Calcium signals in pancreatic $\beta$ cell collectives show a sharp transition from uncorrelated to correlated state resembling a phase transition as the slowly increasing glucose concentration crosses the tipping point. However, the exact nature or the order of this phase transition is not well understood. Using confocal microscopy to record the collective calcium activation of $\beta$ cells in an intact islet under changing glucose concentration in an increasing and then decreasing way, we first show that in, addition to the sharp transition, the coordinated calcium response exhibits a hysteresis indicating a critical, first-order transition. A network model of $\beta$ cells combining link selection and coordination mechanisms capture the observed hysteresis loop and the critical nature of the transition. Our results point towards an understanding of the role of islets as tipping elements in the pancreas that, interconnected by perfusion, diffusion, and innervation, cause the tipping dynamics and abrupt insulin release.

In our ears, inner-hair-cell hair bundles (IHBs) convert sound-induced forces into electrical signals, which are ultimately transmitted to the brain. An IHB comprises filamentous stereocilia emanating from the inner-hair-cell apex. Stereocilium deflections promote ion-channel opening and closing, causing receptor currents. This process is limited by fluctuations in the deflections, which compete with the sound signal, limiting the threshold of hearing. Stereocilia are viscoelastic structures and are coupled by fluid and viscoelastic links. The stiffness and damping of the system's components constrain stereocilium deflections, but increasing damping increases thermal deflection fluctuations. Competition between the constraining forces and thermal forces determines the deflection fluctuations. To better understand the deflection fluctuations, we build a mathematical model that relates the IHB's mechanical properties to deflection fluctuations. We find that the coherency of neighboring stereocilium deflections is less than $0.75$ at frequencies corresponding to the physiological range of sound frequencies. The coherency for pairs of stereocilia decreases exponentially with the distance between them and is approximately zero between stereocilia at the center and edge of the IHB. We determine how the deflection fluctuations depend on the stiffness and damping of the links. In the absence of stiff links between stereocilia, neighboring stereocilia are weakly or negatively correlated in the physiological frequency range. We show how the sign of the coherency between stereocilium pairs is determined by the eigendecomposition of the deflection power spectral density matrix. Increasing the number of stereocilia in the IHB decreases the coherency between stereocilium pairs. The model also predicts that the threshold of hearing corresponds to IHB stereocilium deflections owing to sound of $<$ 1.5 nm and that links of physiological stiffness decrease the threshold of hearing by at least $10\mathrm{dB}$. Predictions of the mathematical model are experimentally testable using recently developed techniques.

The number $n_s$ of clusters (per site) of size $s$, a central quantity in percolation theory, displays at criticality an algebraic scaling behavior of the form $n_s\simeq s^{-\tau }A(1+B{s}^{-\mathrm{\Omega }})$. For the Fortuin-Kasteleyn representation of the $Q$-state Potts model in two dimensions, the Fisher exponent $\tau$ is known as a function of the real parameter $0\le Q\le 4$, and, for bond percolation (the $Q\to 1$ limit), the correction-to-scaling exponent is derived as $\mathrm{\Omega }=72/91$. We derive theoretically the exact formula for the correction-to-scaling exponent $\mathrm{\Omega }=8/\left[\right(2g+1\left)\right(2g+3\left)\right]$ as a function of the Coulomb-gas coupling strength $g$, which is related to $Q$ by $Q=2+2cos\left(2\pi g\right)$. Using an efficient Monte Carlo cluster algorithm, we study the $O\left(n\right)$ loop model on the hexagonal lattice, which is in the same universality class as the $Q=n^2$ Potts model and has significantly suppressed finite-size corrections and critical slowing-down. The predictions of the above formula include the exact value for percolation as a special case and agree well with the numerical estimates of $\mathrm{\Omega }$ for both the critical and tricritical branches of the Potts model.

Hydrocarbon pyrolysis is a complex chemical reaction system at extreme temperature and pressure conditions involving large numbers of chemical reactions and chemical species. Only two kinds of atoms are involved: carbons and hydrogens. Its effective description and predictions for new settings are challenging due to the complexity of the system and the high computational cost of generating data by molecular dynamics simulations. However, the ensemble of molecules present at any moment and the carbon skeletons of these molecules can be viewed as random graphs. Therefore, an adequate random graph model can predict molecular composition at a low computational cost. We propose a random graph model featuring disjoint loops and assortativity correction and a method for learning input distributions from molecular dynamics data. The model uses works of Karrer and Newman [Phys. Rev. E 82, 066118 (2010)] and Newman [Phys. Rev. Lett. 89, 208701 (2002)] as building blocks. We demonstrate that the proposed model accurately predicts the size distribution for small molecules as well as the size distribution of the largest molecule in reaction systems at the pressure of 40.5 GPa, temperature range of 3200–5000 K, and H/C ratio range from 2.25 as in octane through 4 as in methane.

