Evolutionary game theory has provided substantial contributions to explain the emergence of cooperation under unfavorable conditions in ecology, economics, and the social sciences. Recently, inspired by newly available empirical evidence on group interactions, higher-order networks have emerged as a natural framework to encode multiplayer games in structured populations. Here we study the emergence of cooperation in nonlinear public goods games on hypergraphs, where collective reinforcement captures the synergistic or discounting effect associated with each additional cooperator. In well-mixed populations, when all games have the same number of players, the system displays a transition whose nature changes from continuous to discontinuous depending on the form of nonlinearity. By contrast, when games involving different numbers of players coexist, an additional bistability region between an active coexistence state and full cooperation may emerge. We further find that scale-free hypergraphs promote cooperation, highlighting the crucial role played by both the initial placement of cooperators and the presence of hyperdegree correlations. Overall, our results provide a comprehensive characterization of nonlinear public goods games on hypergraphs and open avenues for richer models of evolutionary dynamics of multiplayer games on structured populations.

Neutron scattering is a powerful technique to investigate atomic structures and molecular dynamics of proteins at the nanoscale. When it comes to dynamics, incoherent and coherent scattering respectively provide information on the single and collective dynamics of nuclei. In proteins, hydrogen has the highest incoherent cross section, and it is common practice to overlook the contribution of coherent terms stemming from all nuclei. However, the fast collective dynamics of heavier nuclei could also be studied if coherent scattering and incoherent scattering were experimentally separated. The recent advent of polarized neutron spectroscopy with sufficient flux and energy resolution has made it possible, and opens new perspectives to investigate the relative importance of coherent scattering and the information it provides on biological samples. The present study reports on the use of polarized quasielastic neutron scattering (QENS) and the application of a minimalistic model adapted to both individual and collective dynamics. Using a perdeuterated green fluorescent protein as a model globular protein, the study provides an interpretation of the dynamical parameters obtained with QENS, and a comparative study of the elastic coherent and incoherent scattering factor. Based on both experiments and calculations, we discuss the relative importance of distinct and self components of coherent scattering, which is often wrongly assumed to be representative of collective dynamics only. The results highlight the current impediments rendering complicated a straightforward analysis of fast collective dynamics in hydrated protein samples.

Complex systems are commonly modeled as networks of units that integrate external input and emit brief pulses of activity upon reaching a threshold. Such pulse-coupled interactions can give rise to cascades of activity propagating through the network in the form of avalanches. While the statistics of these collective events are known to depend sensitively on network topology, rigorous analytical descriptions are usually restricted to homogeneous networks or mean-field approximations which are limited to particular aspects of generated avalanches like size and duration. Here we develop a mathematically rigorous theory of avalanche formation in recurrent networks of pulse-coupled units without assuming homogeneity. For arbitrary nonnegative coupling matrices, the framework provides a closed form for the avalanche assembly distribution, which quantifies the probability that a given subset of units is activated during an avalanche. This approach represents a substantial conceptual advance over existing theories allowing analysis of the structure-function relation between network topology and detailed statistics of generated avalanches. This is particularly relevant for the irregular, highly structured, and asymmetric coupling topologies ubiquitous in natural systems, such as brain networks with pronounced columnar, modular, and hierarchical organization.

Laser-driven spherical implosion experiments create some of the most extreme states of matter accessible in the laboratory. However, experimental observables in implosion experiments are highly integrated, meaning that measurements cannot be straightforwardly inverted to characterize the thermodynamic states or material properties in the implosion. Thus, to understand the extreme states of matter typical of implosions, a new generation of experiments and analyses are needed that leverage modern statistical tools. This work presents a comprehensive Bayesian inference framework that enables the analysis of integrated x-ray self-emission measurements from laser-driven implosions at the OMEGA laser, producing equation-of-state data (pressure, density, and temperature) between 0.1 to 1.5 Gbar. The model is benchmarked against synthetic data from radiation-hydrodynamics simulations, and opens avenues for producing quantitative constraints on physical models relevant to dense astrophysical and laboratory fusion plasmas.

Continuous nucleation in nonequilibrium solidification is often treated as an instantaneous response controlled by the current undercooling. In welding, casting, and layer-wise metal additive manufacturing, however, liquid regions can undergo nonmonotonic thermal histories and reach similar undercooling states with different nucleation readiness. Here, an internal activation variable is incorporated into a continuous nucleation description and embedded in an LB-PF solver for dendritic solidification. The variable acts as an effective continuum state for the accumulation, retention, and weakening of prenucleation readiness. Constant cooling, piecewise cooling, low-temperature pretreatment, and high-temperature holding are used to examine the resulting path-dependent nucleation response. The simulations show that different thermal paths lead to different activation states, accepted-nucleus distributions, solid-fraction evolutions, and grain-scale features even under similar later undercooling conditions. The results suggest that time-nonlocal internal variables can help represent thermal-history-dependent nucleation in continuum phase-transformation simulations.

The electrostatic charging of insulators is notoriously irreproducible. Using experiments and simulations we study the charging of a single bouncing ball on a vibrating surface. We show that a ball's final charge results from a coupling between its chaotic dynamics and its evolving charge distribution. This results in a permanent charge dipole which traps the particle in an “orientational absorbing state” preventing further charging. The variability of each particle's final charge is a direct consequence of this dynamical coupling.

We analytically solve the finite-time control problem of driving an overdamped particle via an optical trap under costly measurement. By formulating this mesoscopic information engine within the partially observable Markov decision process framework, we demonstrate that the underlying linear-quadratic-Gaussian dynamics decouples the optimal measurement and driving protocols. We derive the optimal feedback control law for the trap placement, which recovers the discontinuous Schmiedl-Seifert driving protocol in the open-loop limit and extends it to any measurement scheduling. For a costly binary (on-off) sensor, we evaluate the optimal measurement protocol and derive physical bounds on the maximum net gain that can be extracted from thermal fluctuations. We show the emergence of deadline-induced blindness, a phenomenon where all measurements cease as the deadline approaches regardless of their cost. Taking the infinite-horizon limit, we find the exact periodic measurement schedules for the steady state as a function of the measurement cost $C$ and derive the macroscopic velocity envelopes beyond which viscous drag forces the engine into a net-dissipative regime. Finally, we generalize the results to a variable-precision sensor.

We study a minimal model of disordered systems, the random field Ising model (RFIM) on a generalized Petersen Graph, $GP(N,k)$, which consists of an interconnected outer and inner loop with $N$ nodes in each loop. Each node in $GP(N,k)$ has a coordination number of $z=3$, and by varying the parameter $k$ different connections between the nodes in the inner loop can be obtained. The objective is to study whether different connectivities between nodes in these graphs affect the system's response to an external field when the coordination number is fixed. This is of interest because critical behavior is absent for $z\le 3$ on a random graph which has been solved exactly as well as on the honeycomb lattice in the context of RFIM. Using single-spin-flip Glauber dynamics at zero temperature, we compare the system's response with the known case of a $z=3$ random graph and the generalized Petersen graph for various connectivities $k$, albeit for the same $z$. Our study finds the absence of critical behavior on $GP(N,k)$, highlighting the importance of the coordination number over varying connectivities between the nodes. Additionally, we explore the case of directed $GP(N,k)$ and compare it with the undirected $GP(N,k)$ results.

Swarmalators are a class of coupled oscillators that simultaneously self-organize in both space and phase, providing a minimal model for systems ranging from biological microswimmers to robotic swarms. Time delay is ubiquitous in such systems, arising from finite signal propagation speeds and sensory processing lags; however, its structural form, whether symmetric or asymmetric, has received little attention. Here, we study a one-dimensional swarmalator model with asymmetric time delay, in which the delay enters only the self-interaction terms of the spatial and phase dynamics, breaking the symmetry assumed in prior work. Using initial conditions drawn uniformly from $[-\pi ,\pi ]$ for both the position and phase variables, we identify various collective states, such as async, static phase wave, static $\pi$, and active $\pi$, and derive analytical stability boundaries for each state as functions of the coupling parameters and the delay. Our analysis reveals that the asymmetric delay structure fundamentally reshapes the collective phase diagram: in particular, for the asymmetric delay models, increasing the delay systematically expands the active $\pi$ state at the expense of other ordered states. This contrasts with the symmetric delay model, which more strongly promotes unsteady states that are generally not well ordered. By providing closed-form stability conditions validated against numerical simulations, our work establishes that the internal structure of the delay, and not merely its magnitude, is a decisive factor in determining the emergent collective behavior of swarmalator populations.

