Dataset Information

The simplicity of planar networks.

ABSTRACT: Shortest paths are not always simple. In planar networks, they can be very different from those with the smallest number of turns--the simplest paths. The statistical comparison of the lengths of the shortest and simplest paths provides a non trivial and non local information about the spatial organization of these graphs. We define the simplicity index as the average ratio of these lengths and the simplicity profile characterizes the simplicity at different scales. We measure these metrics on artificial (roads, highways, railways) and natural networks (leaves, slime mould, insect wings) and show that there are fundamental differences in the organization of urban and biological systems, related to their function, navigation or distribution: straight lines are organized hierarchically in biological cases, and have random lengths and locations in urban systems. In the case of time evolving networks, the simplicity is able to reveal important structural changes during their evolution.

SUBMITTER: Viana MP

PROVIDER: S-EPMC3861802 | biostudies-other | 2013

REPOSITORIES: biostudies-other

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The simplicity of planar networks.

Viana Matheus P MP Strano Emanuele E Bordin Patricia P Barthelemy Marc M

Scientific reports 20131213

Shortest paths are not always simple. In planar networks, they can be very different from those with the smallest number of turns--the simplest paths. The statistical comparison of the lengths of the shortest and simplest paths provides a non trivial and non local information about the spatial organization of these graphs. We define the simplicity index as the average ratio of these lengths and the simplicity profile characterizes the simplicity at different scales. We measure these metrics on a ...[more]

PMID: 24336510

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Project description:PurposeTo develop a fast and accurate convolutional neural network based method for segmentation of thalamic nuclei.MethodsA cascaded multi-planar scheme with a modified residual U-Net architecture was used to segment thalamic nuclei on conventional and white-matter-nulled (WMn) magnetization prepared rapid gradient echo (MPRAGE) data. A single network was optimized to work with images from healthy controls and patients with multiple sclerosis (MS) and essential tremor (ET), acquired at both 3 T and 7 T field strengths. WMn-MPRAGE images were manually delineated by a trained neuroradiologist using the Morel histological atlas as a guide to generate reference ground truth labels. Dice similarity coefficient and volume similarity index (VSI) were used to evaluate performance. Clinical utility was demonstrated by applying this method to study the effect of MS on thalamic nuclei atrophy.ResultsSegmentation of each thalamus into twelve nuclei was achieved in under a minute. For 7 T WMn-MPRAGE, the proposed method outperforms current state-of-the-art on patients with ET with statistically significant improvements in Dice for five nuclei (increase in the range of 0.05-0.18) and VSI for four nuclei (increase in the range of 0.05-0.19), while performing comparably for healthy and MS subjects. Dice and VSI achieved using 7 T WMn-MPRAGE data are comparable to those using 3 T WMn-MPRAGE data. For conventional MPRAGE, the proposed method shows a statistically significant Dice improvement in the range of 0.14-0.63 over FreeSurfer for all nuclei and disease types. Effect of noise on network performance shows robustness to images with SNR as low as half the baseline SNR. Atrophy of four thalamic nuclei and whole thalamus was observed for MS patients compared to healthy control subjects, after controlling for the effect of parallel imaging, intracranial volume, gender, and age (p < 0.004).ConclusionThe proposed segmentation method is fast, accurate, performs well across disease types and field strengths, and shows great potential for improving our understanding of thalamic nuclei involvement in neurological diseases.

Dataset Information

The simplicity of planar networks.

Publications

The simplicity of planar networks.

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