Projects

Viktor Witkovský

International projects

Precision Neuromodulation for Chronic Pain: Integrating Functional MRI and Focused Ultrasound for Personalised Treatment
Presná neuromodulácia chronickej bolesti: Integrácia funkčnej magnetickej rezonancie a fokusovaného ultrazvuku pre personalizovanú liečbu, skratka „NeuroPain“
Program:	ERANET
Duration:	1.1.2026 – 31.8.2028
Project leader:	Doc. RNDr. Witkovský Viktor, CSc.

National projects

CAUSMET – Methods and algorithms for causal analysis and quantification of measurement uncertainty
Názov projektu Metódy a algoritmy kauzálnej analýzy a kvantifikácie neistôt meraní
Program:	SRDA
Duration:	1.9.2026 – 31.12.2029
Project leader:	Doc. RNDr. Witkovský Viktor, CSc.
Annotation:	The project develops advanced methods and algorithms for causal analysis of stochastic and deterministic processes and for quantifying measurement uncertainties. It addresses methodological challenges in the analysis of time series and dynamical data, where correlation alone is insufficient to reveal the mechanisms governing system behavior. Manyapplications, therefore, require identifying causal relations between variables while reliably characterizing uncertainties arising from measurement processes, noise, and incomplete observations.The project will develop classical and modern approaches to causal analysis of time series based on probabilistic and statistical modeling, and integrate them with algorithms enabling statistical inference and prediction in the presence of randomness, measurement errors, and uncertainty.Modern applications in physical, biomedical, economic, environmental, and linguistic measurements, as well as in the social sciences (education, psychology), generate large and complex datasets with intricate dependence structures and temporal dynamics. A significant project component is hence the study of stochastic dynamical models, including diffusion processes, as a natural framework for modeling random dynamics observed via measurement time series. When modeling complex temporal or spatio-temporal data using kriging, causal structure will serve as a key starting point.The project also advances uncertainty methods for quantifying measurement uncertainties in line with modern metrology and aims to establish a unified methodological framework combining causal analysis, dynamical modeling, and statistical inference and forecasting. Interdisciplinary collaboration among the Institute of Measurement Science of the SAS, theMathematical Institute of the SAS, and the Faculty of Science of P. J. Šafárik University creates favorable conditions for the development of new theoretical results, efficient algorithms, and their applications.

VERISCAN – Metrological framework for the verification of dynamic 3D scanning systems according to ISO GPS in digital manufacturing
Metrologický rámec verifikácie dynamických 3D skenovacích systémov podľa ISO GPS v podmienkach digitálnej výroby
Program:	SRDA
Duration:	1.9.2026 – 31.8.2029
Project leader:	Doc. RNDr. Witkovský Viktor, CSc.
Annotation:	The project addresses the lack of a comprehensive methodological framework for the verification of handheld 3D scanning systems. Despite their massive implementation in digital manufacturing (Industry 4.0/5.0), their metrological assurance lags behind technical hardware capabilities. The core scientific challenge is the missing link between the variable nature of handheld scanning (operator influence, trajectory, strategy) and the strict requirements of the Geometrical ProductSpecifications (ISO GPS) system.The objective is to research and develop a metrological framework that transforms handheld 3D scanning from avisualization tool into a full-fledged system for product conformity decision-making. The project focuses on developing specialized reference artifacts with complex geometry designed for dynamic optical systems. It uniquely combines the technological expertise of UNIZA in digital quality control with the fundamental metrological competencies of the Institute of Measurement SAS in calibration and uncertainty estimation (GUM).The original contribution is an ISO GPS-oriented verification methodology that systematically integrates dynamic measurement uncertainty sources into final conformity assessment. The outputs include a physical reference artifact with SI traceability and verified procedures for the automotive and machinery industries. The project directly supports digital manufacturing chains by enhancing production quality and reducing non-conformance costs through metrologically correctvalidation of complex components.

Characteristic function-based goodness-of-fit test for fuzzy data with application to climate analysis
Testy dobrej zhody založené na charakteristickej funkcii pre neurčité údaje s aplikáciou na analýzu klimatických dát
Program:	SRDA
Duration:	1.1.2026 – 31.8.2028
Project leader:	Doc. RNDr. Witkovský Viktor, CSc.
Annotation:	Modern research faces growing data uncertainty from measurement errors, gaps, and subjective assessments. Traditional statistical methods, assuming precise data, often fail under such conditions. Fuzzy data, which capture vagueness and imprecision, offer a natural framework, yet robust statistical tools for them remain scarce. This interdisciplinary project — combining probability and mathematical statistics, applied mathematics, and measurement science — aims to develop a goodness-of-fit test based on characteristic functions for fuzzy and interval-valued data. This novel methodology addresses both theoretical and applied challenges, with a focus on climate analysis. Objectives include: (1) Developing theoretical and empirical characteristic functions for fuzzy data, defining distance measures, formulating the test, and deriving its statistical properties. (2) Designing and implementing efficient algorithms in R, MATLAB, or Python. (3) Evaluating performance through simulations and benchmarking against existing methods. (4) Applying the method to real climate datasets (e.g., temperature, rainfall) to demonstrate its relevance under uncertainty. The methodology leverages the uniqueness and computational benefits of characteristic functions, extended to fuzzy settings. The project innovatively integrates characteristic functions and fuzzy theory for hypothesis testing, providing a statistically rigorous yet practical approach to imprecise data analysis. Expected outcomes include: a new statistical test, open-source software, simulation and benchmark studies, case studies on climate data, and preparation of a publication in leading journal. This bilateral project brings together expertise in fuzzy theory (University of Montenegro) and measurement science (Institute of Measurement Science of the Slovak Academy of Sciences).

Theoretical properties and applications of special families of probability distributions
Teoretické vlastnosti a aplikácie špeciálnych tried rozdelení pravdepodobnosti
Program:	VEGA
Duration:	1.1.2024 – 31.12.2027
Project leader:	Doc. RNDr. Witkovský Viktor, CSc.
Annotation:	In the project, problems related to probability distributions and their applications in mathematical modeling will be studied. We will analyze some classes of distributions (distributions generated by partial summations, the Schröter family) and study properties of distributions belonging to these classes. Issues related to calibration regression models will be addressed. New methods for solving multivariate statistical problems will be developed. These methods will be based on the calculation of exact probability distributions using the inverse transformation of the characteristic function of the distribution of the output variable. Entropy, another property of probability distributions, plays an important role in detecting causality in time series. The primary area of application is theuse of the distribution of test statistics in hypothesis testing. The new results obtained during the solution of the project will also be applied to mathematical modeling in metrology, linguistics and actuarial mathematics.