This paper presents methods to analyze functional brain networks and signals
from graph spectral perspectives. The notion of frequency and filters
traditionally defined for signals supported on regular domains such as discrete
time and image grids has been recently generalized to irregular graph domains,
and defines brain graph frequencies associated with different levels of spatial
smoothness across the brain regions. Brain network frequency also enables the
decomposition of brain signals into pieces corresponding to smooth or rapid
variations. We relate graph frequency with principal component analysis when
the networks of interest denote functional connectivity. The methods are
utilized to analyze brain networks and signals as subjects master a simple
motor skill. We observe that brain signals corresponding to different graph
frequencies exhibit different levels of adaptability throughout learning.
Further, we notice a strong association between graph spectral properties of
brain networks and the level of exposure to tasks performed, and recognize the
most contributing and important frequency signatures at different task
familiarity.

本文提出一种用图谱谱分析功能性脑网络和信号的方法，其中强调了脑图频率与不同空间平滑程度的关系，并将其与主成分分析联系起来，最终应用于掌握简单运动技能的大脑信号分析中，证明脑图谱性质与任务熟悉度的关联性，并确定了在不同任务熟悉度下的最具贡献及重要标志频率。

脑信号的图频率分析

Graph Frequency Analysis of Brain Signals

Topological analysis of large scale protein-protein interaction networks
(PINs) is important for understanding the organisational and functional
principles of individual proteins. The number of interactions that a protein
has in a PIN has been observed to be correlated with its indispensability.
Essential proteins generally have more interactions than the non-essential
ones. We show here that the lethality associated with removal of a protein from
the yeast proteome correlates with different centrality measures of the nodes
in the PIN, such as the closeness of a protein to many other proteins, or the
number of pairs of proteins which need a specific protein as an intermediary in
their communications, or the participation of a protein in different protein
clusters in the PIN. These measures are significantly better than random
selection in identifying essential proteins in a PIN. Centrality measures based
on graph spectral properties of the network, in particular the subgraph
centrality, show the best performance in identifying essential proteins in the
yeast PIN. Subgraph centrality gives important structural information about the
role of individual proteins and permits the selection of possible targets for
rational drug discovery through the identification of essential proteins in the
PIN.

通过研究蛋白质相互作用网络（PIN）的拓扑结构，使用基于图谱性质的中心度量并观察蛋白质被删除后引起的致命性，从而发现子图中心度重要的结构信息并选择可能的药物靶点来关注。