The spiking activity of neocortical neurons exhibits a striking level of variability, even when these networks are driven by identical stimuli. The approximately Poisson firing of neurons has led to the hypothesis that these neural networks operate in the asynchronous state. In the asynchronous state, neurons fire independently from one another, so that the probability that a neuron experience synchronous synaptic inputs is exceedingly low. While the models of asynchronous neurons lead to observed spiking variability, it is not clear whether the asynchronous state can also account for the level of subthreshold membrane potential variability. We propose a new analytical framework to rigorously quantify the subthreshold variability of a single conductance-based neuron in response to synaptic inputs with prescribed degrees of synchrony. Technically, we leverage the theory of exchangeability to model input synchrony via jump-process-based synaptic drives; we then perform a moment analysis of the stationary response of a neuronal model with all-or-none conductances that neglects postspiking reset. As a result, we produce exact, interpretable closed forms for the first two stationary moments of the membrane voltage, with explicit dependence on the input synaptic numbers, strengths, and synchrony. For biophysically relevant parameters, we find that the asynchronous regime yields realistic subthreshold variability (voltage variance $\simeq 4–9{\mathrm{mV}}^2$) only when driven by a restricted number of large synapses, compatible with strong thalamic drive. By contrast, we find that achieving realistic subthreshold variability with dense cortico-cortical inputs requires including weak but nonzero input synchrony, consistent with measured pairwise spiking correlations. We also show that, without synchrony, the neural variability averages out to zero for all scaling limits with vanishing synaptic weights, independent of any balanced state hypothesis. This result challenges the theoretical basis for mean-field theories of the asynchronous state.

Individuals involved in common group activities or settings, e.g., college students that are enrolled in the same class and/or live in the same dorm, are exposed to recurrent contacts of physical proximity. These contacts are known to mediate the spread of an infectious disease; however, it is not obvious how the properties of the spreading process are determined by the structure of and the interrelation among the group settings that are at the root of those recurrent interactions. Here, we show that reshaping the organization of groups within a population can be used as an effective strategy to decrease the severity of an epidemic. Specifically, we show that when group structures are sufficiently correlated, e.g., the likelihood for two students living in the same dorm to attend the same class is sufficiently high, outbreaks are longer but milder than for uncorrelated group structures. Also, we show that the effectiveness of interventions for disease containment increases as the correlation among group structures increases. We demonstrate the practical relevance of our findings by taking advantage of data about housing and attendance of students at the Indiana University campus in Bloomington. By appropriately optimizing the assignment of students to dorms based on their enrollment, we are able to observe a twofold to fivefold reduction in the severity of simulated epidemic processes.

We develop a multiscale approach to estimate high-dimensional probability distributions. Our approach applies to cases in which the energy function (or Hamiltonian) is not known from the start. Using data acquired from experiments or simulations we can estimate the energy function. We obtain a representation of the approximate probability distribution based on a multiscale cascade of conditional probabilities. This representation allows for fast sampling of many-body systems in various domains, from statistical physics to cosmology. Our method—the wavelet-conditional renormalization group (WCRG)—proceeds scale by scale, estimating models for the conditional probabilities of “fast degrees of freedom” conditioned by coarse-grained fields. These probability distributions are modeled by energy functions associated with scale interactions, and are represented in an orthogonal wavelet basis. The WCRG decomposes the microscopic energy function as a sum of interaction energies at all scales and can efficiently generate new samples by going from coarse to fine scales. Near phase transitions, this representation of the approximate probability distribution completely avoids the “critical slowing-down” of direct estimation and sampling algorithms. This is explained theoretically by combining results from RG and wavelet theories, and verified numerically for the Gaussian and ${\phi }^4$-field theories. We show that multiscale WCRG energy-based models are more general than local potential models and can capture the physics of complex many-body interacting systems at all length scales. This is demonstrated for weak-gravitational-lensing fields reflecting dark-matter distributions in cosmology, which include long-range interactions with long-tail probability distributions. The WCRG has a large number of potential applications in nonequilibrium systems, where the underlying distribution is not known a priori. Finally, we discuss the connection between the WCRG and deep network architectures.

