Acquiring a complex cognitive skill reflects the human brain's remarkable capacity for long‑term plasticity, yet a fine‑grained, temporally dense map of the neural dynamics that unfold from novice to expert remains largely uncharted, limited by sparse sampling and group‑averaged designs. Leveraging longitudinal precision functional imaging, we tracked behavioral and whole‑brain functional dynamics in three individuals over a nine‑month period of real‑world abacus‑based mental calculation learning. This Precision Abacus‑based Representation Learning (PEARL) dataset comprises approximately 4,000 minutes of multimodal MRI data per participant, acquired across more than fifty scanning visits. We delineate a behavioral trajectory marked by initial practice gains, a transient cost of strategy switching, and eventual rapid, stable skill consolidation. Concomitant neuroimaging revealed continuous, individualized reorganization of functional brainwave networks, with each brain progressively diverging from its baseline before converging toward an expert‑like state. This study provides the first integrated, precision map of large‑scale brain plasticity during extended ecological skill learning. As an open‑access resource, the PEARL dataset offers an unprecedented opportunity to uncover the dynamic principles of learning‑induced plasticity, enabling the neuroscience community to explore and model the precise interplay between brain reorganization and behavioral mastery.

Working memory (WM) is a core cognitive function that is both mechanistically tractable and clinically relevant, making it a prime target for noninvasive neuromodulation. However, transcranial magnetic stimulation (TMS) studies targeting the dorsolateral prefrontal cortex (DLPFC) have yielded variable WM outcomes, possibly because single-site protocols fail to engage the distributed network dynamics that support WM and because effects depend on momentary brain states. Here, we tested whether dual-site sequential TMS, excitatory intermittent theta-burst stimulation (iTBS) over left DLPFC combined with inhibitory continuous theta-burst stimulation (cTBS) over medial prefrontal cortex (mPFC), produces state-dependent modulation of WM performance compared with single-site DLPFC stimulation alone. Thirty-seven healthy adults completed a within-subjects protocol with intermixed 0-back and 2-back WM conditions. Self-reported fatigue before each task run served as a coarse indicator of the participant’s cognitive state. Bayesian linear mixed models revealed a clear state-dependent pattern: in the high-load 2-back condition, dual-site stimulation improved accuracy when participants reported low fatigue but impaired accuracy when they reported high fatigue. No reliable effects were found for the 0-back condition or for reaction time. These findings demonstrate that dual-site prefrontal TMS can bidirectionally modulate WM accuracy relative to single-site stimulation depending on the participant’s cognitive state, highlighting the importance of state-aware and network-sensitive stimulation approaches for cognitive enhancement.

We present a data-driven framework to characterize large-scale brain dynamical states directly from correlation matrices at the single-subject level. By treating correlation thresholding as a percolation-like probe of connectivity, the approach tracks multiple cluster- and network-level observables and identifies a characteristic percolation threshold, rc, at which these signatures converge. We use r_c as an operational and physically interpretable descriptor of large-scale brain dynamical state. Applied to resting-state fMRI data from a large cohort of healthy individuals (N = 996), the method yields stable, subject-specific estimates that covary systematically with established dynamical indicators such as temporal autocorrelations. Numerical simulations of a whole-brain model with a known critical regime further show that r_c tracks changes in collective dynamics under controlled variations of excitability. By replacing arbitrary threshold selection with a criterion intrinsic to correlation structure, the r-spectra provides a physically grounded approach for comparing brain dynamical states across individuals.

Against the backdrop of the dual carbon goals and the construction of the new power system, the strong intermittency of wind and photovoltaic (PV) power outputs, coupled with the dynamic coupling of electricity, heat, and cooling loads in park-level integrated energy systems (PIES), renders traditional independent forecasting methods inadequate for safe and economic system operation. To address the limitations of existing approaches, including static coupling modeling, insufficient physical correlation constraints, and physical distortion in probabilistic scenarios, this paper proposes a physics-data hybrid-driven joint forecasting method for wind-solar-load systems. This method integrates mutual information and time-varying Copula theory to quantify the nonlinear dynamic dependence of five-dimensional wind-solar-load sequences, designs a physics-informed wind-solar power reconstruction module with residual learning for error correction, and constructs a CNN-BiLSTM multi-task residual network and feature-enhanced post-calibration framework. Validated using 2023 hourly data from a real industrial park in China, ablation studies confirm the significant synergistic effect of the core modules, which substantially improves both the accuracy and robustness of the wind-solar-load joint forecasting. Then compared with five typical benchmarks, the proposed model achieves MAPEs of 14.0% and 17.6% for wind and PV forecasting, respectively, and as low as 0.9%, 9.0%, and 7.5% for electricity, heat, and cooling loads with R2 values of 0.9919, 0.9646, and 0.9763. The proposed framework thus provides critical technical support for the coordinated source-load scheduling of PIES.

