Modeling stochastic eye tracking data: A comparison of quantum generative adversarial networks and Markov models

We explore the use of quantum generative adversarial networks QGANs for modeling eye movement velocity data. We assess whether the advanced computational capabilities of QGANs can enhance the modeling of complex stochastic distribution beyond the traditional mathematical models, particularly the Markov model. The findings indicate that while QGANs demonstrate potential in approximating complex distributions, the Markov model consistently outperforms in accurately replicating the real data distribution. This comparison underlines the challenges and avenues for refinement in time series data generation using quantum computing techniques. It emphasizes the need for further optimization of quantum models to better align with real-world data characteristics.

A Time-aware tensor decomposition for tracking evolving patterns

Time-evolving data sets can often be arranged as a higher-order tensor with one of the modes being the time mode. While tensor factorizations have been successfully used to capture the underlying patterns in such higher-order data sets, the temporal aspect is often ignored, allowing for the reordering of time points. In recent studies, temporal regularizers are incorporated in the time mode to tackle this issue. Nevertheless, existing approaches still do not allow underlying patterns to change in time (e.g., spatial changes in the brain, contextual changes in topics). In this paper, we propose temporal PARAFAC2 (tPARAFAC2): a PARAFAC2-based tensor factorization method with temporal regularization to extract gradually evolving patterns from temporal data. Through extensive experiments on synthetic data, we demonstrate that tPARAFAC2 can capture the underlying evolving patterns accurately performing better than PARAFAC2 and coupled matrix factorization with temporal smoothness regularization.

Assessing the robustness of critical behavior in stochastic cellular automata

There is evidence that biological systems, such as the brain, work at a critical regime robust to noise, and are therefore able to remain in it under perturbations. In this work, we address the question of robustness of critical systems to noise. In particular, we investigate the robustness of stochastic cellular automata (CAs) at criticality. A stochastic CA is one of the simplest stochastic models showing criticality. The transition state of stochastic CA is defined through a set of probabilities. We systematically perturb the probabilities of an optimal stochastic CA known to produce critical behavior, and we report that such a CA is able to remain in a critical regime up to a certain degree of noise. We present the results using error metrics of the resulting power-law fitting, such as Kolmogorov-Smirnov statistic and Kullback-Leibler divergence. We discuss the implication of our results in regards to future realization of brain-inspired artificial intelligence systems.