One challenge of physics is to explain how collective properties arise from microscopic interactions. Indeed, interactions form the building blocks of almost all physical theories and are described by polynomial terms in the action. The traditional approach is to derive these terms from elementary processes and then use the resulting model to make predictions for the entire system. But what if the underlying processes are unknown? Can we reverse the approach and learn the microscopic action by observing the entire system? We use invertible neural networks to first learn the observed data distribution. By the choice of a suitable nonlinearity for the neuronal activation function, we are then able to compute the action from the weights of the trained model; a diagrammatic language expresses the change of the action from layer to layer. This process uncovers how the network hierarchically constructs interactions via nonlinear transformations of pairwise relations. We test this approach on simulated datasets of interacting theories and on an established image dataset (MNIST). The network consistently reproduces a broad class of unimodal distributions; outside this class, it finds effective theories that approximate the data statistics up to the third cumulant. We explicitly show how network depth and data quantity jointly improve the agreement between the learned and the true model. This work shows how to leverage the power of machine learning to transparently extract microscopic models from data.

Most animal brains present two mirror-symmetric sides, but closer inspection reveals a range of asymmetries (in shape and function) that seem more salient in more cognitively complex species. Sustaining symmetric, redundant neural circuitry has associated metabolic costs, but it might aid in implementing computations within noisy environments or with faulty pieces. It has been suggested that the complexity of a computational task might play a role in breaking bilaterally symmetric circuits into fully lateralized ones; however, a rigorous, mathematically grounded theory of how this mechanism might work is missing. Here, we provide such a mathematical framework, starting with the simplest assumptions but extending our results to a comprehensive range of biologically relevant scenarios. We show mathematically that only fully lateralized or bilateral solutions are relevant within our framework (dismissing configurations in which circuits are only partially engaged). We provide maps that show when each configuration is preferred depending on costs, fitness contributed, circuit reliability, and task complexity. We discuss evolutionary paths leading from bilateral to lateralized configurations and other possible outcomes. The implications of these results for evolution, development, and rehabilitation of damaged or aging brains is discussed. Our work constitutes a limit case that should constrain and underlie similar mappings when other aspects (besides task complexity and circuit reliability) are considered.

A physical self-learning machine can be defined as a nonlinear dynamical system that can be trained on data (similar to artificial neural networks) but where the update of the internal degrees of freedom that serve as learnable parameters happens autonomously. In this way, neither external processing and feedback nor knowledge of (and control of) these internal degrees of freedom is required. We introduce a general scheme for self-learning in any time-reversible Hamiltonian system. It relies on implementing a time-reversal operation and injecting a small error signal on top of the echo dynamics. We show how the physical dynamics itself will then lead to the required gradient update of learnable parameters, independent of the details of the Hamiltonian. We illustrate the training of such a self-learning machine numerically for the case of coupled nonlinear wave fields and other examples.

Pathological morphological changes in tumor tissue enable collective cancer cell unjamming, a cellular motility transition. However, fundamental questions remain: Is unjamming essential for tumor progression? Which different unjamming states can be found in patients? Here, vital cell tracking in patient-derived solid tumor explants ($N=16$) reveals that states of cell unjamming can be recognized by elongated cell and nucleus shape (CeNuS) and low nucleus number density. These static variables serve as a morphodynamic link to map the broad range of morphologies and associated motility states found in histological slides of 1380 breast cancer patients to generate a comprehensive state diagram of cancer cell unjamming. An increase in predicted cell motility in primary tumors through unjamming significantly correlates with distant metastases that may even occur a decade later. Patient risk groups are quantified via a decision boundary in the state space found by machine learning. The resulting clinical prognostic potential is evaluated using a range of quantifiers, including Harrel’s concordance index. Using multivariable Cox models, we find that cell unjamming as a prognostic parameter adds a 26% information gain in the concordance index when combined with the established prognostic criteria (tumor diameter, tumor grade, lymph node status) used in the Nottingham index. Unjamming complements the information on affected lymph nodes in patients regarding metastatic risk. The derived state diagram of cancer cell unjamming reconciles conflicting observations regarding shape- or density-induced unjamming and stresses the nuclei’s mechanical importance, which is not considered in current theories of cell unjamming. We conclude that cancer cell unjamming is part of the metastatic cascade; thus, an emergent physical phenomenon contributes to tumor progression.

