This paper compares Random Forest classification and regression approaches for equity trading strategy development using Zigzag-based price labeling. Both models are trained to identify buy and sell signals derived from Zigzag pivot points and are evaluated against a buy-and-hold benchmark using three exchange-traded funds: S&P 500, Hang Seng, and MSCI UK. A walk-forward framework is implemented using five-year training windows and two-year out-of-sample test windows. The results indicate that the Random Forest classification strategy delivers the strongest performance, particularly in the Hong Kong market, and is found to statistically significantly outperform the regression strategy. Further analysis of pivot timing shows that both models exhibit higher accuracy in predicting buy signals than sell signals, suggesting an asymmetry in model effectiveness across market turning points. As Zigzag labels are retrospective by construction, thus results should be interpreted as an upper bound on achievable performance rather than a direct estimate of live trading returns.

Reliable prediction of financial market movements remains a challenging task due to high volatility, complex interdependencies, and sensitivity to external shocks. This study assessed the performance of advanced machine learning models, including long short-term memory (LSTM), gated recurrent unit (GRU), transformer networks, extreme gradient boosting (XGBoost), and deep multi-layer perceptron (DMLP), as well as proposes their ensemble combinations, in forecasting daily closing prices of five major stock indices (S&P 500, NASDAQ-100, Dow Jones Industrial Average, FTSE 100, and DAX). Results indicate that although all models achieved high predictive accuracy, profitability outcomes varied substantially across models and markets. Among single-model approaches, LSTM generally exhibited more stable positive returns in several indices, while other models showed pronounced variability depending on market conditions. Meanwhile ensemble strategies frequently ranked among the top-performing configurations, often matching or exceeding the performance of adaptive weighting schemes. Performance was strongly index-dependent, with S&P 500 and NASDAQ100 exhibiting comparatively stronger profitability, whereas FTSE and Dow Jones showed weaker and alone is insufficient for profitable trading, underscoring the importance of financial performance metrics, such as total return, drawdown, and risk-adjusted measures, when evaluating predictive models.

Apžvelgiama, remiantis pirminių šaltinių duomenimis, studentų priėmimo į Vilniaus universiteto Matematikos fakulteto (1991–1999 m.m.) bei Matematikos ir informatikos fakulteto (1999–2024 m.m.) pagrindinių studijų matematikos ir informatikos krypčių specialybes raida.

Apžvelgiama, remiantis pirminių šaltinių duomenimis, priėmimo į matematines specialybes raida Vilniaus universiteto Fizikos ir matematikos (1945–1965), Matematikos ir mechanikos (1966–1977) bei Matematikos (1978–1990) fakultete.

The prime zeta function is one of the most under-researched varieties of the class. Very little is known about the irregular distribution of its zeros. The presented study aims - albeit partially - to fill the gap in our understanding of the subject. We consider the zero-free region of the prime zeta function and verify statistically certain conjectures regarding the distribution patterns of the zeroes of the prime zeta function.

Assessing credit risk is essential when making financial decisions, especially investing in debt securities. As the bond market is the largest securities market in the world, a great demand exists for tools to assess issuer creditworthiness. Furthermore, information describing the probability of default is also useful in other areas, such as risk management. In the era of machine learning and big data, new techniques have emerged that allow for automated risk assessment based on large amounts of data. Traditional creditworthiness assessment methods may be inaccurate, as the investor could be biased or misinterpret available information. A review and comparison of modern tools that would allow intelligent processing of large amounts of information will help assess the issuer's credit risk as objectively as possible.

Numbers satisfying a class of triangular arrays, defined by a bivariate first-order linear difference equation with linear coefficients, include a wide range of combinatorial numbers: binomial coefficients, Morgan numbers, Stirling numbers of the first and the second types, non-central Stirling numbers, Eulerian numbers, Lah numbers, and their generalizations. In this work, we derive the general analytic expression of the numbers satisfying a class of triangular arrays and propose problems (both teaching and unsolved ones) for undergraduates studying probability theory and analytical combinatorics subjects in the study programs of the fields of mathematics and computer science. Some of the unsolved challenges can also be used as the basis for a thesis.

