Том 5

Permanent URI for this collection

https://ekmair.ukma.edu.ua/handle/123456789/24881

Browse

Browsing Том 5 by Subject "article"

Now showing 1 - 5 of 5
  • Thumbnail Image
    Item
    A solution of a finitely dimensional Harrington problem for Cantor set
    (2022) Kusinski, Slawomir
    In this paper we are exploring application of fusion lemma - a result about perfect trees, having its origin in forcing theory - to some special cases of a problem proposed by Leo Harrington in a book Analytic Sets. In all generality the problem ask whether given a sequence of functions from Rω to [0; 1] one can find a subsequence of it that is pointwise convergent on a product of perfect subsets of R. We restrict our attention mainly to binary functions on the Cantor set as well as outline the possible direction of generalization of result to other topological spaces and different notions of measurablity.
  • Thumbnail Image
    Item
    Regularization by Denoising for Inverse Problems in Imaging
    (2022) Kravchuk, Oleg; Kriukova, Galyna
    In this work, a generalized scheme of regularization of inverse problems is considered, where a priori knowledge about the smoothness of the solution is given by means of some self-adjoint operator in the solution space. The formulation of the problem is considered, namely, in addition to the main inverse problem, an additional problem is defined, in which the solution is the right-hand side of the equation. Thus, for the regularization of the main inverse problem, an additional inverse problem is used, which brings information about the smoothness of the solution to the initial problem. This formulation of the problem makes it possible to use operators of high complexity for regularization of inverse problems, which is an urgent need in modern machine learning problems, in particular, in image processing problems. The paper examines the approximation error of the solution of the initial problem using an additional problem.
  • Thumbnail Image
    Item
    Remarks on my algebraic problem of determining similarities between certain quotient boolean algebras
    (2022) Frankiewicz, Ryszard
    Remarks on my algebraic problem of determining similarities between certain quotient boolean algebras. In this paper we survey results about quotient boolean algebras of type P(κ)/fin(κ) and condition for them to be or not to be isomorphic for different cardinals к. Our consideration have their root in the classical result of Parovicenko and a less classical, nevertheless really considerable result about non-existence of P-points by S. Shellah. Our main point of interest are the algebras P(ω)/fin(ω) i P(ℵ1)/fin(ℵ1).
  • Thumbnail Image
    Item
    Speech audio modeling by means of causal moving average equipped gated attention
    (2022) Ivaniuk, Andrii
    In the paper we compare different attention mechanisms on the task of audio generation using unsupervised approaches following previous work in language modeling. It is important problem, as far as speech synthesis technology could be used to convert textual information into acoustic waveform signals. These representations can be conveniently integrated into mobile devices and used in such applications as voice messengers or email apps. Sometimes it is difficult to understand and read important messages when being abroad. The lack of appropriate computer systems or some security problems may arise. With this technology, e-mail messages can be listened quickly and efficiently on smartphones, boosting productivity. Apart from that, it is used to assist visually impaired people, so that, for instance, the screen content can be automatically read aloud to a blind user. Nowadays, home appliances, like slow cookers can use this system too for reading culinary recipes, automobiles for voice navigation to the destination spot, or language learners for pronunciation teaching. Speech generation is the opposite problem of automatic speech recognition (ASR) and is researched since the second half of the eighteen’s century. Also, this technology also helps vocally handicapped people find a way to communicate with others who do not understand sign language. However, there is a problem, related to the fact that the audio sampling rate is very high, thus lea,ding to very long sequences which are computationally difficult to model. Second challenge is that speech signals with the same semantic meaning can be represented by a lot of signals with significant variability, which is caused by channel environment, pronunciation or speaker timbre characteristics. To overcome these problems, we train an autoencoder model to discretize continuous audio signal into a finite set of discriminative audio tokens which have a lower sampling rate. Subsequently, autoregressive models, which are not conditioned on text, are trained on this representation space to predict the next token, based on previous sequence elements. Hence, this modeling approach resembles causal language modeling. In our study, we show that unlike in the original MEGA work, traditional attention outperforms moving average equipped gated attention, which shows that EMA gated attention is not stable yet and requires careful hyper-parameter optimization.
  • Thumbnail Image
    Item
    Two approaches for option pricing under illiquidity
    (2022) Pauk, Viktoriia; Petrenko, Oksana; Shchestyuk, Nataliya
    The paper focuses on option pricing under unusual behaviour of the market, when the price may not be changed for some time what is quite a common situation on the modern financial markets. There are some patterns that can cause permanent price gaps to form and lead to illiquidity. For example, global changes that have a negative impact on financial activity, or a small number of market participants, or the market is quite young and is just in the process of developing, etc. In the paper discrete and continuous time approaches for modelling market with illiquidity and evaluation option pricing were considered. Trinomial discrete time model improves upon the binomial model by allowing a stock price not only to move up, down but stay the same with certain probabilities, what is a desirable feature for the illiquid modelling. In the paper parameters for real financial data were identified and the backward induction algorithm for building call option price trinomial tree was applied. Subdiffusive continuous time model allows successfully apply the physical models for describing the trapping events to model financial data stagnation’s periods. In this paper the Inverse Gaussian process IG was proposed as a subordinator for the subdiffusive modelling of illiquidity and option pricing. The simulation of the trajectories for subordinator, inverse subordinator and subdiffusive GBM were performed. The Monte Carlo method for option evaluation was applied. Our aim was not only to compare these two models each with other, but also to show that both models adequately describe the illiquid market and can be used for option pricing on this market. For this purpose absolute relative percentage (ARPE) and root mean squared error (RMSE) for both models were computed and analysed. Thanks to the proposed approaches, the investor gets a tools, which allows him to take into account the illiquidity.