Measures of whole-brain activity, from techniques such as functional Magnetic Resonance Imaging, provide a means to observe the brain’s dynamical operations. However, interpretation of whole-brain dynamics has been stymied by the inherently high-dimensional structure of brain activity. The present research addresses this challenge through a series of scale transformations in the spectral, spatial, and relational domains. Instantaneous multispectral dynamics are first developed from input data via a wavelet filter bank. Voxel-level signals are then projected onto a representative set of spatially independent components. The correlation distance over the instantaneous wavelet-ICA state vectors is a graph that may be embedded onto a lower-dimensional space to assist the interpretation of state-space dynamics. Applying this procedure to a large sample of resting and task data (acquired through the Human Connectome Project), we segment the empirical state space into a continuum of stimulus-dependent brain states. We also demonstrate that resting brain activity includes brain states that are very similar to those adopted during some tasks, as well as brain states that are distinct from experimentally-defined tasks. Back-projection of segmented brain states onto the brain’s surface reveals the patterns of brain activity that support each experimental state.

Measures of whole-brain activity, from techniques such as functional Magnetic Resonance Imaging, provide a means to observe the brain's dynamical operations. However, interpretation of wholebrain dynamics has been stymied by the inherently high-dimensional structure of brain activity. The present research addresses this challenge through a series of scale transformations in the spectral, spatial, and relational domains. Instantaneous multispectral dynamics are first developed from input data via a wavelet filter bank. Voxel-level signals are then projected onto a representative set of spatially independent components. The correlation distance over the instantaneous wavelet-ICA state vectors is a graph that may be embedded onto a lower-dimensional space to assist the interpretation of state-space dynamics. Applying this procedure to a large sample of resting and task data (acquired through the Human Connectome Project), we segment the empirical state space into a continuum of stimulus-dependent brain states. We also demonstrate that resting brain activity includes brain states that are very similar to those adopted during some tasks, as well as brain states that are distinct from experimentally-defined tasks. Back-projection of segmented brain states onto the brain's surface reveals the patterns of brain activity that support each experimental state. Keywords fMRI | connectivity dynamics | functional connectivity | multiscale | dimensionality reduction Highlights• We demonstrate the construction and interrogation of a continuous, two-dimensional map of fMRI dynamics. • Map points represent an individual's multispectral, and multispectral BOLD state centered at a single point in time. • Task-based scans occupy focal state-spaces, reinforcing the utility of study methods to capture salient BOLD dynamics evoked by experimental stimuli. • Resting-state scans occupy a broad state-space, reinforcing the view that the resting mind is highly active.

While functional connectivity has typically been calculated over the entire length of the scan (5-10 min), interest has been growing in dynamic analysis methods that can detect changes in connectivity on the order of cognitive processes (seconds). Previous work with sliding window correlation has shown that changes in functional connectivity can be observed on these time scales in the awake human and in anesthetized animals. This exciting advance creates a need for improved approaches to characterize dynamic functional networks in the brain. Previous studies were performed using sliding window analysis on regions of interest defined based on anatomy or obtained from traditional steady-state analysis methods. The parcellation of the brain may therefore be suboptimal, and the characteristics of the time-varying connectivity between regions are dependent upon the length of the sliding window chosen. This manuscript describes an algorithm based on wavelet decomposition that allows data-driven clustering of voxels into functional regions based on temporal and spectral properties. Previous work has shown that different networks have characteristic frequency fingerprints, and the use of wavelets ensures that both the frequency and the timing of the BOLD fluctuations are considered during the clustering process. The method was applied to resting state data acquired from anesthetized rats, and the resulting clusters agreed well with known anatomical areas. Clusters were highly reproducible across subjects. Wavelet cross-correlation values between clusters from a single scan were significantly higher than the values from randomly-matched clusters that shared no temporal information, indicating that wavelet-based analysis is sensitive to the relationship between areas.

Traditional structural health monitoring techniques based on the vibration response of bridge structures are limited because of several factors — including a poorly formed aggregate system model, very low SNR, and unrealistic boundary conditions. Many times, these methods rely on global parameters to describe the dynamic behavior of local structural elements. In this paper, we proposed a novel efficient SHM technique that employs the use of compactly supported sub-band space/ frequency and time/frequency analysis using local vibration characteristics. To overcome the problem of the low-error sensitivity of features extracted from vibration signals, a near-field adaptive beamforming approach was used. This technique allows the sensor array to `scan' local portions of the structure, resulting in accurate spatial selectivity on the array and high signal-to-noise ratio for any given scan direction. Moreover, the sensor array was in direct contact with the vibrating structure, and thus the measured source is in the near-field of the array. Therefore, compensation of the sensor output was needed. Sub-band analysis and adaptive beamforming were integrated in a wavelet packet sub-band framework. We utilized the 3D energy map of the optimized sub-band signals for any given scan direction and for each sub-band center frequency as the damage detection feature. We validated our method using classical finite elements approximation to the dynamic behavior of the system. The comparison of a simulated undamaged simply supported beam with a damaged equivalent revealed that damage is localized in frequency and aligned with the direction of the simulated damage. The energy signature comparison after the beamforming stage validates these results, localizing the damage in areas of high probability around the direction of the damage. Automatic analysis of the energy comparison map was possible using a pseudo density estimation of the damage location, allowing for an automatic damage detection procedure. The focus of our research was aimed toward the adaptation of this damage detection method to real highway bridges.

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