A fundamental problem associated with the task of network reconstruction from dynamical or behavioral data consists in determining the most appropriate model complexity in a manner that prevents overfitting and produces an inferred network with a statistically justifiable number of edges and their weight distribution. The status quo in this context is based on $L_1$ regularization combined with cross-validation. However, besides its high computational cost, this commonplace approach unnecessarily ties the promotion of sparsity, i.e., abundance of zero weights, with weight “shrinkage.” This combination forces a trade-off between the bias introduced by shrinkage and the network sparsity, which often results in substantial overfitting even after cross-validation. In this work, we propose an alternative nonparametric regularization scheme based on hierarchical Bayesian inference and weight quantization, which does not rely on weight shrinkage to promote sparsity. Our approach follows the minimum description length principle, and uncovers the weight distribution that allows for the most compression of the data, thus avoiding overfitting without requiring cross-validation. The latter property renders our approach substantially faster and simpler to employ, as it requires a single fit to the complete data, instead of many fits for multiple data splits and choice of regularization parameter. As a result, we have a principled and efficient inference scheme that can be used with a large variety of generative models, without requiring the number of reconstructed edges and their weight distribution to be known in advance. In a series of examples, we also demonstrate that our scheme yields systematically increased accuracy in the reconstruction of both artificial and empirical networks. We highlight the use of our method with the reconstruction of interaction networks between microbial communities from large-scale abundance samples involving on the order of ${10}^4–{10}^5$ species and demonstrate how the inferred model can be used to predict the outcome of potential interventions and tipping points in the system.

Biological memory is known to be flexible—memory formation and recall depend on factors such as the behavioral context of the organism. However, this property is often ignored in associative memory models, leaving it unclear how memories can be organized and recalled when subject to contextual control. Because of the lack of a rigorous analytical framework, it is also unknown how contextual control affects memory stability, storage capacity, and information content. Here, we bring the dynamic nature of memory to the fore by introducing a novel model of associative memory, which we refer to as the context-modular memory network. In our model, stored memory patterns are associated to one of several background network states, or contexts. Memories are accessible when their corresponding context is active, and are otherwise inaccessible. Context modulates the effective network connectivity by imposing a specific configuration of neuronal and synaptic gating—gated neurons (synapses) have their activity (weights) momentarily silenced, thereby reducing interference from memories belonging to other contexts. Memory patterns are randomly and independently chosen, while neuronal and synaptic gates may be selected randomly or optimized through a process of contextual synaptic refinement. Through analytic and numerical results, we show that context-modular memory networks can exhibit both improved memory capacity and differential control of memory stability with random gating (especially for neuronal gating). For contextual synaptic refinement, we devise a method in which synapses are gated off for a given context if they destabilize the memory patterns in that context, drastically improving memory capacity and enabling even more precise control over memory stability. Notably, synaptic refinement allows for patterns to be accessible in multiple contexts, stabilizing memory patterns even for weight matrices that alone do not contain any information about the memory patterns, such as Gaussian random matrices. Overall, our model integrates recent ideas about context-dependent memory organization with classic associative memory models and proposes a rigorous theory which can act as a framework for future work. Furthermore, our work carries important implications for the understanding of biological memory storage and recall in the brain, such as highlighting an intriguing trade-off between memory capacity and accessibility.

Glassy materials rapidly quenched from a liquid to a solid state upon flow cessation or cooling solidify in an out-of-equilibrium configuration, trapping residual stresses and retaining the memory of the processing conditions for very long times, which compromises their physical characterization and can adversely affect processing operations. Erasing the mechanical history encoded in disordered materials constitutes a great challenge. Here, we address this problem using experiments and particle dynamic simulations for the case of colloidal glasses made of soft particles densely packed at high volume fractions. We propose a conceptual framework that connects residual stresses, directional memory, and aging of colloidal glasses to the distribution of local shear stresses in the shearing plane. The mean value of the distribution corresponds to the macroscopic stress, the skewness carries information about directional memory, and the standard deviation is related to mechanical aging. Periodically training soft particle glasses near the yield point with a sequence of stress-controlled oscillations provides a fine-tuning of the particle stress distribution. Asymmetric shear stress distributions resulting from previous flow are transformed into symmetric distributions, thereby successfully erasing residual stresses and directional memory. The same methodology is successfully applied to colloidal and polymer gels with thixotropic properties, suggesting that it is general and may be extended to other classes of disordered materials.

