Complexity Thoughts: Issue #41
Unraveling complexity: building knowledge, one paper at a time
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Foundations of network science and complex systems
Tracking the Distance to Criticality in Systems with Unknown Noise
How close your (critical) system is to a bifurcation point? This great paper provides an answer.
Many real-world systems undergo abrupt changes in dynamics as they move across critical points, often with dramatic and irreversible consequences. Much existing theory on identifying the time-series signatures of nearby critical points, such as increased signal variance and slower timescales, is derived from analytically tractable systems, typically considering the case of fixed, low-amplitude noise. However, real-world systems are often corrupted by unknown levels of noise that can distort these temporal signatures. Here we aim to develop noise-robust indicators of the distance to criticality (DTC) for systems affected by dynamical noise in two cases: when the noise amplitude is either fixed or is unknown and variable across recordings. We present a highly comparative approach to this problem that compares the ability of over 7000 candidate time-series features to track the DTC in the vicinity of a supercritical Hopf bifurcation. Our method recapitulates existing theory in the fixed-noise case, highlighting conventional time-series features that accurately track the DTC. But in the variable-noise setting, where these conventional indicators perform poorly, we highlight new types of high-performing time-series features and show that their success is accomplished by capturing the shape of the invariant density (which depends on both the DTC and the noise amplitude) relative to the spread of fast fluctuations (which depends on the noise amplitude). We introduce a new high-performing time-series statistic, the rescaled autodensity (RAD), that combines these two algorithmic components. We then use RAD to provide new evidence that brain regions higher in the visual hierarchy are positioned closer to criticality, supporting existing hypotheses about patterns of brain organization that are not detected using conventional metrics of the DTC. Our results demonstrate how large-scale algorithmic comparison can yield theoretical insights that can motivate new theory and interpretable algorithms for solving important real-world problems.
Disentangling high-order effects in the transfer entropy
Transfer entropy (TE), the primary method for determining directed information flow within a network system, can exhibit bias—either in deficiency or excess—during both pairwise and conditioned calculations, owing to high-order dependencies among the dynamic processes under consideration and the remaining processes in the system used for conditioning. Here, we propose a novel approach. Instead of conditioning TE on all network processes except the driver and the target, as in its fully conditioned version, or not conditioning at all, as in the pairwise approach, our method searches for both the multiplets of variables that maximize information flow and those that minimize it. This provides a decomposition of TE into unique, redundant, and synergistic atoms. Our approach enables the quantification of the relative importance of high-order effects compared to pure two-body effects in information transfer between two processes, while also highlighting the processes that contribute to building these high-order effects alongside the driver. We demonstrate the application of our approach in climatology by analyzing data from El Niño and the Southern Oscillation.
Ecosystems and living systems
Interactions and Migration Rescuing Ecological Diversity
How the movement of species between different ecosystems can help maintain biodiversity and prevent collapse? The authors show that migration can act as a stabilizing force in ecosystems by reducing the likelihood of local extinctions and promoting species coexistence.
This is very interesting. But what about the role of the network? Stay tuned… we’ll discuss about this soon with a paper from the lab.
How diversity is maintained in natural ecosystems is a long-standing question in Theoretical Ecology. By studying a system that combines ecological dynamics, heterogeneous interactions, and spatial structure, we uncover a new mechanism for the survival of diversity-rich ecosystems in the presence of demographic fluctuations. For a single species, one finds a continuous phase transition between an extinction and a survival state, that falls into the universality class of Directed Percolation. Here we show that the case of many species with heterogeneous interactions is different and richer. By merging theory and simulations, we demonstrate that with sufficiently strong demographic noise, the system exhibits behavior akin to the single-species case, undergoing a continuous transition. Conversely, at low demographic noise, we observe unique features indicative of the ecosystem's complexity. The combined effects of the heterogeneity in the interaction network and migration enable the community to thrive, even in situations where demographic noise would lead to the extinction of isolated species. The emergence of mutualism induces the development of global bistability, accompanied by sudden tipping points. We present a way to predict the catastrophic shift from high diversity to extinction by probing responses to perturbations as an early warning signal.
