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Joint estimation of source dynamics and interactions from MEG data. MEG数据源动态和相互作用的联合估计。
IF 3.6 3区 医学 Q2 NEUROSCIENCES Pub Date : 2025-07-17 eCollection Date: 2025-01-01 DOI: 10.1162/netn_a_00453
Narayan Puthanmadam Subramaniyam, Filip Tronarp, Simo Särkkä, Lauri Parkkonen

Current techniques to estimate directed functional connectivity from magnetoencephalography (MEG) signals involve two sequential steps: (a) estimation of the sources and their amplitude time series from the MEG data and (b) estimation of directed interactions between the source time series. However, such a sequential approach is not optimal as it leads to spurious connectivity due to spatial leakage. Here, we present an algorithm to jointly estimate the source and connectivity parameters using Bayesian filtering. We refer to this new algorithm as JEDI-MEG (Joint Estimation of source Dynamics and Interactions from MEG data). By formulating a state-space model for the locations and amplitudes of a given number of sources, we show that estimation of their connections can be reduced to a system identification problem. Using simulated MEG data, we show that the joint approach provides a more accurate reconstruction of connectivity parameters than the conventional two-step approach. Using real MEG responses to visually presented faces in 16 subjects, we also demonstrate that our method gives source and connectivity estimates that are both physiologically plausible and largely consistent across subjects. In conclusion, the proposed joint estimation approach outperforms the traditional two-step approach in determining functional connectivity in MEG data.

目前从脑磁图(MEG)信号中估计定向功能连通性的技术包括两个连续的步骤:(a)从MEG数据中估计源及其振幅时间序列,(b)估计源时间序列之间的定向相互作用。然而,这种顺序方法并不是最优的,因为它会由于空间泄漏而导致虚假连接。在这里,我们提出了一种使用贝叶斯滤波来联合估计源和连通性参数的算法。我们将这种新算法称为JEDI-MEG(联合估计源动态和相互作用)。通过为给定数量的源的位置和振幅制定状态空间模型,我们表明对它们的连接的估计可以简化为系统识别问题。通过模拟MEG数据,我们发现联合方法比传统的两步方法提供了更准确的连接参数重建。通过对16名受试者视觉呈现的面部的真实MEG反应,我们也证明了我们的方法给出的来源和连通性估计在生理上是合理的,并且在受试者之间基本一致。总之,所提出的联合估计方法在确定MEG数据的功能连通性方面优于传统的两步方法。
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引用次数: 0
Longitudinal changes in MEG-based brain network topology of ALS patients with cognitive/behavioral impairment-An exploratory study. 认知/行为障碍ALS患者基于meg的脑网络拓扑结构纵向变化的探索性研究
IF 3.6 3区 医学 Q2 NEUROSCIENCES Pub Date : 2025-07-17 eCollection Date: 2025-01-01 DOI: 10.1162/netn_a_00450
Rosanne Govaarts, Elliz P Scheijbeler, Emma Beeldman, Matteo Fraschini, Alessandra Griffa, Marjolein M A Engels, Anneke J van der Kooi, Yolande A L Pijnenburg, Marianne de Visser, Cornelis J Stam, Joost Raaphorst, Arjan Hillebrand