The disassembly of misfolded protein aggregates is a requirement for the proper functioning of cells. It has implications in multiple neuropathologies, such as Alzheimer’s and Parkinson’s diseases. The active unbundling of fibrillar aggregates has recently been identified as a key rate-limiting step in the disassembly process. However, the nature of the underlying molecular mechanism remains an outstanding question. Here, we develop a coarse-grained computational approach from the atomistic structural information and show that the interactions of molecules tethered to fibrils lead to entropic forces consistent with the unbundling process observed in amyloid α-synuclein disaggregation by Hsp70. We uncover two main types of entropic effects, categorized as intraprotofilament and interprotofilament, which are differentially affected by the system parameters and conditions. Our results show that only highly efficient chaperone systems can overcome the free-energy cost of the lateral association between two protofilaments. Through the analysis of cryoelectron tomography and high-speed atomic force microscopy data, we find that the conditions for highly efficient entropic force generation are those typically achieved with cochaperone networks and ATP hydrolysis, which require energy expenditure but do not provide an enthalpic component to the separation force. We highlight the implications of these results for the design of targeted therapies for the underlying neuropathologies.

In microbial communities, various cell types often coexist by occupying distinct spatial domains. What determines the shape of the interface between such domains—which, in turn, influences the interactions between cells and overall community function? Here, we address this question by developing a continuum model of a 2D spatially structured microbial community with two distinct cell types. We find that, depending on the balance of the different cell proliferation rates and substrate friction coefficients, the interface between domains is either stable and smooth or unstable and develops fingerlike protrusions. We establish quantitative principles describing when these different interfacial behaviors arise and find good agreement with both the results of previous experimental reports as well as new experiments performed here. Our work, thus, helps to provide a biophysical basis for understanding the interfacial morphodynamics of proliferating microbial communities as well as a broader range of proliferating active systems.

Unmeasured causal forces influence diverse experimental time series, such as the transcription factors that regulate genes or the descending neurons that steer motor circuits. Combining the theory of skew-product dynamical systems with topological data analysis, we show that simultaneous recurrence events across multiple time series reveal the structure of their shared unobserved driving signal. We introduce a physics-based unsupervised learning algorithm that reconstructs causal drivers by iteratively building a recurrence graph with glasslike structure. As the amount of data increases, a percolation transition on this graph leads to weak ergodicity breaking for random walks—revealing the shared driver’s dynamics, even from strongly corrupted measurements. We relate reconstruction accuracy to the rate of information transfer from a chaotic driver to the response systems, and we find that effective reconstruction proceeds through gradual approximation of the driver’s dynamical attractor. Through extensive benchmarks against classical signal processing and machine learning techniques, we demonstrate our method’s ability to extract causal drivers from diverse experimental datasets spanning ecology, genomics, fluid dynamics, and physiology.

We consider a dynamic system that is driven by an intensity-modulated Poisson process with intensity $\mathrm{\Lambda }(t)=\lambda (t)+ϵ\nu (t)$. We derive an exact relation between the input-output cross-correlation in the spontaneous state ($ϵ=0$) and the linear response to the modulation ($ϵ>0$). If $ϵ$ is sufficiently small, linear-response theory captures the full response. The relation can be regarded as a variant of the Furutsu-Novikov theorem for the case of shot noise. As we show, the relation is still valid in the presence of additional independent noise. Furthermore, we derive an extension to Cox-process input, which provides an instance of colored shot noise. We discuss applications to particle detection and to neuroscience. Using the new relation, we obtain a fluctuation-response relation for a leaky integrate-and-fire neuron. We also show how the new relation can be used in a remote control problem in a recurrent neural network. The relations are numerically tested for both stationary and nonstationary dynamics. Lastly, extensions to marked Poisson processes and to higher-order statistics are presented.

Understanding if and how the chirality of biomolecules is transferred across scales into larger components and active processes remains elusive. For instance, flagellated bacteria swim in helical trajectories but chirality seems absent from the active turbulence dynamics they display in dense suspensions. We address this question by examining multiscale dynamics in Paenibacillus vortex colonies. We find active turbulence without manifest chirality in the bulk, but wide, clockwise (viewed from the air side) circulation all along the tortuous centimeter-scale external boundary, while similar but counterclockwise flows follow internal boundaries. We trace the origin of these robust edge flows to an unexpected asymmetry at the individual level that is amplified by local interactions. We rationalize our findings with a model of noisy self-propelled particles immersed in a Stokes fluid that accounts faithfully for our observations. Our modeling and experimental efforts reveal that local nematic alignment and hydrodynamic interactions amplify the weak chiral bias in individual motion, promoting the formation of strong edge flows. The likely topological protection of these flows provides robust transport mechanism over large scales. Such robust boundary phenomena in weakly chiral active fluids may inspire new control strategies for active and biological matter.

