Techniques available in graph theory can be applied to signals recorded from human brain. In network analysis of EEG signals, the individual nodes are EEG sensor locations and the edges correspond to functional relations between them that are extracted from EEG time series. In this paper, we study EEG-based directed functional networks in Alzheimer's disease (AD). To this end, directed connectivity matrices of 25 AD patients and 26 healthy subjects are processed and a number of meaningful graph theory metrics are studied. Our data show that functional networks of AD brains have significantly reduced global connectivity in alpha and beta bands (P < 0.05). The AD brains have significantly higher local connectivity than healthy controls in alpha and beta bands. This decreased profile in global connectivity can be linked to compensatory increased local connectivity as a result of wide-spread decline in the long-range connections. We also study resiliency of brain networks against targeted attack to hub nodes and find that AD networks are less resilient than healthy brains in alpha and beta bands.

The effort involved in creating accurate ground truth segmentation maps hinders advances in machine learning approaches to tumor delineation in clinical positron emission tomography (PET) scans. To address this challenge, we propose a fully convolutional network (FCN) model to delineate tumor volumes from PET scans automatically while relying on weak annotations in the form of bounding boxes (without delineations) around tumor lesions. To achieve this, we propose a novel loss function that dynamically combines a supervised component, designed to leverage the training bounding boxes, with an unsupervised component, inspired by the Mumford-Shah piecewise constant level-set image segmentation model. The model is trained end-to-end with the proposed differentiable loss function and is validated on a public clinical PET dataset of head and neck tumors. Using only bounding box annotations as supervision, the model achieves competitive results with state-of-the-art supervised and semiautomatic segmentation approaches. Our proposed approach improves the Dice similarity by approximately 30% and reduces the unsigned distance error by approximately 7 mm compared to a model trained with only bounding boxes (weak supervision). Also, after the post-processing step (morphological operations), our weak supervision approach differs only 7% in terms of the Dice similarity from the quality of the fully supervised model, for segmentation task.

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