Towards Google matrix of brain

Google matrix and Ulam networks of intermittency maps

We study the properties of the Google matrix of an Ulam network generated by intermittency maps. This network is created by the Ulam method which gives a matrix approximant for the Perron-Frobenius operator of dynamical map. The spectral properties of eigenvalues and eigenvectors of this matrix are analyzed. We show that the PageRank of the system is characterized by a power law decay with the exponent $β$ dependent on map parameters and the Google damping factor $α$. Under certain conditions the PageRank is completely delocalized so that the Google search in such a situation becomes inefficie…

Delocalization transition for the Google matrix

We study the localization properties of eigenvectors of the Google matrix, generated both from the World Wide Web and from the Albert-Barabasi model of networks. We establish the emergence of a delocalization phase for the PageRank vector when network parameters are changed. In the phase of localized PageRank, a delocalization takes place in the complex plane of eigenvalues of the matrix, leading to delocalized relaxation modes. We argue that the efficiency of information retrieval by Google-type search is strongly affected in the phase of delocalized PageRank.

Anderson transition for Google matrix eigenstates

We introduce a number of random matrix models describing the Google matrix G of directed networks. The properties of their spectra and eigenstates are analyzed by numerical matrix diagonalization. We show that for certain models it is possible to have an algebraic decay of PageRank vector with the exponent similar to real directed networks. At the same time the spectrum has no spectral gap and a broad distribution of eigenvalues in the complex plain. The eigenstates of G are characterized by the Anderson transition from localized to delocalized states and a mobility edge curve in the complex p…

Spontaneous back-pain alters randomness in functional connections in large scale brain networks: A random matrix perspective

We use randomness as a measure to assess the impact of evoked pain on brain networks. Randomness is defined here as the intrinsic correlations that exist between different brain regions when the brain is in a task-free state. We use fMRI data of three brain states in a set of back pain patients monitored over a period of 6 months. We find that randomness in the task-free state closely follows the predictions of Gaussian orthogonal ensemble of random matrices. However, the randomness decreases when the brain is engaged in attending to painful inputs in patients suffering with early stages of ba…

矩阵分解在fMRI数据上的性能评估

Performance evaluation of matrix factorization for fMRI data

本研究将多种矩阵分解方法应用于人类全脑fMRI数据，验证全脑信息表征的稀疏编码假设，发现高稀疏度稀疏MF及近似稀疏方法的特征分类视觉刺激更准确。

Modeling functional resting-state brain networks through neural message passing on the human connectome

Understanding the relationship between the structure and function of the human brain is one of the most important open questions in Neurosciences. In particular, Resting State Networks (RSN) and more specifically the Default Mode Network (DMN) of the brain, which are defined from the analysis of functional data lack a definitive justification consistent with the anatomical structure of the brain. In this work, we show that a possible connection may naturally rest on the idea that information flows in the brain through a neural message-passing dynamics between macroscopic structures, like those…