Факультет інформатики

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Development of an iOS Application for Task Planning with Consideration of the User’s Emotional State
(2025) Piz, Mariana; Nahirna, Alla
The article focuses on the development of a digital tool designed to address the problem of decreased productivity caused by emotional exhaustion. The main objective of the study is to create an iOS application for task planning that takes into account the user’s emotional state, offers mindful breaks for emotional awareness and recovery, and provides analytics on emotional trends. The research includes a comparative analysis of existing software solutions in the areas of time management and mental well-being. During the development process, modern frameworks, tools, and architectural patterns for iOS development were analyzed. An adaptive planning algorithm was implemented, that takes into accountboth the user’s emotional feedback and the attributes of tasks. As a result of the research, a mobile application named Moodpace was developed using Swift, with SwiftUI for building the user interface, SwiftData for data persistence, and the MVVM architectural pattern to ensure maintainable code structure. During the development process, SwiftLint was used for static code analysis, and SwiftFormat was integrated for automatic code formatting. The app was localized into Ukrainian using String Catalog. The developed application is designed to help users manage their tasks while maintaining balance with their mental well-being. It is suitable for everyday use and especially beneficial for individuals with flexible schedules.
Energy Conservation for Autonomous Agents Using Reinforcement Learning
(2025) Beimuk, Volodymyr; Kuzmenko, Dmytro
Reinforcement learning (RL) has shown strong potential in autonomous racing for its adaptability to complex and dynamic driving environments. However, most research prioritizes performance metrics such as speed and lap time. Limited consideration is given to improving energy efficiency, despite its increasing importance in sustainable autonomous systems. This work investigates the capacity of RL agents to develop multi-objective driving strategies that balance lap time and fuel consumption by incorporating a fuel usage penalty into the reward function. To simulate realistic uncertainty, fuel usage is excluded from the observation space, forcing the agent to infer fuel consumption indirectly. Experiments are conducted using the Soft Actor-Critic algorithm in a high-fidelity racing simulator, Assetto Corsa, across multiple configurations of vehicles and tracks. We compare various penalty strengths against the non-penalized agent and evaluate fuel consumption, lap time, acceleration and braking profiles, gear usage, engine RPM, and steering behavior. Results show that mild to moderate penalties lead to significant fuel savings with minimal or no loss in lap time. Our findings highlight the viability of reward shaping for multi-objective optimization in autonomous racing and contribute to broader efforts in energy-aware RL for control tasks. Results and supplementary material are available on our project website.
Fractional calculus and its application in financial mathematics
(2024) Zubritska, Dariia; Shchestyuk, Nataliya; Sluchynskyi, Dmytro
Fractional calculus extends classical calculus by allowing differentiation and integration of non-integer orders, providing valuable tools for analyzing complex systems. In this part of the paper we demonstrate the main methods of fractional calculus, including Euler’s, Riemann-Liouville, and Caputo approaches. The behavior of functions such as xn, eλx, and sin(x) is analyzed for fractional orders, demonstrating how fractional differentiation results in varying patterns of growth and decay. The second part explores the application of fractal derivatives in financial mathematics. We present the use of the Riemann-Liouville derivative to model stock prices in illiquid markets, where the price of an asset may remain unchanged for some time. For this, subdiffusion processes and a fractal integrodifferential equation with the Riemann-Liouville derivative are used. The idea of subdiffusion models is to replace the calendar time t in the risk-free bond motion and classical GBM by some stochastic process Ht, which represents a hitting time, which is interpreted as the first time at which Gt hits the barrier t. Next, we focus on the pricing of a European option when the underlying asset is illiquid. The option price is found as a solution to a fractal Dupire integro-differential equation, in which the time derivative is replaced by the Dzerbayshan–Caputo (D-K) derivative. The D–K derivative is a generalization of the Caputo approach. The form of the D–K derivative depends on a random process Gt, called the subordinate. We take a standard inverse Gaussian process with parameters (1,1) as the subordinate Gt and formulate the Proposition about the form of the fractal Dupire equation for the chosen subordinate. These approaches provide tools that allow the investor to take into account the illiquidity of the financial markets.
Hybrid AI Model for Financial Market Prediction
(2025) Voitishyn, Mykyta; Kuzmenko, Dmytro
Financial time series modeling is increasingly complex due to volatility, unexpected breakouts, and the impact of external factors, such as macroeconomic indicators, investor sentiment, company fundamentals, and extreme shocks, like geopolitical events or market manipulations. This paper introduces a hybrid artificial intelligence framework that integrates traditional statistical methods, machine learning models, and Bayesian neural networks (BNNs) to improve predictive performance and uncertainty quantification in financial forecasting. The model leverages a variety of engineered features, including rolling statistics, technical indicators, anomaly scores, interpolated macroeconomic data, and transformer-based sentiment scores. A complete ablation study compares various architectures, including ARIMA, SARIMA, MLR, SNN, and BNN, across multiple prediction windows (1, 3, 5 days) and feature combinations. Results show that while linear models yield the lowest MSE for short-term predictions, they fail to capture non-linear dependencies and uncertainty. In contrast, BNNs offer more reliable mid-term predictions by estimating predictive distributions. The best BNN configuration (Normal distribution, constant variation, TanH activation, 1 hidden layer) achieved an MSE of 0.00022, confirming the advantage of uncertainty-adjusted modeling. Sentiment analysis and anomaly detection were especially impactful when combined with macroeconomic indicators, improving signal reliability and behavioral insight. Our findings highlight the importance of integrating diverse data sources and accounting for predictive uncertainty in financial applications. Additionally, the experiments revealed that compact network architectures often outperform deeper ones when paired with engineered features. All experiments were systematically tracked to ensure reproducibility and facilitate future model benchmarking.
