Complexity Thoughts: Issue #25
Unraveling complexity: building knowledge, one paper at a time
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Dall-e 3 representation of this issue’s content
On Jan 24th I was invited by NetPLACE to talk at a panel dedicated about science communication, during the NetSciX 2024 conference. It’s been a really interesting and rewarding experience, convincing me that #ComplexityThoughts is doing a good job in communicating complexity science and should go ahead.
From the lab
Diversity of information pathways drives sparsity in real-world networks
A short #ComplexityThoughts essay dedicated to this work, within a broader context and the “behind the scenes” will appear in about one week from now at this link.
our results suggest that the balance of entropy and free energy, optimizing the trade-off between information flow and response diversity for middle- to long-range signalling, explains the emergence of sparse topological structures, regardless of specific microscopic mechanisms of network formation
Complex systems must respond to external perturbations and, at the same time, internally distribute information to coordinate their components. Although networked backbones help with the latter, they limit the components’ individual degrees of freedom and reduce their collective dynamical range. Here we show that real-world networks balance the loss of response diversity with gain in information flow. Encoding network states as density matrices, we demonstrate that such a trade-off mathematically resembles the thermodynamic efficiency characterized by heat and work in physical systems, providing a variational principle to macroscopically explain the sparsity and empirical scaling law observed in hundreds of real-world networks across multiple domains, both analytically and numerically. We show that the emergence of topological features such as modularity, small-worldness and heterogeneity agrees with maximizing the trade-off between information exchange and response diversity from middle to large temporal scales. Our results suggest that the emergence of some of the most prevalent topological features of real-world networks might have a thermodynamic origin.
Foundations of network science and complex systems
The low-rank hypothesis of complex systems
In a recent paper, it has been shown that it is possible to predict the evolution of some dynamical processes on the top of a network even if the underlying network is not known, which is quite a result. This result suggests that even if the state space of the system is extraordinarily huge, dynamics unfold in a subspace of much smaller dimension.
A new paper tackles the low-rank hypothesis that is widely adopted to make interpretable predictions about the unfolding of complex (high-dimensional) dynamics. I like the whole paper (and its News&Views by Janxi Gao), and it’s difficult to highlight a single sentence. But maybe, the one that most resonates with me is:
Using our framework, a simple example readily provides insights into the emergence of higher-order interactions
What Janxi writes, “As a network can always be described in the language of matrices and tensors, linear algebra provides vital tools to study network properties” remarks one more time the power of the connection between graph theory and linear algebra, especially through the language of tensors (thanks to which we have built a mathematical formulation for multilayer systems a decade ago!).
In fact, the dimension reduction issue can be suitably mapped into the problem of finding the best alignment between a low-dimensional vector field and the original one (with full dynamics). So elegant!
Complex systems are high-dimensional nonlinear dynamical systems with heterogeneous interactions among their constituents. To make interpretable predictions about their large-scale behaviour, it is typically assumed that these dynamics can be reduced to a few equations involving a low-rank matrix describing the network of interactions. Our Article sheds light on this low-rank hypothesis and questions its validity. Using fundamental theorems on singular-value decomposition, we probe the hypothesis for various random graphs, either by making explicit their low-rank formulation or by demonstrating the exponential decrease of their singular values. We verify the hypothesis for real networks by revealing the rapid decrease of their singular values, which has major consequences for their effective ranks. We then evaluate the impact of the low-rank hypothesis for general dynamical systems on networks through an optimal dimension reduction. This allows us to prove that recurrent neural networks can be exactly reduced, and we can connect the rapidly decreasing singular values of real networks to the dimension reduction error of the nonlinear dynamics they support. Finally, we prove that higher-order interactions naturally emerge from the dimension reduction, thus providing insights into the origin of higher-order interactions in complex systems.
Biological Systems
Robust Retrieval of Dynamic Sequences through Interaction Modulation
Many biological systems dynamically rearrange their components through a sequence of configurations in order to perform their functions. Such dynamic processes have been studied using network models that sequentially retrieve a set of stored patterns. Previous models of sequential retrieval belong to a general class in which the components of the system are controlled by feedback (input modulation). In contrast, we introduce a new class of models in which the feedback modifies the interactions among the components (interaction modulation). We show that interaction modulation models not only are capable of retrieving dynamic sequences, but they do so more robustly than input modulation models. In particular, we find that modulation of symmetric interactions allows retrieval of patterns with different activity levels and has a much larger dynamic capacity. Our results suggest that interaction modulation may be a common principle underlying biological systems that show complex collective dynamics.
Beyond reaction norms: the temporal dynamics of phenotypic plasticity
iteratively sampling phenotypic traits over time can help us understand the adaptiveness of plasticity relative to environmental change
Phenotypic plasticity can allow organisms to cope with environmental changes. Although reaction norms are commonly used to quantify plasticity along gradients of environmental conditions, they often miss the temporal dynamics of phenotypic change, especially the speed at which it occurs. Here, we argue that studying the rate of phenotypic plasticity is a crucial step to quantify and understand its adaptiveness. Iteratively measuring plastic traits allows us to describe the actual dynamics of phenotypic changes and avoid quantifying reaction norms at times that do not truly reflect the organism’s capacity for plasticity. Integrating the temporal component in how we describe, quantify, and conceptualise phenotypic plasticity can change our understanding of its diversity, evolution, and consequences.
