Aug 2026· Brain Connectivity· pp.
21580014261479958
· 0 citations· 33 references
Medicine
TL;DR
A diagnostic framework designed to isolate the explanatory contribution of local interaction rules to connectome organization through simulations that identify which structural properties emerge directly from locality and which require additional mechanisms beyond local constraints is provided.
Abstract
INTRODUCTION
The human connectome exhibits nontrivial large-scale organization despite emerging from decentralized local biological interactions. Most existing generative models reproduce connectomic features through global optimization principles, predefined wiring targets, or developmental templates, leaving unresolved which properties arise from locality alone and which require additional nonlocal mechanisms.
Methods
We implemented a simulation framework showing that global coherence can emerge from local compatibility constraints. Networks were generated exclusively through bounded spatial interactions, probabilistic local edge formation, and suppression of incompatible configurations, without global objectives, target topologies, or long-range coordination. Simulated ensembles were analyzed using graph-theoretical metrics, scaling relationships, and rule-based structural classification relative to published reference values of human connectome descriptors.
Results
Simulations consistently generated mesoscopic organization characterized by high clustering, modular structure, motif enrichment, and strong short-range connectivity bias. Degree distributions were broad and right-skewed, while edge-length distributions showed pronounced spatial localization. In contrast, several higher-order integrative properties were not reproduced, including empirical connectivity scale, rich-club organization, and long-range hub-to-hub connectivity. Although global metrics displayed substantial quantitative divergence from reported empirical values, several structural regimes and scaling relationships were preserved across parameter ranges.
Discussion
Our results distinguish connectome properties structurally compatible with local compatibility constraints from those underdetermined under locality alone. We provide a diagnostic framework designed to isolate the explanatory contribution of local interaction rules to connectome organization through simulations that identify which structural properties emerge directly from locality and which require additional mechanisms beyond local constraints.
This work introduces an alternative criterion based on the persistent topological cycles in which each node participates---a measure of mesoscale integration that captures features beyond local connectivity---and demonstrates that persistent topology captures information about brain network control that scalar energy summaries miss.
Carter Sale, Marco Coraggio, Mengsen Zhang et al.· 0 citations
Disordered dynamical systems comprising many interacting units, from ecological communities to neural circuits, are ubiquitous, and understanding how connectivity shapes their collective behavior is a central theoretical challenge. One long-recognized feature of neural circuits is local connectivity balance, in which the excitatory and inhibitory weights converging onto each unit approximately cancel. Although local connectivity balance has been proposed to serve functions such as gating incoming signals, its effect on collective network dynamics remains unclear. Here we analytically study randomly connected recurrent networks with varying degrees of local connectivity balance. We show that this balance leaves the connectivity spectrum unchanged yet drastically reshapes the dynamics in a manner that depends critically on the single-unit nonlinearity. Local balance suppresses unbounded growth of the network state and stabilizes network dynamics when the activation function scales linearly or faster, whereas it drives the network into chaos when the activation function is sub-linear or saturating. Importantly, these effects vanish for odd activation functions, which are commonly assumed in previous work. We further find that, for saturating nonlinearities, the effective dimension of the dynamics varies nonmonotonically with the degree of balance. We show that all these phenomena arise from a unifying mechanism: the suppression of a self-generated feedback input by local connectivity balance. Our results identify local connectivity balance as a previously overlooked control parameter for collective dynamics in realistic disordered networks.
Shotaro Takasu, Richard Gast, Ann Kennedy· 0 citations
A variety of connected systems, ranging from the cytoskeleton to human organizations, dynamically rearrange themselves in order to move through physical or abstract space. However, our understanding of how systems-level behaviors arise from local restructuring actions remains limited, necessitating comparison of real-world data to models that predict network structure and dynamics. To understand these systems, we study an accessible example, the branching slime mold Physarum polycephalum, by imaging the organism as it travels and extracting key fundamental quantities from its continuously remodeling tubular network. By using these quantities as input parameters to a traveling network model, we find that with no further fitting, the model quantitatively matches key emergent properties from P. polycephalum dynamics including path length, relocation time, and search efficiency at different spatial resolutions. These findings demonstrate how a traveling network model can capture P. polycephalum behaviors, highlighting the potential to use traveling networks more broadly for understanding and predicting connected dynamic systems by linking local measurements to emergent, system-wide behaviors.