Amyotrophic lateral sclerosis (ALS) with only motor impairment (ALS-pure motor) and the behavioral variant of frontotemporal dementia (bvFTD) are hypothesized to represent extreme ends of a disease spectrum, which encompasses ALS with cognitive/behavioral impairment (ALSci/bi). In this longitudinal magnetoencephalography (MEG) study, we investigated changes in brain network topology of ALSci/bi over time as compared with ALS-pure motor and bvFTD patients. Resting-state MEG was recorded in ALS-pure motor (n = 9), ALSci/bi (n = 16), and bvFTD (n = 16) at baseline and 5-month follow-up, projected to source space. The corrected version of the amplitude envelope correlation was applied to compute frequency-band-specific functional connectivity between brain regions, from which the backbone of the functional networks was constructed using the minimum spanning tree (MST) approach. Reference MSTs were computed based on the functional connectivity matrices for ALS-pure motor and bvFTD, against which the networks of ALSci/bi were compared. We showed that, at baseline, networks in the theta band of ALSci/bi patients were more similar to ALS-pure motor than bvFTD. At follow-up, ALSci/bi patients' beta-band network similarity had moved away from ALS-pure motor and resembled bvFTD. In conclusion, our findings suggest that brain networks of ALSci/bi patients move along the ALS-bvFTD spectrum over time, from ALS-pure motor to bvFTD-like topology.

肌萎缩侧索硬化症(ALS)仅伴有运动障碍(ALS-纯运动障碍)和额颞叶痴呆(bvFTD)的行为变异被假设代表了一种疾病谱系的极端,其中包括ALS伴有认知/行为障碍(ALSci/bi)。在这项纵向脑磁图(MEG)研究中,我们研究了ALSci/bi患者的大脑网络拓扑结构随时间的变化,并与als -纯运动和bvFTD患者进行了比较。静息状态MEG分别记录als -纯运动(n = 9)、ALSci/bi (n = 16)和bvFTD (n = 16)在基线和5个月随访时的静息状态MEG,投影到源空间。修正后的幅度包络相关性应用于计算脑区之间特定频段的功能连通性,并利用最小生成树(MST)方法构建功能网络的主干。基于als纯运动和bvFTD的功能连接矩阵计算参考mst,并与ALSci/bi网络进行比较。我们发现,在基线时,ALSci/bi患者的θ波段网络更类似于als纯运动,而不是bvFTD。在随访中,ALSci/bi患者的β -频带网络相似性已经从als -纯运动转移到bvFTD。总之,我们的研究结果表明,随着时间的推移,ALSci/bi患者的大脑网络沿着ALS-bvFTD谱移动,从als纯运动到bvftd样拓扑。
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引用次数: 0
Directionality of neural activity in and out of the seizure onset zone in focal epilepsy. 局灶性癫痫发作区内外神经活动的方向性。
IF 3.6 3区 医学 Q2 NEUROSCIENCES Pub Date : 2025-06-30 eCollection Date: 2025-01-01 DOI: 10.1162/netn_a_00454
Hamid Karimi-Rouzbahani, Aileen McGonigal

Epilepsy affects over 50 million people worldwide, with approximately 30% experiencing drug-resistant forms that may require surgical intervention. Accurate localisation of the epileptogenic zone (EZ) is crucial for effective treatment, but how best to use intracranial EEG data to delineate the EZ remains unclear. Previous studies have used the directionality of neural activities across the brain to investigate seizure dynamics and localise the EZ. However, the different connectivity measures used across studies have often provided inconsistent insights about the direction and the localisation power of signal flow as a biomarker for EZ localisation. In a data-driven approach, this study employs a large set of 13 distinct directed connectivity measures to evaluate neural activity flow in and out the seizure onset zone (SOZ) during interictal and ictal periods. These measures test the hypotheses of "sink SOZ" (SOZ dominantly receiving neural activities during interictal periods) and "source SOZ" (SOZ dominantly transmitting activities during ictal periods). While the results were different across connectivity measures, several measures consistently supported higher connectivity directed towards the SOZ in interictal periods and higher connectivity directed away during ictal periods. Comparing six distinct metrics of node behaviour in the network, we found that SOZ separates itself from the rest of the network, allowing for the metric of "eccentricity" to localise the SOZ more accurately than any other metrics including "in strength" and "out strength." This introduced a novel biomarker for localising the SOZ, leveraging the discriminative power of directed connectivity measures in an explainable machine learning pipeline. By using a comprehensive, objective, and data-driven approach, this study addresses previously unresolved questions on the direction of neural activities in seizure organisation and sheds light on dynamics of interictal and ictal activity in focal epilepsy.