Understanding how neural systems efficiently process information through distributed representations is a fundamental challenge at the interface of neuroscience and machine learning. Recent approaches analyze the statistical and geometrical attributes of neural representations as population-level mechanistic descriptors of task implementation. In particular, manifold capacity has emerged as a promising framework linking population geometry to the separability of neural manifolds. However, this metric has been limited to linear readouts. To address this limitation, we introduce a theoretical framework that leverages latent directions in input space, which can be related to contextual information. We derive an exact formula for the context-dependent manifold capacity that depends on manifold geometry and context correlations, and validate it on synthetic and real data. Our framework's increased expressivity captures representation reformatting in deep networks at early stages of the layer hierarchy, previously inaccessible to analysis. As context-dependent nonlinearity is ubiquitous in neural systems, our data-driven and theoretically grounded approach promises to elucidate context-dependent computation across scales, datasets, and models.

Large arrays of active cilia coordinate their beat cycles into metachronal waves. These waves can travel in different directions with respect to the cilium's beat direction and the resulting direction of fluid propulsion. Hydrodynamic interactions provide a mechanism for the individual cilia to coordinate their beat cycles. Using an analytical framework that connects the properties of the individual cilia to the emergent wave behavior, I show how the forcing pattern of the beat cycle breaks the symmetry to select a wave direction. Previously, it was found that the second harmonic in the beat pattern is the dominant term for coordination. Here, I show that the first harmonic in the beat pattern enters the coordination dynamics at higher order and demonstrate the important role the higher order terms play in determining the direction of emerging metachronal waves.

The microscopic organization of dynamical systems coupled via higher-order interactions plays a pivotal role in understanding their collective behavior. In this paper, we introduce a framework for systematically investigating the impact of the interaction structure on dynamical processes. Specifically, we develop an hyperedge overlap matrix whose elements characterize the two main aspects of the microscopic organization of higher-order interactions: the inter-order hyperedge overlap (nondiagonal matrix elements) and the intra-order hyperedge overlap (encapsulated in the diagonal elements). In this way, the first set of terms quantifies the extent of superposition of nodes among hyperedges of different orders, while the second focuses on the number of nodes in common between hyperedges of the same order. Our findings indicate that large values of both types of hyperedge overlap hinder synchronization stability, and that the larger is the order of interactions involved, the more important is their role. Our findings also indicate that the two types of overlap have qualitatively distinct effects on the dynamics of coupled chaotic oscillators. In particular, large values of intra-order hyperedge overlap hamper synchronization by favoring the presence of disconnected sets of hyperedges, while large values of inter-order hyperedge overlap hinder synchronization by increasing the number of shared nodes between groups converging on different trajectories, without necessarily causing disconnected sets of hyperedges.

Fracture propagation is highly sensitive to the conditions at the crack tip. In heterogeneous materials, microscale obstacles can cause propagation instabilities. Macroscopic heterogeneities modify the stress field over scales larger than the tip region. Here we experimentally investigate the propagation of fluid-driven fractures through multilayered materials. We focus on analyzing fracture profiles formed upon injection of a low-viscosity fluid into a two-layer hydrogel block. Experimental observations highlight the influence of the originating layer on fracture dynamics. Fractures that form in the softer layer are confined, with no penetration in the stiffer layer. Conversely, fractures initiated within the stiffer layer experience rapid fluid transfer into the softer layer when reaching the interface. We report the propagation dynamics and show that it is controlled by the toughness contrast between neighboring layers, which drives fluid flow. We model the coupling between elastic deformation, material toughness, and volume conservation. After a short transient regime, scaling arguments capture the dependence of the fracture geometry on material properties, injection parameters, and time. These results show that stiffness contrast can modify fracture propagation over large length scales and demonstrate the importance of macroscopic scale heterogeneities on fracture dynamics. These results have implications for climate change mitigation strategies involving the storage of heat and carbon dioxide in stratified underground rock formations.

The kinesin superfamily of motor proteins is a major driver of anterograde transport of vesicles and organelles within eukaryotic cells via microtubules. Numerous studies have elucidated the step size, velocities, forces, and navigation ability of kinesins both in reconstituted systems and in live cells. Outside of cells, the kinesin-based transport is physically regulated and can be controlled by obstacles or defects in the path or the interaction between several motors on the same cargo. To explore the physical control parameters on kinesin-driven transport, we created increasingly dense microtubule networks in vitro to test how kinesin cargoes made from quantum dots with one to 10 kinesin motors attached are able to navigate the network. We find that many motors on the quantum dot increase the distance walked by a factor of 2, association time increased by a factor of 4 to 5, and the average speed by a factor of 2. We quantified the tortuosity and the trajectory persistence length and found the persistence length increased by a factor of 5 to 8 when multiple motors are on the cargo. We also find that these transport parameters depend linearly on the mesh size of the dense network for cargoes with multiple motors. Thus, both motor number and network density are physical aspects that regulate where cargoes traverse in space and time.

