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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. [ABSTRACT FROM AUTHOR]

Fractional calculus has gained a lot of attention in the last couple of years. Researchers have discovered that processes in various fields follow fractional dynamics rather than ordinary integer-ordered dynamics, meaning that the corresponding differential equations feature non-integer valued derivatives. There are several arguments for why this is the case, one of which is that fractional derivatives inherit spatiotemporal memory and/or the ability to express complex naturally occurring phenomena. Another popular topic nowadays is machine learning, i.e., learning behavior and patterns from historical data. In our ever-changing world with ever-increasing amounts of data, machine learning is a powerful tool for data analysis, problem-solving, modeling, and prediction. It has provided many further insights and discoveries in various scientific disciplines. As these two modern-day topics hold a lot of potential for combined approaches in terms of describing complex dynamics, this article review combines approaches from fractional derivatives and machine learning from the past, puts them into context, and thus provides a list of possible combined approaches and the corresponding techniques. Note, however, that this article does not deal with neural networks, as there is already extensive literature on neural networks and fractional calculus. We sorted past combined approaches from the literature into three categories, i.e., preprocessing, machine learning and fractional dynamics, and optimization. The contributions of fractional derivatives to machine learning are manifold as they provide powerful preprocessing and feature augmentation techniques, can improve physically informed machine learning, and are capable of improving hyperparameter optimization. Thus, this article serves to motivate researchers dealing with data-based problems, to be specific machine learning practitioners, to adopt new tools, and enhance their existing approaches. [ABSTRACT FROM AUTHOR]

The discussion regarding the formal introduction of a new geological age, the Anthropocene, led to the sophisticated attempt of the AWG (Anthropocene Working Group) to investigate the long-term stratigraphical records shaped by human actions and to identify possible GSSAs (Global Standard Stratigraphic Age) and GSSPs (Global boundary Stratotype Section and Point). The present matter tries to contribute to this endeavor and discusses the geochemical and geophysical implications of the global iron ore industry including the associated chains of production. To achieve this goal, a sophisticated literature research was conducted, which was mainly based on various LCAs (Life cycle analysis) and field studies. The results are presented by means of the four stages of the iron ore cycle (Mining, processing, recycling and weathering) and help to illustrate the relation between the physical, chemical, biological, magnetic and sequential markers and the geochemical and geophysical effects of the iron ore industry. The potential markers vary greatly regarding their persistence and measurability, but key findings can be summarized as TMPs (Technogenic magnetic particles), SCPs (Spheroidal carbonaceous fly ash particles), HAHs (Halogenated aromatic hydrocarbons), heavy metals (Vanadium, mercury etc.), species extinction, steel input and steel corrosion as well as the emergence of iron ore related Technosols. Considering the temporal synchrony and global distribution of the stratigraphical records, potential candidates for the GSSP and the GSSA are highlighted. [ABSTRACT FROM AUTHOR]