Complexity Thoughts: Issue #14
Unraveling complexity: building knowledge, one paper at a time
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In a nutshell…
There are a lot of papers after the summer break! Did you miss Complexity Thoughts?
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Ecologists have long sought a unifying equation of state linking species diversity, productivity, abundance, and biomass across ecosystems. By using maximum entropy and metabolic theory, one study finds an equation of state that accurately relates these ecological variables across diverse habitats.
Concerning community detection on networks a new paper offers a solution to a standard problem by associating each community detection objective with its implicit network generative model. This allows principled performance comparisons across diverse algorithms without relying on "ground-truth" labels, revealing biases in some methods and consequences for "no free lunch".
In (network) neuroscience a novel paper presents experimental evidence for the free-energy principle, using in vitro neural networks of rat cortical neurons, demonstrating self-organization and plasticity. Another work presents a novel neural network formalization suggesting that memories consolidate when aiding generalization, reshaping our understanding of cognitive processes. Recent neuroimaging advances reveal the role of network architecture in neurodegenerative diseases: a perspective article explores connectomics, emphasizing individual-level information and dynamic parameter interactions.
In the study of the origin of life, Asgard archaea, potential eukaryotic ancestors, have intrigued researchers for a while: a new paper on cryo-electron tomography unveiled a complex actin-based cytoskeleton in Candidatus Lokiarchaeum ossiferum, shedding light on Asgard phylum evolution and complex cellular structure development.
In Computational Social Science we have novel studies about human behavior and disinformation coming from the collaboration between Meta and a selected pool of academics: I have written a dedicated post about them very recently and refer to that one.
Finally, we have two papers from my lab. In one paper, we propose a mathematical framework to characterize the emergence of information dynamics among networked units. In the second paper we review the most important developments of multilayer network science in the last decade: it comes exactly 10 years later after our first systematic work on the topic!
From the Lab
The constituents of many complex systems are characterized by non-trivial connectivity patterns and dynamical processes that are well captured by network models. However, most systems are coupled with each other through interdependencies, characterized by relationships among heterogeneous units, or multiplexity, characterized by the coexistence of different kinds of relationships among homogeneous units. Multilayer networks provide the framework to capture the complexity typical of systems of systems, enabling the analysis of biophysical, social and human-made networks from an integrated perspective. Here I review the most important theoretical developments in the past decade, showing how the layered structure of multilayer networks is responsible for phenomena that cannot be observed from the analysis of subsystems in isolation or from their aggregation, including enhanced diffusion, emergent mesoscale organization and phase transitions. I discuss applications spanning multiple spatial scales, from the cell to the human brain and to ecological and social systems, and offer perspectives and challenges on future research directions.
The information implicitly represented in the state of physical systems allows for their analysis using analytical techniques from statistical mechanics and information theory. This approach has been successfully applied to complex networks, including biophysical systems such as virus-host protein-protein interactions and whole-brain models in health and disease, drawing inspiration from quantum statistical physics. Here we propose a general mathematical framework for modeling information dynamics on complex networks, where the internal node states are vector valued, allowing each node to carry multiple types of information. This setup is relevant for various biophysical and sociotechnological models of complex systems, ranging from viral dynamics on networks to models of opinion dynamics and social contagion. Instead of focusing on node-node interactions, we shift our attention to the flow of information between network configurations. We uncover fundamental differences between widely used spin models on networks, such as voter and kinetic dynamics, which cannot be detected through classical node-based analysis. We illustrate the mathematical framework further through an exemplary application to epidemic spreading on a low-dimensional network. Our model provides an opportunity to adapt powerful analytical methods from quantum many-body systems to study the interplay between structure and dynamics in interconnected systems.
