arXiv subjects

Kateryna Melnyk

Publications and source records attributed to Kateryna Melnyk.

6 recordsLinked to original sources

arXiv2026

Gaze Prediction as Time-Series Forecasting for Virtual Reality Applications: Quantifying Performance Variability and Extreme-Case Errors

Gaze prediction is essential for addressing motion-to-photon latency and ensuring seamless foveated rendering in Virtual Reality. The reliability of gaze forecasting is highly sensitive to individual differences and the eye movements being predicted. We evaluate recurrent, transformer-based, and classification-guided architectures to assess their generalization capabilities across oculomotor events. Using the GazeBase VR and Meta Quest Pro datasets, we analyzed the relationship between the median (P50) and high-percentile (P95) error profiles across subjects. The analysis reveals significant performance variability, showing that subjects with low P50 errors do not always exhibit the lowest extreme-case errors. Consequently, low median errors do not guarantee the robustness of the utilized solution. We discuss inference performance and address the class imbalance problem in short-term gaze prediction. These results identify a gap in standardized evaluation methods, necessitating a shift toward P95-focused, subject-specific metrics to develop reliable and perceptually stable gaze-contingent systems.

cs.HC↗

arXiv2025

Gaze Prediction as a Function of Eye Movement Type and Individual Differences

Eye movement prediction is a promising area of research with the potential to improve performance and the user experience of systems based on eye-tracking technology. In this study, we analyze individual differences in gaze prediction performance. We use three fundamentally different models within the analysis: the lightweight Long Short-Term Memory network (LSTM), the transformer-based network for multivariate time series representation learning (TST), and the Oculomotor Plant Mathematical Model wrapped in the Kalman Filter framework (OPKF). Each solution was assessed on different eye-movement types. We show important subject-to-subject variation for all models and eye-movement types. We found that fixation noise is associated with poorer gaze prediction in fixation. For saccades, higher velocities are associated with poorer gaze prediction performance. We think these individual differences are important and propose that future research should report statistics related to inter-subject variation. We also propose that future models should be designed to reduce subject-to-subject variation.

cs.HC↗

arXiv2022

Understanding microbiome dynamics via interpretable graph representation learning

Large-scale perturbations in the microbiome constitution are strongly correlated, whether as a driver or a consequence, with the health and functioning of human physiology. However, understanding the difference in the microbiome profiles of healthy and ill individuals can be complicated due to the large number of complex interactions among microbes. We propose to model these interactions as a time-evolving graph whose nodes are microbes and edges are interactions among them. Motivated by the need to analyse such complex interactions, we develop a method that learns a low-dimensional representation of the time-evolving graph and maintains the dynamics occurring in the high-dimensional space. Through our experiments, we show that we can extract graph features such as clusters of nodes or edges that have the highest impact on the model to learn the low-dimensional representation. This information can be crucial to identify microbes and interactions among them that are strongly correlated with clinical diseases. We conduct our experiments on both synthetic and real-world microbiome datasets.

q-bio.QM↗

arXiv2020

GraphKKE: Graph Kernel Koopman Embedding for Human Microbiome Analysis

More and more diseases have been found to be strongly correlated with disturbances in the microbiome constitution, e.g., obesity, diabetes, or some cancer types. Thanks to modern high-throughput omics technologies, it becomes possible to directly analyze human microbiome and its influence on the health status. Microbial communities are monitored over long periods of time and the associations between their members are explored. These relationships can be described by a time-evolving graph. In order to understand responses of the microbial community members to a distinct range of perturbations such as antibiotics exposure or diseases and general dynamical properties, the time-evolving graph of the human microbial communities has to be analyzed. This becomes especially challenging due to dozens of complex interactions among microbes and metastable dynamics. The key to solving this problem is the representation of the time-evolving graphs as fixed-length feature vectors preserving the original dynamics. We propose a method for learning the embedding of the time-evolving graph that is based on the spectral analysis of transfer operators and graph kernels. We demonstrate that our method can capture temporary changes in the time-evolving graph on both created synthetic data and real-world data. Our experiments demonstrate the efficacy of the method. Furthermore, we show that our method can be applied to human microbiome data to study dynamic processes.

q-bio.QM↗

arXiv2019

The semigroup of star partial homeomorphisms of a finite deminsional Euclidean space

In the paper the notion of a star partial homeomorphism of a finite dimensional Euclidean space $\mathbb{R}^n$ is introduced. We describe the structure of the semigroup $\mathbf{PStH}_{\mathbb{R}^n}$ of star partial homeomorphisms of the space $\mathbb{R}^n.$ The structure of the band of $\mathbf{PStH}_{\mathbb{R}^n}$ and Green's relations on $\mathbf{PStH}_{\mathbb{R}^n}$ are described. We show that $\mathbf{PStH}_{\mathbb{R}^n}$ is a bisimple inverse semigroup and every non-unit congruence on $\mathbf{PStH}_{\mathbb{R}^n}$ is a group congruence.

math.GR↗

arXiv2019

The semigroup of monotone co-finite partial homeomorphisms of the real line

In the paper we investigate the semigroup of monotone co-finite partial homeomorphisms of the space of the usual real line $\mathbb{R}$. We prove that the inverse semigroup $\mathscr{P\!\!H}^+_{\!\!\operatorname{\textsf{cf}}}\!(\mathbb{R})$ is factorizable and $F$-inverse. We describe the structure of the band of the semigroup $\mathscr{P\!\!H}^+_{\!\!\operatorname{\textsf{cf}}}\!(\mathbb{R})$, its two-sided ideals, maximal subgroups and Green's relations. We prove that the quotient semigroup $\mathscr{P\!\!H}^+_{\!\!\operatorname{\textsf{cf}}}\!(\mathbb{R})/\mathfrak{C}_{\textsf{mg}}$, where $\mathfrak{C}_{\textsf{mg}}$ is the maximum group congruence on $\mathscr{P\!\!H}^+_{\!\!\operatorname{\textsf{cf}}}\!(\mathbb{R})/\mathfrak{C}_{\textsf{mg}}$, is isomorphic to the group of all oriental homeomorphisms of the space $\mathbb{R}$, and showe that the semigroup $\mathscr{P\!\!H}^+_{\!\!\operatorname{\textsf{cf}}}\!(\mathbb{R})$ is isomorphic to a semidirect product $\mathscr{H}^+\!(\mathbb{R})\ltimes_\mathfrak{h}\mathscr{P}_{\!\infty}(\mathbb{R})$ of the free semilattice with unit $(\mathscr{P}_{\!\infty}(\mathbb{R}),\cup)$ by the group $\mathscr{H}^+\!(\mathbb{R})$.

math.GR↗