Bridging the gap between atomistic detail and continuum mechanics is a central challenge in modeling biological membranes, particularly for mesoscopic phenomena spanning large length and time scales. In this work, we introduce a new, solvent-free, one-particle-thick, coarse-grained model for lipid bilayers, governed by an additive potential. Our approach treats orientational elasticity through distinct additive energy terms for tilt and splay, offering an unbiased potential form. The model is implemented in the lammps molecular-dynamics engine. Our simulations show spontaneous self-assembly of lamellar structures and stable vesicles from disordered states. We map the dynamical phase diagram of the system, identifying distinct gel-like, fluid, and gas regimes, controlled by temperature and the steepness of the isotropic attraction. The model accurately reproduces the theoretical $1/q^4$ fluctuation spectrum for tensionless membranes and exhibits tunable mechanical properties, including biologically relevant bending rigidities. We show how we can include osmotic pressure and spontaneous curvature in our model. Finally, we demonstrate the model's applicability to complex membrane remodeling by simulating the adhesive wrapping of colloidal nanoparticles, recovering the predicted dependency on particle size and adhesion strength.

We study generalization in overparameterized deep neural networks using a thermal deep learning machine with a well-defined Hamiltonian. We find that learning dynamics organize the network into a solid–liquid–solid structure, where boundary layers are constrained while central layers remain flexible. These layers exhibit distinct dynamical behaviors, including timescale separation and nonequilibrium aging. We show that the solution space is structureless in liquid layers but hierarchically organized in solid layers, indicating a direct link between dynamics and landscape geometry. These results suggest a physical perspective for generalization, arising from the interplay between flexible representations and boundary-induced constraints.

We investigate collective behavior in a $Q$-species Vicsek model with a nonreciprocal velocity alignment interaction. This system is characterized by a constant phase shift $\alpha$ in the interspecies velocity alignment rule. While the phase shift renders the interaction nonreciprocal, the system is globally invariant under any permutations of particle species, possessing Potts symmetry. The combination of Potts symmetry and nonreciprocity gives rise to a rich phase diagram. The nonreciprocal phase shift generates either counterclockwise or clockwise chirality. Potts symmetry can be broken spontaneously. Consequently, the system exhibits four distinct phases: A species-mixed chiral phase where particles perform counterclockwise chiral motion with quasi-long-range order, a species separation phase where Potts symmetry is broken and species-separated particles form vortex cells with clockwise chirality, a coexistence phase, and a disordered phase, for $0<\alpha <\pi$. We derive a Boltzmann equation and a hydrodynamic equation describing the system in the continuum limit, and present analytic arguments for the emergence of chirality and species separation.

In nondegenerate integrable Hamiltonian systems, invariant tori can be parametrized by action variables or fundamental frequencies. We introduce an invariant-flow formulation, consistent with the Liouville-Arnold geometry, for extracting these frequencies. Treating invariants as generators of commuting Hamiltonian flows yields the frequencies from time-of-flight parameters, providing a direct alternative to action-angle constructions and long-time spectral analysis. The resulting numerical procedure extends naturally to multiple degrees of freedom and achieves high accuracy for the McMillan map. More broadly, the framework provides an invariant-centered view of near-integrable dynamics, recovering frequencies and other dynamical information from high-quality approximate invariants.

Synchronous update schemes in p-bit annealing offer a natural route to massive parallelism, but they can also induce period-2 oscillations that degrade optimization performance. In practical solvers, such oscillations matter only if they become observable within the finite runtime of the device or simulation. However, most existing analyses are formulated in terms of asymptotic stability and therefore do not directly address when oscillatory modes appear during finite-duration annealing. Here we develop a finite-time observability framework for synchronous tick-random p-bit dynamics. Starting from a linearized mean-field description, we derive a graph-dependent criterion that predicts whether unstable modes amplify sufficiently within a finite observation window to produce visible signatures in quantities such as the one-step autocorrelation and the energy trace. This shifts the analysis from asymptotic instability to practical detectability and yields a principled estimate of the reduction in synchrony required to suppress oscillations. We validate the framework on benchmark max-cut graph instances and illustrative graph families. The predicted thresholds capture both the graph dependence of oscillation onset and the finite-time conditions under which oscillations become observable. These results provide a graph-aware basis for selecting the update probability in synchronous p-bit annealers without relying on exhaustive instance-by-instance parameter sweeps.