全世界有5000多万人患有癫痫,其中约30%患有可能需要手术干预的耐药形式。准确定位癫痫区(EZ)对于有效治疗至关重要,但如何最好地使用颅内脑电图数据来划定EZ仍不清楚。以前的研究已经利用整个大脑的神经活动的方向性来调查癫痫发作的动态和定位EZ。然而,研究中使用的不同连通性测量方法通常对信号流的方向和定位能力作为EZ定位的生物标志物提供了不一致的见解。在数据驱动的方法中,本研究采用了大量的13种不同的定向连接测量来评估癫痫发作区(SOZ)在间歇期和发作期的神经活动流。这些测量方法验证了“sink SOZ”(在间歇期主要接收神经活动)和“source SOZ”(在间歇期主要传递神经活动)的假设。虽然不同连接性测量的结果不同,但有几个测量一致支持在间隔期指向SOZ的更高连接性和在临界期指向SOZ的更高连接性。比较网络中节点行为的六个不同指标,我们发现SOZ将自己与网络的其余部分分开,允许“偏心”指标比任何其他指标(包括“强度”和“强度”)更准确地定位SOZ。这为定位SOZ引入了一种新的生物标志物,在可解释的机器学习管道中利用定向连接测量的判别能力。通过使用全面、客观和数据驱动的方法,本研究解决了以前未解决的癫痫发作组织中神经活动方向的问题,并阐明了局灶性癫痫发作间期和发作期活动的动态。
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引用次数: 0
Diffusion wavelets on connectome: Localizing the sources of diffusion mediating structure-function mapping using graph diffusion wavelets. 连接组上的扩散小波:用图扩散小波定位扩散中介结构-函数映射的源。
IF 3.6 3区 医学 Q2 NEUROSCIENCES Pub Date : 2025-06-27 eCollection Date: 2025-01-01 DOI: 10.1162/netn_a_00456
Chirag Jain, Sravanthi Upadrasta Naga Sita, Avinash Sharma, Raju Surampudi Bapi

The intricate link between brain functional connectivity (FC) and structural connectivity (SC) is explored through models performing diffusion on SC to derive FC, using varied methodologies from single to multiple graph diffusion kernels. However, existing studies have not correlated diffusion scales with specific brain regions of interest (RoIs), limiting the applicability of graph diffusion. We propose a novel approach using graph diffusion wavelets to learn the appropriate diffusion scale for each RoI to accurately estimate the SC-FC mapping. Using the open Human Connectome Project dataset, we achieve an average Pearson's correlation value of 0.833, surpassing the state-of-the-art methods for the prediction of FC. It is important to note that the proposed architecture is entirely linear, computationally efficient, and notably demonstrates the power-law distribution of diffusion scales. Our results show that the bilateral frontal pole, by virtue of it having large diffusion scale, forms a large community structure. The finding is in line with the current literature on the role of the frontal pole in resting-state networks. Overall, the results underscore the potential of graph diffusion wavelet framework for understanding how the brain structure leads to FC.

通过对大脑功能连接(FC)和结构连接(SC)进行扩散的模型来探索大脑功能连接(FC)和结构连接(SC)之间的复杂联系,使用从单个到多个图扩散核的各种方法来推导FC。然而,现有的研究并没有将扩散量表与特定的大脑兴趣区域(roi)联系起来,这限制了图扩散的适用性。我们提出了一种新的方法,使用图扩散小波来学习每个RoI的适当扩散尺度,以准确估计SC-FC映射。使用开放的人类连接组项目数据集,我们实现了平均Pearson相关值为0.833,超过了最先进的FC预测方法。值得注意的是,所提出的体系结构是完全线性的,计算效率高,并且显著地展示了扩散尺度的幂律分布。结果表明,双侧额极具有较大的扩散规模,形成了较大的群落结构。这一发现与目前关于额极在静息状态网络中的作用的文献一致。总的来说,结果强调了图扩散小波框架在理解大脑结构如何导致FC方面的潜力。
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引用次数: 0
Increased functional network segregation in glioma patients posttherapy: A neurological compensatory response or catastrophe for cognition? 神经胶质瘤患者治疗后功能网络分离增加:神经代偿反应或认知灾难?
IF 3.6 3区 医学 Q2 NEUROSCIENCES Pub Date : 2025-06-27 eCollection Date: 2025-01-01 DOI: 10.1162/netn_a_00449
Laurien De Roeck, Rob Colaes, Patrick Dupont, Stefan Sunaert, Steven De Vleeschouwer, Paul M Clement, Charlotte Sleurs, Maarten Lambrecht