Noisy Circumnutations Facilitate Self-Organized Shade Avoidance in Sunflowers
Sunflowers self-organize to maximize their exposure to the light. How?
Circumnutations are widespread in plants and typically associated with exploratory movements; however, a quantitative understanding of their role remains elusive. In this study we report, for the first time, the role of noisy circumnutations in facilitating an optimal growth pattern within a crowded group of mutually shading plants. We revisit the problem of self-organization observed for sunflowers, mediated by shade response interactions. Our analysis reveals that circumnutation movements conform to a bounded random walk characterized by a remarkably broad distribution of velocities, covering 3 orders of magnitude. In motile animal systems such wide distributions of movement velocities are frequently identified with enhancement of behavioral processes, suggesting that circumnutations may serve as a source of functional noise. To test our hypothesis, we developed a Langevin-type parsimonious model of interacting growing disks, informed by experiments, successfully capturing the characteristic dynamics of individual and multiple interacting plants. Employing our simulation framework we examine the role of circumnutations in the system, and find that the observed breadth of the velocity distribution represents a sharp transition in the force-noise ratio, conferring advantageous effects by facilitating exploration of potential configurations, leading to an optimized arrangement with minimal shading. These findings represent the first report of functional noise in plant movements and establish a theoretical foundation for investigating how plants navigate their environment by employing computational processes such as task-oriented processes, optimization, and active sensing. Since plants move by growing, space and time are coupled, and dynamics of self-organization lead to emergent 3D patterns. As such, this system provides conceptual insight for other interacting growth-driven systems such as fungal hyphae, neurons and self-growing robots, as well as active matter systems where agents interact with past trajectories of their counterparts, such as stigmergy in social insects. This foundational insight has implications in statistical physics, ecological dynamics, agriculture, and even swarm robotics.
Morphological Entanglement in Living Systems
Many organisms exhibit branching morphologies that twist around each other and become entangled. Entanglement occurs when different objects interlock with each other, creating complex and often irreversible configurations. This physical phenomenon is well studied in nonliving materials, such as granular matter, polymers, and wires, where it has been shown that entanglement is highly sensitive to the geometry of the component parts. However, entanglement is not yet well understood in living systems, despite its presence in many organisms. In fact, recent work has shown that entanglement can evolve rapidly and play a crucial role in the evolution of tough, macroscopic multicellular groups. Here, through a combination of experiments, simulations, and numerical analyses, we show that growth generically facilitates entanglement for a broad range of geometries. We find that experimentally grown entangled branches can be difficult or even impossible to disassemble through translation and rotation of rigid components, suggesting that there are many configurations of branches that growth can access that agitation cannot. We use simulations to show that branching trees readily grow into entangled configurations. In contrast to nongrowing entangled materials, these trees entangle for a broad range of branch geometries. We, thus, propose that entanglement via growth is largely insensitive to the geometry of branched trees but, instead, depends sensitively on timescales, ultimately achieving an entangled state once sufficient growth has occurred. We test this hypothesis in experiments with snowflake yeast, a model system of undifferentiated, branched multicellularity, showing that lengthening the time of growth leads to entanglement and that entanglement via growth can occur for a wide range of geometries. Taken together, our work demonstrates that entanglement is more readily achieved in living systems than in their nonliving counterparts, providing a widely accessible and powerful mechanism for the evolution of novel biological material properties.
