Band separation and electric field prediction in square Bravais-Moiré photonic crystals

In this study, we address three key challenges in photonic crystals: modeling of isolated flat bands, electric field prediction, and band separation in dispersion relations. Using twisted square Bravais lattices at specific angles, we create Bravais-Moiré photonic crystals exhibiting unique characteristics. These include band pairing and parallelism in certain Brillouin zones, enabling predictable electric field behavior and identification of isolated, flat band pairs within extensive band gaps. We apply advanced Shape theory-based classification methods for precise band separation, offering significant contributions to photonics research and light manipulation applications.

Riemannian distance based channel selection and feature extraction combining discriminative time-frequency bands and Riemannian tangent space for MI-BCIs

OBJECTIVE

Motor imagery-based brain computer interfaces (MI-BCIs) have been widely researched because they do not demand external stimuli and have a high degree of maneuverability. In most scenarios, superabundant selected channels, fixed time windows, and frequency bands would certainly affect the performance of MI-BCIs due to the neurophysiological diversities between different individuals. In this study, we tended to effectively use the Riemannian geometry of spatial covariance matrix to extract more robust features and thus enhance the decoding efficiency.

APPROACH

First, we propose a Riemannian distance-based EEG channel selection method (RDCS), which preliminarily reduces the information redundancy in the first stage. Second, we extract discriminative Riemannian Tangent Space features of EEG signals of selected channels from the most discriminant time-frequency bands (DTFRTS) to further enhance decoding accuracy for MI-BCIs. Finally, we trained a support vector machine (SVM) model with a linear kernel to classify our extracted discriminative Riemannian features and evaluated our proposed method using publicly available BCI Competition Ⅳ dataset Ⅰ (DS1) and Competition Ⅲ dataset Ⅲa (DS2).

MAIN RESULTS

The experimental results showed that the average classification accuracy with the selected 10-channel EEG signals of our method is 88.1% and 91.6% in DS1 and DS2 respectively. The average improvements are 24.3% & 27.1% on DS1 and 4.4% & 14.2% on DS2 for 10 & 20 selected channels, respectively.

SIGNIFICANCE

These results showed that our proposed method is a promising candidate for performance improvement of MI-BCIs.

A Riemannian Revisiting of Structure-Function Mapping Based on Eigenmodes

Understanding the link between brain structure and function may not only improve our knowledge of brain organization, but also lead to better quantification of pathology. To quantify this link, recent studies have attempted to predict the brain's functional connectivity from its structural connectivity. However, functional connectivity matrices live in the Riemannian manifold of the symmetric positive definite space and a specific attention must be paid to operate on this appropriate space. In this work we investigated the implications of using a distance based on an affine invariant Riemannian metric in the context of structure-function mapping. Specifically, we revisit previously proposed structure-function mappings based on eigendecomposition and test them on 100 healthy subjects from the Human Connectome Project using this adapted notion of distance. First, we show that using this Riemannian distance significantly alters the notion of similarity between subjects from a functional point of view. We also show that using this distance improves the correlation between the structural and functional similarity of different subjects. Finally, by using a distance appropriate to this manifold, we demonstrate the importance of mapping function from structure under the Riemannian manifold and show in particular that it is possible to outperform the group average and the so-called glass ceiling on the performance of mappings based on eigenmodes.

CSP-TSM: Optimizing the performance of Riemannian tangent space mapping using common spatial pattern for MI-BCI

BACKGROUND

Classification of electroencephalography (EEG) signals for motor imagery based brain computer interface (MI-BCI) is an exigent task and common spatial pattern (CSP) has been extensively explored for this purpose. In this work, we focused on developing a new framework for classification of EEG signals for MI-BCI.

METHOD

We propose a single band CSP framework for MI-BCI that utilizes the concept of tangent space mapping (TSM) in the manifold of covariance matrices. The proposed method is named CSP-TSM. Spatial filtering is performed on the bandpass filtered MI EEG signal. Riemannian tangent space is utilized for extracting features from the spatial filtered signal. The TSM features are then fused with the CSP variance based features and feature selection is performed using Lasso. Linear discriminant analysis (LDA) is then applied to the selected features and finally classification is done using support vector machine (SVM) classifier.

RESULTS

The proposed framework gives improved performance for MI EEG signal classification in comparison with several competing methods. Experiments conducted shows that the proposed framework reduces the overall classification error rate for MI-BCI by 3.16%, 5.10% and 1.70% (for BCI Competition III dataset IVa, BCI Competition IV Dataset I and BCI Competition IV Dataset IIb, respectively) compared to the conventional CSP method under the same experimental settings.

CONCLUSION

The proposed CSP-TSM method produces promising results when compared with several competing methods in this paper. In addition, the computational complexity is less compared to that of TSM method. Our proposed CSP-TSM framework can be potentially used for developing improved MI-BCI systems.

Wideband Spectrum Sensing Based on Riemannian Distance for Cognitive Radio Networks

Detecting the signals of the primary users in the wideband spectrum is a key issue for cognitive radio networks. In this paper, we consider the multi-antenna based signal detection in a wideband spectrum scenario where the noise statistical characteristics are assumed to be unknown. We reason that the covariance matrices of the spectrum subbands have structural constraints and that they describe a manifold in the signal space. Thus, we propose a novel signal detection algorithm based on Riemannian distance and Riemannian mean which is different from the traditional eigenvalue-based detector (EBD) derived with the generalized likelihood ratio criterion. Using the moment matching method, we obtain the closed expression of the decision threshold. From the considered simulation settings, it is shown that the proposed Riemannian distance detector (RDD) has a better performance than the traditional EBD in wideband spectrum sensing.