arXiv subjects

Guido Nolte

Publications and source records attributed to Guido Nolte.

10 recordsLinked to original sources

arXiv2026

A Generalized Framework of Antisymmetric Polyspectral Indices for Identifying High-Order Neural Interactions

Cross-frequency interactions are fundamental brain mechanisms for integrating information across temporal scales. However, accurate identification of these couplings is hindered by complex multi-frequency nonlinearities and by spurious, zero-lag artifacts caused by volume conduction. To our knowledge, conventional metrics lack a robust framework to characterize genuine interactions among multiple time series where a frequency of interest $f_N$ arises from the combination of $N-1$ components such that $f_N = \sum_{i=1}^{N-1} f_i$. We introduce a general family of antisymmetric cross-polyspectral indices designed to quantify these harmonic dependencies while being intrinsically robust to instantaneous mixing. We derive the theoretical properties of these quantities and validate them through simulations of cubic nonlinearities. As a proof of concept, we apply the indices to empirical EEG recordings; the results reveal significant higher-order dependencies that elude standard analytical approaches. We further discuss how these indices can inform novel, personalized multi-site transcranial magnetic stimulation (mTMS) protocols by enabling the selective monitoring and modulation of specific multi-frequency network interactions.

q-bio.NC↗

arXiv2025

Estimating Time Delays between Signals under Mixed Noise Influence with Novel Cross- and Bispectral Methods

A common problem to signal processing are biases introduced by correlated noise. When quantifying time delays between two signals, mixed noise introduces a bias towards zero delay in conventional delay estimates based on the cross- or bispectrum. Here we propose two novel time delay estimators that address these shortcomings: (1) A cross-spectrum based approach that relies on estimating the periodicity of the phase spectrum rather than its slope, and (2) a bispectrum based approach, bispectral antisymmetrization, which removes contributions from not just Gaussian but all independent sources. In a simulation study, we compare conventional and novel TDE approaches and resolve differences in performance with respect to noise Gaussianity and auto-correlation structure. As a proof-of concept, we also perform TDE analysis on a neural stimulation dataset (n=3). We find that antisymmetrization consistently outperforms conventional bispectral methods at low signal-to-noise ratios (SNR) and prevents spurious zero-delay estimates in all mixed-noise environments. Time delay estimation based on phase periodicity also improves signal sensitivity compared to conventional cross-spectral methods. These observations are stable with respect to the magnitude of the delay and the statistical properties of the noise.

eess.SP↗

arXiv2019

Bispectral pairwise interacting source analysis for identifying systems of cross-frequency interacting brain sources from electroencephalographic or magnetoencephalographic signals

Brain cognitive functions arise through the coordinated activity of several brain regions, which actually form complex dynamical systems operating at multiple frequencies. These systems often consist of interacting subsystems, whose characterization is of importance for a complete understanding of the brain interaction processes. To address this issue, we present a technique, namely the bispectral Pairwise Interacting Source Analysis (biPISA), for analyzing systems of cross-frequency interacting brain sources when multichannel electroencephalographic (EEG) or magnetoencephalographic (MEG) data are available. Specifically, the biPISA allows to identify one or many subsystems of cross-frequency interacting sources by decomposing the antisymmetric components of the cross-bispectra between EEG or MEG signals, based on the assumption that interactions are pairwise. Thanks to the properties of the antisymmetric components of the cross-bispectra, biPISA is also robust to spurious interactions arising from mixing artifacts, i.e. volume conduction or field spread, which always affect EEG or MEG functional connectivity estimates. This method is an extension of the Pairwise Interacting Source Analysis (PISA), which was originally introduced for investigating interactions at the same frequency, to the study of cross-frequency interactions. The effectiveness of this approach is demonstrated in simulations for up to three interacting source pairs, and for real MEG recordings of spontaneous brain activity. Simulations show that the performances of biPISA in estimating the phase difference between the interacting sources are affected by the increasing level of noise rather than by the number of the interacting subsystems. The analysis of real MEG data reveals an interaction between two pairs of sources of central mu and beta rhythms, localizing in the proximity of the left and right central sulci.

