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Mathematics
Special Issues
Mathematical Approaches for Brain Dynamics and Connectivity
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Special Issue "Mathematical Approaches for Brain Dynamics and Connectivity"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Network Science".

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 1652

Special Issue Editors

Dr. Hua-Liang Wei

E-Mail Website
Guest Editor
Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield S10 2TN, UK
Interests: bioscience signal processing; data modeling
Special Issues, Collections and Topics in MDPI journals
Dr. Yuzhu Guo

E-Mail Website
Guest Editor
School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China
Interests: brain dynamics and brain activities; brain–computer interfaces; AI for clinical disease diagnosis; neurorehabilitation; hybrid-augmented intelligence
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Yang Li

E-Mail Website
Guest Editor
School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China
Interests: brain informatics; medical image processing; deep learning; brain–computer interfaces
Special Issues, Collections and Topics in MDPI journals
Dr. Jingjing Luo

E-Mail Website
Guest Editor
Fudan University, Shanghai, China
Interests: system identification and modeling of complex systems; biomedical time series processing; human–machine interfaces

Special Issue Information

Dear Colleagues,

Brain connectivity of the human brain represents the statistical dependence and information flow between cortical regions. Brain connectivity, including structural connectivity, functional connectivity and effective connectivity, significantly contributes to the study of brain functions and underlying mechanisms. Brain connectivity has a wide range of applications in brain–computer interfaces, neural modulation, neural rehabilitations, plasticity and learning, and brain-inspired intelligences, etc. Recent advances in data acquisition make data-driven analysis methods possible and have had a fruitful contribution to our knowledge about the brain dynamics and its connections.

The aim of this Special Issue is to gather the efforts of experts from various disciplines and to publish original research articles covering advances in the theory, technique, and applied aspects of brain dynamics and connectivity. In this framework, diverse information processing analysis and modeling techniques will be discussed to study the statistical and dynamical properties of brain activities.

Potential topics include but are not limited to the following:

  • Brain dynamics and connectivity;
  • Brain connectivity;
  • Brain–computer interfaces;
  • Neural rehabilitation;
  • Brain disorders;
  • Neural plasticity;
  • Brain images;
  • Brain-inspired intelligence;
  • Neuronal dynamics;
  • Spiking neural networks.

Herewith, I encourage the authors to submit their recent results to this Special Issue to capture state-of-the-art research in the various aspects of complex network theory.

Dr. Hua-Liang Wei
Prof. Dr. Yuzhu Guo
Prof. Dr. Yang Li
Dr. Jingjing Luo
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • dynamic mode decomposition
  • nonlinear modelling of brain dynamics
  • qualitative and quantitative description of brain connectivity
  • brain image analysis
  • brain disorders
  • neural plasticity
  • brain-inspired intelligence
  • neuronal dynamics
  • spiking neural networks
  • brain–computer interfaces
  • neural rehabilitation

Published Papers (1 paper)

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Research

17 pages, 3459 KiB  
Article
Phase Analysis of Event-Related Potentials Based on Dynamic Mode Decomposition
by
Li Li
,
Jingjing Luo
,
Yang Li
,
Lei Zhang
and
Yuzhu Guo
Mathematics 2022, 10(23), 4406; https://doi.org/10.3390/math10234406 - 22 Nov 2022
Viewed by 883
Abstract
Real-time detection of event-related potentials (ERPs) and exploration of ERPs generation mechanisms are vital to practical application of brain–computer interfaces (BCI). Traditional methods for ERPs analysis often fall into time domain, time–frequency domain, or spatial domain. Methods which can reveal spatiotemporal interactions by [...] Read more.
Real-time detection of event-related potentials (ERPs) and exploration of ERPs generation mechanisms are vital to practical application of brain–computer interfaces (BCI). Traditional methods for ERPs analysis often fall into time domain, time–frequency domain, or spatial domain. Methods which can reveal spatiotemporal interactions by simultaneously analyzing multi-channel EEG signals may provide new insights into ERP research and is highly desired. Additionally, although phase information has been investigated to describe the phase consistency of a certain frequency component across different ERP trials, it is of research significance to analyze the phase reorganization across different frequency components that constitute a single-trial ERP signal. To address these problems, dynamic mode decomposition (DMD) was applied to decompose multi-channel EEG into a series of spatial–temporal coherent DMD modes, and a new metric, called phase variance distribution (PVD) is proposed as an index of the phase reorganization of DMD modes during the ERP in a single trial. Based on the PVD, a new error-related potential (ErrP) detection method based on symmetric positive defined in Riemann manifold is proposed to demonstrate the significant PVD differences between correct and error trials. By including the phase reorganization index, the 10-fold cross-validation results of an ErrP detection task showed that the proposed method is 4.98%, 27.99% and 7.98% higher than the counterpart waveform-based ErrP detection method in the terms of weighted accuracy rate, precision and recall of the ErrP class, respectively. The resulting PVD curve shows that with the occurrence of ERP peaks, the phases of different frequency rhythms are getting to aligned and yields a significant smaller PVD. Since the DMD modes of different frequencies characterize spatiotemporal coherence of multi-channel EEG at different functional regions, the new phase reorganization index, PVD, may indicate the instantaneous phase alignment of different functional networks and sheds light on a new interpretation of ERP generation mechanism. Full article
(This article belongs to the Special Issue Mathematical Approaches for Brain Dynamics and Connectivity)
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