The brain is a complex, multiscale dynamical system composed of many interacting regions. Knowledge of the spatiotemporal organization of these interactions is critical for establishing a solid understanding of the brain’s functional architecture and the relationship between neural dynamics and cognition in health and disease. The possibility of studying these dynamics through careful analysis of neuroimaging data has catalyzed substantial interest in methods that estimate time-resolved fluctuations in functional connectivity (often referred to as “dynamic” or time-varying functional connectivity; TVFC). At the same time, debates have emerged regarding the application of TVFC analyses to resting fMRI data, and about the statistical validity, physiological origins, and cognitive and behavioral relevance of resting TVFC. These and other unresolved issues complicate interpretation of resting TVFC findings and limit the insights that can be gained from this promising new research area. This article brings together scientists with a variety of perspectives on resting TVFC to review the current literature in light of these issues. We introduce core concepts, define key terms, summarize controversies and open questions, and present a forward-looking perspective on how resting TVFC analyses can be rigorously and productively applied to investigate a wide range of questions in cognitive and systems neuroscience.

Attention-deficit/hyperactivity disorder (ADHD) is among the most common psychiatric disorders of childhood, and there is great interest in understanding its neurobiological basis. A prominent neurodevelopmental hypothesis proposes that ADHD involves a lag in brain maturation. Previous work has found support for this hypothesis, but examinations have been limited to structural features of the brain (e.g., gray matter volume or cortical thickness). More recently, a growing body of work demonstrates that the brain is functionally organized into a number of large-scale networks, and the connections within and between these networks exhibit characteristic patterns of maturation. In this study, we investigated whether individuals with ADHD (age 7.2-21.8 y) exhibit a lag in maturation of the brain's developing functional architecture. Using connectomic methods applied to a large, multisite dataset of resting state scans, we quantified the effect of maturation and the effect of ADHD at more than 400,000 connections throughout the cortex. We found significant and specific maturational lag in connections within default mode network (DMN) and in DMN interconnections with two task positive networks (TPNs): frontoparietal network and ventral attention network. In particular, lag was observed within the midline core of the DMN, as well as in DMN connections with right lateralized prefrontal regions (in frontoparietal network) and anterior insula (in ventral attention network). Current models of the pathophysiology of attention dysfunction in ADHD emphasize altered DMN-TPN interactions. Our finding of maturational lag specifically in connections within and between these networks suggests a developmental etiology for the deficits proposed in these models.resting state | connectomics | default network A ttention-deficit/hyperactivity disorder (ADHD) is a serious neuropsychiatric disorder characterized by inattention, hyperactivity, and impulsivity. One influential neurodevelopmental model of the disorder posits a lag in the maturational trajectories of key features of the brain (1-4). This model has mostly been investigated by examining developmental pathways of structural features of the brain (3,(5)(6)(7)(8). In recent years, however, theorists have increasingly used resting state functional MRI (fMRI)-scanning participants in a task-free resting state-to explore the brain's functional architecture. This work has led to the recognition that the human brain is organized into several large-scale intrinsic connectivity networks (ICNs), each associated with specific neurocognitive functions (9, 10). ICNs have been shown to undergo significant maturation from childhood to early adulthood, with individual ICNs exhibiting spatially specific reliable patterns of integration (increased connectivity with age) and segregation (decreased connectivity with age) with other ICNs (11-17). These advances raise possibilities for investigating maturational lag in ADHD in the developing ICN architecture of the brain (18).Independent lines of res...

Consistent with existing theoretical models, these results provide evidence that default network-ventral attention network interconnections are a key locus of dysfunction in ADHD. Moreover, these findings contribute to growing evidence that distributed dysconnectivity within and between large-scale networks is present in ADHD.

Increased connectivity between DMN and executive control regions following mindfulness training could underlie increased capacity for volitional shifting of attention. The increased PCC-DLPFC rsFC following MBET was related to PTSD symptom improvement, pointing to a potential therapeutic mechanism of mindfulness-based therapies.

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A recent wave of studies—over 100 conducted over the last decade—shows that exerting effort at controlling impulses or behavioral tendencies leaves a person depleted and less able to engage in subsequent rounds of regulation. Regulatory depletion is thought to play an important role in everyday problems (e.g., excessive spending, overeating) as well as psychiatric conditions, but its neurophysiological basis is poorly understood. Using a placebo-controlled, double-blind design, we demonstrate that the psychostimulant methylphenidate (commonly known as ‘Ritalin’), a catecholamine reuptake blocker that increases dopamine and norepinephrine at the synaptic cleft, fully blocks effort-induced depletion of regulatory control. Spectral analysis of trial-by-trial reaction times found specificity of methylphenidate effects on regulatory depletion in the slow-4 frequency band. This band is associated with the operation of resting state brain networks that produce mind wandering, raising potential connections between our results and recent brain network-based models of control over attention.

Abstract.Phase-field models, the simplest of which is Allen-Cahn's problem, are characterized by a small parameter ε that dictates the interface thickness. These models naturally call for mesh adaptation techniques, which rely on a posteriori error control. However, their error analysis usually deals with the underlying non-monotone nonlinearity via a Gronwall argument which leads to an exponential dependence on ε −2 . Using an energy argument combined with a topological continuation argument and a spectral estimate, we establish an a posteriori error control result with only a low order polynomial dependence in ε −1 . Our result is applicable to any conforming discretization technique that allows for a posteriori residual estimation. Residual estimators for an adaptive finite element scheme are derived to illustrate the theory.Mathematics Subject Classification. 65M15, 65M50, 65M60.

Previous neuroimaging investigations in attention-deficit/hyperactivity disorder (ADHD) have separately identified distributed structural and functional deficits, but interconnections between these deficits have not been explored. To unite these modalities in a common model, we used joint independent component analysis, a multivariate, multimodal method that identifies cohesive components that span modalities. Based on recent network models of ADHD, we hypothesized that altered relationships between large-scale networks, in particular, default mode network (DMN) and task-positive networks (TPNs), would co-occur with structural abnormalities in cognitive regulation regions. For 756 human participants in the ADHD-200 sample, we produced gray and white matter volume maps with voxel-based morphometry, as well as whole-brain functional connectomes. Joint independent component analysis was performed, and the resulting transmodal components were tested for differential expression in ADHD versus healthy controls. Four components showed greater expression in ADHD. Consistent with our a priori hypothesis, we observed reduced DMN-TPN segregation co-occurring with structural abnormalities in dorsolateral prefrontal cortex and anterior cingulate cortex, two important cognitive control regions. We also observed altered intranetwork connectivity in DMN, dorsal attention network, and visual network, with co-occurring distributed structural deficits. There was strong evidence of spatial correspondence across modalities: For all four components, the impact of the respective component on gray matter at a region strongly predicted the impact on functional connectivity at that region. Overall, our results demonstrate that ADHD involves multiple, cohesive modality spanning deficits, each one of which exhibits strong spatial overlap in the pattern of structural and functional alterations.