Revised NODDI model for diffusion MRI data with multiple b-tensor encodings

This work proposes a revision of the NODDI model to relate brain tissue microstructure to the new generation of diffusion MRI data with multiple b-tensor encodings. NODDI was developed originally for conventional multi-shell diffusion data acquired with linear tensor encoding (LTE). While adequate for LTE data, it has been shown to be incompatible with data using spherical tensor encoding (STE). We embed a different set of assumptions in NODDI, while retaining the tortuosity constraint, to accommodate both LTE and STE data. Experiments with human data with multiple b-tensor encodings confirm the efficacy of the revision

Stay on the Beat With Tensor-Valued Encoding: Time-Dependent Diffusion and Cell Size Estimation in ex vivo Heart

Diffusion encoding with free gradient waveforms can provide increased microstructural specificity in heterogeneous tissues compared to conventional encoding approaches. This is achieved by considering specific aspects of encoding, such as b-tensor shape, sensitivity to bulk motion and to time-dependent diffusion (TDD). In tensor-valued encoding, different b-tensor shapes are used, such as in linear tensor encoding (LTE) or spherical tensor encoding (STE). STE can be employed for estimation of mean diffusivity (MD) or in combination with LTE to probe average microscopic anisotropy unconfounded by orientation dispersion. While tensor-valued encoding has been successfully applied in the brain and other organs, its potential and limitations have not yet been fully explored in cardiac applications. To avoid artefacts due to motion, which are particularly challenging in cardiac imaging, arbitrary b-tensors can be designed with motion compensation, i.e. gradient moment nulling, while also nulling the adverse effects of concomitant gradients. Encoding waveforms with varying degrees of motion compensation may however have significantly different sensitivities to TDD. This effect can be prominent in tissues with relatively large cell sizes such as in the heart and can be used advantageously to provide further tissue information. To account for TDD in tensor-valued encoding, the interplay between asynchronous gradients simultaneously applied along different directions needs to be considered. As the first step toward in vivo cardiac applications, our overarching goal was to explore the feasibility of acceleration compensated tensor-valued encoding on preclinical and clinical scanners ex vivo. We have demonstrated strong and predictable variation of MD due to TDD in mouse and pig hearts using a wide range of LTE and STE with progressively increasing degrees of motion compensation. Our preliminary data from acceleration compensated STE and LTE at high b-values, attainable on the preclinical scanner, indicate that TDD needs to be considered in experiments with varying b-tensor shapes. We have presented a novel theoretical framework, which enables cell size estimation, helps to elucidate limitations and provides a basis for further optimizations of experiments probing both mean diffusivity and microscopic anisotropy in the heart

Charge separation relative to the reaction plane in Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm NN}}= 2.76 TeV

Measurements of charge dependent azimuthal correlations with the ALICE detector at the LHC are reported for Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV. Two- and three-particle charge-dependent azimuthal correlations in the pseudo-rapidity range $|\eta| < 0.8$ are presented as a function of the collision centrality, particle separation in pseudo-rapidity, and transverse momentum. A clear signal compatible with a charge-dependent separation relative to the reaction plane is observed, which shows little or no collision energy dependence when compared to measurements at RHIC energies. This provides a new insight for understanding the nature of the charge dependent azimuthal correlations observed at RHIC and LHC energies.Comment: 12 pages, 3 captioned figures, authors from page 2 to 6, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/286

Transverse sphericity of primary charged particles in minimum bias proton-proton collisions at s=0.9\sqrt{s}=0.9, 2.76 and 7 TeV

Measurements of the sphericity of primary charged particles in minimum bias proton--proton collisions at $\sqrt{s}=0.9$, 2.76 and 7 TeV with the ALICE detector at the LHC are presented. The observable is linearized to be collinear safe and is measured in the plane perpendicular to the beam direction using primary charged tracks with $p_{\rm T}\geq0.5$ GeV/c in $|\eta|\leq0.8$. The mean sphericity as a function of the charged particle multiplicity at mid-rapidity ($N_{\rm ch}$) is reported for events with different $p_{\rm T}$ scales ("soft" and "hard") defined by the transverse momentum of the leading particle. In addition, the mean charged particle transverse momentum versus multiplicity is presented for the different event classes, and the sphericity distributions in bins of multiplicity are presented. The data are compared with calculations of standard Monte Carlo event generators. The transverse sphericity is found to grow with multiplicity at all collision energies, with a steeper rise at low $N_{\rm ch}$, whereas the event generators show the opposite tendency. The combined study of the sphericity and the mean $p_{\rm T}$ with multiplicity indicates that most of the tested event generators produce events with higher multiplicity by generating more back-to-back jets resulting in decreased sphericity (and isotropy). The PYTHIA6 generator with tune PERUGIA-2011 exhibits a noticeable improvement in describing the data, compared to the other tested generators.Comment: 21 pages, 9 captioned figures, 3 tables, authors from page 16, published version, figures from http://aliceinfo.cern.ch/ArtSubmission/node/308

A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE

In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio