For the brain to recognize local orientations within images, neurons must spontaneously break the translation and rotation symmetry of their response functions—an archetypal example of unsupervised learning. The dominant framework for unsupervised learning in biology is Hebb’s principle, but how Hebbian learning could break such symmetries is a longstanding biophysical riddle. Theoretical studies argue that this requires inputs to the visual cortex to invert the relative magnitude of their correlations at long distances. Empirical measurements have searched in vain for such an inversion and report the opposite to be true. We formally approach the question through the Hermitianization of a multilayer model, which maps it into a problem of zero-temperature phase transitions. In the emerging phase diagram, both symmetries break spontaneously as long as (i) recurrent interactions are sufficiently long range and (ii) Hebbian competition is duly accounted for. A key ingredient for symmetry breaking is competition among connections sprouting from the same afferent cell. Such a competition, along with simple monotonic falloff of input correlations with distance, is capable of triggering the broken-symmetry phase required by image processing. We provide analytic predictions on the relative magnitudes of the relevant length scales needed for this novel mechanism to occur. These results reconcile experimental observations to the Hebbian paradigm, shed light on a new mechanism for visual cortex development, and contribute to our growing understanding of the relationship between learning and symmetry breaking.

Quantifying and comparing patterns of dynamical ecological systems requires averaging over measurable quantities. For example, to infer variation in movement and behavior, metrics such as step length and velocity are averaged over large ensembles. Yet, in nonergodic systems, such averaging is inconsistent; thus, identifying ergodicity breaking is essential in ecology. Using rich, high-resolution, movement data sets (greater than $7\times {10}^7$ localizations) from 70 individuals and continuous-time random walk modeling, we find subdiffusive behavior and ergodicity breaking in the localized movement of three species of avian predators. Small-scale, within-patch movement was found to be qualitatively different, not inferrable and separated from large-scale interpatch movement. Local search is characterized by long, power-law-distributed waiting times with a diverging mean, giving rise to ergodicity breaking in the form of considerable variability uniquely observed at this scale. This implies that wild animal movement is scale specific, with no typical waiting time at the local scale.

Power-law distributions are widely used in computational and statistical investigations of extreme events and complex systems. The usual technique to generate power-law distributed data is to first infer the scale exponent $\alpha$ using the observed data of interest and then sample from the associated distribution. This approach has important limitations because it relies on a fixed $\alpha$ (e.g., it has limited applicability in testing the family of power-law distributions) and on the hypothesis of independent observations (e.g., it ignores temporal correlations and other constraints typically present in complex systems data). Here we propose a constrained surrogate method that overcomes these limitations by choosing uniformly at random from a set of sequences exactly as likely to be observed under a discrete power law as the original sequence (i.e., regardless of $\alpha$) and by showing how additional constraints can be imposed in the sequence (e.g., the Markov transition probability between states). This nonparametric approach involves redistributing observed prime factors to randomize values in accordance with a power-law model but without restricting ourselves to independent observations or to a particular $\alpha$. We test our results in simulated and real data, ranging from the intensity of earthquakes to the number of fatalities in disasters.

The threat of global warming and the demand for reliable climate predictions pose a formidable challenge because the climate system is multiscale, high-dimensional and nonlinear. Spatiotemporal recurrences of the system hint to the presence of a low-dimensional manifold containing the high-dimensional climate trajectory that could make the problem more tractable. Here we argue that reproducing the geometrical and topological properties of the low-dimensional attractor should be a key target for models used in climate projections. In doing so, we propose a general data-driven framework to characterize the climate attractor and showcase it in the tropical Pacific Ocean using a reanalysis as observational proxy and two state-of-the-art models. The analysis spans four variables simultaneously over the periods 1979–2019 and 2060–2100. At each time $t$, the system can be uniquely described by a state space vector parametrized by $N$ variables and their spatial variability. The dynamics is confined on a manifold with dimension lower than the full state space that we characterize through manifold learning algorithms, both linear and nonlinear. Nonlinear algorithms describe the attractor through fewer components than linear ones by considering its curved geometry, allowing for visualizing the high-dimensional dynamics through low-dimensional projections. The local geometry and local stability of the high-dimensional, multivariable climate attractor are quantified through the local dimension and persistence metrics. Model biases that hamper climate predictability are identified and found to be similar in the multivariate attractor of the two models during the historical period while diverging under the warming scenario considered. Finally, the relationships between different subspaces (univariate fields), and therefore among climate variables, are evaluated. The proposed framework provides a comprehensive, physically based, test for assessing climate feedbacks and opens new avenues for improving their model representation.

