We initiate the study of graph sketching, i.e., algorithms that use a limited number of linear measurements of a graph to determine the properties of the graph. While a graph on n nodes is essentially O(n 2 )-dimensional, we show the existence of a distribution over random projections into d-dimensional "sketch" space (d n 2 ) such that the relevant properties of the original graph can be inferred from the sketch with high probability. Specifically, we show that:including connectivity, k-connectivity, bipartiteness, and to return any constant approximation of the weight of the minimum spanning tree.2. d = O(n 1+γ ) suffices to compute graph sparsifiers, the exact MST, and approximate the maximum weighted matchings if we permit O(1/γ)-round adaptive sketches, i.e., a sequence of projections where each projection may be chosen dependent on the outcome of earlier sketches.Our results have two main applications, both of which have the potential to give rise to fruitful lines of further research. First, our results can be thought of as giving the first compressed-sensing style algorithms for graph data. Secondly, our work initiates the study of dynamic graph streams. There is already extensive literature on processing massive graphs in the data-stream model. However, the existing work focuses on graphs defined by a sequence of inserted edges and does not consider edge deletions. We think this is a curious omission given the existing work on both dynamic graphs in the non-streaming setting and dynamic geometric streaming. Our results include the first dynamic graph semi-streaming algorithms for connectivity, spanning trees, sparsification, and matching problems.

The GM/WM ratio correlates with the outcome of hypoxic ischaemic encephalopathy and may be useful as an objective early predictor of vegetative state or death in comatose patients after cardiac arrest.

Previous studies have shown an association between late-onset depression (LOD) and cognitive impairment in older adults. However, the neural correlates of this relationship are not yet clear. The aim of this study was to investigate the differences in both cortical thickness and subcortical volumes between drug-naive LOD patients and healthy controls and explore the relationship between LOD and cognitive impairments. A total of 48 elderly, drug-naive patients with LOD and 47 group-matched healthy control subjects underwent 3T MRI scanning, and the cortical thickness was compared between the groups in multiple locations, across the continuous cortical surface. The subcortical volumes were also compared on a structure-by-structure basis. Subjects with LOD exhibited significantly decreased cortical thickness in the rostral anterior cingulate cortex, the medial orbitofrontal cortex, dorsolateral prefrontal cortex, the superior and middle temporal cortex, and the posterior cingulate cortex when compared with healthy subjects (all p<0.05, false discovery rate corrected). Reduced volumes of the right hippocampus was also observed in LOD patients when compared with healthy controls (p<0.001). There were significant correlations between memory functions and cortical thickness of medial temporal, isthmus cingulate, and precuneus (p<0.001). This study was the first study to explore the relationships between the cortical thickness/subcortical volumes and cognitive impairments of drug-naive patients with LOD. These structural changes might explain the neurobiological mechanism of LOD as a risk factor of dementia.

Mild cognitive impairment (MCI) has been defined as a transitional state between normal aging and Alzheimer disease. Diffusion tensor imaging (DTI) can estimate the microstructural integrity of white matter tracts in MCI. We evaluated the microstructural changes in the white matter of MCI patients with DTI. We recruited 11 patients with MCI who met the working criteria of MCI and 11 elderly normal controls. The mean diffusivity (MD) and fractional anisotropy (FA) were measured in 26 regions of the brain with the regions of interest (ROIs) method. In the MCI patients, FA values were significantly decreased in the hippocampus, the posterior limb of the internal capsule, the splenium of corpus callosum, and in the superior and inferior longitudinal fasciculus compared to the control group. MD values were significantly increased in the hippocampus, the anterior and posterior limbs of the internal capsules, the splenium of the corpus callosum, the right frontal lobe, and in the superior and the inferior longitudinal fasciculus. Microstructural changes of several corticocortical tracts associated with cognition were identified in patients with MCI. FA and MD values of DTI may be used as novel biomarkers for the evaluation of neurodegenerative disorders.