We consider an inequality concerning absolute values of the Riemann zeta function at places symmetric with respect to the critical line. The study concludes the investigations started by Spira and complements Trudgian's results.

The Baltic States equity market is a challenge for investors and financial analysts. Unfortunately strong assivity is observed in ``young'' markets, therefore any (Gaussian, α-stable etc) distribution fitting tests (Anderson–Darling, Kolmogorov–Smirnov, etc.) are poorly applicable. Improvement based on mixed distributions is proposed and its adequacy in the Baltic States market is tested. In this paper we use Koutrouvelis goodness-of-fit test and modified χ2 test.

The twin primes conjecture states that there are infinitely many twin primes. While studying this hypothesis, many important results were obtained, but the problem remains unsolved. In this work, the problem is studied from the side of experimental mathematics. Using the probabilistic Miller–Rabin primality test and parallel computing technologies, the distribution of prime pairs in the intervals (2n; 2n+1] is studied experimentally.

The paper investigates the asymptotic behavior of the geometric polynomials, when the polynomial degree tends to infinity. Using the contour integration technique, we obtain an asymptotic formula, given explicitly in terms of the polynomial degree and variable. This type of asymptotics will be applied to derive limit theorems for combinatorial numbers.

The article presents formulas for powers of repdigits in the different numeral systems. This task can be used as an exercise for computer science students to help them master the corresponding mathematical apparatus.

The paper extends the research on the series with binomial-like coefficients for the computation of zeta functions on the complex plane. It offers alternative perspectives on the proof of central limit theorems for the coefficients of the series. The moment generating function of the coefficients and exact expressions for the first moments of the coefficients of the series are established.

In this paper, we continue the study of efficient algorithms for the computation of the Riemann zeta function on the complex plane. We introduce two precalculated arrays-based modifications of MB-method. We perform numerical experiments with these algorithms using Zetafast as a benchmark and apply the algorithms for the visualizations of fractal structures associated with the Riemann zeta function.

In this paper, we study limit theorems for numbers satisfying a class of triangular arrays, which are defined by a bivariate linear recurrence with bivariate linear coefficients. We obtain analytical expressions for the semi-exponential generating function of several classes of the numbers, including combinatorial numbers associated with Laguerre polynomials. We apply these results to prove the numbers' asymptotic normality and specify the convergence rate to the limiting distribution.

In this research we generalize our result for numbers satisfying the Delannoy triangle. We obtain a central limit theorem and a local limit theorem for weighted numbers of the triangle and establish the rate of convergence to the limiting (normal) distribution.

The paper extends the study of efficient algorithms for the computation of the Riemann zeta function on the complex plane. It is dedicated to numerical aspects of the implementation of the algorithm. Since the straightforward computation of the coefficients of the method is difficult and time-consuming, we propose a new perspective, taking into account the asymptotic normality of the coefficients. We show that the presented approach accelerates computations of the Riemann zeta function. To increase the performance, we propose several modifications of the algorithm for the Riemann zeta function. We compare both ordinary and parallel versions and evaluate accuracy, efficiency, and speedup.

The paper continues the study of efficient algorithms for the computation of zeta functions over the complex plane. We aim to apply the modifications of algorithms to the investigation of underlying fractal structures associated with the Riemann zeta function. We discuss the computational complexity and numerical aspects of the implemented algorithms based on series with binomial-like coefficients.

The paper extends the investigations of limit theorems for numbers satisfying a class of triangular arrays. We obtain analytical expressions for the semiexponential generating function the numbers, associated with Hermite polynomials. We apply the results to prove the asymptotic normality of the numbers and specify the convergence rate to the limiting distribution.