Recent developments in stochastic thermodynamics have elucidated various relations between the entropy production rate (thermodynamic dissipation) and the physical limits of information processing in nonequilibrium dynamical systems. These findings have been actively utilized and have opened new perspectives in the analysis of real biological systems. In neuroscience also, the importance of quantifying entropy production has attracted increasing attention as a means to understand the properties of information processing in the brain. However, the relationship between entropy production rate and oscillations, which is prevalent in many biological systems, is unclear. For example, neural oscillations, such as delta, theta, and alpha waves, play crucial roles in brain information processing. Here, we derive a novel decomposition of the entropy production rate of linear Langevin systems. We show that one of the components of the entropy production rate, called the housekeeping entropy production rate, can be decomposed into independent positive contributions from oscillatory modes. Our decomposition enables us to calculate the contribution of oscillatory modes to the housekeeping entropy production rate. In addition, when the noise matrix of the Langevin equation is diagonal, the contribution of each oscillatory mode is further decomposed into the contribution of each element of the system. To demonstrate the utility of our decomposition, we apply our decomposition to an electrocorticography dataset recorded during awake and anesthetized conditions in monkeys, wherein the properties of oscillations change drastically. We show the consistent trends across different monkeys; i.e., the contribution of oscillatory modes from the delta band are larger in the anesthetized condition than in the awake condition, while those from the higher-frequency bands, such as the theta band, are smaller. These results allow us to interpret the change in neural oscillation in terms of stochastic thermodynamics and the physical limit of information processing.

Quantifying how difficult it is to control an emerging infectious disease is crucial to public health decision-making, providing valuable evidence on if targeted interventions, e.g., quarantine and isolation, can contain spread or when population wide controls, e.g., lockdowns, are warranted. The disease reproduction number $R$ or growth rate $r$ are universally assumed to measure controllability because $R=1$ and $r=0$ define when infections stop growing and hence the state of critical stability. Outbreaks with larger $R$ or $r$ are therefore interpreted as less controllable and requiring more stringent interventions. We prove this common interpretation is impractical and incomplete. We identify a positive feedback loop among infections intrinsically underlying disease transmission and evaluate controllability from how interventions disrupt this loop. The epidemic gain and delay margins, which, respectively, define how much we can scale infections (this scaling is known as gain) or delay interventions on this loop before stability is lost, provide rigorous measures of controllability. Outbreaks with smaller margins necessitate more control effort. Using these margins, we quantify how presymptomatic spread, surveillance limitations, variant dynamics, and superspreading shape controllability and demonstrate that $R$ and $r$ measure controllability only when interventions do not alter timings between the infections and are implemented without delay. Our margins are easily computed, interpreted, and reflect complex relationships among interventions, their implementation, and epidemiological dynamics.

Despite the widespread adoption of higher-order mathematical structures such as hypergraphs, methodological tools for their analysis lag behind those for traditional graphs. This work addresses a critical gap in this context by proposing two microcanonical random null models for directed hypergraphs: the directed hypergraph degree model (dhdm) and the directed hypergraph JOINT model (dhjm). These models preserve essential structural properties of directed hypergraphs such as node in- and out-degree sequences and hyperedge head- and tail-size sequences, or their joint tensor. We also describe two efficient Markov chain Monte Carlo algorithms, nudhy-degs and nudhy-joint, to sample random hypergraphs from these ensembles. To showcase the interdisciplinary applicability of the proposed null models, we present three distinct use cases in sociology, epidemiology, and economics. First, we reveal the oscillatory behavior of increased homophily in opposition parties in the U.S. Congress over a 40-year span, emphasizing the role of higher-order structures in quantifying political group homophily. Second, we investigate a nonlinear contagion in contact hypernetworks, demonstrating that disparities between simulations and theoretical predictions can be explained by considering higher-order joint degree distributions. Last, we examine the economic complexity of countries in the global trade network, showing that local network properties preserved by nudhy explain the main structural economic complexity indexes. This work advances the development of null models for directed hypergraphs, addressing the intricate challenges posed by their complex entity relations, and providing a versatile suite of tools for researchers across various domains.

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.