Arnold Chen, Shenghao Tan, Yash V. Mundewadi et al.· bioRxiv· 0 citations
Complex systems are difficult to study not only because they are nonlinear, multiscale, and nonstationary, but because their scientifically relevant organization is often distributed across components, relations, and interaction orders. Topology provides a mathematical language for describing that organization through connectedness, recurrence, branching, closure, cavities, and persistence across scale. This review synthesizes persistent homology, Mapper, simplicial complexes, hypergraphs, and relation-level operator methods through a unified workflow from empirical data to representation, topological construction, output, and scientific interpretation. Across nonlinear dynamics, finance, neuroscience, biology, ecology, materials, and engineered systems, topological and topology-inspired methods make state-space organization, collective constraints, and structural reorganization available as observables that can be integrated with statistics, dynamics, mechanistic models, and machine learning. The review distinguishes the claim that a representation makes structure visible from the stronger claim that it improves detection or prediction, and it summarizes comparative evidence where such benchmarks exist. Prospective early-warning evidence remains uneven, but several studies demonstrate useful structural diagnostics, data-efficient classification, anomaly detection, and reductions in false alarms. The central conclusion is that topology is most valuable when representation is treated as a scientific hypothesis and topological descriptions are connected to domain-matched inference and mechanism.
The human brain exhibits a complex and hierarchical organization that supports efficient information integration across local and global scales. Accurately characterizing such topological organization from neuroimaging data remains challenging. Conventional graph neural networks (GNNs) effectively capture local dependencies through neighborhood aggregation but often overlook higher-order topological structures that reflect the brain's small-world organization. Although Transformer architectures enable global dependency modeling, their high computational cost limits scalability for large connected brain networks. To address these challenges, we propose a Topology-Constrained Graph Transformer Network (TC-GTN) that explicitly integrates brain network topology into graph learning. TC-GTN combines two complementary modules: a cycle-constrained graph convolution, which captures localized edge aggregation and models modular brain organization, and an MST-guided Transformer, which constrains global attention along minimum spanning tree (MST) pathways to efficiently model long-range dependencies while reducing redundant communication. Moreover, we introduce cycle-based edge positional encodings (CEPE) that provide a topological coordinate system for distinguishing edges with similar local structures but different cycle-level contexts. We evaluate TC-GTN on both structural and functional brain networks, extracted from diffusion-weighted imaging (DWI) and functional MRI (fMRI) respectively, using large-scale datasets, including UK Biobank (38557 participants; 18100 females/20457 males; age 40-70 years) and ABCD (7684 participants; 3782 females/3902 males; age 9-10 years). Experiments on sex classification and brain-age estimation demonstrate that TC-GTN consistently outperforms state-of-the-art graph network approaches, achieving superior accuracy, interpretability, and generalizability. Clinical significance analysis further demonstrates that the model accurately characterizes neuroanatomical divergence across pathological states. Using the brain age gap (BAG) as a biomarker, systemic accelerated aging is identified in multiple sclerosis and dementia, alongside heterogeneous structural alterations in stroke and Parkinson's disease. Our code is available at https://github.com/bieqa/TC-GTN.
Jundan Ji, Mengjun Liu, Nanguang Chen et al.· Medical Image Anal.· 0 citations
We derive a one-dimensional reduction for nonlinear dynamics on simplicial complexes containing both pairwise and triangular (higher-order) interactions. The effective state is defined using a mixed weight determined by the pairwise and triangular degrees of each node. The resulting reduced equation retains two structural coefficients, associated separately with the pairwise and higher-order coupling channels. A fluctuation expansion identifies the closure assumptions underlying the reduction and shows how deviations of individual node states from the effective state contribute to the approximation error. We numerically validate the proposed framework on Gene-regulatory dynamics, the double-well system, and SIS spreading. The states of the reduced model are compared with full-network simulations through coupling-parameter sweeps, steady-state branch calculations, and progressive node-removal experiments on synthetic and real-world networks. The reduced model successfully reproduces the principal transitions and steady-state branches in all three dynamical systems considered. Agreement is strongest for relatively homogeneous networks and deteriorates when structural heterogeneity produces a broader distribution of node states. The closure diagnostics account for this loss of accuracy and indicate when a single effective state is no longer sufficient. The reduction therefore provides a tractable description of resilience in systems with coexisting pairwise and higher-order interactions.
Amit Tiwari, C. Hens, Prosenjit Kundu· 0 citations
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