The mapping of the wiring diagrams of neural circuits promises to allow us to link the structure and function of neural networks. Current approaches to analyzing such connectomes rely mainly on graph-theoretical tools, but these may downplay the complex nonlinear dynamics of single neurons and the way networks respond to their inputs. Here, we measure the functional similarity of simulated networks of neurons, by quantifying the similitude of their spiking patterns in response to the same stimuli. We find that common graph-theory metrics convey little information about the similarity of networks’ responses. Instead, we learn a functional metric between networks based on their synaptic differences and show that it accurately predicts the similarity of novel networks, for a wide range of stimuli. We then show that a sparse set of architectural features—the sum of synaptic inputs that each neuron receives and the sum of each neuron’s synaptic outputs—predicts the functional similarity of networks of up to 1000 neurons, with high accuracy. We thus suggest new architectural design principles that shape the function of neural networks. These architectural features conform with experimental evidence of homeostatic synaptic mechanisms.

Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning. Quantum mechanical systems can produce probability distributions that exhibit quantum correlations which are difficult to capture using classical models. We show theoretically that such quantum-inspired correlations provide a powerful resource for generative modeling. In particular, we provide an unconditional proof of separation in expressive power between a class of widely used generative models, known as Bayesian networks, and its minimal quantum-inspired extension. We show that this expressivity enhancement is associated with quantum nonlocality and quantum contextuality. Furthermore, we numerically test this separation on standard machine-learning data sets and show that it holds for practical problems. The possibility of quantum-inspired enhancement demonstrated in this work not only sheds light on the design of useful quantum machine-learning protocols but also provides inspiration to draw on ideas from quantum foundations to improve purely classical algorithms.

Cortical neurons are characterized by irregular firing and a broad distribution of rates. The balanced state model explains these observations with a cancellation of mean excitatory and inhibitory currents, which makes fluctuations drive firing. In networks of neurons with current-based synapses, the balanced state emerges dynamically if coupling is strong, i.e., if the mean number of synapses per neuron $K$ is large and synaptic efficacy is of the order of $1/\sqrt{K}$. When synapses are conductance-based, current fluctuations are suppressed when coupling is strong, questioning the applicability of the balanced state idea to biological neural networks. We analyze networks of strongly coupled conductance-based neurons and show that asynchronous irregular activity and broad distributions of rates emerge if synaptic efficacy is of the order of $1/\log (K)$. In such networks, unlike in the standard balanced state model, current fluctuations are small and firing is maintained by a drift-diffusion balance. This balance emerges dynamically, without fine-tuning, if inputs are smaller than a critical value, which depends on synaptic time constants and coupling strength, and is significantly more robust to connection heterogeneities than the classical balanced state model. Our analysis makes experimentally testable predictions of how the network response properties should evolve as input increases.

Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) and neuroscience. Prior theoretical work has focused on RNNs with additive interactions. However, gating, i.e., multiplicative, interactions are ubiquitous in real neurons and also the central feature of the best-performing RNNs in ML. Here, we show that gating offers flexible control of two salient features of the collective dynamics: (i) timescales and (ii) dimensionality. The gate controlling timescales leads to a novel, marginally stable state, where the network functions as a flexible integrator. Unlike previous approaches, gating permits this important function without parameter fine-tuning or special symmetries. Gates also provide a flexible, context-dependent mechanism to reset the memory trace, thus complementing the memory function. The gate modulating the dimensionality can induce a novel, discontinuous chaotic transition, where inputs push a stable system to strong chaotic activity, in contrast to the typically stabilizing effect of inputs. At this transition, unlike additive RNNs, the proliferation of critical points (topological complexity) is decoupled from the appearance of chaotic dynamics (dynamical complexity). The rich dynamics are summarized in phase diagrams, thus providing a map for principled parameter initialization choices to ML practitioners.

The statistics of gap ratios between consecutive energy levels is a widely used tool—in particular, in the context of many-body physics—to distinguish between chaotic and integrable systems, described, respectively, by Gaussian ensembles of random matrices and Poisson statistics. In this work, we extend the study of the gap ratio distribution $P(r)$ to the case where discrete symmetries are present. This is important since in certain situations it may be very impractical, or impossible, to split the model into symmetry sectors, let alone in cases where the symmetry is not known in the first place. Starting from the known expressions for surmises in the Gaussian ensembles, we derive analytical surmises for random matrices comprised of several independent blocks. We check our formulas against simulations from large random matrices, showing excellent agreement. We then present a large set of applications in many-body physics, ranging from quantum clock models and anyonic chains to periodically driven spin systems. In all these models, the existence of a (sometimes hidden) symmetry can be diagnosed through the study of the spectral gap ratios, and our approach furnishes an efficient way to characterize the number and size of independent symmetry subspaces. We finally discuss the relevance of our analysis for existing results in the literature, as well as its practical usefulness, and point out possible future applications and extensions.

