed as linear orthogonal combinations of spatial values. The coefficients obtain as eigenvectors of the standardised exchange matrix appearing in spectral clustering, and generalise to the weighted case the concept of spatial filtering for connectivity matrices. Also, two proposals aimed at transforming an acessibility matrix into a exchange matrix with with a priori fixed margins are presented. Two examples (inter-regional migratory flows and binary adjacency networks) illustrate the formalism, rooted in the theory of spectral decomposition for reversible Markov chains.

Energy-weighted sum rules for mesons in hot and dense matter

We study energy-weighted sum rules of the pion and kaon propagator in nuclear matter at finite temperature. The sum rules are obtained from matching the Dyson form of the meson propagator with its spectral Lehmann representation at low and high energies. We calculate the sum rules for specific models of the kaon and pion self-energy. The in-medium spectral densities of the K and (K) over bar mesons are obtained from a chiral unitary approach in coupled channels that incorporates the S and P waves of the kaon-nucleon interaction. The pion self-energy is determined from the P-wave coupling to particle-hole and Delta-hole excitations, modified by short-range correlations. The sum rules for the lower-energy weights are fulfilled satisfactorily and reflect the contributions from the different quasiparticle and collective modes of the meson spectral function. We discuss the sensitivity of the sum rules to the distribution of spectral strength and their usefulness as quality tests of model calculations.

Method for performing cerebral perfusion-weighted MRI in neonates

Cerebral perfusion-weighted imaging (PWI) in neonates is known to be technically difficult and there are very few published studies on its use in preterm infants. In this paper, we describe one convenient method to perform PWI in neonates, a method only recently used in newborns. A device was used to manually inject gadolinium contrast material intravenously in an easy, quick and reproducible way. We studied 28 newborn infants, with various gestational ages and weights, including both normal infants and those suffering from different brain pathologies. A signal intensity-time curve was obtained for each infant, allowing us to build perfusion maps. This technique offered a fast and easy method to manually inject a bolus gadolinium contrast material, which is essential in performing PWI in neonates. Cerebral PWI is technically feasible and reproducible in neonates of various gestational age and with various pathologies.

Correlations in weighted networks

We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of structural constraints. We also introduce an algorithm for generating maximally random weighted networks with arbitrary P(k,s) to be used as null models. The application of our measures to real networks reveals the importance of weights in a correct understanding and modeling of these heterogeneous systems.

Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces

We characterize the Schatten class membership of the canonical solution operator to $\overline{\partial}$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in terms of $\Delta\phi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\phi})$