Methods of computational quantum chemistry provide accurate approximations of molecular properties crucial for computer-aided drug discovery and other areas of chemical science. However, high computational complexity limits the scalability of their applications. Neural network potentials (NNPs) are a promising alternative to quantum chemistry methods, but they require large and diverse datasets for training. This work presents a new dataset and benchmark called $\nabla^2$DFT that is based on the nablaDFT. It contains twice as much molecular structures, three times more conformations, new data types and tasks, and state-of-the-art models. The dataset includes energies, forces, 17 molecular properties, Hamiltonian and overlap matrices, and a wavefunction object. All calculations were performed at the DFT level ($\omega$B97X-D/def2-SVP) for each conformation. Moreover, $\nabla^2$DFT is the first dataset that contains relaxation trajectories for a substantial number of drug-like molecules. We also introduce a novel benchmark for evaluating NNPs in molecular property prediction, Hamiltonian prediction, and conformational optimization tasks. Finally, we propose an extendable framework for training NNPs and implement 10 models within it.

3D mesh segmentation is an important task with many biomedical applications. The human body has bilateral symmetry and some variations in organ positions. It allows us to expect a positive effect of rotation and inversion invariant layers in convolutional neural networks that perform biomedical segmentations. In this study, we show the impact of weight symmetry in neural networks that perform 3D mesh segmentation. We analyze the problem of 3D mesh segmentation for pathological vessel structures (aneurysms) and conventional anatomical structures (endocardium and epicardium of ventricles). Local geometrical features are encoded as sampling from the signed distance function, and the neural network performs prediction for each mesh node. We show that weight symmetry gains from 1 to 3% of additional accuracy and allows decreasing the number of trainable parameters up to 8 times without suffering the performance loss if neural networks have at least three convolutional layers. This also works for very small training sets.

Atrial fibrillation (AF) is one of the most common arrhythmias with challenging public health implications. Therefore, automatic detection of AF episodes on ECG is one of the essential tasks in biomedical engineering. In this paper, we applied the recently introduced method of compressor-based text classification with gzip algorithm for AF detection (binary classification between heart rhythms). We investigated the normalized compression distance applied to RR-interval and $\Delta$RR-interval sequences ($\Delta$RR-interval is the difference between subsequent RR-intervals). Here, the configuration of the k-nearest neighbour classifier, an optimal window length, and the choice of data types for compression were analyzed. We achieved good classification results while learning on the full MIT-BIH Atrial Fibrillation database, close to the best specialized AF detection algorithms (avg. sensitivity = 97.1\%, avg. specificity = 91.7\%, best sensitivity of 99.8\%, best specificity of 97.6\% with fivefold cross-validation). In addition, we evaluated the classification performance under the few-shot learning setting. Our results suggest that gzip compression-based classification, originally proposed for texts, is suitable for biomedical data and quantized continuous stochastic sequences in general.

There are hundreds of methods for analysis of data obtained in mRNA-sequencing. The most of them are focused on small number of genes. In this study, we propose an approach that reduces the analysis of several thousand genes to analysis of several clusters. The list of genes is enriched with information from open databases. Then, the descriptions are encoded as vectors using the pretrained language model (BERT) and some text processing approaches. The encoded gene function pass through the dimensionality reduction and clusterization. Aiming to find the most efficient pipeline, 180 cases of pipeline with different methods in the major pipeline steps were analyzed. The performance was evaluated with clusterization indexes and expert review of the results.

Heart rate variability (HRV) indices describe properties of interbeat intervals in electrocardiogram (ECG). Usually HRV is measured exclusively in normal sinus rhythm (NSR) excluding any form of paroxysmal rhythm. Atrial fibrillation (AF) is the most widespread cardiac arrhythmia in human population. Usually such abnormal rhythm is not analyzed and assumed to be chaotic and unpredictable. Nonetheless, ranges of HRV indices differ between patients with AF, yet physiological characteristics which influence them are poorly understood. In this study, we propose a statistical model that describes relationship between HRV indices in NSR and AF. The model is based on Mahalanobis distance, the k-Nearest neighbour approach and multivariate normal distribution framework. Verification of the method was performed using 10 min intervals of NSR and AF that were extracted from long-term Holter ECGs. For validation we used Bhattacharyya distance and Kolmogorov-Smirnov 2-sample test in a k-fold procedure. The model is able to predict at least 7 HRV indices with high precision.