Optimizing vaccine prioritization is often treated as the default policy response when vaccine supply is limited. Yet optimized prioritization carries administrative, ethical and communication costs, motivating an upstream question: whether differences among vaccine allocations can alter epidemic outcomes enough to make optimization epidemiologically necessary. We show that optimization is not always worth pursuing: in some regimes, vaccination markedly reduces epidemic burden, but many feasible allocation rules perform almost equally well, making the necessity of optimization low. We quantify this necessity as the range of epidemic outcomes generated by different allocations under fixed supply and show that it is governed by competition between vaccinating high-contact groups to slow transmission and vaccinating groups that benefit most directly: necessity is low when these protection routes are balanced and high when one dominates. Increasing transmission intensity changes this balance and drives a transition in the optimal allocation from transmission-focused prioritization toward direct protection. Different prevention objectives exhibit distinct transition thresholds, creating regimes in which optimizing one objective substantially compromises another, thereby revealing when the choice of prevention target matters most. This framework reframes vaccine prioritization as a prior decision problem, identifying when optimization is warranted, when simpler rules suffice, and when prevention goals conflict.

As a complex system, the brain always operates as a functional whole, with multiple brain networks collectively facilitating the interaction between the intrinsic system and the external environment. On one hand, in the resting state without specific tasks, the brain maintains organized intrinsic neural activity and synchronizes the functions of different regions within the networks. Previous neuroimaging studies have identified a set of brain regions that exhibit relatively high energy consumption in the resting state and consistently show non-task-dependent negative activation in response to various task stimuli. The neural activities in these brain regions are highly synchronized, forming a functional network known as the default network (DN). On the other hand, when the brain is engaged in high-load, goal-oriented external tasks, it exhibits cognitive characteristics such as high arousal levels, focused attention, and the generation of action plans. The latest neuroimaging research has revealed that in this task-action state, there is also a set of brain regions that show non-task-dependent positive activation in response to various task stimuli, forming a functional network termed the action network (AN). From the perspective of working mechanism, the DN and the AN are complementary and constitute the "yin" and "yang" poles of the brain's complex dynamical system. The discovery of the AN not only deepens and completes our understanding of the brain's working principles but also provides a new perspective for the study of brain disease mechanisms and the development of brain-inspired intelligence. This paper first reviews the naming process of the DN and explores the naming of the AN. It then summarizes the discovery process and neuroimaging evidence of the AN, analyzes its anatomical composition and functional characteristics, and proposes a three-dimensional hierarchical view of the AN's anatomical structure from a clinical perspective (cortex-basal ganglia/thalamus-cerebellum). It is suggested that future research should integrate considerations from the three dimensions of cortex, basal ganglia/thalamus, and cerebellum to provide a systematic framework for clinical and basic research in neuroscience. Thirdly, the paper elaborates on the theoretical insight into the functional opposition and unity of the AN and the DN, emphasizing the need for future in-depth studies on the network neuroscience laws of the AN's anatomy and function, its development and evolution across the entire life span, and the innovation of multi-level, interdisciplinary scientific paradigms to reveal the cross-scale neurophysiological mechanisms underlying its neuroimaging findings. Finally, the paper looks forward to the important scientific significance and application value of the brain's AN for brain science and brain-inspired research.

Human functional brain networks, originating from coherent fluctuations in brain activity, are organized along a hierarchical axis. However, how this stable hierarchical architecture emerges from time-varying co-fluctuations remains unknown. Existing dynamic analyses have primarily focused on high-amplitude co-fluctuations, largely overlooking the contribution of lower-amplitude activity. Here, we investigated the amplitude-dependent configurations of regional co-fluctuation. We found that these patterns were hierarchically aligned with the sensorimotor-association (SA) axis: sensorimotor networks are preferentially expressed during high-amplitude co-fluctuations, associative systems prevailed during intermediate amplitudes, and limbic system preferentially engaged in low-amplitude states. This amplitude-stratified hierarchy underwent developmental refinement from childhood to adulthood and adaptively reconfigured under naturalistic stimuli. Replicated across four independent datasets including 7 T fMRI, these findings uncover a fundamental principle whereby the brain's hierarchical architecture is actively preserved through a structured, amplitude-dependent cascade of functional co-fluctuations. Our framework bridges dynamic coordination and stable architecture, demonstrating how the brain balances external processing with internal cognition through amplitude-stratified interactions.