The initial immune response to an acute primary infection is a coupled process of antigen proliferation, molecular recognition by naive B cells, and their subsequent clonal expansion. This process contains a fundamental problem: the recognition of an exponentially time-dependent antigen signal. Here, we show that an efficient immune response must be stringently constrained to B-cell lineages with high antigen binding affinity. We propose a tuned proofreading mechanism for primary recognition of new antigens, where the molecular recognition machinery is adapted to the complexity of the immune repertoire. We show that this process produces potent, specific, and fast recognition of antigens, maintaining a spectrum of genetically distinct B-cell lineages as input for affinity maturation. Our analysis maps the proliferation-recognition dynamics of a primary infection to a generalized Luria-Delbrück process, akin to the dynamics of the classic fluctuation experiment. This map establishes a link between signal recognition dynamics and evolution. We derive the resulting statistics of the activated immune repertoire: Antigen binding affinity, expected size, and frequency of active B-cell clones are related by power laws, which define the class of generalized Luria-Delbrück processes. Their exponents depend on the antigen and B-cell proliferation rate, the number of proofreading steps, and the lineage density of the naive repertoire. We extend the model to include spatiotemporal processes, including the diffusion-recognition dynamics of a vaccination. Empirical data of activated mouse immune repertoires are found to be consistent with activation involving about three proofreading steps. The model predicts key clinical characteristics of acute infections and vaccinations, including the emergence of elite neutralizers and the effects of immune aging. More broadly, our results establish infections and vaccinations as a new probe into the global architecture and functional principles of immune repertoires.

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.

Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional data representations. However, how many training examples are required to learn such representations remains unknown. To quantitatively study this question, we introduce the random hierarchy model: a family of synthetic tasks inspired by the hierarchical structure of language and images. The model is a classification task where each class corresponds to a group of high-level features, chosen among several equivalent groups associated with the same class. In turn, each feature corresponds to a group of subfeatures chosen among several equivalent groups and so on, following a hierarchy of composition rules. We find that deep networks learn the task by developing internal representations invariant to exchanging equivalent groups. Moreover, the number of data required corresponds to the point where correlations between low-level features and classes become detectable. Overall, our results indicate how deep networks overcome the curse of dimensionality by building invariant representations and provide an estimate of the number of data required to learn a hierarchical task.

Paramagnetic transition metals play a crucial role as cofactors in various cellular catalytic processes. However, their high concentrations in reactive oxidation states can induce oxidative stress, resulting in cell dysfunction or death. Hence, it is vital to have methods to monitor metal concentrations and paramagnetic properties in cells for medicine and cell biology. Here we present a novel multimodal method for in-cell magnetometry enabling direct measurement of metal magnetic properties within individual cells in tissue, without prior isolation and at room temperature. Individual cell magnetic moments are measured using superresolution magnetic resonance imaging (MRI) microscopy at 9.4 T by detecting microscopic magnetic-field perturbations around the cells. The cellular metal content is quantified using ion-beam microscopy or synchrotron micro-x-ray fluorescence for the same cells. The metal magnetic susceptibility at 9.4 T is then obtained from the slope of the cell magnetic moments’ dependence on cell metal content. To estimate the susceptibility at lower fields, multifield MR relaxometry and biophysical modeling are employed, extrapolating the 9.4-T susceptibility values to fields as low as 3 T. We apply the new method to determine the susceptibility of iron accumulated in human dopaminergic neurons inside neuromelanin, the by-product of dopamine synthesis. The susceptibility of iron in neuromelanin is measured to be ${\chi }_{\rho }=(2.98\pm 0.19)\times {10}^{-6}{\mathrm{m}}^3/\mathrm{kg}$ providing unique insights into the biochemistry of iron inside dopaminergic neurons. The obtained value reveals a predominant monoatomic low-affinity iron-binding site within neuromelanin, indicating a higher neurotoxicity of iron than previously suggested. Furthermore, the measured susceptibility value establishes a quantitative relationship between cellular iron concentration and iron-sensitive MRI parameters, which can be noninvasively measured in vivo. This breakthrough paves the way for the in vivo detection of dopaminergic neuron density and iron load, requiring a standard clinical MRI scanner only. It promises to facilitate early diagnosis of Parkinson’s disease. In conclusion, our presented novel method enables the direct measurements of magnetic properties of paramagnetic metals within single cells with high sensitivity and across large cell groups within a macroscopic volume, providing invaluable information about the cellular biology of metals.