Neuroscience
The robust differences that were uncovered demonstrate that Ca2+ and BOLD also capture some complementary features of brain organization
Large-scale functional networks have been characterized in both rodent and human brains, typically by analyzing fMRI-BOLD signals. However, the relationship between fMRI-BOLD and underlying neural activity is complex and incompletely understood, which poses challenges to interpreting network organization obtained using this technique. Additionally, most work has assumed a disjoint functional network organization (i.e., brain regions belong to one and only one network). Here, we employ wide-field Ca2+ imaging simultaneously with fMRI-BOLD in mice expressing GCaMP6f in excitatory neurons. We determine cortical networks discovered by each modality using a mixed-membership algorithm to test the hypothesis that functional networks exhibit overlapping organization. We find that there is considerable network overlap (both modalities) in addition to disjoint organization. Our results show that multiple BOLD networks are detected via Ca2+ signals, and networks determined by low-frequency Ca2+ signals are only modestly more similar to BOLD networks. In addition, the principal gradient of functional connectivity is nearly identical for BOLD and Ca2+ signals. Despite similarities, important differences are also detected across modalities, such as in measures of functional connectivity strength and diversity. In conclusion, Ca2+ imaging uncovers overlapping functional cortical organization in the mouse that reflects several, but not all, properties observed with fMRI-BOLD signals.
Understanding neural circuit function through synaptic engineering
Synapses are a key component of neural circuits, facilitating rapid and specific signalling between neurons. Synaptic engineering — the synthetic insertion of new synaptic connections into in vivo neural circuits — is an emerging approach for neural circuit interrogation. This approach is especially powerful for establishing causality in neural circuit structure–function relationships, for emulating synaptic plasticity and for exploring novel patterns of circuit connectivity. Contrary to other approaches for neural circuit manipulation, synaptic engineering targets specific connections between neurons and functions autonomously with no user-controlled external activation. Synaptic engineering has been successfully implemented in several systems and in different forms, including electrical synapses constructed from ectopically expressed connexin gap junction proteins, synthetic optical synapses composed of presynaptic photon-emitting luciferase coupled with postsynaptic light-gated channels, and artificial neuropeptide signalling pathways. This Perspective describes these different methods and how they have been applied, and examines how the field may advance.
Circuit topology for synchronizing neurons in spontaneously active networks
Spike synchronization underlies information processing and storage in the brain. But how can neurons synchronize in a noisy network? By exploiting a high-speed (500–2,000 fps) multineuron imaging technique and a large-scale synapse mapping method, we directly compared spontaneous activity patterns and anatomical connectivity in hippocampal CA3 networks ex vivo. As compared to unconnected pairs, synaptically coupled neurons shared more common presynaptic neurons, received more correlated excitatory synaptic inputs, and emitted synchronized spikes with approximately 107 times higher probability. Importantly, common presynaptic parents per se synchronized more than unshared upstream neurons. Consistent with this, dynamic-clamp stimulation revealed that common inputs alone could not account for the realistic degree of synchronization unless presynaptic spikes synchronized among common parents. On a macroscopic scale, network activity was coordinated by a power-law scaling of synchronization, which engaged varying sets of densely interwired (thus highly synchronized) neuron groups. Thus, locally coherent activity converges on specific cell assemblies, thereby yielding complex ensemble dynamics. These segmentally synchronized pulse packets may serve as information modules that flow in associatively parallel network channels.
Climate change
Significantly wetter or drier future conditions for one to two thirds of the world’s population
These findings can directly assist with designing ‘fit for purpose’ climate adaptation policies and reduce uncertainty in which direction precipitation is projected to change globally under different emissions levels
Future projections of precipitation are uncertain, hampering effective climate adaptation strategies globally. Our understanding of changes across multiple climate model simulations under a warmer climate is limited by this lack of coherence across models. Here, we address this challenge introducing an approach that detects agreement in drier and wetter conditions by evaluating continuous 120-year time-series with trends, across 146 Global Climate Model (GCM) runs and two elevated greenhouse gas (GHG) emissions scenarios. We show the hotspots of future drier and wetter conditions, including regions already experiencing water scarcity or excess. These patterns are projected to impact a significant portion of the global population, with approximately 3 billion people (38% of the world’s current population) affected under an intermediate emissions scenario and 5 billion people (66% of the world population) under a high emissions scenario by the century’s end (or 35-61% using projections of future population). We undertake a country- and state-level analysis quantifying the population exposed to significant changes in precipitation regimes, offering a robust framework for assessing multiple climate projections.
Integrating climate change induced flood risk into future population projections
Flood exposure has been linked to shifts in population sizes and composition. Traditionally, these changes have been observed at a local level providing insight to local dynamics but not general trends, or at a coarse resolution that does not capture localized shifts. Using historic flood data between 2000-2023 across the Contiguous United States (CONUS), we identify the relationships between flood exposure and population change. We demonstrate that observed declines in population are statistically associated with higher levels of historic flood exposure, which may be subsequently coupled with future population projections. Several locations have already begun to see population responses to observed flood exposure and are forecasted to have decreased future growth rates as a result. Finally, we find that exposure to high frequency flooding (5 and 20-year return periods) results in 2-7% lower growth rates than baseline projections. This is exacerbated in areas with relatively high exposure to frequent flooding where growth is expected to decline over the next 30 years.
Remotely sensing potential climate change tipping points across scales
The resulting fine-resolution spatial-temporal sensing of tipping systems can support policy-making and risk management at regional, national, and international scales. It can actively help to protect numerous human lives and livelihoods that are at risk from climate change tipping points
Potential climate tipping points pose a growing risk for societies, and policy is calling for improved anticipation of them. Satellite remote sensing can play a unique role in identifying and anticipating tipping phenomena across scales. Where satellite records are too short for temporal early warning of tipping points, complementary spatial indicators can leverage the exceptional spatial-temporal coverage of remotely sensed data to detect changing resilience of vulnerable systems. Combining Earth observation with Earth system models can improve process-based understanding of tipping points, their interactions, and potential tipping cascades. Such fine-resolution sensing can support climate tipping point risk management across scales.