We illuminate the many-body effects underlying the structure, formation, and dissolution of cellular adhesion domains in the presence and absence of forces. We consider mixed Glauber-Kawasaki dynamics of a two-dimensional model of nearest-neighbor-interacting adhesion bonds with intrinsic binding affinity under the action of a shared pulling or pushing force. We consider adhesion bonds that are immobile due to being anchored to the underlying cytoskeleton, as well as adhesion molecules that are transiently diffusing. Highly accurate analytical results are obtained on the pair-correlation level of the Bethe-Guggenheim approximation for the complete thermodynamics and kinetics of adhesion clusters of any size, including the thermodynamic limit. A new kind of dynamical phase transition is uncovered—the mean formation and dissolution times per adhesion bond change discontinuously with respect to the bond-coupling parameter. At the respective critical points, cluster formation and dissolution are the fastest, while the statistically dominant transition path undergoes a qualitative change—the entropic barrier to a completely bound or unbound state is rate-limiting below, and the phase transition between dense and dilute phases above the dynamical critical point. In the context of the Ising model, the dynamical phase transition reflects a first-order discontinuity in the magnetization-reversal time. Our results provide a potential explanation for the mechanical regulation of cell adhesion and suggest that the quasistatic and kinetic responses to changes in the membrane stiffness or applied forces is largest near the statical and dynamical critical points, respectively.

Multiple aspects of an economy can be regulated, tampered with, or left to chance. Economic actors can exploit these degrees of freedom, at a cost, to bend the flow of wealth in their favor. If intervention becomes widespread, microeconomic strategies of different actors can build into emergent macroeconomic effects. How viable is a “rigged” economy? How do growing economic complexity and wealth affect it? We study rigged economies with a toy model. In it, economic degrees of freedom progress from minority to coordination games as intervention increases. Growing economic complexity spontaneously defuses cartels. But excessive complexity leads to large-fluctuations regimes, threatening the system’s stability. Simulations suggest that wealth must grow faster than linearly with economic complexity to avoid this regime and keep economies viable in the long run. We discuss a real-case scenario of multiple economic actors coordinated to result in an emergent upset of the stock market.

Many biological systems synchronize their movement through physical interactions. By far, the most well-studied examples concern physical interactions through a fluid: Beating cilia, swimming sperm and worms, and flapping wings all display synchronization behavior through fluid mechanical interactions. However, as the density of a collective increases, individuals may also interact with each other through physical contact. In the field of “active matter” systems, it is well known that inelastic contact between individuals can produce long-range correlations in position, orientation, and velocity. In this work, we demonstrate that contact interactions between undulating robots yield novel phase dynamics such as synchronized motions. We consider undulatory systems in which rhythmic motion emerges from time-independent oscillators that sense and respond to an undulatory bending angle and speed. In pair experiments, we demonstrate that robot joints will synchronize to in-phase and antiphase oscillations through collisions, and a phase-oscillator model describes the stability of these modes. To understand how contact interactions influence the phase dynamics of larger groups, we perform simulations and experiments of simple three-link undulatory robots that interact only through contact. Collectives synchronize their movements through contact as predicted by the theory, and when the robots can adjust their position in response to contact, we no longer observe antiphase synchronization. Lastly, we demonstrate that synchronization dramatically reduces the interaction forces within confined groups of undulatory robots, indicating significant energetic and safety benefits from group synchronization. The theory and experiments in this study illustrate how contact interactions in undulatory active matter can lead to novel collective motion and synchronization.