The brain operates through networks of interconnected regions, which can be disrupted by glial tumors and their treatment. This study investigates associations between this altered functional network topology and cognition in gliomas. We studied 50 adult glioma survivors (>1-year posttherapy) and 50 healthy controls. Participants underwent cognitive assessments across six domains and an 8-min resting-state functional MRI. Based on the BOLD signal, partial correlations were computed among 78 brain regions. From their absolute values, whole-brain and nodal graph metrics were derived and normalized to random graphs. Group differences in whole-brain and nodal graph metrics were assessed with Mann-Whitney U tests and mixed-design analyses of variance, respectively. Metrics exhibiting significant intergroup differences were correlated with cognitive scores, with p bonf < 0.050 indicating significance. Among controls, 8 of 78 nodes were identified as hubs. Patients exhibited significantly higher whole-brain clustering, correlating with intelligence (r(98) = -0.409, p bonf < 0.001) and executive functioning (r(98) = 0.300, p bonf = 0.014). Lower centrality, higher nodal clustering, and assortativity were also observed in patients, particularly in hubs, correlating with language and executive functioning, respectively (all r(98) > 0.300, p bonf < 0.050). Glioma patients commonly experience cognitive deficits alongside posttreatment alterations in functional network topology. Alterations in clustering, assortativity, and centrality may specifically act as compensatory mechanisms, significantly influencing cognitive functioning.

大脑通过相互连接的区域网络运作,神经胶质肿瘤及其治疗可能会破坏这些区域。这项研究调查了神经胶质瘤中这种改变的功能网络拓扑与认知之间的关系。我们研究了50名成年胶质瘤幸存者(治疗后1年)和50名健康对照。参与者接受了六个领域的认知评估和8分钟静息状态功能MRI。基于BOLD信号,计算了78个脑区之间的部分相关性。根据它们的绝对值,导出全脑和节点图度量并归一化为随机图。采用Mann-Whitney U检验和混合设计方差分析分别评估全脑和节点图指标的组间差异。组间差异显著的指标与认知评分相关,p < 0.050为显著性差异。在对照组中,78个节点中有8个被确定为枢纽。患者表现出更高的全脑聚类,与智力(r(98) = -0.409, p bonf < 0.001)和执行功能(r(98) = 0.300, p bonf = 0.014)相关。在患者中也观察到较低的中心性,较高的节点聚类和分类性,特别是在中心,分别与语言和执行功能相关(所有r(98) bb0 0.300, p < 0.050)。神经胶质瘤患者通常会经历认知缺陷以及治疗后功能网络拓扑结构的改变。聚类性、分类性和中心性的改变可能作为补偿机制,显著影响认知功能。
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引用次数: 0
A graph neural network approach to investigate brain critical states over neurodevelopment. 研究神经发育过程中脑临界状态的图神经网络方法。
IF 3.6 3区 医学 Q2 NEUROSCIENCES Pub Date : 2025-06-27 eCollection Date: 2025-01-01 DOI: 10.1162/netn_a_00451
Rodrigo M Cabral-Carvalho, Walter H L Pinaya, João R Sato