Network & Complex Systems foundations
To advance understanding of biodiversity and ecosystem function, ecologists seek widely applicable relationships among species diversity and other ecosystem characteristics such as species productivity, biomass, and abundance. These metrics vary widely across ecosystems and no relationship among any combination of them that is valid across habitats, taxa, and spatial scales, has heretofore been found. Here we derive such a relationship, an equation of state, among species richness, energy flow, biomass, and abundance by combining results from the Maximum Entropy Theory of Ecology and the Metabolic Theory of Ecology. It accurately captures the relationship among these state variables in 42 data sets, including vegetation and arthropod communities, that span a wide variety of spatial scales and habitats. The success of our ecological equation of state opens opportunities for estimating difficult-to-measure state variables from measurements of others, adds support for two current theories in ecology, and is a step toward unification in ecology.
The task of community detection, which aims to partition a network into clusters of nodes to summarize its large-scale structure, has spawned the development of many competing algorithms with varying objectives. Some community detection methods are inferential, explicitly deriving the clustering objective through a probabilistic generative model, while other methods are descriptive, dividing a network according to an objective motivated by a particular application, making it challenging to compare these methods on the same scale. Here we present a solution to this problem that associates any community detection objective, inferential or descriptive, with its corresponding implicit network generative model. This allows us to compute the description length of a network and its partition under arbitrary objectives, providing a principled measure to compare the performance of different algorithms without the need for “ground-truth” labels. Our approach also gives access to instances of the community detection problem that are optimal to any given algorithm and in this way reveals intrinsic biases in popular descriptive methods, explaining their tendency to overfit. Using our framework, we compare a number of community detection methods on artificial networks and on a corpus of over 500 structurally diverse empirical networks. We find that more expressive community detection methods exhibit consistently superior compression performance on structured data instances, without having degraded performance on a minority of situations where more specialized algorithms perform optimally. Our results undermine the implications of the “no free lunch” theorem for community detection, both conceptually and in practice, since it is confined to unstructured data instances, unlike relevant community detection problems which are structured by requirement.
Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges and give perspectives on future research directions, looking to inspire interdisciplinary approaches.
Empirical applications of the free-energy principle are not straightforward because they entail a commitment to a particular process theory, especially at the cellular and synaptic levels. Using a recently established reverse engineering technique, we confirm the quantitative predictions of the free-energy principle using in vitro networks of rat cortical neurons that perform causal inference. Upon receiving electrical stimuli—generated by mixing two hidden sources—neurons self-organised to selectively encode the two sources. Pharmacological up- and downregulation of network excitability disrupted the ensuing inference, consistent with changes in prior beliefs about hidden sources. As predicted, changes in effective synaptic connectivity reduced variational free energy, where the connection strengths encoded parameters of the generative model. In short, we show that variational free energy minimisation can quantitatively predict the self-organisation of neuronal networks, in terms of their responses and plasticity. These results demonstrate the applicability of the free-energy principle to in vitro neural networks and establish its predictive validity in this setting.
Memorization and generalization are complementary cognitive processes that jointly promote adaptive behavior. For example, animals should memorize safe routes to specific water sources and generalize from these memories to discover environmental features that predict new ones. These functions depend on systems consolidation mechanisms that construct neocortical memory traces from hippocampal precursors, but why systems consolidation only applies to a subset of hippocampal memories is unclear. Here we introduce a new neural network formalization of systems consolidation that reveals an overlooked tension—unregulated neocortical memory transfer can cause overfitting and harm generalization in an unpredictable world. We resolve this tension by postulating that memories only consolidate when it aids generalization. This framework accounts for partial hippocampal–cortical memory transfer and provides a normative principle for reconceptualizing numerous observations in the field. Generalization-optimized systems consolidation thus provides new insight into how adaptive behavior benefits from complementary learning systems specialized for memorization and generalization.