Neuroscience
Moving beyond processing- and analysis-related variation in resting-state functional brain imaging
fMRI under scrutiny (again! See also Carp 2012, Bowring et al 2019, Botvinik-Nezer et al 2020)
When fields lack consensus standard methods and accessible ground truths, reproducibility can be more of an ideal than a reality. Such has been the case for functional neuroimaging, where there exists a sprawling space of tools and processing pipelines. We provide a critical evaluation of the impact of differences across five independently developed minimal preprocessing pipelines for functional magnetic resonance imaging. We show that, even when handling identical data, interpipeline agreement was only moderate, critically shedding light on a factor that limits cross-study reproducibility. We show that low interpipeline agreement can go unrecognized until the reliability of the underlying data is high, which is increasingly the case as the field progresses. Crucially we show that, when interpipeline agreement is compromised, so too is the consistency of insights from brain-wide association studies. We highlight the importance of comparing analytic configurations, because both widely discussed and commonly overlooked decisions can lead to marked variation.
This is huge, and honestly I could not go through the whole supplementary materials. It is a great effort to build a near-comprehensive anatomical description and annotation of neurons in a male Drosophila ventral nerve cord. I strongly recommend to read also this Insight.
Nervous systems function as ensembles of neurons communicating via synaptic connections, and a functional understanding of nervous systems requires extensive knowledge of their connectomes. In a companion paper (Takemura et al., 2023), we describe the acquisition of a complete fruit fly nerve cord connectome, the first for an animal that can walk or fly. Here, to efficiently navigate and to appreciate the biological significance of this connectome, we categorise and name nearly all neurons systematically and link them to the experimental literature. We employ a system of hierarchical coarse annotations and group similar neurons across the midline and across segments, then define systematic cell types for sensory neurons, intrinsic neurons, ascending neurons, and non-motor efferent neurons. Stereotyped arrays of neuroblasts generate related neuron populations called hemilineages that repeat across the segments of the nerve cord. We confirm that larval-born neurons from a given hemilineage generally express the same neurotransmitter but find that earlier born neurons often express a different one. We match over 35% of intrinsic, ascending, and non-motor efferent neurons across segments, defining serial sets which were crucial for systematic typing of motor neurons and sensory neurons. We assign a sensory modality to over 5000 sensory neurons, cluster them by connectivity, and identify serially homologous cell types and a layered organisation likely corresponding to peripheral topography. Finally, we present selected examples of sensory circuits predicated on programmatic analysis of a complete VNC connectome. Our annotations are critical for analysing the structure of descending input to the nerve cord and of motor output, both described in a third companion paper (Cheong et al., 2023). These annotations are being released as part of the neuprint.janelia.org and clio.janelia.org web applications and also serve as the basis for programmatic analysis of the connectome through dedicated tools that we describe in this paper.
Structure–function coupling in macroscale human brain networks
Precisely how the anatomical structure of the brain gives rise to a repertoire of complex functions remains incompletely understood. A promising manifestation of this mapping from structure to function is the dependency of the functional activity of a brain region on the underlying white matter architecture. Here, we review the literature examining the macroscale coupling between structural and functional connectivity, and we establish how this structure–function coupling (SFC) can provide more information about the underlying workings of the brain than either feature alone. We begin by defining SFC and describing the computational methods used to quantify it. We then review empirical studies that examine the heterogeneous expression of SFC across different brain regions, among individuals, in the context of the cognitive task being performed, and over time, as well as its role in fostering flexible cognition. Last, we investigate how the coupling between structure and function is affected in neurological and psychiatric conditions, and we report how aberrant SFC is associated with disease duration and disease-specific cognitive impairment. By elucidating how the dynamic relationship between the structure and function of the brain is altered in the presence of neurological and psychiatric conditions, we aim to not only further our understanding of their aetiology but also establish SFC as a new and sensitive marker of disease symptomatology and cognitive performance. Overall, this Review collates the current knowledge regarding the regional interdependency between the macroscale structure and function of the human brain in both neurotypical and neuroatypical individuals.
Human behavior
Computational evolution of social norms in well-mixed and group-structured populations
Fugaku has been the most powerful supercomputer for a while. Now it has been use to explore the evolution of social norms. The authors focused on third-order norms, which define how people are judged based on their actions and those of others. They found that cooperative norms are easier to establish in populations divided into smaller communities rather than in a single well-mixed one. In fact, the population structure significantly influences which social norms will prevail and how effectively cooperation can be sustained within a society. That’s quite a simulation!