We investigate mixed eigenstates in systems with sharply divided phase space, using different piecewise-linear maps whose regular-chaotic boundaries are formed by marginally unstable periodic orbits (MUPOs) or by quasiperiodic orbits. With the overlap index and the entropy localization length, we classify mixed eigenstates and show that the contribution from dynamical tunneling scales as $\sim \hslash exp(-b/\hslash )$, with $b>0$ associated with the relative size of the regular region. The dominant fraction of states that remain sticky to the boundaries, referred to as sticky eigenstates, scales approximately as ${\hslash }^{1/2}$ in the MUPO case and oscillates around this algebraic behavior in the quasiperiodic case. This behavior generalizes established predictions for hierarchical states in Kolmogorov-Arnold-Moser (KAM) systems, which scale as ${\hslash }^{1-1/\gamma }$, with $\gamma$ set by the corresponding classical stickiness reflected in the algebraic decay of cumulative recurrence-time distributions $t^{-\gamma }$. For the piecewise-linear maps studied here, $\gamma =2$. These results reveal a clear quantum signature of classical stickiness in non-KAM systems.

We study the one-dimensional swarmalator model with self-propulsion $v_{0}sin{\theta }_i$, where ${\theta }_i$ is the body orientation. The static states of the ordinary model unfold into traveling, breathing, split-wave, and chaotic states, two of which admit analytic reductions: A traveling two-cluster branch with a closed-form stability spectrum, and a split-wave ansatz whose active pair obeys an Adler equation. At large propulsion the chaos is transient rather than a chaotic attractor: the accumulated tangent growth saturates—at every propulsion speed across the chaos window, and at every system size we can integrate far enough to test—and trajectories end on the cluster states. The transient lifetime grows with system size, leaving the continuum limit open. The resulting states may serve as qualitative signatures for confined active oscillator arrays.

In networks that grow by isotropic redirection (IR), a new node selects an initial target node uniformly at random and attaches to a randomly chosen neighbor of the target. The emerging networks exhibit leaf proliferation, in which the number of nonleaves scales sublinearly as $N^{\mu }$ and the degree distribution has an algebraic tail with exponent $1+\mu$. To understand these mysterious properties, we introduce a class of models with redirection to leaves whenever possible. The resulting networks exhibit qualitatively similar phenomenology to IR networks, but avoid the inherent nonlocality of the IR growth rule. These networks admit an analytical description of the leaf degree distribution, from which we extract the exponent $\mu$.

Many real systems can be efficiently represented by complex networks. Recently, the robustness of these networks under random or targeted attacks has been of interest. One of the strategies to dismantle a network involves identifying and removing articulation points. These are nodes that are critical to the network's connectivity; their removal causes the network to break into separate components. Most real-world networks are not isolated, but interacting, and can be viewed as multiplex networks. Inherent cascading failure within multiplex structures makes the definition of articulation points evading; an articulation point of a single monoplex layer loses this property due to removal by cascading failure within the parent multiplex network. We extend a consistent definition of articulation points and apply it to real and random multiplex networks. Moreover, we find that most of the real networks are vulnerable to the articulation points removal process. Through extensive simulations, we establish criteria for network resilience to this process across different types of random multiplex network models. These include two- and three-layer Erdős-Rényi multiplex networks, two-layer scale-free multiplex networks with varying degree exponents, and hyperbolic multiplex networks.

With the development of microfluidics, it has now become possible to assess the susceptibility of bacteria to antibiotics at the single-cell level instead of relying on population measurements. Such studies are particularly relevant when the growth of a bacterial population in the presence of antibiotics is heterogeneous. Here, we build a model to describe such a case and apply it to experimental measurements on a small population of E. coli exposed to ciprofloxacin, a drug which is well-known for triggering a bistable response.

This work demonstrates the impact of ion-electron collisions on ion transport for strongly inhomogeneous plasmas in the nonlocal regime, where collisionality is insufficient to enforce local thermal equilibrium due to sharp gradients. Ion heat conduction and viscous stress in both unmagnetized and magnetized plasmas are considered, as well as interspecies diffusion in multispecies plasmas. Most notably, even for equal ion and electron temperatures, ion-electron collisions are found to substantially modify the peak nonlocal heat flow, whereas nonlocal preheats are strongly suppressed since streaming suprathermal particles are further out in the tail of the cold ion distribution where ion-electron collisions become dominant.