physics.med-ph↗

arXiv2009

Modeling sparse connectivity between underlying brain sources for EEG/MEG

We propose a novel technique to assess functional brain connectivity in EEG/MEG signals. Our method, called Sparsely-Connected Sources Analysis (SCSA), can overcome the problem of volume conduction by modeling neural data innovatively with the following ingredients: (a) the EEG is assumed to be a linear mixture of correlated sources following a multivariate autoregressive (MVAR) model, (b) the demixing is estimated jointly with the source MVAR parameters, (c) overfitting is avoided by using the Group Lasso penalty. This approach allows to extract the appropriate level cross-talk between the extracted sources and in this manner we obtain a sparse data-driven model of functional connectivity. We demonstrate the usefulness of SCSA with simulated data, and compare to a number of existing algorithms with excellent results.

stat.ME↗

arXiv2009

Sparse Causal Discovery in Multivariate Time Series

Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on non-vanishing coefficients belonging to respective time-lagged instances. As in most cases a parsimonious causality structure is assumed, a promising approach to causal discovery consists in fitting VAR models with an additional sparsity-promoting regularization. Along this line we here propose that sparsity should be enforced for the subgroups of coefficients that belong to each pair of time series, as the absence of a causal relation requires the coefficients for all time-lags to become jointly zero. Such behavior can be achieved by means of l1-l2-norm regularized regression, for which an efficient active set solver has been proposed recently. Our method is shown to outperform standard methods in recovering simulated causality graphs. The results are on par with a second novel approach which uses multiple statistical testing.

stat.ME↗

arXiv2007

Robustly estimating the flow direction of information in complex physical systems

We propose a new measure to estimate the direction of information flux in multivariate time series from complex systems. This measure, based on the slope of the phase spectrum (Phase Slope Index) has invariance properties that are important for applications in real physical or biological systems: (a) it is strictly insensitive to mixtures of arbitrary independent sources, (b) it gives meaningful results even if the phase spectrum is not linear, and (c) it properly weights contributions from different frequencies. Simulations of a class of coupled multivariate random data show that for truly unidirectional information flow without additional noise contamination our measure detects the correct direction as good as the standard Granger causality. For random mixtures of independent sources Granger Causality erroneously yields highly significant results whereas our measure correctly becomes non-significant. An application of our novel method to EEG data (88 subjects in eyes-closed condition) reveals a strikingly clear front-to-back information flow in the vast majority of subjects and thus contributes to a better understanding of information processing in the brain.

stat.ME↗

arXiv1995

Observing instantons directly on the lattice without cooling

Based on the study of the simple Abelian Higgs model in $1+1$ dimensions we will present a new method to identify and localize extended instantons. The idea is to measure the topological charge on regions somewhat larger than the extended instantons so as to average out the ultraviolet fluctuations but without losing the detailed topological information when going to the full space. The instanton size and probability density can be directly extracted from this analysis. Local dislocations, which can be avoided for fine enough lattices, can be reinterpreted as modified boundary conditions producing sectors with net topological charge.

hep-lat↗

arXiv1995

Nondegenerate Fermions in the Background of the Sphaleron Barrier

We consider level crossing in the background of the sphaleron barrier for nondegenerate fermions. The mass splitting within the fermion doublets allows only for an axially symmetric ansatz for the fermion fields. In the background of the sphaleron we solve the partial differential equations for the fermion functions. We find little angular dependence for our choice of ansatz. We therefore propose a good approximate ansatz with radial functions only. We generalize this approximate ansatz with radial functions only to fermions in the background of the sphaleron barrier and argue, that it is a good approximation there, too.

hep-ph↗

arXiv1994

Gradient Approach to the Sphaleron Barrier

We apply the gradient approach to obtain a path over the sphaleron barrier and to demonstrate the fermionic level crossing phenomenon. Neglecting the mixing angle dependence and assuming that the fermions of a doublet are degenerate in mass we employ spherically symmetric ansätze for the fields. The gradient path over the barrier is smooth, even for large values of the Higgs boson mass or of the fermion mass, where the extremal energy path bifurcates.

hep-ph↗

arXiv1993

The Sphaleron Barrier in the Presence of Fermions

We calculate the minimal energy path over the sphaleron barrier in the pre\-sen\-ce of fermions, assuming that the fermions of a doublet are degenerate in mass. This allows for spherically symmetric ansätze for the fields, when the mixing angle dependence is neglected. While light fermions have little influence on the barrier, the presence of heavy fermions ($M_F \sim$ TeV) strongly deforms the barrier, giving rise to additional sphalerons for very heavy fermions ($M_F \sim$ 10 TeV). Heavy fermions form non-topological solitons in the vacuum sector.

hep-ph↗