Models of indirect reciprocity study how social norms promote cooperation. In these models, cooperative individuals build up a positive reputation, which in turn helps them in their future interactions. The exact reputational benefits of cooperation depend on the norm in place, which may change over time. Previous research focused on the stability of social norms. Much less is known about how social norms initially evolve when competing with many others. A comprehensive evolutionary analysis, however, has been difficult. Even among the comparably simple space of so-called third-order norms, there are thousands of possibilities, each one inducing its own reputation dynamics. To address this challenge, we use large-scale computer simulations. We study the reputation dynamics of each third-order norm and all evolutionary transitions between them. In contrast to established work with only a handful of norms, we find that cooperation is hard to maintain in well-mixed populations. However, within group-structured populations, cooperation can emerge. The most successful norm in our simulations is particularly simple. It regards cooperation as universally positive, and defection as usually negative—unless defection takes the form of justified punishment. This research sheds light on the complex interplay of social norms, their induced reputation dynamics, and population structure.
Machine learning and bio-inspired computing
Fully nonlinear neuromorphic computing with linear wave scattering
Linear systems – which are typically unable to performing nonlinear operations – can be adapted to achieve nonlinear computations. Black magic? Not really.
Even if the finding sounds paradoxical because nonlinear computations are generally assumed to require nonlinear systems, the authors solved the issue by encoding input parameters within the linear system, enabling it to mimic nonlinear behavior. That’s the trick! I suggest to read also this News&Views.
The increasing size of neural networks for deep learning applications and their energy consumption create a need for alternative neuromorphic approaches, for example, using optics. Current proposals and implementations rely on physical nonlinearities or optoelectronic conversion to realize the required nonlinear activation function. However, there are considerable challenges with these approaches related to power levels, control, energy efficiency and delays. Here we present a scheme for a neuromorphic system that relies on linear wave scattering and yet achieves nonlinear processing with high expressivity. The key idea is to encode the input in physical parameters that affect the scattering processes. Moreover, we show that gradients needed for training can be directly measured in scattering experiments. We propose an implementation using integrated photonics based on racetrack resonators, which achieves high connectivity with a minimal number of waveguide crossings. Our work introduces an easily implementable approach to neuromorphic computing that can be widely applied in existing state-of-the-art scalable platforms, such as optics, microwave and electrical circuits.
Machine learning without a processor: Emergent learning in a nonlinear analog network
We demonstrate that the system learns tasks unachievable in linear systems, including XOR (exclusive or) and nonlinear regression, without a computer
The capabilities of digital artificial neural networks grow rapidly with their size. Unfortunately, so do the time and energy required to train them. By contrast, brains function rapidly and power-efficiently at scale because their analog constituent parts (neurons) update their connections without knowing what all the other neurons are doing; in other words, they update using local rules. Recently introduced analog electronic contrastive local learning networks (CLLNs) share this important property. However, unlike brains and artificial neural networks, their capabilities were limited and could not grow with size because they are linear. Here, we experimentally demonstrate that nonlinearity enhances machine-learning capabilities in an analog CLLN, establishing a paradigm for scalable learning systems.
Urban systems
A typology of activities over a century of urban growth
Contemporary literature on the dynamics of economic activities in growing cities has mainly focused on time frames of a few years or decades. Using a new geohistorical database constructed from historical directories with about 1 million entries, we present a comprehensive analysis of the dynamics of activities in a major city, Paris, over almost a century (1829–1907). Our analysis suggests that activities that accompany city growth can be classified in different categories according to their dynamics and their scaling with population: (1) linear for everyday needs of residents (food stores, clothing retailers, health care practitioners), (2) sublinear for public services (legal, administrative, educational) and (3) superlinear for the city’s specific features (passing fads, specialization, timely needs). The dynamics of these activities is in addition very sensitive to historical perturbations such as large-scale public works or political conflicts. These results shed light on the evolution of activities, a crucial component of growing cities.