arXiv subjects

Pedro A. Valdes-Sosa

Publications and source records attributed to Pedro A. Valdes-Sosa.

11 recordsLinked to original sources

arXiv2025

Redundant and synergistic interactions in a complex network of single-transistor electronic chaotic oscillators and in neurophysiological recordings

Complex networks often exhibit emergent behaviors, where simple dyadic interactions yield collective dynamics that cannot be explained by examining the system's units individually or in pairs. Understanding how redundant and synergistic interaction emerges from elementary connectivity patterns is important in characterizing the behavior of physical, biological, and engineering systems. In this study, the information-theoretic framework of Partial Information Decomposition (PID) is employed to investigate how pairs of signals measured at the nodes of large network systems contribute individually and in cooperation with each other to determine the overall state of the network. The analyzed systems are networks of numerically simulated Roessler oscillators and physical single-transistor electronic chaotic oscillators, reproducing purely pairwise and symmetric links in biological neuronal cultures, and cortical electroencephalographic networks assessed in humans. In the two settings, PID was extensively applied to decompose the information brought by pairs of signals to the overall state of the system, assessed respectively as the dynamic regime (from asynchronous chaos to synchronization) and the subject condition (open vs. closed eyes). Our approach highlights the coexistence of redundant and synergistic interplay in determining the effect of the pairwise dynamics on the system's state. Specifically, we demonstrate how, in a highly synchronized system, where units act following overlapped redundant behaviors, their joint consideration helps determine the system's state though their synergistic interactions. Our findings reveal the emergence of non-trivial behaviors in networked system based on pairwise connections and straightforward neural states, highlighting the need for using appropriate analytical tools to capture complex phenomena.

nlin.CD↗

arXiv2025

GANORM: Lifespan Normative Modeling of EEG Network Topology based on Multinational Cross-Spectra

Charting the lifespan evolutionary trajectory of brain function serves as the normative standard for preventing mental disorders during brain development and aging. Although numerous MRI studies have mapped the structural connectome for young cohorts, the EEG-based functional connectome is unknown to characterize human lifespan, limiting its practical applications for the early detection of brain dysfunctions at the community level. This work aimed to undertake normative modeling from the perspective of EEG network topology. Frequency-dependent scalp EEG functional networks were constructed based on EEG cross-spectra aged 5-97 years from 9 countries and network characteristics were quantified. First, GAMLSS were applied to describe the normative curves of the network characteristics in different frequency bands. Subsequently, addressing the limitations of existing regression approaches for whole brain network analysis, this paper proposed an interpretable encoder-decoder framework, Generative Age-dependent brain Network nORmative Model (GANORM). Building upon this framework, we established an age-dependent normative trajectory of the complete brain network for the entire lifespan. Finally, we validated the effectiveness of the norm using EEG datasets from multiple sites. Subsequently, we evaluated the effectiveness of GANORM, and the tested performances of BPNN showed the R^2 was 0.796, the MAE was 0.081, and the RMSE was 0.013. Following established lifespan brain network norm, GANORM also exhibited good results upon verification using healthy and disease data from various sites. The deviation scores from the normative mean for the healthy control group were significantly smaller than those of the disease group.

cs.NE↗

arXiv2022

Identification of oscillatory brain networks with Hidden Gaussian Graphical Spectral models of EEG/MEG

Identifying the functional networks underpinning indirectly observed processes poses an inverse problem for neurosciences or other fields. A solution of such inverse problems estimates as a first step the activity emerging within functional networks from EEG or MEG data. These EEG or MEG estimates are a direct reflect functional brain network activity with a temporal resolution that no other in vivo neuroimage may provide. A second step estimating functional connectivity from such activity pseudodata unveil the oscillatory brain networks that strongly correlate with all cognition and behavior. Simulations of such MEG or EEG inverse problem also reveal estimation errors of the functional connectivity determined by any of the state-of-the-art inverse solutions. We disclose a significant cause of estimation errors originating from misspecification of the functional network model incorporated into either inverse solution steps. We introduce the Bayesian identification of a Hidden Gaussian Graphical Spectral (HIGGS) model specifying such oscillatory brain networks model. In human EEG alpha rhythm simulations estimation errors measured as ROC performance do not surpass 2% in our HIGGS inverse solution and reach 20% in state-of-the-art methods. Macaque simultaneous EEG/ECoG recordings provide experimental confirmation for our inverse-solution with 1/3 more congruence according to Riemannian distances than state-of-the-art methods.

