62 research outputs found
Paraquaternionic CR-submanifolds of paraquaternionic Kahler manifolds and semi-Riemannian submersions
In this paper we introduce paraquaternionic CR-submanifolds of almost
paraquaternionic hermitian manifolds and state some basic results on their
differential geometry. We also study a class of semi-Riemannian submersions
from paraquaternionic CR-submanifolds of paraquaternionic Kaehler manifolds.Comment: 19 page
Effects of nongaussian diffusion on "isotropic diffusion measurements'': an ex-vivo microimaging and simulation study
Designing novel diffusion-weighted pulse sequences to probe tissue
microstructure beyond the conventional Stejskal-Tanner family is currently of
broad interest. One such technique, multidimensional diffusion MRI, has been
recently proposed to afford model-free decomposition of diffusion signal
kurtosis into terms originating from either ensemble variance of isotropic
diffusivity or microscopic diffusion anisotropy. This ability rests on the
assumption that diffusion can be described as a sum of multiple Gaussian
compartments, but this is often not strictly fulfilled. The effects of
nongaussian diffusion on single shot isotropic diffusion sequences were first
considered in detail by de Swiet and Mitra in 1996. They showed theoretically
that anisotropic compartments lead to anisotropic time dependence of the
diffusion tensors, which causes the measured isotropic diffusivity to depend on
gradient frame orientation. Here we show how such deviations from the multiple
Gaussian compartments assumption conflates orientation dispersion with ensemble
variance in isotropic diffusivity. Second, we consider additional contributions
to the apparent variance in isotropic diffusivity arising due to
intracompartmental kurtosis. These will likewise depend on gradient frame
orientation. We illustrate the potential importance of these confounds with
analytical expressions, numerical simulations in simple model geometries, and
microimaging experiments in fixed spinal cord using isotropic diffusion
encoding waveforms with 7.5 ms duration and 3000 mT/m maximum amplitude.Comment: 26 pages, 9 figures. Appearing in J. Magn. Reso
Ruled CR-submanifolds of locally conformal K\"{a}hler manifolds
The purpose of this paper is to study the canonical totally real foliations
of CR-submanifolds in a locally conformal K\"{a}hler manifold.Comment: 10 pages, Journal of Geometry and Physics (to appear
Riemannian submersions from almost contact metric manifolds
In this paper we obtain the structure equation of a contact-complex
Riemannian submersion and give some applications of this equation in the study
of almost cosymplectic manifolds with Kaehler fibres.Comment: Abh. Math. Semin. Univ. Hamb., to appea
On paraquaternionic submersions between paraquaternionic K\"ahler manifolds
In this paper we deal with some properties of a class of semi-Riemannian
submersions between manifolds endowed with paraquaternionic structures, proving
a result of non-existence of paraquaternionic submersions between
paraquaternionic K\"ahler non locally hyper paraK\"ahler manifolds. Then we
examine, as an example, the canonical projection of the tangent bundle, endowed
with the Sasaki metric, of an almost paraquaternionic Hermitian manifold.Comment: 13 pages, no figure
Double oscillating diffusion encoding and sensitivity to microscopic anisotropy
PURPOSE: To introduce a novel diffusion pulse sequence, namely double oscillating diffusion encoding (DODE), and to investigate whether it adds sensitivity to microscopic diffusion anisotropy (µA) compared to the well-established double diffusion encoding (DDE) methodology. METHODS: We simulate measurements from DODE and DDE sequences for different types of microstructures exhibiting restricted diffusion. First, we compare the effect of varying pulse sequence parameters on the DODE and DDE signal. Then, we analyse the sensitivity of the two sequences to the microstructural parameters (pore diameter and length) which determine µA. Finally, we investigate specificity of measurements to particular substrate configurations. RESULTS: Simulations show that DODE sequences exhibit similar signal dependence on the relative angle between the two gradients as DDE sequences, however, the effect of varying the mixing time is less pronounced. The sensitivity analysis shows that in substrates with elongated pores and various orientations, DODE sequences increase the sensitivity to pore diameter, while DDE sequences are more sensitive to pore length. Moreover, DDE and DODE sequence parameters can be tailored to enhance/suppress the signal from a particular range of substrates. CONCLUSIONS: A combination of DODE and DDE sequences maximize sensitivity to µA, compared to using just the DDE method. Magn Reson Med, 2016. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine
Some constructions of almost para-hyperhermitian structures on manifolds and tangent bundles
In this paper we give some examples of almost para-hyperhermitian structures
on the tangent bundle of an almost product manifold, on the product manifold
, where is a manifold endowed with a mixed 3-structure
and on the circle bundle over a manifold with a mixed 3-structure.Comment: 10 pages; This paper has been presented in the "4th German-Romanian
Seminar on Geometry" Dortmund, Germany, 15-18 July 200
Accurate estimation of microscopic diffusion anisotropy and its time dependence in the mouse brain
Microscopic diffusion anisotropy (μA) has been recently gaining increasing attention for its ability to decouple the average compartment anisotropy from orientation dispersion. Advanced diffusion MRI sequences, such as double diffusion encoding (DDE) and double oscillating diffusion encoding (DODE) have been used for mapping μA, usually using measurements from a single b shell. However, the accuracy of μA estimation vis-à-vis different b-values was not assessed. Moreover, the time-dependence of this metric, which could offer additional insights into tissue microstructure, has not been studied so far. Here, we investigate both these concepts using theory, simulation, and experiments performed at 16.4T in the mouse brain, ex-vivo. In the first part, simulations and experimental results show that the conventional estimation of microscopic anisotropy from the difference of D(O)DE sequences with parallel and orthogonal gradient directions yields values that highly depend on the choice of b-value. To mitigate this undesirable bias, we propose a multi-shell approach that harnesses a polynomial fit of the signal difference up to third order terms in b-value. In simulations, this approach yields more accurate μA metrics, which are similar to the ground-truth values. The second part of this work uses the proposed multi-shell method to estimate the time/frequency dependence of μA. The data shows either an increase or no change in μA with frequency depending on the region of interest, both in white and gray matter. When comparing the experimental results with simulations, it emerges that simple geometric models such as infinite cylinders with either negligible or finite radii cannot replicate the measured trend, and more complex models, which, for example, incorporate structure along the fibre direction are required. Thus, measuring the time dependence of microscopic anisotropy can provide valuable information for characterizing tissue microstructure
Hidden symmetries and Killing tensors on curved spaces
Higher order symmetries corresponding to Killing tensors are investigated.
The intimate relation between Killing-Yano tensors and non-standard
supersymmetries is pointed out. In the Dirac theory on curved spaces,
Killing-Yano tensors generate Dirac type operators involved in interesting
algebraic structures as dynamical algebras or even infinite dimensional
algebras or superalgebras. The general results are applied to space-times which
appear in modern studies. One presents the infinite dimensional superalgebra of
Dirac type operators on the 4-dimensional Euclidean Taub-NUT space that can be
seen as a twisted loop algebra. The existence of the conformal Killing-Yano
tensors is investigated for some spaces with mixed Sasakian structures.Comment: 12 pages; talk presented at Group 27 Colloquium, Yerevan, Armenia,
August 200
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