Pursuing fractionalized particles that do not bear properties of conventional measurable objects, exemplified by bare particles in the vacuum such as electrons and elementary excitations such as magnons, is a challenge in physics. Here we show that a machine-learning method for quantum many-body systems that has achieved state-of-the-art accuracy reveals the existence of a quantum spin liquid (QSL) phase in the region $0.49\lesssim J_2/J_1\lesssim 0.54$ convincingly in spin-$1/2$ frustrated Heisenberg model with the nearest and next-nearest-neighbor exchanges, $J_1$ and $J_2$, respectively, on the square lattice. This is achieved by combining with the cutting-edge computational schemes known as the correlation ratio and level spectroscopy methods to mitigate the finite-size effects. The quantitative one-to-one correspondence between the correlations in the ground state and the excitation spectra found in the present analyses enables the reliable identification and estimation of the QSL and its nature. The spin excitation spectra containing both singlet and triplet gapless Dirac-like dispersions signal the emergence of gapless fractionalized spin-$1/2$ Dirac-type spinons in the distinctive QSL phase. Unexplored critical behavior with coexisting and dual power-law decays of Néel antiferromagnetic and dimer correlations is revealed. The power-law decay exponents of the two correlations differently vary with $J_2/J_1$ in the QSL phase and thus have different values except for a single point satisfying the symmetry of the two correlations. The isomorph of excitations with the cuprate $d$-wave superconductors revealed here implies a tight connection between the present QSL and superconductivity. This achievement demonstrates that the quantum-state representation using machine-learning techniques, which had mostly been limited to benchmarks, is a promising tool for investigating grand challenges in quantum many-body physics.

Epithelia are ubiquitous tissues that display a large diversity of functions and forms, from totally flat to highly curved. Various morphogenetic events, such as gastrulation or branching morphogenesis, correlate to changes in the curvature of epithelia. Building a physical framework to account for the shape of cells in epithelia is thus an important challenge to understand various normal and pathological biological processes, such as epithelial morphogenesis or cancer metastasis. It is widely recognized that the shape of epithelial cells is determined by the tension generated by the actomyosin cortex and the adhesion of cells to the substrate and to each other. These tensions and adhesions are not homogeneously distributed on the cell surface, which makes a 3D view of the problem valuable. To account for these biological and structural contributions to cell shape, different physical models have been proposed, which include surface energies, adhesions, line tensions, volume compressibility, or elasticity terms. However, an experimental procedure that would allow a validation of a minimal physical model for the shape of epithelial cells in 3D has not yet been proposed. In this study, we first made a quantitative analysis of the correlation between cell thickness and curvature during the formation of the ventral furrow in the early Drosophila embryo. We then cultured Madin-Darby Canine Kidney (MDCK) epithelial cells on substrates with a sinusoidal profile, allowing us to measure the shape of the cells on various positive and negative curvatures. We found that both in the early Drosophila ventral furrow and in MDCK epithelia cells are thicker when positively curved (on valleys of sinusoidal substrates) than when negatively curved (on the crests). The influence of curvature on the shape of epithelial cells could not be understood with a model using only differential apical, basal, and lateral surface energies. However, the addition of an apical line tension was sufficient to quantitatively account for the experimental measurements. The model also accounts for the shape of MDCK cells that overexpress E-cadherin. On the other hand, when reducing myosin II activity with blebbistatin, we measured a saturation of the difference in cell thickness between valleys and crests, suggesting the need for a term limiting large cell deformations. Our results show that a minimal model that accounts for epithelial cell shape needs to include an apical line tension in addition to differential surface energies, highlighting the importance of structures that produce anisotropic tension in epithelial cells, such as the actin belt linking adherens junctions. In the future, the model could be used to account for the shape of epithelial cells in different contexts, such as branching morphogenesis. Furthermore, our experimental procedure could be used to test a wider range of physical models for the shape of epithelia in curved environments, including, for example, continuous models.

Cells coexist together in colonies or as tissues. Their behavior is controlled by an interplay between intercellular forces and biochemical regulation. We develop a simple model of the cell cycle, the fundamental regulatory network controlling growth and division, and couple this to the physical forces arising within the cell collective. We analyze this model using both particle-based computer simulations and a continuum theory. We focus on 2D colonies confined in a channel. These develop moving growth fronts of dividing cells with quiescent cells in the interior. The profile and speed of these fronts are nontrivially related to the substrate friction and the cell-cycle parameters, providing a possible approach to measure such parameters in experiments.

We devise a machine learning technique to solve the general problem of inferring network links that have time delays using only time series data of the network nodal states. This task has applications in many fields, e.g., from applied physics, data science, and engineering to neuroscience and biology. Our approach is to first train a type of machine learning system known as reservoir computing to mimic the dynamics of the unknown network. We then use the trained parameters of the reservoir system output layer to deduce an estimate of the unknown network structure. Our technique, by its nature, is noninvasive but is motivated by the widely used invasive network inference method, whereby the responses to active perturbations applied to the network are observed and employed to infer network links (e.g., knocking down genes to infer gene regulatory networks). We test this technique on experimental and simulated data from delay-coupled optoelectronic oscillator networks, with both identical and heterogeneous delays along the links. We show that the technique often yields very good results, particularly if the system does not exhibit synchrony. We also find that the presence of dynamical noise can strikingly enhance the accuracy and ability of our technique, especially in networks that exhibit synchrony.

