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

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

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

Microstructure Imaging Sequence Simulation Toolbox

This work describes Microstructure Imaging Sequence Simulation Toolbox (MISST), a practical diffusion MRI simulator for development, testing, and optimisation of novel MR pulse sequences for microstructure imaging. Diffusion MRI measures molecular displacement at microscopic level and provides a non-invasive tool for probing tissue microstructure. The measured signal is determined by various cellular features such as size, shape, intracellular volume fraction, orientation, etc., as well as the acquisition parameters of the diffusion sequence. Numerical simulations are a key step in understanding the effect of various parameters on the measured signal, which is important when developing new techniques for characterizing tissue microstructure using diffusion MRI. Here we present MISST - a semi-analytical simulation software, which is based on a matrix method approach and computes diffusion signal for fully general, user specified pulse sequences and tissue models. Its key purpose is to provide a deep understanding of the restricted diffusion MRI signal for a wide range of realistic, fully flexible scanner acquisition protocols, in practical computational time

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

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 $M\times\mathbb{R}$, where $M$ 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

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

PGSE, OGSE, and sensitivity to axon diameter in diffusion MRI: Insight from a simulation study

Purpose To identify optimal pulsed gradient spin-echo (PGSE) and oscillating gradient spin-echo (OGSE) sequence settings for maximizing sensitivity to axon diameter in idealized and practical conditions. Methods Simulations on a simple two-compartment white matter model (with nonpermeable cylinders) are used to investigate a wide space of clinically plausible PGSE and OGSE sequence parameters with trapezoidal diffusion gradient waveforms. Signal sensitivity is measured as a derivative of the signal with respect to axon diameter. Models of parallel and dispersed fibers are investigated separately to represent idealized and practical conditions. Results Simulations show that, for the simple case of gradients perfectly perpendicular to straight parallel fibers, PGSE always gives maximum sensitivity. However, in real-world scenarios where fibers have unknown and dispersed orientation, low-frequency OGSE provides higher sensitivity. Maximum sensitivity results show that on current clinical scanners (Gmax = 60 mT/m, signal to noise ratio (SNR) = 20) axon diameters below 6 µm are indistinguishable from zero. Scanners with stronger gradient systems such as the Massachusetts General Hospital (MGH) Connectom scanner (Gmax = 300 mT/m) can extend this sensitivity limit down to 2–3 µm, probing a much greater proportion of the underlying axon diameter distribution. Conclusion Low-frequency OGSE provides additional sensitivity to PGSE in practical situations. OGSE is particularly advantageous for systems with high performance gradients

Hidden Symmetries for Ellipsoid-Solitonic Deformations of Kerr-Sen Black Holes and Quantum Anomalies

We prove the existence of hidden symmetries in the general relativity theory defined by exact solutions with generic off-diagonal metrics, nonholonomic (non-integrable) constraints, and deformations of the frame and linear connection structure. A special role in characterization of such spacetimes is played by the corresponding nonholonomic generalizations of Stackel-Killing and Killing-Yano tensors. There are constructed new classes of black hole solutions and studied hidden symmetries for ellipsoidal and/or solitonic deformations of "prime" Kerr-Sen black holes into "target" off-diagonal metrics. In general, the classical conserved quantities (integrable and not-integrable) do not transfer to the quantized systems and produce quantum gravitational anomalies. We prove that such anomalies can be eliminated via corresponding nonholonomic deformations of fundamental geometric objects (connections and corresponding Riemannian and Ricci tensors) and by frame transforms.Comment: latex2e, 11pt, 34 pages, the variant accepted by EPJC, with additional explanations, modifications and new references requested by refere