Non-invasive EEG-based speech decoding typically treats the neural-to-text mapping as a black box, offering limited interpretability and few explicit links to the brain’s language networks. Here we present a framework that reconstructs language-network dynamics in source space from scalp EEG by integrating neural perturbational inference with geometric constraints derived from cortical eigenmodes. A meta-learning diffusion decoder then translates these dynamics into text with few-shot adaptation. Evaluated on Chinese and English reading EEG, the framework achieves state-of-the-art decoding performance, reducing the character error rate by up to 11% relative to existing methods. The decoded semantic fields localize to temporal regions that match the ventral language pathway, and cross-modal experiments reveal shared semantic representations between reading and listening. Moreover, orthographic, omission, and semantic errors map onto distinct electrophysiological signatures—the N170, P200, and N400 components, respectively—and error-informed correction using these signatures further reduces the character error rate by 8.3%. By establishing an interpretable signal-to-language-network-to-text pathway, this work advances non-invasive brain–computer interfaces toward physiologically grounded, cross-modally generalizable, and diagnostically meaningful communication

Multiple lines of research have studied how complex brain dynamics emerge from underlying connectivity by using Ising models as simplified neural mass models. However, limitations on parameter estimation have prevented their use with individual, high-resolution human neuroimaging data. Furthermore, most studies focus only on connectivity, ignoring node heterogeneity, even though real brain regions have different structural and dynamical properties. Here we present an improved approach to fitting Ising models to 360-region functional MRI data: derivation of an initial guess model from group data, optimization of simulation temperature, and two stages of Boltzmann learning, first with group data, then with individual data. Our implementation uses GPU acceleration to mitigate the high computational cost of this approach. We then analyze how data binarization threshold affects goodness-of-fit, the role of the external field in model behavior, consistency among models fitted to different scans of the same individual, and correlations between model parameters and features from structural MRI, including measures of myelination and cortical folding. We find that binarizing fMRI data at higher thresholds decreases correlation between model and data functional connectivity but increases the heterogeneity of node external fields and their correlations with structural features. A choice of threshold that achieves both goodness-of-fit and intrinsic heterogeneity of regions results in a model that better reflects the reality of the brain as a network of intrinsically heterogeneous nodes. By enabling personalized, biophysically interpretable modeling of structure-function mapping across the whole brain, this approach can aid understanding of individual differences in brain network organization and bridge the gap between the network-focused methodology of connectomics and the region-focused paradigm typical of translational research.

Effective vaccine prioritization is critical for epidemic control, yet real outbreaks exhibit memory effects that inflate state space and make long-term prediction and optimization challenging. Many strategies are therefore tuned to short-term objectives and overlook indirect protection. We develop a general age-stratified non-Markovian epidemic model that captures memory dynamics and unifies diverse models through state aggregation. Here we map non-Markovian final states to an equivalent Markovian representation, enabling real-time direct prediction of long-term vaccination effects. Leveraging this mapping, we design a dynamic prioritization strategy that continually allocates doses to minimize the predicted long-term epidemic burden, explicitly balancing indirect transmission blocking with direct protection of important groups and outperforming static policies and short-term heuristics that target only immediate direct effects. We further identify the mechanism driving shifts in vaccine prioritization as the epidemic progresses and coverage accumulates, underscoring the importance of adaptive allocations. This study makes long-term prediction tractable in systems with memory and provides actionable guidance for optimal vaccine deployment. Vaccine prioritization must account for both direct protection and indirect transmission blocking. This study develops a non-Markovian epidemic framework that predicts final outbreak burden and dynamically allocates vaccines, showing when priority should shift between groups.

Explaining individual differences in cognitive abilities requires both identifying brain parameters that vary across individuals and understanding how brain networks are recruited for specific tasks. Typically, task performance relies on the integration and segregation of functional subnetworks, often captured by parameters like regional excitability and connectivity. Yet, the high dimensionality of these parameters hinders pinpointing their functional relevance. Here, we apply stiff-sloppy analysis to human brain data, revealing that certain subtle parameter combinations ("stiff dimensions") powerfully influence neural activity during task processing, whereas others ("sloppy dimensions") vary more extensively but exert minimal impact. Using a pairwise maximum entropy model of task fMRI, we show that even small deviations in stiff dimensions-derived through Fisher Information Matrix analysis-govern the dynamic interplay of segregation and integration between the default mode network (DMN) and a working memory network (WMN). Crucially, separating a 0-back task (vigilant attention) from a 2-back task (working memory updating) uncovers partially distinct stiff dimensions predicting performance in each condition, along with a global DMN-WMN segregation shared across both tasks. Altogether, stiff-sloppy analysis challenges the conventional focus on large parameter variability by highlighting these subtle yet functionally decisive parameter combinations.