Neurodegenerative diseases are the most common cause of dementia. Although their underlying molecular pathologies have been identified, there is substantial heterogeneity in the patterns of progressive brain alterations across and within these diseases. Recent advances in neuroimaging methods have revealed that pathological proteins accumulate along specific macroscale brain networks, implicating the network architecture of the brain in the system-level pathophysiology of neurodegenerative diseases. However, the extent to which ‘network-based neurodegeneration’ applies across the wide range of neurodegenerative disorders remains unclear. Here, we discuss the state-of-the-art of neuroimaging-based connectomics for the mapping and prediction of neurodegenerative processes. We review findings supporting brain networks as passive conduits through which pathological proteins spread. As an alternative view, we also discuss complementary work suggesting that network alterations actively modulate the spreading of pathological proteins between connected brain regions. We conclude this Perspective by proposing an integrative framework in which connectome-based models can be advanced along three dimensions of innovation: incorporating parameters that modulate propagation behaviour on the basis of measurable biological features; building patient-tailored models that use individual-level information and allowing model parameters to interact dynamically over time. We discuss promises and pitfalls of these strategies for improving disease insights and moving towards precision medicine.
Network link inference from measured time series data of the behavior of dynamically interacting network nodes is an important problem with wide-ranging applications, e.g., estimating synaptic connectivity among neurons from measurements of their calcium fluorescence. Network inference methods typically begin by using the measured time series to assign to any given ordered pair of nodes a numerical score reflecting the likelihood of a directed link between those two nodes. In typical cases, the measured time series data may be subject to limitations, including limited duration, low sampling rate, observational noise, and partial nodal state measurement. However, it is unknown how the performance of link inference techniques on such datasets depends on these experimental limitations of data acquisition. Here, we utilize both synthetic data generated from coupled chaotic systems as well as experimental data obtained from Caenorhabditis elegans neural activity to systematically assess the influence of data limitations on the character of scores reflecting the likelihood of a directed link between a given node pair. We do this for three network inference techniques: Granger causality, transfer entropy, and, a machine learning-based method. Furthermore, we assess the ability of appropriate surrogate data to determine statistical confidence levels associated with the results of link-inference techniques.
Origin of life
One of the currently most popular evolutionary theories assumes that eukaryotes (including animals, plants and fungi) arose from the fusion of an Asgard archaeon with a bacterium. Credit: © Florian Wollweber, ETH Zürich
Asgard archaea are considered to be the closest known relatives of eukaryotes. Their genomes contain hundreds of eukaryotic signature proteins (ESPs), which inspired hypotheses on the evolution of the eukaryotic cell1,2,3. A role of ESPs in the formation of an elaborate cytoskeleton and complex cellular structures has been postulated4,5,6, but never visualized. Here we describe a highly enriched culture of ‘Candidatus Lokiarchaeum ossiferum’, a member of the Asgard phylum, which thrives anaerobically at 20 °C on organic carbon sources. It divides every 7–14 days, reaches cell densities of up to 5 × 107 cells per ml and has a significantly larger genome compared with the single previously cultivated Asgard strain7. ESPs represent 5% of its protein-coding genes, including four actin homologues. We imaged the enrichment culture using cryo-electron tomography, identifying ‘Ca. L. ossiferum’ cells on the basis of characteristic expansion segments of their ribosomes. Cells exhibited coccoid cell bodies and a network of branched protrusions with frequent constrictions. The cell envelope consists of a single membrane and complex surface structures. A long-range cytoskeleton extends throughout the cell bodies, protrusions and constrictions. The twisted double-stranded architecture of the filaments is consistent with F-actin. Immunostaining indicates that the filaments comprise Lokiactin—one of the most highly conserved ESPs in Asgard archaea. We propose that a complex actin-based cytoskeleton predated the emergence of the first eukaryotes and was a crucial feature in the evolution of the Asgard phylum by scaffolding elaborate cellular structures.
Computational Social Science
There are four papers, published simultaneously, for this section:
→ I have written a dedicated post about them very recently.
Book of the month
Complexity Science: The Study of Emergence (2022) by Henrik J. Jensen
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