Recent studies show that functional resting-state dynamics may be modeled by lattice models near criticality, such as the 2D Ising model. The Ising temperature, which is the control parameter dictating the phase transitions of the model, can provide insight into the large-scale dynamics and is being used to better understand different brain states and neurodevelopment. This period is categorized by intricate changes in the microcircuits to consolidate networks. These changes influence the macroscopic brain dynamics and also its functional relations, which can be observed in functional magnetic resonance imaging (fMRI). Therefore, this work investigates neurodevelopment through a novel method to estimate the Ising temperature of the brain from fMRI data using functional connectivity and graph neural networks trained on Ising model networks. The main finding indicates a statistically significant negative correlation between age and temperature for typically developing children (r = -0.48, p < 0.0001) and also children with attention-deficit/hyperactivity disorder (r = -0.49, p < 0.0001). This study suggests that the brain gets distant from criticality as age increases, leading to a more ordered state.

最近的研究表明,功能静态动力学可以用接近临界的晶格模型来建模,例如二维Ising模型。伊辛温度是决定模型相变的控制参数,它可以提供对大尺度动力学的洞察,并被用来更好地理解不同的大脑状态和神经发育。这一时期是通过微电路的复杂变化来巩固网络的。这些变化影响了宏观脑动力学及其功能关系,可以在功能磁共振成像(fMRI)中观察到。因此,这项工作通过一种新的方法来研究神经发育,该方法使用功能连接和在Ising模型网络上训练的图神经网络,从fMRI数据中估计大脑的Ising温度。主要发现表明,正常发育儿童的年龄和温度之间存在统计学上显著的负相关(r = -0.48, p < 0.0001),注意缺陷/多动障碍儿童的年龄和温度之间也存在统计学上显著的负相关(r = -0.49, p < 0.0001)。这项研究表明,随着年龄的增长,大脑离临界状态越来越远,从而导致更有序的状态。
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引用次数: 0
Interdependence patterns of multifrequency oscillations predict visuomotor behavior. 多频振荡的相互依赖模式预测视觉运动行为。
IF 3.6 3区 医学 Q2 NEUROSCIENCES Pub Date : 2025-05-08 eCollection Date: 2025-01-01 DOI: 10.1162/netn_a_00440
Jyotika Bahuguna, Antoine Schwey, Demian Battaglia, Nicole Malfait

We show that sensorimotor behavior can be reliably predicted from single-trial EEG oscillations fluctuating in a coordinated manner across brain regions, frequency bands, and movement time epochs. We define high-dimensional oscillatory portraits to capture the interdependence between basic oscillatory elements, quantifying oscillations occurring in single trials at specific frequencies, locations, and time epochs. We find that the general structure of the element interdependence networks (effective connectivity) remains stable across task conditions, reflecting an intrinsic coordination architecture and responds to changes in task constraints by subtle but consistently distinct topological reorganizations. Trial categories are reliably and significantly better separated using oscillatory portraits than from the information contained in individual oscillatory elements, suggesting an interelement coordination-based encoding. Furthermore, single-trial oscillatory portrait fluctuations are predictive of fine trial-to-trial variations in movement kinematics. Remarkably, movement accuracy appears to be reflected in the capacity of the oscillatory coordination architecture to flexibly update as an effect of movement-error integration.