Linking synaptic-level perturbations to distributed brain-network dynamics remains a central challenge for understanding and treating mental illness. Although recent whole-brain models can reproduce individual brain activity patterns, they largely function as descriptive simulators rather than mechanistic, intervention-capable systems. Here we present an intervention-capable digital twin of the human brain, integrating individual neuroanatomy and task-evoked dynamics within a neuronal-scale framework. Individualised digital twin brains recapitulate a participant-specific compact cortico-subcortical network phenotype that captures transdiagnostic psychopathology across population and clinical cohorts. In silico modulation of excitatory and inhibitory synaptic conductance produces bidirectional, heterogeneous network responses across individuals. Population-scale simulations stratify individuals and predict longitudinal symptom trajectories from DTB-derived response profiles. Independent pharmacological functional MRI data further validate the predicted baseline-dependent network responses in vivo. Together, these findings establish digital brain models as experimental platforms for mechanistic perturbation, behavioural prediction and stratification, providing a foundation for precision neuroscience and psychiatry.

Transcranial magnetic stimulation (TMS) has evolved from a focal brain stimulation method to a network-level neuromodulation tool. This review examines the emerging field of multi-site TMS—approaches that target two or more brain regions to influence inter-regional dynamics and large-scale networks underlying cognition and clinical disorders. Three major forms are described: sequential multi-site TMS, which stimulates different targets in succession and is applied in disorders such as depression and Alzheimer’s disease; dual-site TMS, exemplified by cortico-cortical paired associative stimulation (ccPAS), which employs precisely timed pulses to alter directional connectivity and synaptic plasticity; and multi-locus TMS, a hardware-based method enabling simultaneous, electronically guided stimulation of distributed cortical areas with millisecond precision. While each offers distinct advantages for probing and modulating brain networks, challenges remain, such as parameter variability, individual differences, and technical complexity. Adaptive, personalized protocols guided by neuroimaging are needed to address anatomical and functional variability. In parallel, unified computational models are being developed to optimize protocol design and improve reproducibility. Overall, multi-site TMS represents a promising frontier in neuroscience and neurotherapeutics, bridging local stimulation with global brain dynamics to enable more effective and individualized interventions.

Macroscale functional connectivity emerges from a complex interplay between structural wiring and non-tract-mediated mechanisms. However, the intrinsic entanglement of these contributions obscures their specific roles in brain organization. Here, we introduce a computational modeling framework to disentangle functional synchrony into two fundamentally distinct components: tract-explainable and tract-underexplained synchrony. Validated across two large-scale human cohorts ($n = 1214$) and an independent marmoset dataset ($n = 24$), this dissociation reveals an evolutionarily conserved architectural principle. We show that tract-explainable synchrony aligns closely with structural connectomes to facilitate global integration. Conversely, tract-underexplained synchrony drives local modularity and is anchored by multiscale cortical similarity, encompassing microstructural, receptor, and transcriptomic profiles. Crucially, these components gradually dissociate from sensorimotor to higher-order association cortices, with the importance of tract-underexplained synchrony progressively increasing. Furthermore, the tract-underexplained synchrony exhibits greater individual variability and demonstrates a stronger association with individual cognitive performance.Ultimately, tract-based and non-tract-mediated mechanisms serve distinct yet complementary roles, jointly shaping a functional organization that balances conserved macroscopic stability with higher-order cognitive flexibility.

A prominent hypothesis in neuroscience proposes that brains achieve optimal performance by operating near a critical point. However, this framework, which often assumes a universal critical point, fails to account for the extensive individual variability observed in neural dynamics and cognitive functions. These variabilities are not noise but rather an inherent manifestation of a fundamental systems-biology principle: the necessary trade-off between robustness and flexibility in human populations. Here, we propose that the Griffiths phase (GP), an extended critical regime synergically induced by two kinds of heterogeneities in brain network region and connectivity, offers a unified framework for brain criticality that better reconciles robustness and flexibility and accounts for individual variability. Using Human Connectome Project data and whole-brain modeling, we demonstrated that the synergic interplay between structural network modularity and regional heterogeneity in local excitability yields biologically viable GP featured with widely extended global excitability ranges, with an embedded optimal point that balances global/local information transmission. Crucially, an individua's position within the GP gives rise to unique global network dynamics, which in turn confer a distinctive cognitive profile via flexible configuration of functional connectivity for segregation, integration, and balance between them. These results establish GP as an evolved adaptive mechanism resolving the robustness-flexibility trade-off, fulfilling diverse cognitive demands through individualized criticality landscapes, providing a new framework of brain criticality.

