In this work, we focus on silent speech recognition in electroencephalography (EEG) data of healthy individuals to advance brain–computer interface (BCI) development to include people with neurodegeneration and movement and communication difficulties in society. Our dataset was recorded from 270 healthy subjects during silent speech of eight different Russia words (commands): ‘forward’, ‘backward’, ‘up’, ‘down’, ‘help’, ‘take’, ‘stop’, and ‘release’, and one pseudoword. We began by demonstrating that silent word distributions can be very close statistically and that there are words describing directed movements that share similar patterns of brain activity. However, after training one individual, we achieved 85% accuracy performing 9 words (including pseudoword) classification and 88% accuracy on binary classification on average. We show that a smaller dataset collected on one participant allows for building a more accurate classifier for a given subject than a larger dataset collected on a group of people. At the same time, we show that the learning outcomes on a limited sample of EEG-data are transferable to the general population. Thus, we demonstrate the possibility of using selected command-words to create an EEG-based input device for people on whom the neural network classifier has not been trained, which is particularly important for people with disabilities.

The article formulates the Dictionary Recognition problem, which is relevant for a wide range of applied problems: word recognition in a noisy audio signal for natural language processing tasks or in a noisy electromagnetic signal, recognition of visual patterns in limited visibility, and much more. A Dictionary Recognition problem is finding a set of words from a given set to maximize the classification accuracy of the words in the dictionary without losing semantic representation. The idea of solving the problem is to represent a set of objects (encoded as a sequence of symbols or visual sequences) in the form of a k-partite graph, where each partite of the graph corresponds to a group of objects with a certain common feature (equivalence class). The task is to find such a set of representatives of the k equivalence classes on which the k-classification accuracy by the classifier H meets certain criteria: (1) maximum classification accuracy; (2) maximin accuracy—the binary classification accuracy of every two objects is not lower than a certain value. The proposed Maximin Algorithm provides k-partite cliques with a maximin worst-case classification accuracy and belongs to the P-class. The Maximal Algorithm provides k-partite cliques with the maximum total weight (the problem belongs to the NP-hard class). The presented algorithms select a set of representatives optimally in terms of classification accuracy for the certain classifier and runtime. The algorithms increase classification accuracy when using classical classification methods without additional optimization of the classifiers themselves. We tested the algorithms on simulated data and provide an open-source project on GitHub. The results of the Maximin and Maximal Algorithms give 4-, 8- and 16-classification accuracy close to the best accuracy (obtained by brute-force enumeration) and better than the median accuracy by more than 20% for the support vector machine classifiers. Furthermore, the algorithms increase the selection speed of representatives by five orders of magnitude compared to the brute-force algorithm with a slight loss of accuracy.

Accurate segmentation of brain vessels in magnetic resonance angiography (MRA) is essential for surgical procedures. Neural networks are powerful tools for medical image segmentation, but their development requires well-annotated datasets. However, publicly available MRA datasets with detailed vessel annotations are scarce. We present a dataset of 100 manually annotated brain MRA images from the IXI Dataset, representing one of the largest publicly available collections with detailed vessel segmentation. We focused on the Circle of Willis and associated vessels, critical for neurovascular surgery planning. The annotation pipeline involved automated segmentation using the Frangi vesselness filter, followed by manual refinement by three annotators under supervision of three neurovascular surgeons. Images were acquired using 1.5T and 3T MRI scanners. The dataset includes demographic metadata, with clustering analysis revealing four distinct morphological patterns. This resource enables development of automated segmentation algorithms, investigation of cerebrovascular morphology variations, and advancement of AI-driven diagnostic tools.

In many modern applications, such as intrusion detection and prevention systems, expert knowledge can be formalized in the form of regular expressions. After this formalization, a finite automaton checks whether a word belongs to a regular language. Deterministic finite automata have an optimal time complexity, but the number of automaton states (space com­plexity) can grow exponentially with the length of the regular expression. At the same time, the time complexity is the main disadvantage of non-deterministic finite automata. Therefore, reducing spatial complexity while maintaining low time complexity is highly relevant. In applied problems of regular language recognition, a significant problem is the problem of the exponentially growing number of states of the recognizing deterministic finite automaton depending on the length of regular expressions of the recognized language — the exponential explosion problem. There are the following three main approaches to solving this problem using finite automata: 1) restriction on signatures given by experts; 2) regular language modification — this approach assumes the appearance in the solution of a practical problem of recognizing errors of the first and second kind; 3) finite automata modification without recognizing regular language changing. The third approach can be implemented as a finite automata modification through compression algorithms and particular structural elements. The paper presents a review of modern solutions, the main idea of which is the transition from an abstract finite automaton, represented by a table-specified function, to a structural automaton that combines the abstract part stored in the memory and various structural elements such as bit arrays and counters. Some ideas and algorithms have become especially successful when solving the exponential explosion problem by adding special structural elements. First, such successful solutions include the use of counters. Second, the idea of storing additional information about the state machine. Third, the combination of non-deterministic and deterministic finite automata. Fourth, the economic attitude to the state machine regarding its location to fast and slow memory allows us to consider the em­pirical experience of accumulated malicious traffic in intrusion detection systems.

EEG-based BCIs face noise and computational constraints for on-device deployment. We present a lightweight pipeline using Hankel embeddings: projecting EEG blocks onto paired eigenvectors yields oscillators-closed-orbit components. Our approach provides three contributions: (1) jPCA-based oscillator dynamics with mechanics-inspired descriptors for stable, class-separable features; (2) adaptive band-pass filtering by reconstructing signals from selected oscillators, suppressing noise without preset frequencies; (3) consistent spatiotemporal oscillator localization across channels. The pipeline uses only matrix operations, enabling GPU-free streaming. On motor-imagery benchmarks, our Hankel-based filter improves classifier accuracy by 6%, providing a resource-efficient EEG representation for edge BCI systems.

This paper introduces a Polyharmonic Brain Signal Model. The model is introduced to justify the use of trajectory embedding and low-rank approximations, and is not intended as a direct biophysical description of neuronal generators. We introduce a lightweight method to solve the reverse problem “Evaluating the Number of Sources” for electroencephalography (EEG) or magnetoencephalography (MEG) based non-invasive brain-computer interfaces (BCIs). Each EEG/MEG time series trace is mapped to a Hankel matrix which rank equals the number of oscillatory components in the noise-free case under the Polyharmonic Brain Signal Model. In practice, we infer the active oscillator count by examining the singular spectrum of the unfolded data. The method combines unfolding analysis, singular spectrum analysis with noise-aware thresholds (e.g., eigenvalue gaps or random-matrix-inspired cutoffs) and aggregates estimates across channels and sliding windows for robustness. This yields a lightweight preprocessing tool that outputs both the estimated source number and associated subspaces, facilitating downstream denoising and classification. We validate the approach on recordings from an authordeveloped non-invasive BCI.