我们表明,感觉运动行为可以可靠地预测单次脑电图振荡在大脑区域,频带和运动时间的协调方式波动。我们定义了高维振荡画像,以捕捉基本振荡元素之间的相互依存关系,量化在特定频率、位置和时间时代的单次试验中发生的振荡。我们发现,元素相互依赖网络(有效连接)的总体结构在不同的任务条件下保持稳定,反映了内在的协调架构,并通过微妙但始终不同的拓扑重组来响应任务约束的变化。与单个振荡元素中包含的信息相比,使用振荡肖像可靠且显著地更好地分离了试验类别,这表明基于元素间协调的编码。此外,单次试验的振荡肖像波动预测了运动运动学中精细的试验对试验的变化。值得注意的是,运动精度似乎反映在振荡协调体系结构灵活更新的能力上,作为运动误差积分的影响。
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引用次数: 0
Modelling low-dimensional interacting brain networks reveals organising principle in human cognition. 对低维相互作用的大脑网络进行建模,揭示了人类认知的组织原理。
IF 3.6 3区 医学 Q2 NEUROSCIENCES Pub Date : 2025-05-08 eCollection Date: 2025-01-01 DOI: 10.1162/netn_a_00434
Yonatan Sanz Perl, Sebastian Geli, Eider Pérez-Ordoyo, Lou Zonca, Sebastian Idesis, Jakub Vohryzek, Viktor K Jirsa, Morten L Kringelbach, Enzo Tagliazucchi, Gustavo Deco

The discovery of resting-state networks shifted the focus from the role of local regions in cognitive tasks to the ongoing spontaneous dynamics in global networks. Recently, efforts have been invested to reduce the complexity of brain activity recordings through the application of nonlinear dimensionality reduction algorithms. Here, we investigate how the interaction between these networks emerges as an organising principle in human cognition. We combine deep variational autoencoders with computational modelling to construct a dynamical model of brain networks fitted to the whole-brain dynamics measured with functional magnetic resonance imaging (fMRI). Crucially, this allows us to infer the interaction between these networks in resting state and seven different cognitive tasks by determining the effective functional connectivity between networks. We found a high flexible reconfiguration of task-driven network interaction patterns and we demonstrate that this reconfiguration can be used to classify different cognitive tasks. Importantly, compared with using all the nodes in a parcellation, we obtain better results by modelling the dynamics of interacting networks in both model and classification performance. These findings show the key causal role of manifolds as a fundamental organising principle of brain function, providing evidence that interacting networks are the computational engines' brain during cognitive tasks.

静息状态网络的发现将焦点从局部区域在认知任务中的作用转移到全球网络中持续的自发动态。近年来,人们致力于通过应用非线性降维算法来降低大脑活动记录的复杂性。在这里,我们研究这些网络之间的相互作用如何作为人类认知的组织原则出现。我们将深度变分自编码器与计算建模相结合,构建了一个与功能磁共振成像(fMRI)测量的全脑动力学相适应的脑网络动力学模型。至关重要的是,这使我们能够通过确定这些网络之间的有效功能连接来推断静息状态下这些网络与七种不同认知任务之间的相互作用。我们发现了任务驱动的网络交互模式的高度灵活的重新配置,并证明了这种重新配置可以用于分类不同的认知任务。重要的是,与在一个分组中使用所有节点相比,我们通过对交互网络的动态建模在模型和分类性能上都获得了更好的结果。这些发现显示了流形作为大脑功能基本组织原则的关键因果作用,提供了交互网络是认知任务中计算引擎大脑的证据。
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引用次数: 0
Whole-brain modular dynamics at rest predict sensorimotor learning performance. 休息时全脑模块化动态预测感觉运动学习表现。
IF 3.6 3区 医学 Q2 NEUROSCIENCES Pub Date : 2025-05-08 eCollection Date: 2025-01-01 DOI: 10.1162/netn_a_00420
Dominic I Standage, Daniel J Gale, Joseph Y Nashed, J Randall Flanagan, Jason P Gallivan

Neural measures that predict cognitive performance are informative about the mechanisms underlying cognitive phenomena, with diagnostic potential for neuropathologies with cognitive symptoms. Among such markers, the modularity (subnetwork composition) of whole-brain functional networks is especially promising due to its longstanding theoretical foundations and recent success in predicting clinical outcomes. We used functional magnetic resonance imaging to identify whole-brain modules at rest, calculating metrics of their spatiotemporal dynamics before and after a sensorimotor learning task on which fast learning is widely believed to be supported by a cognitive strategy. We found that participants' learning performance was predicted by the degree of coordination of modular reconfiguration and the strength of recruitment and integration of networks derived during the task itself. Our findings identify these whole-brain metrics as promising network-based markers of cognition, with relevance to basic neuroscience and the potential for clinical application.