The human brain dynamically organizes its activity through coordinated fluctuations, whose spatiotemporal interactions form the foundation of functional networks. While large-scale co-fluctuations are well-studied, the principles governing their amplitude-dependent transitions-particularly across high, intermediate, and low-amplitude regimes-remain unknown. We introduce a co-fluctuation score to quantify how instantaneous functional interactions reorganize with global amplitude dynamics. Using resting-state fMRI data, we identified amplitude-dependent co-fluctuation transitions between functional systems hierarchically aligned with the sensorimotor-association (SA) axis: sensorimotor networks dominated high-amplitude co-fluctuations, associative systems prevailed during intermediate amplitudes, and limbic system preferentially engaged in low-amplitude states. This hierarchy underwent developmental refinement from childhood to adulthood and adaptively reconfigured under external stimuli. Replicated across four independent samples including 7T fMRI, these findings establish the SA axis as infrastructure for amplitude-dependent transitions of co-fluctuation states. Our framework bridges transient coordination and stable functional architecture, demonstrating how brain networks balance external processing (high-amplitude states) with internal cognition/emotion (mid-to-low amplitude states) through amplitude-stratified interactions.

Human cognition depends on large scale communication constrained by white matter architecture. Although weak connections are abundant in mammalian connectomes, they have long been treated as noise and downweighted because of tractography uncertainty in the human brain, and their relevance to human cognition and large scale functional organization remains unresolved. Across multiple datasets and tractography pipelines, we show that, when tractography derived connectivity weights are interpreted through a nonlinear weighting framework, weak connections make measurable contributions to cognitive prediction, functional connectivity simulation, and structure-function coupling. These effects are selective: nonlinear weighting improves the prediction of general cognitive ability and memory more than that of crystallized intelligence or processing speed, consistent with the notion that weak connections preferentially expand the modal repertoire of brain networks to enhance both large scale integration and fine grained segregation, thereby supporting the functional balance essential for diverse cognitive abilities. Importantly, these effects are replicated in a reliability aware connectome generated by integrating two post tractography filtering methods, in which preserving weak links consistently outperforms conventional thresholding strategies. Finally, we show that weak connections contain functionally informative subsets organized along systems level and transcriptomic gradients. In particular, a specific class of weak connections, predominantly linking visual and motor systems with limbic regions and characterized by negative gene coexpression, exerts a disproportionately large influence on brain function.

Neural criticality has emerged as a unified framework that reconciles diverse multiscale neuronal dynamics such as the irregular firing of individual neurons, sparse synchrony in neuronal populations, and the emergence of scale-free avalanches. However, the functional role of neuronal criticality remains ambiguous. Here, we investigate the neural dynamics and representations in response to external signals in excitation-inhibition balanced networks. We reveal that, in contrast with the case for the traditional critical branching model, the critical state of the balanced network simultaneously achieves maximal response sensitivity, maximal response reliability, and the optimal representation of external signals due to the presence of reliable avalanches induced by external signals. We further demonstrate that heterogeneity in inhibitory connections is a mechanism underlying the reliable critical avalanches and optimal representation. Our study addresses a longstanding challenge concerning the functional significance of neuronal criticality, namely the intricate coexistence of reliability and sensitivity.

Accurate retrieval of the maintained information is crucial for working memory. This process primarily occurs during post-delay epochs, when subjects receive cues and generate responses. However, the computational and neural mechanisms that underlie these post-delay epochs to support robust memory remain poorly understood. To address this, we trained recurrent neural networks (RNNs) on a color delayed-response task, where certain colors (referred to as common colors) were more frequently presented for memorization. We found that the trained RNNs reduced memory errors for common colors by decoding a broader range of neural states into these colors through the post-delay epochs. This decoding process was driven by convergent neural dynamics and a non-dynamic, biased readout process during the post-delay epochs. Our findings highlight the importance of post-delay epochs in working memory and suggest that neural systems adapt to environmental statistics by using multiple mechanisms across task epochs.