Complexity Thoughts: Issue #38
Unraveling complexity: building knowledge, one paper at a time
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Dall-e 3 representation of this issue’s content
From the Lab
Unraveling the mesoscale organization induced by network-driven processes
This is a new work where we push further the analysis of network function to better understand the interplay between structure and dynamics. It has two flavors: theoretical and applied. I plan a dedicated post soon, stay tuned.
Complex systems are characterized by emergent patterns created by the nontrivial interplay between dynamical processes and the networks of interactions on which these processes unfold. Topological or dynamical descriptors alone are not enough to fully embrace this interplay in all its complexity, and many times one has to resort to dynamics-specific approaches that limit a comprehension of general principles. To address this challenge, we employ a metric—that we name Jacobian distance—which captures the spatiotemporal spreading of perturbations, enabling us to uncover the latent geometry inherent in network-driven processes. We compute the Jacobian distance for a broad set of nonlinear dynamical models on synthetic and real-world networks of high interest for applications from biological to ecological and social contexts. We show, analytically and computationally, that the process-driven latent geometry of a complex network is sensitive to both the specific features of the dynamics and the topological properties of the network. This translates into potential mismatches between the functional and the topological mesoscale organization, which we explain by means of the spectrum of the Jacobian matrix. Finally, we demonstrate that the Jacobian distance offers a clear advantage with respect to traditional methods when studying human brain networks. In particular, we show that it outperforms classical network communication models in explaining functional communities from structural data, therefore highlighting its potential in linking structure and function in the brain.
Maximum entropy network states for coalescence processes
We have introduced the formalism of network density matrices in 2016, we have interpreted it in terms of a statistical field theory in 2020 and it extended to a more general formalism based on signaling in 2023. Recently, the formalism has been used for developing the Laplacian Renormalization Group and to understand, under an elegant variational principle, the emergence of sparsity in complex networks (we have also a dedicated post about the latter).
In this new technical work, we demonstrate under which conditions a network density matrix can be obtained through a maximum-entropy approach, defining maximum-entropy network states. Since nodes and sub-systems can interact in different ways, we focus on three coalescence processes that are useful for modeling a variety of complex systems.
Complex network states are characterized by the interplay between system’s structure and dynamics. One way to represent such states is by means of network density matrices, whose von Neumann entropy characterizes the number of distinct microstates compatible with given topology and dynamical evolution. In this Letter, we propose a maximum entropy principle to characterize network states for systems with heterogeneous, generally correlated, connectivity patterns and non-trivial dynamics. We focus on three distinct coalescence processes, widely encountered in the analysis of empirical interconnected systems, and characterize their entropy and transitions between distinct dynamical regimes across distinct temporal scales. Our framework allows one to study the statistical physics of systems that aggregate, such as in transportation infrastructures serving the same geographic area, or correlate, such as inter-brain synchrony arising in organisms that socially interact, and active matter that swarm or synchronize.
Foundations of network science and complex systems
Chimera states in mechanical oscillator networks
The synchronization of coupled oscillators is a fascinating manifestation of self-organization that nature uses to orchestrate essential processes of life, such as the beating of the heart. Although it was long thought that synchrony and disorder were mutually exclusive steady states for a network of identical oscillators, numerous theoretical studies in recent years have revealed the intriguing possibility of “chimera states,” in which the symmetry of the oscillator population is broken into a synchronous part and an asynchronous part. However, a striking lack of empirical evidence raises the question of whether chimeras are indeed characteristic of natural systems. This calls for a palpable realization of chimera states without any fine-tuning, from which physical mechanisms underlying their emergence can be uncovered. Here, we devise a simple experiment with mechanical oscillators coupled in a hierarchical network to show that chimeras emerge naturally from a competition between two antagonistic synchronization patterns. We identify a wide spectrum of complex states, encompassing and extending the set of previously described chimeras. Our mathematical model shows that the self-organization observed in our experiments is controlled by elementary dynamical equations from mechanics that are ubiquitous in many natural and technological systems. The symmetry-breaking mechanism revealed by our experiments may thus be prevalent in systems exhibiting collective behavior, such as power grids, optomechanical crystals, or cells communicating via quorum sensing in microbial populations.