Turing patterns, arising from the interplay between competing species of diffusive particles, have long been an important concept for describing nonequilibrium self-organization in nature and have been extensively investigated in many chemical and biological systems. Historically, these patterns have been studied in extended systems and lattices. Recently, the Turing instability was found to produce topological patterns in networks with scale-free degree distributions and the small-world property, although with an apparent absence of geometric organization. While hints of explicitly geometric patterns in simple network models (e.g., Watts-Strogatz) have been found, the question of the exact nature and morphology of geometric Turing patterns in heterogeneous complex networks remained unresolved. In this work, we study the Turing instability in the framework of geometric random graph models, where the network topology is explained using an underlying geometric space. We demonstrate that not only can geometric patterns be observed, their wavelength can also be estimated by studying the eigenvectors of the annealed graph Laplacian. Finally, we show that Turing patterns can be found in geometric embeddings of real networks. These results indicate that there is a profound connection between the function of a network and its hidden geometry, even when the associated dynamical processes are exclusively determined by the network topology.

Fluctuation-dissipation relations (FDRs) connect the internal spontaneous fluctuations of a system with its response to an external perturbation. In this work we propose a nonlinear generalized FDR (NL FDR) as a test for Markovianity of the considered nonequilibrium system; i.e., the violation of the NL FDR indicates a non-Markovian process. Previously suggested FDRs are based on linear response and require a significant number of measurements. However, the nonlinear relation holds for systems out of equilibrium and for strong perturbations. Therefore, its verification requires significantly less data than the standard linear relation. We test the NL FDR for two theoretical model systems: a particle in a tilted periodic potential and a harmonically bound particle, each driven either by white noise (leading to Markovian test cases, which should obey the NL FDR) or by colored noise (resulting in non-Markovian systems, which may not obey the relation). The degree of violation is systematically explored for the non-Markovian variants of our theoretical models. For the particle in the harmonically bound potential, all statistical measures entering the NL FDR can be calculated explicitly and can be used to elucidate why the relation is violated in the non-Markovian case. In addition, we apply our formalism and test for Markovianity in an inherently out-of-equilibrium experimental system, a tracer particle, embedded in an active bath of self-propelled agents (bristlebots) and subject to a force applied by an external air stream. An experimental violation of the NL FDR is witnessed by introducing an additional timescale to the process, when using bristlebots with two metastable speed states.

The adaptive immune system constantly remodels its lymphocyte repertoire for better protection against future pathogens. Its ability to improve antigen recognition on the fly relies on somatic mutation and selective expansion of B lymphocytes expressing high-affinity antigen receptors. However, this rapid evolution inside an individual appears ineffective, hitting a modest ceiling of antigen-binding affinity. Only recently, experiments began to reveal that evolving B cells physically extract antigens from presenting cells using active forces, and that the extraction level dictates clonal fitness. These observations challenge the prevailing view that the equilibrium constant of receptor-antigen binding determines selective advantage of a B cell clone. Here, we present a theoretical framework to explore ways in which tug-of-war antigen extraction impacts the quality and diversity of an evolved B cell repertoire. We propose that the apparent “ineffectiveness” of in vivo selection can be a direct consequence of nonequilibrium antigen recognition. Our theory predicts, on the one hand, that the physical limits of antigen tether strength, under tugging forces, set the affinity ceiling. On the other hand, intriguingly, cells can use force heterogeneity to diversify binding phenotype without compromising fitness, thus remaining plastic under resource constraint. These results suggest that active probing of receptor quality—via a molecular tug of war during antigen recognition—limits the potency of response to current antigens, but confer adaptive benefit against future variants. By bridging physical mechanisms and evolved functions, this work reveals a multifaceted role of active forces in immune adaptation, which rationalizes key observations on repertoire dynamics.

The planted-coloring problem is a prototypical inference problem for which thresholds for Bayes-optimal algorithms, like belief propagation (BP), can be computed analytically. In this paper, we analyze the limits and performances of simulated annealing (SA), a Monte-Carlo-based algorithm that is more general and robust than BP, and thus of broader applicability. We show that SA is suboptimal in the recovery of the planted solution because it gets attracted by glassy states that, instead, do not influence the BP algorithm. At variance with previous conjectures, we propose an analytic estimation for the SA algorithmic threshold by comparing the spinodal point of the paramagnetic phase and the dynamical critical temperature. This is a fundamental connection between thermodynamical phase transitions and out-of-equilibrium behavior of Glauber dynamics. We also study an improved version of SA, called replicated SA (RSA), where several weakly coupled replicas are cooled down together. We show numerical evidence that the algorithmic threshold for the RSA coincides with the Bayes-optimal one. Finally, we develop an approximated analytical theory explaining the optimal performances of RSA and predicting the location of the transition toward the planted solution in the limit of a very large number of replicas. Our results for RSA support the idea that mismatching the parameters in the prior with respect to those of the generative model may produce an algorithm that is optimal and very robust.

Multipolar spindles are very rare in normal tissues, but they are much more prevalent in many tumors, which might be induced by the mechanical confinements from overcrowding microenvironments in tumors. However, little is known about what the difference is between various forms of mechanical confinements that cells encounter in normal tissues and tumor tissues, and how they affect multipolarity and chromosome segregation fidelity. Here, we use microchannels with different heights and widths to mimic diverse forms and degrees of mechanical constraints within the tissue architecture. We find that multipolar spindles occur frequently under two-wall confinement but that they are rare under four-wall confinement, suggesting that multipolar-spindle assembly depends on the form of the three-dimensional mechanical confinement. We reveal that two-wall confinement leads to an increased fraction of multipolar spindles by pole splitting, while four-wall confinement restrains multipolarity by the enhancement of pole clustering and the inhibition of pole splitting. We further conduct numerical simulations and develop a theoretical model to investigate how mechanical confinement influences pole splitting and clustering. By exploring the energy landscape of pole-pole interactions and pole-cortex interactions and treating pole splitting and clustering as reversible reactions, we demonstrate that mechanical confinement controls cell shape and pole-cortex interactions, which, in turn, change the energy barriers of pole splitting and clustering as well as the probability of multipolar mitosis. Further experiments confirm the theoretical prediction that the pole-cortex interaction determines the probability of the multipolar spindles under various mechanical confinements. Our findings demonstrate the extent to which extracellular microenvironments and tissue architecture can affect complex cellular behaviors, indicating that normal tissue architecture may have the ability to suppress the progress of cancers. Thus, our findings would provide essential cues for cancer therapies targeting the tumor microenvironment.

Thermodynamics serves as a universal means for studying physical systems from an energy perspective. In recent years, with the establishment of the field of stochastic and quantum thermodynamics, the ideas of thermodynamics have been generalized to small fluctuating systems. Independently developed in mathematics and statistics, the optimal transport theory concerns the means by which one can optimally transport a source distribution to a target distribution, deriving a useful metric between probability distributions, called the Wasserstein distance. Despite their seemingly unrelated nature, an intimate connection between these fields has been unveiled in the context of continuous-state Langevin dynamics, providing several important implications for nonequilibrium systems. In this study, we elucidate an analogous connection for discrete cases by developing a thermodynamic framework for discrete optimal transport. We first introduce a novel quantity called dynamical state mobility, which significantly improves the thermodynamic uncertainty relation and provides insights into the precision of currents in nonequilibrium Markov jump processes. We then derive variational formulas that connect the discrete Wasserstein distances to stochastic and quantum thermodynamics of discrete Markovian dynamics described by master equations. Specifically, we rigorously prove that the Wasserstein distance equals the minimum product of irreversible entropy production and dynamical state mobility over all admissible Markovian dynamics. These formulas not only unify the relationship between thermodynamics and the optimal transport theory for discrete and continuous cases, but also generalize it to the quantum case. In addition, we demonstrate that the obtained variational formulas lead to remarkable applications in stochastic and quantum thermodynamics, such as stringent thermodynamic speed limits and the finite-time Landauer principle. These bounds are tight and can be saturated for arbitrary temperatures, even in the zero-temperature limit. Notably, the finite-time Landauer principle can explain finite dissipation even at extremely low temperatures, which cannot be explained by the conventional Landauer principle.

