Dataset Information

Variational principle for scale-free network motifs.

ABSTRACT: For scale-free networks with degrees following a power law with an exponent τ ∈ (2, 3), the structures of motifs (small subgraphs) are not yet well understood. We introduce a method designed to identify the dominant structure of any given motif as the solution of an optimization problem. The unique optimizer describes the degrees of the vertices that together span the most likely motif, resulting in explicit asymptotic formulas for the motif count and its fluctuations. We then classify all motifs into two categories: motifs with small and large fluctuations.

SUBMITTER: Stegehuis C

PROVIDER: S-EPMC6494877 | biostudies-other | 2019 May

REPOSITORIES: biostudies-other

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Variational principle for scale-free network motifs.

Stegehuis Clara C Hofstad Remco van der RV van Leeuwaarden Johan S H JSH

Scientific reports 20190501 1

For scale-free networks with degrees following a power law with an exponent τ ∈ (2, 3), the structures of motifs (small subgraphs) are not yet well understood. We introduce a method designed to identify the dominant structure of any given motif as the solution of an optimization problem. The unique optimizer describes the degrees of the vertices that together span the most likely motif, resulting in explicit asymptotic formulas for the motif count and its fluctuations. We then classify all motif ...[more]

PMID: 31043621

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Project description:PurposeFree-breathing Magnetization Transfer Contrast Bright blOOd phase SensiTive (MTC-BOOST) is a prototype balanced-Steady-State Free Precession sequence for 3D whole-heart imaging, that employs the endogenous magnetisation transfer contrast mechanism. This achieves reduction of flow and off-resonance artefacts, that often arise with the clinical T2prepared balanced-Steady-State Free Precession sequence, enabling high quality, contrast-agent free imaging of the thoracic cardiovascular anatomy. Fully-sampled MTC-BOOST acquisition requires long scan times (~10-24 min) and therefore acceleration is needed to permit its clinical incorporation. The aim of this study is to enable and clinically validate the 5-fold accelerated MTC-BOOST acquisition with joint Multi-Scale Variational Neural Network (jMS-VNN) reconstruction.MethodsThirty-six patients underwent free-breathing, 3D whole-heart imaging with the MTC-BOOST sequence, which is combined with variable density spiral-like Cartesian sampling and 2D image navigators for translational motion estimation. This sequence acquires two differently weighted bright-blood volumes in an interleaved fashion, which are then joined in a phase sensitive inversion recovery reconstruction to obtain a complementary fully co-registered black-blood volume. Data from eighteen patients were used for training, whereas data from the remaining eighteen patients were used for testing/evaluation. The proposed deep-learning based approach adopts a supervised multi-scale variational neural network for joint reconstruction of the two differently weighted bright-blood volumes acquired with the 5-fold accelerated MTC-BOOST. The two contrast images are stacked as different channels in the network to exploit the shared information. The proposed approach is compared to the fully-sampled MTC-BOOST and 5-fold undersampled MTC-BOOST acquisition with Compressed Sensing (CS) reconstruction in terms of scan/reconstruction time and bright-blood image quality. Comparison against conventional 2-fold undersampled T2-prepared 3D bright-blood whole-heart clinical sequence (T2prep-3DWH) is also included.ResultsAcquisition time was 3.0 ± 1.0 min for the 5-fold accelerated MTC-BOOST versus 9.0 ± 1.1 min for the fully-sampled MTC-BOOST and 11.1 ± 2.6 min for the T2prep-3DWH (p < 0.001 and p < 0.001, respectively). Reconstruction time was significantly lower with the jMS-VNN method compared to CS (10 ± 0.5 min vs 20 ± 2 s, p < 0.001). Image quality was higher for the proposed 5-fold undersampled jMS-VNN versus conventional CS, comparable or higher to the corresponding T2prep-3DWH dataset and similar to the fully-sampled MTC-BOOST.ConclusionThe proposed 5-fold accelerated jMS-VNN MTC-BOOST framework provides efficient 3D whole-heart bright-blood imaging in fast acquisition and reconstruction time with concomitant reduction of flow and off-resonance artefacts, that are frequently encountered with the clinical sequence. Image quality of the cardiac anatomy and thoracic vasculature is comparable or superior to the clinical scan and 5-fold CS reconstruction in faster reconstruction time, promising potential clinical adoption.

Dataset Information

Variational principle for scale-free network motifs.

Publications

Variational principle for scale-free network motifs.

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