Properties of the ideal-intersection graph of the ring Zn
(2023) Utenko, Yelizaveta
In this paper we study properties of the ideal-intersection graph of the ring 𝑍𝑛. The graph of ideal intersections is a simple graph in which the vertices are non-zero ideals of the ring, and two vertices (ideals) are adjacent if their intersection is also a non-zero ideal of the ring. These graphs can be referred to as the intersection scheme of equivalence classes (See: Laxman Saha, Mithun Basak Kalishankar Tiwary "Metric dimension of ideal-intersection graph of the ring 𝑍𝑛" [1] ). In this article we prove that the triameter of graph is equal to six or less than six. We also describe maximal clique of the ideal-intersection graph of the ring 𝑍𝑛. We prove that the chromatic number of this graph is equal to the sum of the number of elements in the zero equivalence class and the class with the largest number of element. In addition, we demonstrate that eccentricity is equal to 1 or it is equal to 2. And in the end we describe the central vertices in the ideal-intersection graph of the ring 𝑍𝑛.
Risk modelling approaches for student-like models with fractal activity time
(2021) Solomanchuk, Georgiy; Shchestyuk, Nataliia
The paper focuses on value at risk (V@R) measuring for Student-like models of markets with fractal activity time (FAT). The fractal activity time models were introduced by Heyde to try to encompass the empirically found characteristics of read data and elaborated on for Variance Gamma, normal inverse Gaussian and skewed Student distributions. But problem of evaluating an value at risk for this model was not researched. It is worth to mention that if we use normal or symmetric Student‘s models than V@R can be computed using standard statistical packages. For calculating V@R for Student-like models we need Monte Carlo method and the iterative scheme for simulating N scenarios of stock prices. We model stock prices as a diffusion processes with the fractal activity time and for modeling increments of fractal activity time we use another diffusion process, which has a given marginal inverse gamma distribution. The aim of the paper is to perform and compare V@R Monte Carlo approach and Markowitz approach for Student-like models in terms of portfolio risk. For this purpose we propose procedure of calculating V@R for two types of investor portfolios. The first one is uniform portfolio, where d assets are equally distributed. The second is optimal Markowitz portfolio, for which variance of return is the smallest out of all other portfolios with the same mean return. The programmed model which was built using R-statistics can be used as to the simulations for any asset and for construct optimal portfolios for any given amount of assets and then can be used for understanding how this optimal portfolio behaves compared to other portfolios for Student-like models of markets with fractal activity time. Also we present numerical results for evaluating V@R for both types of investor portfolio. We show that optimal Markowitz portfolio demonstrates in the most of cases the smallest possible Value at Risk comparing with other portfolios. Thus, for making investor decisions under uncertainty we recommend to apply portfolio optimization and value at risk approach jointly.
Validating Architectural Hypotheses in Neural Decision Trees with Neural Architecture Search
(2025) Mykytyshyn, Artem; Shvai, Nadiia
This article introduces an automated and unbiased framework for validating architectural hypotheses for neural network models, with a particular focus on Neural Decision Trees (NDTs). The proposed methodology employs Neural Architecture Search (NAS) as an unbiased tool to explore architectural variations and empirically assess theoretical claims. To demonstrate this framework, we investigate a hypothesis found in the literature: that the complexity of decision nodes in NDTs decreases monotonically with tree depth. This assumption, initially motivated by the task of monocular depth estimation, suggests that deeper nodes in the tree require fewer parameters due to simpler split functions. To rigorously test this hypothesis, we conduct a series of NAS campaigns over the CIFAR-10 image and fully connected layers, while all other architectural components are held constant to isolate the effect of node depth. By applying Tree-structured Parzen Estimator (TPE)-based NAS and evaluating over 300 architectures, we quantify complexity metrics across tree levels and analyze their correlations using Spearman’s rank coefficient. The results provide no statistical or visual evidence supporting the hypothesized trend: node complexity does not decrease with depth. Instead, complexity remains nearly constant across levels, regardless of tree depth or search space size. These results suggest that assumptions derived from specific applications may not generalize to other domains, underscoring the importance of empirical validation and careful searchspace design. The presented framework may serve as a foundation for verifying other structural assumptions across various neural network families and applications.
Аналіз програмних систем підтримки розумного будинку
(2019) Глибовець, Андрій; Моголівський, Віталій
Проведено аналіз досліджень у сфері "розумного будинку". Визначено ключові проблеми галузі. Розглянуто наявні Saas системи, здійснено порівняння між ними та знайдено сильні та слабкі сторони кожної із систем. Визначено ключові характеристики системи підтримки "розумного будинку".

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