Bacterial aggregate formation and surface accumulation are increasingly viewed as alternative pathways for biofilm colonization. However, little is known about the dynamics of bacterial aggregate cluster-cluster assembly and their subsequent microstructural and mechanical properties. To this end, we studied experimentally and computationally an aggregating bacterial system that forms a space-spanning interconnected network via cluster-cluster assembly. By controllably inducing bacterial filamentation, we aimed to understand how cell length distribution and cell surface hydrophobicity control the dynamics of aggregation and sedimentation, as well as the microstructure and mechanics of the settled bacterial networks. We found that filamentation lowers the percolation threshold, leading to gelation at a lower number density with distinct assembly dynamics and lower network connectivity. Furthermore, we analyzed the mechanical properties of the bacterial networks. Static stress tests reveal three yielding modes: discrete cluster-cluster disassembly, collective delamination, and subregional network fracture. The yielding modes are consistent with the gel-like viscoelastic properties of the cluster-cluster assembled networks observed during macroscale rheometry. In particular, we observe a scaling relationship between the storage modulus and the volume fraction, characteristic of an attractive rod gel. Our experimental observations are supported by Langevin dynamic simulations, providing mechanistic insights into the factors determining network self-assembly and connectivity. Our findings elucidate the gel-like structure-function dynamics in cluster-cluster aggregated bacterial systems, and they underscore the fundamental importance of filamentation in their properties and mechanical behavior.

Choosing the correct free energy functional is critical when developing thermodynamically consistent phase field models. We show that the grand-potential phase field model minimizes the Helmholtz free energy when mass conservation is imposed. While both functionals are at a minimum at equilibrium, the Helmholtz free energy decreases monotonically with time in the grand-potential phase field model, whereas the grand potential does not. Minimizing the grand potential implies a different problem where a system can exchange mass with its surroundings at every point, leading to a condition of isochemical potential and invalidating mass conservation of the system.

Kinetic proofreading (KPR) is a commonly invoked mechanism for specificity enhancement of receptor signaling. However, specificity enhancement comes at a cost of nonequilibrium energy input and signal attenuation. We show that ligand-induced multimeric receptor assembly can enhance receptor specificity to the same degree as KPR, yet without the need for out-of-equilibrium energy expenditure and signal loss. We show how multimeric receptor specificity enhancement arises from the amplification of affinity differences via sequential progression down a free energy landscape. We also show that multimeric receptor ligand recognition is more robust to stochastic fluctuations and molecular noise than KPR receptors. Finally, we show that multimeric receptors perform signaling tasks beyond specificity enhancement like absolute discrimination and aspects of ligand antagonism. Our results suggest that multimeric receptors may serve as a potent mechanism of ligand discrimination comparable to and potentially with more advantages than traditional proofreading.

Time-series analysis often involves the characterization of order or predictability, qualities that are related to internal structure and autocorrelation. Investigating a recently proposed algorithm for solving a density prediction task, we demonstrate that if the same system can be viewed on multiple time scales, there is an inevitable degree of expected order and predictability that increases as the system size grows. In particular, we introduce bounds on the expected second-order structure function and autocorrelation function of a time series where multiple observation scales are available, and conclude with a lower bound on the expected correlation time. Such a lower bound shows that there is an inevitable degree of correlation induced when time-series data is aggregated, quantifying a previously overlooked source of bias towards high correlations.

The physics of planetary climate features a variety of complex systems that are challenging to model as they feature turbulent flows. A key example is the heat flux from the upper ocean to the underside of sea ice which provides a key contribution to the evolution of the Arctic sea ice cover. Here, we develop a model of the turbulent ice-ocean heat flux using coupled ordinary stochastic differential equations to model fluctuations in the vertical velocity and temperature in the Arctic mixed layer. All the parameters in the model are determined from observational data. A detailed comparison between the model results and measurements made during the Surface Heat Budget of the Arctic Ocean (SHEBA) project reveals that the model is able to capture the probability density functions (PDFs) of velocity, temperature, and heat flux fluctuations. Furthermore, we show that the temperature in the upper layer of the Arctic Ocean can be treated as a passive scalar during the whole year of SHEBA measurements. The stochastic model developed here provides a computationally inexpensive way to compute an observationally consistent PDF of this heat flux and has implications for its parametrization in regional and global climate models.

Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard DMs, this is done by learning a “score function” that reverses the effect of adding diffusive noise to the distribution of interest. Here we consider the generalisation of DMs to lattice systems with discrete degrees of freedom, and where noise is added via Markov chain jump dynamics. We show how to use tensor networks (TNs) to efficiently define and sample such “discrete diffusion models” (DDMs) without explicitly having to solve a stochastic differential equation. We show the following: (i) by parametrising the data and evolution operators as TNs, the denoising dynamics can be represented exactly; (ii) the auto-regressive nature of TNs allows to generate samples efficiently and without bias; (iii) for sampling Boltzmann-like distributions, TNs allow to construct an efficient learning scheme that integrates well with Monte Carlo. We illustrate this approach to study the equilibrium of two models with non-trivial thermodynamics, the $d=1$ constrained Fredkin chain and the $d=2$ Ising model.

Close to the yielding transition, amorphous solids exhibit a jerky dynamics characterized by plastic avalanches. The statistics of these avalanches have been measured experimentally and numerically using a variety of different triggering protocols, assuming that all of them were equivalent for this purpose. In particular, two main classes of protocols have been studied, deformation under controlled strain or under controlled stress. In this work, we investigate different protocols to generate plasticity avalanches and conduct two-dimensional simulations of an elastoplastic model to examine the protocol dependence of avalanche statistics in yield-stress fluids. We demonstrate that when stress is controlled, the value and even the existence of the exponent governing the probability distribution function of avalanche sizes strongly depend on the protocol chosen to initiate avalanches. This confirms in finite dimension a scenario presented in a previous mean-field analysis. We identify a consistent stress-controlled protocol whose associated avalanches differ from the quasi-static ones in their fractal dimension and dynamical exponent. Remarkably, this protocol also seems to satisfy the scaling relations among exponents previously proposed. Our results underscore the necessity for a cautious interpretation of avalanche universality within elastoplastic models, and more generally within systems where several control parameters exist.

Finding self-similarity is a key step for understanding the governing law behind complex physical phenomena. Traditional methods for identifying self-similarity often rely on specific models, which can introduce significant bias. In this paper, we present a neural network-based approach that discovers self-similarity directly from observed data, without presupposing any models. The presence of self-similar solutions in a physical problem signals that the governing law contains a function whose arguments are given by power-law monomials of physical parameters, which are characterized by power-law exponents. The basic idea is to enforce such particular forms structurally in a neural network in a parametrized way. We train the neural network model using the observed data, and when the training is successful, we can extract the power exponents that characterize scale-transformation symmetries of the physical problem. We demonstrate the effectiveness of our method with both synthetic and experimental data, validating its potential as a robust, model-independent tool for exploring self-similarity in complex systems.

This study deals with polymer looping, an important process in many chemical and biological systems. We investigate basic questions on the looping dynamics of a polymer under tension using the freely jointed chain (FJC) model. Previous theoretical approaches to polymer looping under tension have relied on barrier escape methods, which assume local equilibrium, an assumption that may not always hold. As a starting point, we use an analytical expression for the equilibrium looping probability as a function of the number of monomers and applied force, predicting an inverse relationship between looping time and looping probability. Using molecular dynamics simulations, the predictions of this theoretical approach are validated within the numerical precision achieved. We compare our predictions to those of the barrier escape approach by way of a calculation of the mean first passage time (MFPT) for the ends of a polymer to cross. For this purpose, we derive the exact free energy landscape, but the resulting temporal predictions do not agree with the observed inverse scaling. We conclude that the traditional barrier escape approach does not provide satisfactory predictions for polymer looping dynamics and that the inverse scaling with looping probability offers a more reliable alternative.

We investigate the statistics of the first-passage time (FPT) to a fractal self-similar boundary of the Koch snowflake. When the starting position is fixed near the absorbing boundary, the FPT distribution exhibits an apparent power-law decay over a broad range of timescales, culminated by an exponential cutoff. By extensive Monte Carlo simulations, we compute the local persistence exponent of the survival probability and reveal its log-periodic oscillations in time due to self-similarity of the boundary. The effect of the starting point on this behavior is analyzed in depth. Theoretical bounds on the survival probability are derived from the analysis of diffusion in a circular sector. Physical rationales for the refined structure of the survival probability are presented.

We investigate a large ensemble of quadratic integrate-and-fire neurons with heterogeneous input currents and adaptation variables. Our analysis reveals that, for a specific class of adaptation, termed quadratic spike-frequency adaptation, the high-dimensional system can be exactly reduced to a low-dimensional system of ordinary differential equations, which describes the dynamics of three mean-field variables: the population's firing rate, the mean membrane potential, and a mean adaptation variable. The resulting low-dimensional firing rate equations (FREs) uncover a key generic feature of heterogeneous networks with spike-frequency adaptation: Both the center and width of the distribution of the neurons' firing frequencies are reduced, and this largely promotes the emergence of collective synchronization in the network. Our findings are further supported by the bifurcation analysis of the FREs, which accurately captures the collective dynamics of the spiking neuron network, including phenomena such as collective oscillations, bursting, and macroscopic chaos.