stat.ME↗

arXiv2019

Caulking the Leakage Effect in MEEG Source Connectivity Analysis

Simplistic estimation of neural connectivity in MEEG sensor space is impossible due to volume conduction. The only viable alternative is to carry out connectivity estimation in source space. Among the neuroscience community this is claimed to be impossible or misleading due to Leakage: linear mixing of the reconstructed sources. To address this problematic we propose a novel solution method that caulks the Leakage in MEEG source activity and connectivity estimates: BC-VARETA. It is based on a joint estimation of source activity and connectivity in the frequency domain representation of MEEG time series. To achieve this, we go beyond current methods that assume a fixed gaussian graphical model for source connectivity. In contrast we estimate this graphical model in a Bayesian framework by placing priors on it, which allows for highly optimized computations of the connectivity, via a new procedure based on the local quadratic approximation under quite general prior models. A further contribution of this paper is the rigorous definition of leakage via the Spatial Dispersion Measure and Earth Movers Distance based on the geodesic distances over the cortical manifold. Both measures are extended for the first time to quantify Connectivity Leakage by defining them on the cartesian product of cortical manifolds. Using these measures, we show that BC-VARETA outperforms most state of the art inverse solvers by several orders of magnitude.

q-bio.NC↗

arXiv2019

Third Generation MEEG Source Connectivity Analysis Toolbox (BC-VARETA 1.0) and Validation Benchmark

This paper presents a new toolbox for MEEG source activity and connectivity estimation: Brain Connectivity Variable Resolution Tomographic Analysis version 1.0 (BC-VARETA 1.0). It relies on the third generation of nonlinear methods for the analysis of resting state MEEG Time Series. Into the state of the art of MEEG analysis, the methodology underlying our tool (BC-VARETA) brings out several assets. First: Constitutes a Bayesian Identification approach of Linear Dynamical Systems in the Frequency Domain, grounded in more consistent models (third generation). Second: Achieves Super-Resolution, through the iterative solution of a Sparse Hermitian Source Graphical Model. Third: Tackles efficiently in High Dimensional and Complex set up the estimation of connectivity. Fourth: Incorporates priors at the connectivity level by penalizing the groups of variables, corresponding to the Gray Matter anatomical segmentation, and including a probability mask of the anatomically plausible connections. Along with the implementation of our method, we include in this toolbox a benchmark for the validation of MEEG source analysis methods, that would serve for the evaluation of sophisticated methodologies (third generation). It incorporates two elements. First: A realistic simulation framework, for the generation of MEEG synthetic data, given an underlying source connectivity structure. Second: Sensitive quality measures that allow for a reliable evaluation of the source activity and connectivity reconstruction performance, based on the Spatial Dispersion and Earth Movers Distance, in both source and connectivity space.

q-bio.NC↗

arXiv2018

Restate the reference for EEG microstate analysis

Despite the decades of efforts, the choice of EEG reference is still a debated fundamental issue. Non-neutral reference can inevitably inject the uncontrolled temporal biases into all EEG recordings, which may influence the spatiotemporal analysis of brain activity. A method, termed microstates, identifying spatiotemporal EEG features as the quasi-stable topography states in milliseconds, suggests its potential as biomarkers of neurophysiological disease. As reference electrode standardization technique (REST) could reconstruct an infinity reference approximately, it is a question whether REST or the other references will be more reliable than average reference (AR) for the microstates analysis. In this study, we design the microstate-based EEG forward model, and apply different references for microstates analysis. The spatial similarity between the generated and assumed cluster maps is mainly investigated. Furthermore, the real EEG data by the parametric bootstrap method is used to validate the performance of the references. Finally, we find that REST is robust to recover more similar cluster maps to the assumption than AR in the simulation, and the cluster maps between REST and AR on the real EEG data are quite different. This study may indicate that REST contributes to identifying more objective microstates features than AR.

q-bio.QM↗

arXiv2018

Unified Bayesian estimator of EEG reference at infinity: rREST

The choice of reference for electroencephalogram (EEG) is a long-lasting unsolved issue resulting in inconsistent usages and endless debates. Currently, both average reference (AR) and reference electrode standardization technique (REST) are two primary, irreconcilable contenders. We propose a theoretical framework to resolve this issue by formulating both a) estimation of potentials at infinity, and, b) determination of the reference, as a unified Bayesian linear inverse problem. We find that AR and REST are very particular cases of this unified framework: AR results from biophysically non-informative prior; while REST utilizes the prior of EEG generative model. We develop the regularized versions of AR and REST, named rAR, and rREST, respectively. Both depend on a regularization parameter that is the noise to signal ratio. Traditional and new estimators are evaluated with this framework, by both simulations and analysis of real EEGs. Generated artificial EEGs, show that relative error in estimating the EEG potentials at infinity is lowest for rREST. It also reveals that realistic volume conductor models improve the performances of REST and rREST. For practical applications, it is shown that average lead field gives the results comparable to the individual lead field. Finally, it is shown that the selection of the regularization parameter with Generalized Cross-Validation (GCV) is close to the 'oracle' choice based on the ground truth. When evaluated with the real 89 resting state EEGs, rREST consistently yields the lowest GCV. This study provides a novel perspective on the EEG reference problem by means of a unified inverse solution framework. It may allow additional principled theoretical formulations and numerical evaluation of performance.

