The magnetic susceptibility of tissue can be determined in gradient echo MRI by deconvolving the local magnetic field with the magnetic field generated by a unit dipole. This Quantitative Susceptibility Mapping (QSM) problem is unfortunately ill-posed. By transforming the problem to the Fourier domain, the susceptibility appears to be undersampled only at points where the dipole kernel is zero, suggesting that a modest amount of additional information may be sufficient for uniquely resolving susceptibility. A Morphology Enabled Dipole Inversion (MEDI) approach is developed that exploits the structural consistency between the susceptibility map and the magnitude image reconstructed from the same gradient echo MRI. Specifically, voxels that are part of edges in the susceptibility map but not in the edges of the magnitude image are considered to be sparse. In this approach an L1 norm minimization is used to express this sparsity property. Numerical simulations and phantom experiments are performed to demonstrate the superiority of this L1 minimization approach over the previous L2 minimization method. Preliminary brain imaging results in healthy subjects and in patients with intracerebral hemorrhages illustrate that QSM is feasible in practice.

Magnetic susceptibility varies among brain structures and provides insights into the chemical and molecular composition of brain tissues. However, the determination of an arbitrary susceptibility distribution from the measured MR signal phase is a challenging, ill-conditioned inverse problem. Although a previous method named calculation of susceptibility through multiple orientation sampling (COSMOS) has solved this inverse problem both theoretically and experimentally using multiple angle acquisitions, it is often impractical to carry out on human subjects. Recently, the feasibility of calculating the brain susceptibility distribution from a singleangle acquisition was demonstrated using morphology enabled dipole inversion (MEDI). In this study, we further improved the original MEDI method by sparsifying the edges in the quantitative susceptibility map that do not have a corresponding edge in the magnitude image. Quantitative susceptibility maps generated by the improved MEDI were compared qualitatively and quantitatively with those generated by calculation of susceptibility through multiple orientation sampling. The results show a high degree of agreement between MEDI and calculation of susceptibility through multiple orientation sampling, and the practicality of MEDI allows many potential clinical applications. Magn Reson Med 66:777-783,

Using the entire CLEO-c c ð3770Þ ! D " D event sample, corresponding to an integrated luminosity of 818 pb À1 and approximately 5:4 Â 10 6 D " D events, we present a study of the decays D 0 ! À e þ e , D 0 ! K À e þ e , D þ ! 0 e þ e , and D þ ! " K 0 e þ e . Via a tagged analysis technique, in which one D is fully reconstructed in a hadronic mode, partial rates for semileptonic decays by the other D are measured in several q 2 bins. We fit these rates using several form factor parametrizations and report the results, including form factor shape parameters and the branching fractions BðD 0 ! À e þ e Þ ¼ ð0:288 AE 0:008 AE 0:003Þ%, BðD 0 ! K À e þ e Þ ¼ ð3:50 AE 0:03 AE 0:04Þ%, BðD þ ! 0 e þ e Þ ¼ ð0:405 AE 0:016 AE 0:009Þ%, and BðD þ ! "K 0 e þ e Þ ¼ ð8:83 AE 0:10 AE 0:20Þ%, where the first uncertainties are statistical and the second are systematic. Taking input from lattice quantum chromodynamics, we also find jV cd j ¼ 0:234 AE 0:007 AE 0:002 AE 0:025 and jV cs j ¼ 0:985 AE 0:009 AE 0:006 AE 0:103, where the third uncertainties are from lattice quantum chromodynamics.

Reactions in solvothermal conditions between hexanuclear rare earth complexes and H2bdc, where H2bdc symbolizes terephthalic acid, lead to a family of monodimensional coordination polymers in which hexanuclear complexes act as metallic nodes. The hexanuclear cores can be either homometallic with general chemical formula [Ln6O(OH)8(NO3)6](2+) (Ln = Pr-Lu plus Y) or heterometallic with general chemical formula [Ln(6x)Ln'(6-6x)O(OH)8(NO3)6](2+) (Ln and Ln' = Pr-Lu plus Y). Whatever the hexanuclear entity is, the resulting coordination polymer is iso-structural to [Y6O(OH)8(NO3)2(bdc)(Hbdc)2·2NO3·H2bdc]∞, a coordination polymer that we have previously reported. The random distribution of the lanthanide ions over the six metallic sites of the hexanuclear entities is demonstrated by (89)Y solid state NMR, X-ray diffraction (XRD), and luminescent measurements. The luminescent and colorimetric properties of selected compounds that belong to this family have been studied. These studies demonstrate that some of these compounds exhibit very promising optical properties and that there are two ways of modulating the luminescent properties: (i) playing with the composition of the heterohexanuclear entities or (ii) playing with the relative ratio between two different hexanuclear entities. This enables the independent tuning of luminescence intensity and color.

We measure the branching ratio of the purely leptonic decay of the D + meson with unprecedented precision as B(D + → µ + ν) = (3.82 ± 0.32 ± 0.09) × 10 −4 , using 818 pb −1 of data taken on the ψ(3770) resonance with the CLEO-c detector at the CESR collider. We use this determination to derive a value for the pseudoscalar decay constant f D + , combining with measurements of the D + lifetime and assuming |V cd | = |V us |. We find f D + = (205.8 ± 8.5 ± 2.5) MeV. The decay rate asymmetry.08 ± 0.08, consistent with no CP violation. We also set 90% confidence level upper limits on B(D + → τ + ν) < 1.2 × 10 −3 and B(D + → e + ν) < 8.8 × 10 −6 .

In this paper, we address whether a (probabilistic) function of a finite homogeneous Markov chain still enjoys a Markov-type property. We propose a complete answer to this question using a linear algebra approach. At the core of our approach is the concept of invariance of a set under a matrix. In that sense, the framework of this paper is related to the so-called "geometric approach" in control theory for linear dynamical systems. This allows us to derive a collection of new results under generic assumptions on the original Markov chain. In particular, we obtain a new criterion for a function of a Markov chain to be a homogeneous Markov chain. We provide a deterministic polynomial-time algorithm for checking this criterion. Moreover, a non-standard notion of observability for a linear system will be used. This allows one to show that the set of all stochastic matrices for which our criterion holds, is nowhere dense in the set of stochastic matrices.

We perform a Dalitz plot analysis of D + → K − π + π + decay with the CLEO-c data set of 572 pb −1 of e + e − collisions accumulated at the ψ(3770). This corresponds to 1.6 × 10 6 D + D − pairs from which we select 140793 candidate events with a small background of 1.1%. We compare our results with previous measurements using the isobar model. We modify the isobar model with an improved description of some of the contributing resonances, and get better agreement with our data. We also consider a quasi-model-independent approach and measure the magnitude and phase of the contributing Kπ S wave in the range of invariant masses from the threshold to the maximum in this decay. This gives an improved descriptions of our data over the isobar model. Finally we allow for an isospin-two π + π + S wave contribution, and find that adding this to both the isobar model and the quasi-model-independent approach gives the best description of our data.