Assembly Theory provides a promising framework to explain the complexity of systems such as molecular structures and the origins of life, with broad applicability across various disciplines. In this study, we explore and consolidate different aspects of Assembly Theory by introducing a simplified Toy Model to simulate the autocatalytic formation of complex structures. This model abstracts the molecular formation process, focusing on the probabilistic control of catalysis rather than the intricate interactions found in organic chemistry. We establish a connection between probabilistic catalysis events and key principles of Assembly Theory, particularly the probability of a possible construction path in the formation of a complex object, and examine how the assembly of complex objects is impacted by the presence of autocatalysis. Our findings suggest that this presence of autocatalysis tends to favor longer consecutive construction sequences in environments with a low probability of catalysis, while this bias diminishes in environments with higher catalysis probabilities, highlighting the significant influence of environmental factors on the assembly of complex structures.

Ensuring reliability, availability, and security in modern software systems hinges on early fault detection, yet predicting which parts of a codebase are most at risk remains a significant challenge. In this paper, we analyze 2.4 million commits drawn from 33 heterogeneous open-source projects, spanning healthcare, security tools, data processing, and more. By examining each repository per file and per commit, we derive process metrics (e.g., churn, file age, revision frequency) alongside size metrics and entropy-based indicators of how scattered changes are over time. We train and tune a gradient boosting model to classify bug-prone commits under realistic class-imbalance conditions, achieving robust predictive performance across diverse repositories. Moreover, a comprehensive feature-importance analysis shows that files with long lifespans (high age), frequent edits (revision count), and widely scattered changes (entropy metrics) are especially vulnerable to defects. These insights can help practitioners and researchers prioritize testing and tailor maintenance strategies, ultimately strengthening software dependability.

This study introduces a data obfuscation technique that leverages the exponential map of Lie-group generators. Originating from quantum machine learning frameworks, the method injects controlled noise into these generators, deliberately breaking symmetry and obscuring the source data while retaining predictive utility. Experiments on open medical datasets show that classifiers trained on obfuscated features match or slightly exceed the baseline accuracy obtained on raw data. This work demonstrates how Lie-group theory can advance privacy in sensitive domains by providing simultaneous data obfuscation and augmentation.

We present a supervised learning method to estimate two local descriptors of time-series dynamics, the mean-reversion rate $\theta$ and a heavy-tail estimate $\alpha$, from short windows of data. These parameters summarize recovery behavior and tail heaviness and are useful for interpreting stochastic signals in sensing applications. The method is trained on synthetic, dimensionless Ornstein–Uhlenbeck processes with $\alpha$-stable noise, ensuring robustness for non-Gaussian and heavy-tailed inputs. Gradient-boosted tree models (CatBoost) map window-level statistical features to discrete $\alpha$ and $\theta$ categories with high accuracy and predominantly adjacent-class confusion. Using the same trained models, we analyze daily financial returns, daily sunspot numbers, and NASA POWER climate fields for Austria. The method detects changes in local dynamics, including shifts in the financial tail structure after 2010, weaker and more irregular solar cycles after 2005, and a redistribution in clear-sky shortwave irradiance around 2000. Because it relies only on short windows and requires no domain-specific tuning, the framework provides a compact diagnostic tool for signal processing, supporting the characterization of local variability, detection of regime changes, and decision making in settings where long-term stationarity is not guaranteed.

We present a supervised method to estimate two local descriptors of time-series dynamics, the mean-reversion rate θ and a heavy tail estimate α, from short windows of data. These parameters summarize recovery behavior and tail heaviness and are useful for interpreting stochastic signals in sensing applications. The method is trained on synthetic, dimensionless Ornstein–Uhlenbeck processes with α-stable noise, ensuring robustness for non-Gaussian and heavy-tailed inputs. Gradient-boosted tree models (CatBoost) map window-level statistical features to discrete (α, θ) categories with high accuracy and predominantly adjacent-class confusion. Using the same trained models, we analyze daily financial returns, daily sunspot numbers, and NASA POWER climate fields for Austria. The method detects changes in local dynamics, including shifts in financial tail structure after 2010, weaker and more irregular solar cycles after 2005, and a redistribution in clear-sky shortwave irradiance around 2000. Because it relies only on short windows and requires no domain-specific tuning, the framework provides a compact diagnostic tool for signal processing, supporting characterization of local variability, detection of regime changes, and decision making in settings where long-term stationarity is not guaranteed.