q-bio.QM↗

arXiv2015

Tensor Analysis and Fusion of Multimodal Brain Images

Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks that underpin human cognitive processes by analysis of different neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the multimodal, multi-scale nature of neuroimaging data is well reflected by a multi-way (tensor) structure where the underlying processes can be summarized by a relatively small number of components or "atoms". We introduce Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network notation in order to analyze these models. These diagrams not only clarify matrix and tensor EEG and fMRI time/frequency analysis and inverse problems, but also help understand multimodal fusion via Multiway Partial Least Squares and Coupled Matrix-Tensor Factorization. We show here, for the first time, that Granger causal analysis of brain networks is a tensor regression problem, thus allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI recordings shows the potential of the methods and suggests their use in other scientific domains.

stat.ME↗

arXiv2014

Bidirectional Control of Absence Seizures by the Basal Ganglia: A Computational Evidence

Absence epilepsy is believed to be associated with the abnormal interactions between the cerebral cortex and thalamus. Besides the direct coupling, anatomical evidence indicates that the cerebral cortex and thalamus also communicate indirectly through an important intermediate bridge--basal ganglia. It has been thus postulated that the basal ganglia might play key roles in the modulation of absence seizures, but the relevant biophysical mechanisms are still not completely established. Using a biophysically based model, we demonstrate here that the typical absence seizure activities can be controlled and modulated by the direct GABAergic projections from the substantia nigra pars reticulata (SNr) to either the thalamic reticular nucleus (TRN) or the specific relay nuclei (SRN) of thalamus, through different biophysical mechanisms. Under certain conditions, these two types of seizure control are observed to coexist in the same network. More importantly, due to the competition between the inhibitory SNr-TRN and SNr-SRN pathways, we find that both decreasing and increasing the activation of SNr neurons from the normal level may considerably suppress the generation of SWDs in the coexistence region. Overall, these results highlight the bidirectional functional roles of basal ganglia in controlling and modulating absence seizures, and might provide novel insights into the therapeutic treatments of this brain disorder.

q-bio.NC↗

arXiv2013

Spatio-temporal Granger causality: a new framework

That physiological oscillations of various frequencies are present in fMRI signals is the rule, not the exception. Herein, we propose a novel theoretical framework, spatio-temporal Granger causality, which allows us to more reliably and precisely estimate the Granger causality from experimental datasets possessing time-varying properties caused by physiological oscillations. Within this framework, Granger causality is redefined as a global index measuring the directed information flow between two time series with time-varying properties. Both theoretical analyses and numerical examples demonstrate that Granger causality is a monotonically increasing function of the temporal resolution used in the estimation. This is consistent with the general principle of coarse graining, which causes information loss by smoothing out very fine-scale details in time and space. Our results confirm that the Granger causality at the finer spatio-temporal scales considerably outperforms the traditional approach in terms of an improved consistency between two resting-state scans of the same subject. To optimally estimate the Granger causality, the proposed theoretical framework is implemented through a combination of several approaches, such as dividing the optimal time window and estimating the parameters at the fine temporal and spatial scales. Taken together, our approach provides a novel and robust framework for estimating the Granger causality from fMRI, EEG, and other related data.

stat.AP↗

arXiv2011

Cortical current source connectivity by means of partial coherence fields

An important field of research in functional neuroimaging is the discovery of integrated, distributed brain systems and networks, whose different regions need to work in unison for normal functioning. The EEG is a non-invasive technique that can provide information for massive connectivity analyses. Cortical signals of time varying electric neuronal activity can be estimated from the EEG. Although such techniques have very high time resolution, two cortical signals even at distant locations will appear to be highly similar due to the low spatial resolution nature of the EEG. In this study a method for eliminating the effect of common sources due to low spatial resolution is presented. It is based on an efficient estimation of the whole-cortex partial coherence matrix. Using as a starting point any linear EEG tomography that satisfies the EEG forward equation, it is shown that the generalized partial coherences for the cortical grey matter current density time series are invariant to the selected tomography. It is empirically shown with simulation experiments that the generalized partial coherences have higher spatial resolution than the classical coherences. The results demonstrate that with as little as 19 electrodes, lag-connected brain regions can often be missed and misplaced even with lagged coherence measures, while the new method detects and localizes correctly the connected regions using the lagged partial coherences.

stat.AP↗