Analysis of occurrence the modes.

<p>Boxplots of occurrence rates of each individual frequency mode in ICA networks. Networks with significantly higher (filled boxplots) or lower (dashed boxplots) occurrence of the given mode than majority (85%) of all networks are identified.</p

Analysis of co-occurrence rates of the modes.

<p>Cco-occurrence maps of frequency mode pairs. An entry (column <i>m</i>, row <i>n</i>)(1…50, 1…50) of a matrix at column <i>i</i> (1…4) and row <i>j</i> (1…4) of the figure shows cco-occurrence of frequency mode <i>i</i> in network <i>m</i>, given that frequency mode <i>j</i> is occurred at the same time-point in network <i>n</i>. Positive cc-occurrence (color coded as red) corresponds to <i>reinforcement effect</i> and negative cc-occurrence (color coded as blue) is corresponding to <i>suppression effect</i>.</p

Time-varying spectral power of resting-state fMRI networks reveal cross-frequency dependence in dynamic connectivity

<div><p>Brain oscillations and synchronicity among brain regions (brain connectivity) have been studied in resting-state (RS) and task-induced settings. RS-connectivity which captures brain functional integration during an unconstrained state is shown to vary with the frequency of oscillations. Indeed, high temporal resolution modalities have demonstrated both between and cross-frequency connectivity spanning across frequency bands such as theta and gamma. Despite high spatial resolution, functional magnetic resonance imaging (fMRI) suffers from low temporal resolution due to modulation with slow-varying hemodynamic response function (HRF) and also relatively low sampling rate. This limits the range of detectable frequency bands in fMRI and consequently there has been no evidence of cross-frequency dependence in fMRI data. In the present work we uncover recurring patterns of spectral power in network timecourses which provides new insight on the actual nature of frequency variation in fMRI network activations. Moreover, we introduce a new measure of dependence between pairs of rs-fMRI networks which reveals significant cross-frequency dependence between functional brain networks specifically default-mode, cerebellar and visual networks. This is the first strong evidence of cross-frequency dependence between functional networks in fMRI and our subject group analysis based on age and gender supports usefulness of this observation for future clinical applications.</p></div

Outline of our framework for capturing instantaneous spectra of ICA time-courses and its variation in time in the form of “frequency modes”.

<p>(A) First, fMRI time-series is pre-processed and feed into the ICA to be decomposed into 50 ICA networks and the associated time-courses (detail of these ICA networks is provided in supplementary material of (Allen, 2014 #510)). Complex morlet wavelet is used to map the time-courses to the time-frequency domain. Finally, canonical patterns of power spectra are estimated by k-means clustering which we refer to as “frequency modes”. (B) "Frequency modes" as the representatives of the variation in spectral powers of networks time-courses, Each mode is formed by similar instantaneous frequency content of time-courses which have been clustered together.</p

Analysis of age and gender effect on.

<p>(A) occurrence rate of individual frequency modes and (B) cco-occurrence rate of pair of modes. In (A) specific networks and in (B) pairs of networks are highlighted [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0171647#pone.0171647.ref013" target="_blank">13</a>] in which occurrence rate of given mode and cco-occurrence of pair of modes are significantly effected by age or gender</p

Planar projection of the discrete five-dimensional state space.

<p>Planar projection of the discrete five-dimensional state space.</p

The Structure of the Shih-chi 史記 and the Theory of Five Virtues

The Shih-chi is written from the viewpoint of the circular theory of history 循環史觀, which reflects the system of cognition that the creation and destruction repeat each other eternally, shared commonly by the people of antiquity. According to the Shih-chi, history began with the Yellow Emperor 黄帝 and then developed into a succession of dynasties, each of which enjoyed the protection of one of the five elements. The fall of a dynasty is due to either cataclysm or tyranny, a notion also common in the folk legends of the time. With the tyranny of the First Emperor of Ch'in 秦始皇, the greatest catastrophe befell and destroyed the civilization continued since the Yellow Emperor. Soon, however, from the chaos emerged Liu Pang 劉邦, who by slaying a serpent realized the cosmos and brought new life to China. What the author of the Shih-chi intended to write was a history of one full cycle, beginning with the Yellow Emperor and coining to Han Wu-ti 漢武帝, the ruler of his time. Both of them, thought he, enjoyed the protection of the element earth ; accordingly, he consciously tried to draw a parallel between the deeds of the two. The theory which tries to explain the succession of dynasties in terms of the five elements is being usually referred to as the wu-hsing hsiang-sheng 五行相勝説. The author of the Shih-chi, however, terms it as the wu-te chung-shih shuo 五徳終始説 or the theory of five virtues. The Shih-chi, it can be said, was written on the basis of this theory and the Taoist philosophy

Demographic Information.

<p>Demographic Information.</p

Age and gender-corrected effects of SZ on four general dynamism measures (rows) under four different decompositions of the wFNC data into sets of five correlation patterns (columns).

<p>Age and gender-corrected effects of SZ on four general dynamism measures (rows) under four different decompositions of the wFNC data into sets of five correlation patterns (columns).</p

Effect of Schizophrenia on Dynamic Roles of Individual tICA Correlation Patterns (Fig 4(A), Row 1).

<p>Red (or bars pointing upward) indicate positive correlation with SZ. Only effects significant at the 0.05 level following FDR-correction are displayed. (A) SZ effects on the number of times each discretized CP timecourse (y-axis), assumes values indicated on the x-axis; (B) SZ effects on binned counts (x-axis) of the number of timepoints each discretized CP timecourse spends <i>consecutively</i> the most negative level, -4; (C) SZ effect on the number of correlation patterns <i>simultaneously</i> contributing in their <i>anti-state</i> form, ie. on the number of timepoints at which a subject's meta-state contains the indicated number (x-axis) of negative values; (D) SZ effects, component-wise for CPs that exhibit strong positive AVSN correlations, on the number of transitions between levels indicated on x-axis and y-axis; All diagnosis effects and p-values are from the regression model specified in the Methods section.</p