In the present paper, we study dynamical systems generated by stochastic operators which are superpositions of extremal Volterra and non-Volterra quadratic stochastic operators defined on the two-dimensional simplex. It is described the set of all periodic and the set of all fixed points of such operators. Further for such operator we showed that for an initial point their trajectory either converges to a periodic trajectory or diverges.
The paper analyses the correlation of change in word concreteness ratings with semantic change. To perform the analysis, we apply a neural network to diachronic data to obtain concreteness ratings of English words. As input to the model, we use co-occurrence statistics with the most frequent words extracted from the Google Books Ngram diachronic corpus. It is shown that the model, initially trained on data averaged over a long time interval, predicts the concreteness ratings with high accuracy (based on the word co-occurrence data in a particular year). The impact of lexical semantic change on the change in the concreteness rating is analyzed using 69 words borrowed from previous works. As the considered cases show, the neural network estimate of the word concreteness rating is very sensitive to changes in semantics. Among the factors that influence changes in the concreteness rating, we reveal the emergence of new meanings of a word, the competition of word meanings related to different parts of speech, the use of a word as a proper name, and the use of the word as a part of collocations. It is shown in the paper that changes in the concreteness rating can (along with changes in other word properties) serve as a marker of semantic change.
This article focuses on the analysis of quasilinear equations influenced by the two-phase operator, commonly referred to as the ‘‘double-phase operator’’, while also incorporating a non-linear boundary condition. We prove the multiplicity of solutions through the utilization the method of Nehari manifold, complemented through the utilization of comparative techniques and critical point theory. Furthermore, determine the polarity of these solutions, distinctly identifying one as positive, another as negative, and a third as nodal.
Neural networks are progressively assuming a larger role in individuals daily routines, as their complexity continues to grow. While the model demonstrates satisfactory performance when evaluated on the test data, it often yields unforeseen outcomes in real-world scenarios. To diagnose the source of these errors, understanding the decision-making process employed by the model becomes crucial. In this paper, we consider various methods of interpreting the BERT model in classification tasks, and also consider methods for evaluating interpretation methods using vector representations fastText, GloVe and Sentence-BERT.
We prove some new Berezin number inequalities for sums and products of operators acting on a reproducing kernel Hilbert space. Among other applications of our inequalities, we present refinements of the triangle inequality for the Berezin norm.
The object of research is solvability of a boundary value problem with a nonlocal condition for an equation of elliptic-hyperbolic type of the second kind. Characteristic of boundary value problem is arbitrarily divided into two parts and the Bitsadze–Samarsky condition is given on one part. The second part is freed from the boundary condition and this missing Bitsadze–Samarsky condition is replaced by an analog Frankl conditions on the degeneracy interval. The uniqueness of the solution to the problem is proved, using the extremum principle method. The existence of a solution to the problem is proved, using the theories of singular integral equations and by the Wiener–Hopf equation. As a result, formulated and proved the solvability theorem for the posed problem.
We study constant expansions of quite o-minimal theories. We prove that any non-essential expansion (expansion by finitely many new constants) of a quite o-minimal Ehrenfeucht theory of finite convexity rank preserves Ehrenfeuchtness. We also establish that the countable spectrum of such an expanded theory is not decreased.
Given second-order Ito stochastic equations, we construct almost surely equivalent stochastic equations of the Lagrangian structure. We establish the conditions for the direct and indirect analytical representations of the Lagrangian in the presence of random perturbations. The results obtained are illustrated by examples.
Summarization aims at discovering a small set of typical subsequences (patterns) in the given long time series that represent the whole series. Further, one can implement unsupervised labeling of the given time series by assigning each subsequence a tag that corresponds to its most similar pattern. In the previous research, we developed the PSF (Parallel Snippet-Finder) algorithm for the time series summarization on GPU, where a snippet is the given-length subsequence, which is similar to many other subsequences w.r.t. the bespoke distance measure MPdist. However, PSF is limited by the demand that the snippet length be predefined by a domain expert. In this article, we introduce the novel parallel algorithm PaSTiLa (Parallel Snippet-based Time series Labeling) that discovers snippets and produces the labeling of the given time series on an HPC cluster with GPU nodes. As opposed to its predecessor, PaSTiLa employs the automatic selection of the snippet length from the specified range through our proposed heuristic criterion. In the experiments on labeling quality over time series from the TSSB (Time Series Segmentation Benchmark) dataset, PaSTiLa outperforms state-of-the-art segmentation-based competitors in average (textrm{F}_{1}) score. In the case of long-length time series (typically more than 8–10 K points), PaSTiLa outruns the rivals. Finally, over the million-length time series, our algorithm demonstrates a close-to-linear speedup.
We consider the singular integral operator acting between two weighted Hölder spaces and give an estimate for its norm.
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