Neutrons are powerful tools for investigating the structure and properties of materials used in science and technology. Recently, laser-driven neutron sources (LDNS) have attracted the attention of different communities, from science to industry, in a variety of applications, including radiography, spectroscopy, security, and medicine. However, the laser-driven ion acceleration mechanism for neutron generation and for establishing the scaling law on the neutron yield is essential to improve the feasibility of LDNS. In this paper, we report the mechanism that accelerates ions with spectra suitable for neutron generation. We show that the neutron yield increases with the fourth power of the laser intensity, resulting in the neutron generation of $3\times {10}^{11}$ in $4\pi$ at a maximum, with $1.1\times {10}^{19}\mathrm{W}{\mathrm{cm}}^{-2}$, 900 J, 1.5 ps lasers. By installing a “hand-size” moderator, which is specially designed for the LDNS, it is demonstrated that the efficient generation of epithermal (0.1–100 eV) neutrons enables the single-shot analysis of composite materials by neutron resonance transmission analysis (NRTA). We achieve the energy resolution of 2.3% for 5.19-eV neutrons 1.8 m downstream of the LDNS. This leads to the analysis of elements and isotopes within sub-$\mathrm{\mu }\mathrm{s}$ times and allows for high-speed nondestructive inspection.

Attractor networks are an influential theory for memory storage in brain systems. This theory has recently been challenged by the observation of strong temporal variability in neuronal recordings during memory tasks. In this work, we study a sparsely connected attractor network where memories are learned according to a Hebbian synaptic plasticity rule. After recapitulating known results for the continuous, sparsely connected Hopfield model, we investigate a model in which new memories are learned continuously and old memories are forgotten, using an online synaptic plasticity rule. We show that for a forgetting timescale that optimizes storage capacity, the qualitative features of the network’s memory retrieval dynamics are age dependent: most recent memories are retrieved as fixed-point attractors while older memories are retrieved as chaotic attractors characterized by strong heterogeneity and temporal fluctuations. Therefore, fixed-point and chaotic attractors coexist in the network phase space. The network presents a continuum of statistically distinguishable memory states, where chaotic fluctuations appear abruptly above a critical age and then increase gradually until the memory disappears. We develop a dynamical mean field theory to analyze the age-dependent dynamics and compare the theory with simulations of large networks. We compute the optimal forgetting timescale for which the number of stored memories is maximized. We found that the maximum age at which memories can be retrieved is given by an instability at which old memories destabilize and the network converges instead to a more recent one. Our numerical simulations show that a high degree of sparsity is necessary for the dynamical mean field theory to accurately predict the network capacity. To test the robustness and biological plausibility of our results, we study numerically the dynamics of a network with learning rules and transfer function inferred from in vivo data in the online learning scenario. We found that all aspects of the network’s dynamics characterized analytically in the simpler model also hold in this model. These results are highly robust to noise. Finally, our theory provides specific predictions for delay response tasks with aging memoranda. In particular, it predicts a higher degree of temporal fluctuations in retrieval states associated with older memories, and it also predicts fluctuations should be faster in older memories. Overall, our theory of attractor networks that continuously learn new information at the price of forgetting old memories can account for the observed diversity of retrieval states in the cortex, and in particular, the strong temporal fluctuations of cortical activity.

The distant projection of high-peak and average-power laser beams in the atmosphere is a long-standing goal with a wide range of applications. Our early proof-of-principle experiments [Phys. Rev. X 4, 011027 (2014)] presented one solution to this problem, employing the energy deposition of femtosecond filaments in air to sculpt millisecond-lifetime sub-meter-length air waveguides. Here, we demonstrate air waveguiding at the 50-m scale, $60\times \text{longer}$, making many practical applications now possible. We employ a new method for filament energy deposition: multifilamentation of Laguerre-Gaussian ${\mathrm{LG}}_{01}$ “donut” modes. We first investigate the detailed physics of this scheme over a shorter 8-m in-lab propagation range corresponding to 13 Rayleigh lengths of the guided pulse. We then use these results to demonstrate optical guiding over 45 m in the hallway adjacent to the lab, corresponding to 70 Rayleigh lengths. Injection of a continuous-wave probe beam into these waveguides demonstrates very long lifetimes of tens of milliseconds.

