Complexity Thoughts: Issue #33
Unraveling complexity: building knowledge, one paper at a time
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Dall-e 3 representation of this issue’s content
Foundations of network science and complex systems
Relevant to read for putting the subsequent paper in a better context:
Message passing on networks with loops
Message passing is a fundamental technique for performing calculations on networks and graphs with applications in physics, computer science, statistics, and machine learning, including Bayesian inference, spin models, satisfiability, graph partitioning, network epidemiology, and the calculation of matrix eigenvalues. Despite its wide use, however, it has long been recognized that the method has a fundamental flaw: It works poorly on networks that contain short loops. Loops introduce correlations that can cause the method to give inaccurate answers or to fail completely in the worst cases. Unfortunately, most real-world networks contain many short loops, which limits the usefulness of the message-passing approach. In this paper we demonstrate how to rectify this shortcoming and create message-passing methods that work on any network. We give 2 example applications, one to the percolation properties of networks and the other to the calculation of the spectra of sparse matrices.
Tensor Network Message Passing
When studying interacting systems, computing their statistical properties is a fundamental problem in various fields such as physics, applied mathematics, and machine learning. However, this task can be quite challenging due to the exponential growth of the state space as the system size increases. Many standard methods have significant weaknesses. For instance, message-passing algorithms can be inaccurate and even fail to converge due to short loops, while tensor network methods can have exponential computational complexity in large graphs due to long loops. In this Letter, we propose a new method called “tensor network message passing.” This approach allows us to compute local observables like marginal probabilities and correlations by combining the strengths of tensor networks in contracting small subgraphs with many short loops and the strengths of message-passing methods in globally sparse graphs, thus addressing the crucial weaknesses of both approaches. Our algorithm is exact for systems that are globally treelike and locally dense-connected when the dense local graphs have a limited tree width. We have conducted numerical experiments on synthetic and real-world graphs to compute magnetizations of Ising models and spin glasses, and have demonstrated the superiority of our approach over standard belief propagation and the recently proposed loopy message-passing algorithm. In addition, we discuss the potential applications of our method in inference problems in networks, combinatorial optimization problems, and decoding problems in quantum error correction.
Geometric renormalization of weighted networks
The geometric renormalization technique for complex networks has successfully revealed the multiscale self-similarity of real network topologies and can be applied to generate replicas at different length scales. Here, we extend the geometric renormalization framework to weighted networks, where the intensities of the interactions play a crucial role in their structural organization and function. Our findings demonstrate that the weighted organization of real networks exhibits multiscale self-similarity under a renormalization protocol that selects the connections with the maximum weight across increasingly longer length scales. We present a theory that elucidates this symmetry, and that sustains the selection of the maximum weight as a meaningful procedure. Based on our results, scaled-down replicas of weighted networks can be straightforwardly derived, facilitating the investigation of various size-dependent phenomena in downstream applications.
Identifying hubs in directed networks
Nodes in networks that exhibit high connectivity, also called “hubs,” play a critical role in determining the structural and functional properties of networked systems. However, there is no clear definition of what constitutes a hub node in a network, and the classification of network hubs in existing work has either been purely qualitative or relies on ad hoc criteria for thresholding continuous data that do not generalize well to networks with certain degree sequences. Here we develop a set of efficient nonparametric methods that classify hub nodes in directed networks using the Minimum Description Length principle, effectively providing a clear and principled definition for network hubs. We adapt our methods to both unweighted and weighted networks, and we demonstrate them in a range of example applications using real and synthetic network data.
Ecosystems
Diversity begets stability: Sublinear growth and competitive coexistence across ecosystems
We propose that population growth may scale as a sublinear power law with biomass. Not only is sublinear population density dependence consistent with extensive time-series data, but the sublinear community model is more parsimonious and realistic than the logistic for modeling several macroecological patterns. But why should sublinear population growth have such an opposing collective effect on community stability from what classic theory predicts?
Editor’s summary:
Some of Earth’s most biodiverse ecosystems are also its most stable over time, yet ecological theory predicts that communities become less stable when more species co-occur. The most commonly used models of species coexistence are derived from the Lotka-Volterra model, which assumes that populations follow logistic growth patterns and that self-regulation is required to allow multiple species to stably coexist. Hatton et al. show that an alternative model with sublinear population growth provides nearly identical predictions to generalized Lotka-Volterra models at the population level but very different predictions for communities. Under the sublinear model, diversity promotes stability. This model is consistent with published population time series and macroecological scaling relationships.