Ecosystems
Ecological modelling approaches for predicting emergent properties in microbial communities
Recent studies have brought forward the critical role of emergent properties in shaping microbial communities and the ecosystems of which they are a part. Emergent properties—patterns or functions that cannot be deduced linearly from the properties of the constituent parts—underlie important ecological characteristics such as resilience, niche expansion and spatial self-organization. While it is clear that emergent properties are a consequence of interactions within the community, their non-linear nature makes mathematical modelling imperative for establishing the quantitative link between community structure and function. As the need for conservation and rational modulation of microbial ecosystems is increasingly apparent, so is the consideration of the benefits and limitations of the approaches to model emergent properties. Here we review ecosystem modelling approaches from the viewpoint of emergent properties. We consider the scope, advantages and limitations of Lotka–Volterra, consumer–resource, trait-based, individual-based and genome-scale metabolic models. Future efforts in this research area would benefit from capitalizing on the complementarity between these approaches towards enabling rational modulation of complex microbial ecosystems.
Biological Systems
Selective social interactions and speed-induced leadership in schooling fish
A very interesting paper about the emergence of collective behavior (schooling fish). Interestingly, this is the second paper in a row making in #ComplexityThoughts, nice to see that the interest in this topic is still high. For an introduction to collective motion, I recommend this extentive review.
The experimental evidence for alignment and antialignment is worth exploring!
Animals moving together in groups are believed to interact among each other with effective social forces, such as attraction, repulsion, and alignment. Such forces can be inferred using “force maps,” i.e., by analyzing the dependency of the acceleration of a focal individual on relevant variables. Here, we introduce a force map technique suitable for the analysis of the alignment forces experienced by individuals. After validating it using an agent-based model, we apply the force map to experimental data of schooling fish. We observe signatures of an effective alignment force with faster neighbors and an unexpected antialignment with slower neighbors. Instead of an explicit antialignment behavior, we suggest that the observed pattern is the result of a selective attention mechanism, where fish pay less attention to slower neighbors. This mechanism implies the existence of temporal leadership interactions based on relative speeds between neighbors. We present support for this hypothesis both from agent-based modeling as well as from exploring leader–follower relationships in the experimental data.
Bio-inspired computing
Neuromorphic dendritic network computation with silent synapses for visual motion perception
Neuromorphic technologies typically employ a point neuron model, neglecting the spatiotemporal nature of neuronal computation. Dendritic morphology and synaptic organization are structurally tailored for spatiotemporal information processing, such as visual perception. Here we report a neuromorphic computational model that integrates synaptic organization with dendritic tree-like morphology. Based on the physics of multigate silicon nanowire transistors with ion-doped sol–gel films, our model—termed dendristor—performs dendritic computation at the device and neural-circuit level. The dendristor offers the bioplausible nonlinear integration of excitatory/inhibitory synaptic inputs and silent synapses with diverse spatial distribution dependency, emulating direction selectivity, which is the feature that reacts to signal direction on the dendrite. We also develop a neuromorphic dendritic neural circuit—a network of interconnected dendritic neurons—that serves as a building block for the design of a multilayer network system that emulates three-dimensional spatial motion perception in the retina.
Books & Volumes
Foundational papers in complexity science
An interesting attempt from SFI community and surroundings to collect less than one hundred papers that have made a great contribution to the development of complexity science up to AD 2000.
McCulloch was a pioneer in the field of cybernetics, with fundamental works to understanding the brain's computational functions and cognitive processes. This volume is a collection of essays that encapsulates his work in cybernetics, neural networks, and the philosophy of mind. A bit dated (1965) but full of influential papers exploring the intersection of biology and computation.