Phase separation of biomolecules gives rise to membraneless organelles that contribute to the spatiotemporal organization of the cell. In most cases, such biomolecular condensates contain multiple components, but the manner in which interactions between components control the stability of condensates have remained challenging to elucidate. Here, we develop an approach to determine tie-line gradients in ternary biomolecular phase-separation systems based on measurements of the dilute phase concentration of only one component. We show that the sign of the tie-line gradient is related to the cross-interaction energy between the polymers in the system and discriminates between associative and segregative phase separation. Using this approach, we study the interaction between protein fused in sarcoma (FUS) and polyethylene glycol (PEG) polymer chains and measure positive tie-line gradients. Our results show that PEG drives phase separation through an associative interaction with FUS, other than through acting as an inert crowder. We further study the interaction between poly(A) ribonucleic acid (RNA) ($\text{700}–\text{3500\hspace{0.17em}\hspace{0.17em}}\mathrm{kDa}$ [kilodalton]) and the protein G3BP1, and using the tie-line gradient as a reporter for the stoichiometry of polymers in the condensate, we determine a G3BP1-to-poly(A) RNA molar ratio of $1:0.003–0.015$ in the dense phase. Our framework for measuring tie-line gradients opens up a route for the characterization of interaction types and compositions in ternary phase-separation systems.

Interfacing electrons and light enables ultrafast electron microscopy and quantum control of electrons, as well as new optical elements for high-sensitivity imaging. Here, we demonstrate for the first time programmable transverse electron-beam shaping in free space based on ponderomotive potentials from short intense laser pulses. We can realize both convex and concave electron lenses with a focal length of a few millimeters, comparable to those in state-of-the-art electron microscopes. We further show that we can realize almost arbitrary deflection patterns by shaping the ponderomotive potentials using a spatial light modulator. Our modulator is lossless and programmable, has unity fill factor, and could pave the way to electron wave-front shaping with hundreds of individually addressable pixels.

Cell migration in confining physiological environments relies on the concerted dynamics of several cellular components, including protrusions, adhesions with the environment, and the cell nucleus. However, it remains poorly understood how the dynamic interplay of these components and the cell polarity determine the emergent migration behavior at the cellular scale. Here, we combine data-driven inference with a mechanistic bottom-up approach to develop a model for protrusion and polarity dynamics in confined cell migration, revealing how the cellular dynamics adapt to confining geometries. Specifically, we use experimental data of joint protrusion-nucleus migration trajectories of cells on confining micropatterns to systematically determine a mechanistic model linking the stochastic dynamics of cell polarity, protrusions, and nucleus. This model indicates that the cellular dynamics adapt to confining constrictions through a switch in the polarity dynamics from a negative to a positive self-reinforcing feedback loop. Our model further reveals how this feedback loop leads to stereotypical cycles of protrusion-nucleus dynamics that drive the migration of the cell through constrictions. These cycles are disrupted upon perturbation of cytoskeletal components, indicating that the positive feedback is controlled by cellular migration mechanisms. Our data-driven theoretical approach therefore identifies polarity feedback adaptation as a key mechanism in confined cell migration.

Biological evolution of a population is governed by the fitness landscape, which is a map from genotype to fitness. However, a fitness landscape depends on the organism’s environment, and evolution in changing environments is still poorly understood. We study a particular model of antibiotic resistance evolution in bacteria where the antibiotic concentration is an environmental parameter and the fitness landscapes incorporate trade-offs between adaptation to low and high antibiotic concentration. With evolutionary dynamics that follow fitness gradients, the evolution of the system under slowly changing antibiotic concentration resembles the athermal dynamics of disordered physical systems under external drives. Exploiting this resemblance, we show that our model can be described as a system with interacting hysteretic elements. As in the case of the driven disordered systems, adaptive evolution under antibiotic concentration cycling is found to exhibit hysteresis loops and memory formation. We derive a number of analytical results for quasistatic concentration changes. We also perform numerical simulations to study how these effects are modified under driving protocols in which the concentration is changed in discrete steps. Our approach provides a general framework for studying motifs of evolutionary dynamics in biological systems in a changing environment.