As a schematic model of the complexity economic agents are confronted with, we introduce the “Sherrington-Kirkpatrick game,” a discrete time binary choice model inspired from mean-field spin glasses. We show that, even in a completely static environment, agents are unable to learn collectively optimal strategies. This is either because the learning process gets trapped in a suboptimal fixed point or because learning never converges and leads to a never-ending evolution of agent intentions. Contrarily to the hope that learning might save the standard “rational expectation” framework in economics, we argue that complex situations are generically unlearnable and agents must do with satisficing solutions, as argued long ago by Simon [Q. J. Econ. 69, 99 (1955)]. Only a centralized, omniscient agent endowed with enormous computing power could qualify to determine the optimal strategy of all agents. Using a mix of analytical arguments and numerical simulations, we find that (i) long memory of past rewards is beneficial to learning, whereas overreaction to recent past is detrimental and leads to cycles or chaos; (ii) increased competition (nonreciprocity) destabilizes fixed points and leads first to chaos and, in the high competition limit, to quasicycles; (iii) some amount of randomness in the learning process, perhaps paradoxically, allows the system to reach better collective decisions; (iv) nonstationary, “aging” behavior spontaneously emerges in a large swath of parameter space of our complex but static world. On the positive side, we find that the learning process allows cooperative systems to coordinate around satisficing solutions with rather high (but markedly suboptimal) average reward. However, hypersensitivity to the game parameters makes it impossible to predict ex ante who will be better or worse off in our stylized economy. The statistical description of the space of satisficing solutions is an open problem.

Complex systems are characterized by multiple spatial and temporal scales. A natural framework to capture their multiscale nature is that of multilayer networks, where different layers represent distinct physical processes that often regulate each other indirectly. We model these regulatory mechanisms through triadic higher-order interactions between nodes and edges. In this work, we focus on how the different timescales associated with each layer impact their reciprocal effective couplings. First, we rigorously derive a decomposition of the joint probability distribution of any dynamical process acting on such multilayer networks. By inspecting this probabilistic structure, we unravel the general principles governing how information propagates across timescales, elucidating the interplay between mutual information and causality in multiscale systems. In particular, we show that feedback interactions, i.e., those representing regulatory mechanisms from slow to fast variables, generate mutual information between layers. On the contrary, direct interactions, i.e., from fast to slow layers, can propagate this information only under certain conditions that depend solely on the structure of the underlying higher-order couplings. We introduce the mutual information matrix for multiscale observables to capture these emergent functional couplings. We apply our results to study archetypal examples of biological signaling networks and effective environmental dependencies in stochastic processes. Our framework generalizes to any dynamics on multilayer networks, paving the way for a deeper understanding of how the multiscale nature of real-world systems shapes their information content and complexity.

Natural and manmade complex systems are comprised of different elementary units, being either system components or diverse subsystems as in the case of networked systems. These units interact with each other in a possibly nonlinear way, which results in a complex dynamics that is generally dissipative and nonstationary. One of the challenges in the modeling of such systems is the identification of not only pairwise but, more importantly, higher-order interactions, together with their directions and strengths from measured multivariate time series. Here, we propose a novel data-driven approach for characterizing interactions of different orders. Our approach is based on solving a set of linear equations constructed from Kramers-Moyal coefficients derived from statistical moments of $\mathcal{N}$-dimensional multivariate time series. We demonstrate the substantial potential for applications by a data-driven reconstruction of interactions in various multidimensional and networked dynamical systems.

We demonstrate the controlled spatiotemporal transfer of transverse orbital angular momentum (OAM) to electromagnetic waves: the spatiotemporal torquing of light. This is a radically different situation from OAM transfer to longitudinal, spatially defined OAM light by stationary or slowly varying refractive-index structures such as phase plates or air turbulence. We show that net transverse OAM per photon can be spatiotemporally imparted to a light pulse only if (1) a transient phase perturbation is well overlapped with the pulse in spacetime, or (2) the pulse initially has nonzero transverse OAM density, and the perturbation removes energy from it. Physical insight is provided by the mechanical analogy of torquing a wheel or removing mass as it spins. Our OAM theory for spatiotemporal optical vortex (STOV) pulses [S. W. Hancock et al.,Phys. Rev. Lett. 127, 193901 (2021)] correctly quantifies the light-matter interaction of our experiments and provides a spatiotemporal-torque-based explanation for the first measurement of STOVs [N. Jhajj et al., Phys. Rev. X 6, 031037 (2016)].