Mario Franco, Gerardo Febres, Nelson Fernández, Carlos Gershenson

Classification is a ubiquitous and fundamental problem in artificial intelligence and machine learning, with extensive efforts dedicated to developing more powerful classifiers and larger datasets. However, the classification task is ultimately constrained by the intrinsic properties of datasets, independently of computational power or model complexity. In this work, we introduce a formal entropy-based measure of classificability, which quantifies the inherent difficulty of a classification problem by assessing the uncertainty in class assignments given feature representations. This measure captures the degree of class overlap and aligns with human intuition, serving as an upper bound on classification performance for classification problems. Our results establish a theoretical limit beyond which no classifier can improve the classification accuracy, regardless of the architecture or amount of data, in a given problem. Our approach provides a principled framework for understanding when classification is inherently fallible and fundamentally ambiguous.

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Matthew Russell Barnes, Vincenzo Nicosia, Richard G. Clegg
In complex networks, the rich-get-richer effect (nodes with high degree at one point in time gain more degree in their future) is commonly observed. In practice this is often studied on a static network snapshot, for example, a preferential attachment model assumed to explain the more highly connected nodes or a rich-club}effect that analyses the most highly connected nodes. In this paper, we consider temporal measures of how success (measured here as node degree) propagates across time. By analogy with social mobility (a measure people moving within a social hierarchy through their life) we define hierarchical mobility to measure how a node’s propensity to gain degree changes over time. We introduce an associated taxonomy of temporal correlation statistics including mobility, philanthropy and community. Mobility measures the extent to which a node’s degree gain in one time period predicts its degree gain in the next. Philanthropy and community measure similar properties related to node neighbourhood.
We apply these statistics both to artificial models and to 26 real temporal networks. We find that most of our networks show a tendency for individual nodes and their neighbourhoods to remain in similar hierarchical positions over time, while most networks show low correlative effects between individuals and their neighbourhoods. Moreover, we show that the mobility taxonomy can discriminate between networks from different fields. We also generate artificial network models to gain intuition about the behaviour and expected range of the statistics. The artificial models show that the opposite of the “rich-get-richer” effect requires the existence of inequality of degree in a network. Overall, we show that measuring the hierarchical mobility of a temporal network is an invaluable resource for discovering its underlying structural dynamics.

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Competence Modelling From the Perspective of Complex Systems Theories: A Systematic Literature Review

Pedagogika Vol. 156 No. 4

This article aims to investigate how the notion of competence is conceptualised and modelled from the point of view of complex systems theories. Although the importance of competences and competency-based education is widely acknowledged, the concept of competence keeps evolving and it remains difficult to define it in today’s constantly changing and uncertain VUCA world. Therefore, this study explores how the approach of complex systems, which is increasingly more often applied in educational research, can contribute to the definition of competence. The article presents a systematic review of 21 articles published in various databases in 2000-2023, revealing that from the perspective of complex systems, competence can be conceptualised both at the individual level and at the level of the whole system or organisation; it can follow a functionalist or contextual approach. Based on the research findings, it is assumed that in certain cases competence can be treated as emergence or even as an entire complex system, characterised by such properties as non-linearity, chaos, emergence, feedback loops, etc. Finally, this article reviews the variety of complexity-informed mathematical/computational and theoretical models utilised in the reviewed studies, the application of which opens up new avenues in overall educational research.

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Liad Mudrik, Melanie Boly, Stanislas Dehaene, Stephen M. Fleming, Victor Lamme, Anil Seth, Lucia Melloni

Neuroscience & Biobehavioral Reviews

As the field of consciousness science matures, the research agenda has expanded from an initial focus on the neural correlates of consciousness, to developing and testing theories of consciousness. Several theories have been put forward, each aiming to elucidate the relationship between consciousness and brain function. However, there is an ongoing, intense debate regarding whether these theories examine the same phenomenon. And, despite ongoing research efforts, it seems like the field has so far failed to converge around any single theory, and instead exhibits significant polarization. To advance this discussion, proponents of five prominent theories of consciousness—Global Neuronal Workspace Theory (GNWT), Higher-Order Theories (HOT), Integrated Information Theory (IIT), Recurrent Processing Theory (RPT), and Predictive Processing (PP)—engaged in a public debate in 2022, as part of the annual meeting of the Association for the Scientific Study of Consciousness (ASSC). They were invited to clarify the explananda of their theories, articulate the core mechanisms underpinning the corresponding explanations, and outline their foundational premises. This was followed by an open discussion that delved into the testability of these theories, potential evidence that could refute them, and areas of consensus and disagreement. Most importantly, the debate demonstrated that at this stage, there is more controversy than agreement between the theories, pertaining to the most basic questions of what consciousness is, how to identify conscious states, and what is required from any theory of consciousness. Addressing these core questions is crucial for advancing the field towards a deeper understanding and comparison of competing theories.

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