Biological Systems
CryoEM structures reveal how the bacterial flagellum rotates and switches direction
Chemotaxis is a fascinating phenomenon, crucial for some (micro)organisms.
“How bacterial chemotaxis is performed is much better understood than why.” — Keegstra et al
Bacterial chemotaxis requires bidirectional flagellar rotation at different rates. Rotation is driven by a flagellar motor, which is a supercomplex containing multiple rings. Architectural uncertainty regarding the cytoplasmic C-ring, or ‘switch’, limits our understanding of how the motor transmits torque and direction to the flagellar rod. Here we report cryogenic electron microscopy structures for Salmonella enterica serovar typhimurium inner membrane MS-ring and C-ring in a counterclockwise pose (4.0 Å) and isolated C-ring in a clockwise pose alone (4.6 Å) and bound to a regulator (5.9 Å). Conformational differences between rotational poses include a 180° shift in FliF/FliG domains that rotates the outward-facing MotA/B binding site to inward facing. The regulator has specificity for the clockwise pose by bridging elements unique to this conformation. We used these structures to propose how the switch reverses rotation and transmits torque to the flagellum, which advances the understanding of bacterial chemotaxis and bidirectional motor rotation.
Neuroscience
A precision functional atlas of personalized network topography and probabilities
Although the general location of functional neural networks is similar across individuals, there is vast person-to-person topographic variability. To capture this, we implemented precision brain mapping functional magnetic resonance imaging methods to establish an open-source, method-flexible set of precision functional network atlases—the Masonic Institute for the Developing Brain (MIDB) Precision Brain Atlas. This atlas is an evolving resource comprising 53,273 individual-specific network maps, from more than 9,900 individuals, across ages and cohorts, including the Adolescent Brain Cognitive Development study, the Developmental Human Connectome Project and others. We also generated probabilistic network maps across multiple ages and integration zones (using a new overlapping mapping technique, Overlapping MultiNetwork Imaging). Using regions of high network invariance improved the reproducibility of executive function statistical maps in brain-wide associations compared to group average-based parcellations. Finally, we provide a potential use case for probabilistic maps for targeted neuromodulation. The atlas is expandable to alternative datasets with an online interface encouraging the scientific community to explore and contribute to understanding the human brain function more precisely.
Bio-inspired computing
Recently, machine learning methods, including reservoir computing (RC), have been tremendously successful in predicting complex dynamics in many fields. However, a present challenge lies in pushing for the limit of prediction accuracy while maintaining the low complexity of the model. Here, we design a data-driven, model-free framework named higher-order Granger reservoir computing (HoGRC), which owns two major missions: The first is to infer the higher-order structures incorporating the idea of Granger causality with the RC, and, simultaneously, the second is to realize multi-step prediction by feeding the time series and the inferred higher-order information into HoGRC. We demonstrate the efficacy and robustness of the HoGRC using several representative systems, including the classical chaotic systems, the network dynamical systems, and the UK power grid system. In the era of machine learning and complex systems, we anticipate a broad application of the HoGRC framework in structure inference and dynamics prediction.
Oldies but goldies
From the concept of system to the paradigm of complexity
I had the great opportunity to listen to an Edgard Morin’s seminar at the University of Messina (the city where I was born), when I was a teenager, more than 20 years ago. His thoughts have deeply influenced my perspective about nature and the universe in general. This paper is a gem.
Curiosity: in 2002, a center for the philosophy of complexity was founded in Messina.
This paper is an overview of the author's ongoing reflections on the need for a new paradigm of complexity capable of informing all theories, whatever their field of application or the phenomena in question. Beginning with a critique of General System Theory and the principle of holism with which it is associated, the author suggests that contemporary advances in our knowledge of organization call for a radical reformation in our organization of knowledge. This reformation involves the mobilization of recursive thinking, which is to say a manner of thinking capable of establishing a dynamic and generative feedback loop between terms or concepts (such as whole and part, order and disorder, observer and observed, system and ecosystem, etc.) that remain both complementary and antagonistic. The paradigm of complexity thus stands as a bold challenge to the fragmentary and reductionistic spirit that continues to dominate the scientific enterprise.
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