Lukas Kuzma
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Lukas Kuzma has a total of 5 co-authors. Here are the top co-authors by number of shared publications:
- Igoris Belovas
Vilnius University
3 shared publications - Martynas Sabaliauskas
Vilnius University
3 shared publications - Povilas Daniušis
Neurotechnology Laisvės pr. 125A LT-06118 Vilnius Lithuania
1 shared publication - Shubham Juneja
Institute of Data Science and Digital Technologies, Vilnius University, Akademijos Str. 4, 08412 Vilnius, Lithuania
1 shared publication - Virginijus Marcinkevičius
Institute of Data Science and Digital Technologies, Vilnius University, Vilnius, Lithuania
1 shared publication
Latest Publications
- Open Access
- 1 January 2026
- Published by Vilnius University Press in Informatica
- p. 1-27
Visualization of Mandelbulbs Associated with the Zeta Functions
This research builds upon our previous work on efficient algorithms for calculating and visualizing fractal structures associated with zeta functions, shifting the focus from two-dimensional to three-dimensional structures. Specifically, we introduce Zetabulbs – a class of Mandelbulbs (three-dimensional analogues of Mandelbrot sets) derived from the zeta functions. The visualization of Mandelbulbs poses substantial computational and algorithmic challenges, while also carrying practical relevance in areas such as digital visual effects, where Mandelbulb-based structures have been used in the production of high-budget films. By introducing Zetabulbs, we expand the landscape of zeta-function–driven fractal geometry and open new opportunities for its application in both artistic visualization and scientific exploration.
- 1 January 2026
- Published by Vilnius University Press in Informatica
- p. 1-27
Open AccessVisualization of Mandelbulbs Associated with the Zeta Functions
This research builds upon our previous work on efficient algorithms for calculating and visualizing fractal structures associated with zeta functions, shifting the focus from two-dimensional to three-dimensional structures. Specifically, we introduce Zetabulbs – a class of Mandelbulbs (three-dimensional analogues of Mandelbrot sets) derived from the zeta functions. The visualization of Mandelbulbs poses substantial computational and algorithmic challenges, while also carrying practical relevance in areas such as digital visual effects, where Mandelbulb-based structures have been used in the production of high-budget films. By introducing Zetabulbs, we expand the landscape of zeta-function–driven fractal geometry and open new opportunities for its application in both artistic visualization and scientific exploration.
- Open Access
Measuring Statistical Dependence via Characteristic Function IPM
We study statistical dependence in the frequency domain using the integral probability metric (IPM) framework. We propose the uniform Fourier dependence measure (UFDM) defined as the uniform norm of the difference between the joint and product-marginal characteristic functions. We provide a theoretical analysis, highlighting key properties, such as invariances, monotonicity in linear dimension reduction, and a concentration bound. For the estimation of the UFDM, we propose a gradient-based algorithm with singular value decomposition (SVD) warm-up and show that this warm-up is essential for stable performance. The empirical estimator of UFDM is differentiable, and it can be integrated into modern machine learning pipelines. In experiments with synthetic and real-world data, we compare UFDM with distance correlation (DCOR), Hilbert–Schmidt independence criterion (HSIC), and matrix-based Rényi’s -entropy functional (MEF) in permutation-based statistical independence testing and supervised feature extraction. Independence test experiments showed the effectiveness of UFDM at detecting some sparse geometric dependencies in a diverse set of patterns that span different linear and nonlinear interactions, including copulas and geometric structures. In feature extraction experiments across 16 OpenML datasets, we conducted 160 pairwise comparisons: UFDM statistically significantly outperformed other baselines in 20 cases and was outperformed in 13.Open AccessMeasuring Statistical Dependence via Characteristic Function IPM
We study statistical dependence in the frequency domain using the integral probability metric (IPM) framework. We propose the uniform Fourier dependence measure (UFDM) defined as the uniform norm of the difference between the joint and product-marginal characteristic functions. We provide a theoretical analysis, highlighting key properties, such as invariances, monotonicity in linear dimension reduction, and a concentration bound. For the estimation of the UFDM, we propose a gradient-based algorithm with singular value decomposition (SVD) warm-up and show that this warm-up is essential for stable performance. The empirical estimator of UFDM is differentiable, and it can be integrated into modern machine learning pipelines. In experiments with synthetic and real-world data, we compare UFDM with distance correlation (DCOR), Hilbert–Schmidt independence criterion (HSIC), and matrix-based Rényi’s -entropy functional (MEF) in permutation-based statistical independence testing and supervised feature extraction. Independence test experiments showed the effectiveness of UFDM at detecting some sparse geometric dependencies in a diverse set of patterns that span different linear and nonlinear interactions, including copulas and geometric structures. In feature extraction experiments across 16 OpenML datasets, we conducted 160 pairwise comparisons: UFDM statistically significantly outperformed other baselines in 20 cases and was outperformed in 13. - Open Access
- 29 May 2022
- Published by MDPI AG in Fractal and Fractional
- Vol. 6 (6) , 300
Series with Binomial-like Coefficients for the Investigation of Fractal Structures Associated with the Riemann Zeta Function
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.
- 29 May 2022
- Published by MDPI AG in Fractal and Fractional
- Vol. 6 (6) , 300
Open AccessSeries with Binomial-like Coefficients for the Investigation of Fractal Structures Associated with the Riemann Zeta Function
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.
- Open Access
- 10 May 2022
- Published by MDPI AG in Preprints.org
Series with Binomial-Like Coefficients for the Investigation of Fractal Structures Associated with the Riemann Zeta Function
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.
- 10 May 2022
- Published by MDPI AG in Preprints.org
Open AccessSeries with Binomial-Like Coefficients for the Investigation of Fractal Structures Associated with the Riemann Zeta Function
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.