预测认知表现的神经测量对认知现象的潜在机制提供了信息,对具有认知症状的神经病理学具有诊断潜力。在这些标记中,全脑功能网络的模块化(子网络组成)由于其长期的理论基础和最近在预测临床结果方面的成功而特别有希望。我们使用功能性磁共振成像来识别静止的全脑模块,计算它们在感觉运动学习任务前后的时空动态度量,在这种任务中,快速学习被广泛认为是由认知策略支持的。我们发现,参与者的学习绩效是由任务本身中产生的模块重构的协调程度和网络的招募和整合强度预测的。我们的研究结果表明,这些全脑指标是有前途的基于网络的认知标记,与基础神经科学和临床应用潜力相关。
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引用次数: 0
Metric structural human connectomes: Localization and multifractality of eigenmodes. 度量结构人类连接体:特征模态的局部化和多重分形。
IF 3.6 3区 医学 Q2 NEUROSCIENCES Pub Date : 2025-05-08 eCollection Date: 2025-01-01 DOI: 10.1162/netn_a_00439
Anna Bobyleva, Alexander Gorsky, Sergei Nechaev, Olga Valba, Nikita Pospelov

We explore the fundamental principles underlying the architecture of the human brain's structural connectome through the lens of spectral analysis of Laplacian and adjacency matrices. Building on the idea that the brain balances efficient information processing with minimizing wiring costs, our goal is to understand how the metric properties of the connectome relate to the presence of an inherent scale. We demonstrate that a simple generative model combining nonlinear preferential attachment with an exponential penalty for spatial distance between nodes can effectively reproduce several key features of the human connectome. These include spectral density, edge length distribution, eigenmode localization, local clustering, and topological properties. Additionally, we examine the finer spectral characteristics of human structural connectomes by evaluating the inverse participation ratios (IPR q ) across various parts of the spectrum. Our analysis shows that the level statistics in the soft cluster region of the Laplacian spectrum (where eigenvalues are small) deviate from a purely Poisson distribution due to interactions between clusters. Furthermore, we identify localized modes with large IPR values in the continuous spectrum. Multiple fractal eigenmodes are found across different parts of the spectrum, and we evaluate their fractal dimensions. We also find a power-law behavior in the return probability-a hallmark of critical behavior-and conclude by discussing how our findings are related to previous conjectures that the brain operates in an extended critical phase that supports multifractality.

我们通过拉普拉斯矩阵和邻接矩阵的光谱分析来探索人脑结构连接体结构的基本原理。基于大脑在有效的信息处理和最小化连接成本之间取得平衡的观点,我们的目标是了解连接体的度量属性是如何与固有尺度的存在相关联的。我们证明了一个简单的生成模型结合了非线性优先依恋和节点之间空间距离的指数惩罚,可以有效地再现人类连接组的几个关键特征。这些包括谱密度、边长分布、特征模定位、局部聚类和拓扑性质。此外,我们通过评估频谱各部分的反向参与比率(IPR q)来检查人类结构连接体的更精细的频谱特征。我们的分析表明,由于聚类之间的相互作用,拉普拉斯谱的软聚类区域(特征值较小)中的水平统计量偏离了纯粹的泊松分布。此外,我们在连续光谱中识别出具有大IPR值的局域模式。在光谱的不同部分发现了多个分形特征模态,并评估了它们的分形维数。我们还在返回概率中发现了幂律行为——临界行为的标志——并通过讨论我们的发现如何与先前的猜测有关,即大脑在支持多重分形的扩展临界阶段中运行。
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Network Neuroscience
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