We study the stability of quasinormal modes (QNM) in asymptotically flat black hole spacetimes by means of a pseudospectrum analysis. The construction of the Schwarzschild QNM pseudospectrum reveals the following: (i) the stability of the slowest-decaying QNM under perturbations respecting the asymptotic structure, reassessing the instability of the fundamental QNM discussed by Nollert [H. P. Nollert, About the Significance of Quasinormal Modes of Black Holes, Phys. Rev. D 53, 4397 (1996)] as an “infrared” effect; (ii) the instability of all overtones under small-scale (“ultraviolet”) perturbations of sufficiently high frequency, which migrate towards universal QNM branches along pseudospectra boundaries, shedding light on Nollert’s pioneer work and Nollert and Price’s analysis [H. P. Nollert and R. H. Price, Quantifying Excitations of Quasinormal Mode Systems, J. Math. Phys. (N.Y.) 40, 980 (1999)]. Methodologically, a compactified hyperboloidal approach to QNMs is adopted to cast QNMs in terms of the spectral problem of a non-self-adjoint operator. In this setting, spectral (in)stability is naturally addressed through the pseudospectrum notion that we construct numerically via Chebyshev spectral methods and foster in gravitational physics. After illustrating the approach with the Pöschl-Teller potential, we address the Schwarzschild black hole case, where QNM (in)stabilities are physically relevant in the context of black hole spectroscopy in gravitational-wave physics and, conceivably, as probes into fundamental high-frequency spacetime fluctuations at the Planck scale.

The stochasticity of gene expression is manifested in the fluctuations of messenger ribonucleic acid and protein copy numbers within a cell lineage over time. While data of this type can be obtained for many generations, most mathematical models are unsuitable to interpret such data since they assume nongrowing cells. Here we develop a theoretical approach that quantitatively links the frequency content of lineage data to subcellular dynamics. We elucidate how the position, height, and width of the peaks in the power spectrum provide a distinctive fingerprint that encodes a wealth of information about mechanisms controlling transcription, translation, replication, degradation, bursting, promoter switching, cell cycle duration, cell division, gene dosage compensation, and cell-size homeostasis. Predictions are confirmed by analysis of single-cell Escherichia coli data obtained using fluorescence microscopy. Furthermore, by matching the experimental and theoretical power spectra, we infer the temperature-dependent gene expression parameters, without the need of measurements relating fluorescence intensities to molecule numbers.

Icosahedral virus capsids are closed shells built up with a hexagonal lattice of proteins, which incorporate pentamers at their fivefold vertices. Human adenovirus particles lose pentamers (pentons) during infection under a variety of physicochemical cues, including mechanical pulling of molecular motors and the viscous drag of the cytoplasm. By combining atomic force microscopy experiments with survival analysis and Markovian transition state theory, we investigate the sequence of adenovirus penton disassembly that reveals the aging of the virus structure. We show evidence that the lifetime of pentons gradually decreases, accompanied by capsid softening as neighboring pentons are lost. This cooperative dismantling process, which involves first-neighbor penton-penton distances of at least 45 nm, leads to a 50% increase in the virus disassembling rate of the virus particle. Theory and experiments fit remarkably well, allowing us to obtain the spontaneous escape rate and the energy barrier of penton disassembly ($\sim 30k_{B}T$). The observed increase in the penton’s loss rate reveals long-range structural correlations within the capsid. Our estimations suggest that the mechanical cues arising from the strokes of protein motors carrying the virus to the nucleus could help penton disassembly and warrant the timely delivery of weak-enough capsids for adenovirus infection.

Community detection methods attempt to divide a network into groups of nodes that share similar properties, thus revealing its large-scale structure. A major challenge when employing such methods is that they are often degenerate, typically yielding a complex landscape of competing answers. As an attempt to extract understanding from a population of alternative solutions, many methods exist to establish a consensus among them in the form of a single partition “point estimate” that summarizes the whole distribution. Here, we show that it is, in general, not possible to obtain a consistent answer from such point estimates when the underlying distribution is too heterogeneous. As an alternative, we provide a comprehensive set of methods designed to characterize and summarize complex populations of partitions in a manner that captures not only the existing consensus but also the dissensus between elements of the population. Our approach is able to model mixed populations of partitions, where multiple consensuses can coexist, representing different competing hypotheses for the network structure. We also show how our methods can be used to compare pairs of partitions, how they can be generalized to hierarchical divisions, and how they can be used to perform statistical model selection between competing hypotheses.