Riemannian classification of single-trial surface EEG and sources during checkerboard and navigational images in humans

Objective Different visual stimuli are classically used for triggering visual evoked potentials comprising well-defined components linked to the content of the displayed image. These evoked components result from the average of ongoing EEG signals in which additive and oscillatory mechanisms contribute to the component morphology. The evoked related potentials often resulted from a mixed situation (power variation and phase-locking) making basic and clinical interpretations difficult. Besides, the grand average methodology produced artificial constructs that do not reflect individual peculiarities. This motivated new approaches based on single-trial analysis as recently used in the brain-computer interface field. Approach We hypothesize that EEG signals may include specific information about the visual features of the displayed image and that such distinctive traits can be identified by state-of-the-art classification algorithms based on Riemannian geometry. The same classification algorithms are also applied to the dipole sources estimated by sLORETA. Main results and significance We show that our classification pipeline can effectively discriminate between the display of different visual items (Checkerboard versus 3D navigational image) in single EEG trials throughout multiple subjects. The present methodology reaches a single-trial classification accuracy of about 84% and 93% for inter-subject and intra-subject classification respectively using surface EEG. Interestingly, we note that the classification algorithms trained on sLORETA sources estimation fail to generalize among multiple subjects (63%), which may be due to either the average head model used by sLORETA or the subsequent spatial filtering failing to extract discriminative information, but reach an intra-subject classification accuracy of 82%.

Simultaneous Classification of Both Mental Workload and Stress Level Suitable for an Online Passive Brain–Computer Interface

Research studies on EEG-based mental workload detection for a passive BCI generally focus on classifying cognitive states associated with the performance of tasks at different levels of difficulty, with no other aspects of the user’s mental state considered. However, in real-life situations, different aspects of the user’s state such as their cognitive (e.g., level of mental workload) and affective (e.g., level of stress/anxiety) states will often change simultaneously, and performance of a BCI system designed considering just one state may be unreliable. Moreover, multiple mental states may be relevant to the purposes of the BCI—for example both mental workload and stress level might be related to an aircraft pilot’s risk of error—and the simultaneous prediction of states may be critical in maximizing the practical effectiveness of real-life online BCI systems. In this study we investigated the feasibility of performing simultaneous classification of mental workload and stress level in an online passive BCI. We investigated both subject-specific and cross-subject classification approaches, the latter with and without the application of a transfer learning technique to align the distributions of data from the training and test subjects. Using cross-subject classification with transfer learning in a simulated online analysis, we obtained accuracies of 77.5 ± 6.9% and 84.1 ± 5.9%, across 18 participants for mental workload and stress level detection, respectively.

Characteristics of Regular Functions Defined on a Semicommutative Subalgebra of 4-Dimensional Complex Matrix Algebra

In this paper, we give an extended quaternion as a matrix form involving complex components. We introduce a semicommutative subalgebra ℂ ℂ 2 of the complex matrix algebra M 4 , ℂ . We exhibit regular functions defined on a domain in ℂ 4 but taking values in ℂ ℂ 2 . By using the characteristics of these regular functions, we propose the corresponding Cauchy–Riemann equations. In addition, we demonstrate several properties of these regular functions using these novel Cauchy–Riemann equations. Mathematical Subject Classification is 32G35, 32W50, 32A99, and 11E88.

A mathematical justification for metronomic chemotherapy in oncology

We mathematically justify metronomic chemotherapy as the best strategy to apply most cytotoxic drugs in oncology for both curative and palliative approaches, assuming the classical pharmacokinetic model together with the Emax pharmacodynamic and the Norton-Simon hypothesis.From the mathematical point of view, we will consider two mixed-integer nonlinear optimization problems, where the unknowns are the number of the doses and the quantity of each one, adjusting the administration times a posteriori.Mathematics Subject Classification: 93C15, 92C50, 90C30

Higher-order tensor decomposition based scalp-to-intracranial EEG projection for detection of interictal epileptiform discharges

Objective. Interictal epileptiform discharges (IEDs) occur between two seizures onsets. IEDs are mainly captured by intracranial recordings and are often invisible over the scalp. This study proposes a model based on tensor factorization to map the time-frequency (TF) features of scalp EEG (sEEG) to the TF features of intracranial EEG (iEEG) in order to detect IEDs from over the scalp with high sensitivity. Approach. Continuous wavelet transform is employed to extract the TF features. Time, frequency, and channel modes of IED segments from iEEG recordings are concatenated into a four-way tensor. Tucker and CANDECOMP/PARAFAC decomposition techniques are employed to decompose the tensor into temporal, spectral, spatial, and segmental factors. Finally, TF features of both IED and non-IED segments from scalp recordings are projected onto the temporal components for classification. Main results. The model performance is obtained in two different approaches: within- and between-subject classification approaches. Our proposed method is compared with four other methods, namely a tensor-based spatial component analysis method, TF-based method, linear regression mapping model, and asymmetric-symmetric autoencoder mapping model followed by convolutional neural networks. Our proposed method outperforms all these methods in both within- and between-subject classification approaches by respectively achieving 84.2% and 72.6% accuracy values. Significance. The findings show that mapping sEEG to iEEG improves the performance of the scalp-based IED detection model. Furthermore, the tensor-based mapping model outperforms the autoencoder- and regression-based mapping models.

Analysis and Mining of Internet Public Opinion Based on LDA Subject Classification

This paper uses Python, R language, Gephi and other software to crawl and classify the comment content of Weibo hot search events. Using word cloud, co-occurrence social network graphs, LDA topic classification visualization methods, this paper regularizes and integrates public opinions of hot events. Through this research, we can get the influence of public opinion mediators, public opinion objects, and government forces on the network public opinion and put forward corresponding improvement suggestions. We hope to contribute to the government’s governance and prevention of online public opinion during the spread of COVID-19 and other public hot events.

Cubic Polynomial for the Series of Consecutive Cubes under Alternating Signs

This paper aims to develop an elegant formula for the series of consecutive cubes of natural numbers under alternating signs. In addition, this paper investigates the formula under odd and even number of terms and discuss some important findings.Keywords: Consecutive cubes; alternating signs; odd and even terms.2010 Mathematics Subject Classification: 11B13, 11B50, 97I30AbstrakPaper ini bertujuan membangun formula yang elegan untuk deret berganti tanda bilangan-bilangan kubik berurutan. Paper ini juga menyelidiki formula untuk banyak suku ganjil dan untuk banyak suku genap, dan mendiskusikan beberapa temuan penting.Kata kunci:. Bilangan kubik berurutan, berganti tanda, suku ganjil dan suku genap

Subgraph of generalized co-maximal graph of commutative rings

Let R be a commutative ring with 1. In [3], we introduced a graph G(R) whose vertices are elements of R and two distinct vertices a, b are adjacent if and only if aR + bR = eR for some non-zero idempotent e in R. Let G′(R) be the subgraph of G(R) generated by the non-units of R. In this paper, we characterize those rings R for which the graph G′(R) is connected and Eulerian. Also we characterize those rings R for which genus of the graph G′(R) is ≤ 2. Finally, we show that the graph G′(R) is a line graph of some graph if and only if R is either a regular ring or a local ring.AMS Subject Classification 2020 : 05C25

Zα Open and Closed Mappings in Double Fuzzy Topological Spaces

We introduce and investigate some new class of mappings called double fuzzy Zα-open map and double fuzzy Zα-closed map in double fuzzy topological spaces. Also, some of their fundamental properties are studied. Moreover, we investigate the relationships between double fuzzy Z α-open and other existing mappings. AMS (2000) subject classification: 54A40.