Neural entrainment, the phenomenon of adjusting the dynamics of a neural system to that of an external stimulus, underlies various cognitive phenomena. Traditionally, most entrainment studies focus on an external periodic drive. However, most naturalistic stimuli are rarely periodic and often have a spread in frequency domain rendering an intrinsic aperiodic component. One intuitive way to account for this variability is by introducing a spread around the forcing frequency to mimic the temporal structure of more naturalistic inputs. In this work, we investigate how such variability affects the dynamics of a canonical neural mass model namely the Jansen and Rit Neural Mass Model. The stimulant frequency is shuffled and drawn from a Gaussian distribution with mean = system frequency. It is seen that a stimulated Jansen and Rit model shows an optimal amount of energy pumping for an intermediate amount of shuffling (standard deviation of frequencies). Furthermore, this optimality is lost if the shuffling rate is higher than the system frequency.

We set out to explore the possibility of investigating the critical behavior of systems with first-order phase transition using deep machine learning. We propose a machine learning protocol with ternary classification of instantaneous spin configurations using known values of disordered phase energy and ordered phase energy. The trained neural network is used to predict whether a given sample belong to one or another phase of matter. This allows us to estimate for the first time the probability that configurations with a certain energy belong to the ordered phase, coexistence phase, and disordered phase. Based on these probabilities, we obtained estimates of the values of the critical energies and latent heat for the Potts model with 10 and 20 components, which undergoes a strong discontinuous transition. We also found that the probabilities may reflect geometric transitions in the coexistence phase.

Self-propulsion in run-and-tumble particles (RTPs) generates effective attractive interactions that can drive motility-induced phase separation (MIPS), a phenomenon absent in passive systems. Here we investigate RTPs in the presence of explicit attractive interactions and show that, at high motility, such interactions can suppress MIPS, yielding a homogeneous phase. Upon further increasing the attraction strength, phase separation reappears, giving rise to a re-entrant transition. We characterize this transition by analyzing the percolation properties of dense clusters, which provide geometric signatures of phase separation. Along the resulting critical line, we find continuously varying critical exponents, while certain scaling functions remain unchanged and coincide with those of equilibrium lattice gas models undergoing interacting percolation, which is in the Ising-percolation universality class. These results reveal that the MIPS transition in interacting RTP systems exhibit Ising superuniversality, thereby establishing a connection between nonequilibrium active matter and classical critical behavior.

We show that, on a $d$-dimensional hypercubic lattice with $d>1$, conserved-mass transport processes, with multidirectional hopping that respect all symmetries of the lattice, exhibit power-law correlations for generic parameter values—even far from phase transition point, if any. The key idea for generating the algebraic decay is the notion of multidirectional hopping, which means that several chunks of masses, or several particles, can hop out simultaneously from a lattice site in multiple directions, consequently breaking detailed balance. Notably, the systems we consider are described by a continuous-time Markov process, are diffusive, lattice-rotation symmetric, spatially homogeneous and thus have $\mathit{no}$ net mass current. Using hydrodynamic and exact microscopic theory, we show that, for spatial dimensions $d>1$, the steady-state static density-density and “activity”-density correlation functions in the thermodynamic limit typically decay as $\sim 1/r^{(d+2)}$ at large distance $r=\left|\mathbf{r}\right|$; the strength of the power law is exactly calculated for several models and expressed in terms of the density-dependent bulk-diffusion coefficient and Onsager matrix (or, mobility tensor). In particular, our theory explains why center-of-mass-conserving dynamics, used to model novel disordered hyperuniform state of matter, result in generic long-ranged correlations. However, in a restricted parameter regime, the correlations can also be short ranged and are characterized through the Onsager matrix.

We consider jump processes with finite variance which, from the point of view of experimental studies, apparently do not converge to the expected Gaussian behavior. A mathematically tractable example of such processes are those with a distribution of jump lengths in the form of a weighted sum of exponential distributions. For such processes on a half-line and on a finite interval, we calculate the probability densities of arrival at a given time at a given point on the line. The found probability densities allow us to calculate many quantities important for applications: coordinate probability density functions, first passage times, leapover-length distributions, splitting probabilities, conditional exit times, and others. The following results are obtained: for a given variance of the jump-length distribution, the ratio of the mean leapover length to the mean jump length can be arbitrarily large; for a given variance of the jump-length distribution and a given interval length, the transmission probability can be arbitrarily small; for a given variance of the jump-length distribution, a given interval length, and a given mean waiting time, the mean exit time can be arbitrarily large. These results are radically different from those previously obtained using the continuous limit for processes rapidly converging to Gaussian behavior.

Cooperation often depends on individuals avoiding exploitation and interacting preferentially with other cooperators. We explore how context-dependent migration influences the evolution of cooperation in spatially structured populations. Individuals interact in small groups through public goods games and reproduce with possible dispersal. Cooperators migrate more frequently when surrounded by defectors, while defectors disperse uniformly. This behavioral asymmetry reflects realistic differences in mobility and social responsiveness. Our results show that conditional migration can promote cooperation by enabling cooperators to escape defector-rich environments and cluster together. The effectiveness of this mechanism depends on baseline migration rates, group size, and the sensitivity of cooperators to local conditions. We identify parameter ranges where cooperation is favored even under conditions that would typically hinder its evolution. These findings highlight how behavioral plasticity and dispersal strategies can interact with population structure to support the emergence of cooperation.

In an increasingly interconnected world, understanding congestion-related phenomena in transportation and their underlying mechanisms is crucial for improving efficiency. As the transportation system becomes denser, different modes of transportation have more opportunities to interact with each other, giving rise to emergent dynamics that simple models cannot explain. In this study, we investigate the synchronized motion of indirectly coupled transportation modes. We develop a numerical simulation model on a one-dimensional periodic lattice, where each point represents a bus station. In this system, two types of buses operate: multiple local buses with nonoverlapping routes, each serving a specific zone, and a single global bus that partially overlaps with the routes of the local buses. We perform numerical simulations to examine how close the arrival times of these buses are to each other—that is, how synchronized their motions are. When the number of zones is two, three, or five, robust synchronization occurs not only between the global bus and the local buses but also among the local buses themselves. In contrast, no synchronization is found for other numbers of zones. We developed a mathematical model using self-consistent equations and found that two distinct arrival patterns at the terminals must be considered. A stability analysis reveals which pattern is ultimately realized in the simulations. Our results show that transportation modes can exhibit coherent motion even when sharing only partial or no direct route overlaps. This outcome highlights that emergent behavior depends not only on local interactions but is also strongly shaped by the system's overall structural configuration.

Polarization significantly influences societal divisions across economic, political, religious, and ideological lines. Understanding these mechanisms is key to devising strategies to mitigate such divisions and promote depolarization. Our study examines how asymmetric opinion perception, modeled through nonlinear incidence terms, affects polarization and depolarization within structured communities. In particular, we leverage the fact that the modular structure of the social network yields adjacency matrix eigenvectors with approximately constant values within each community, which enables us to predict the spatial profile of polarization patterns. We demonstrate that such asymmetry leads to explosive polarization and causes a hysteresis effect responsible for abrupt depolarization. We develop a mean-field approximation to explain how nonlinear incidence results in first-order phase transitions and the nature of bifurcations. This approach also helps in understanding how opinions polarize according to underlying social network communities and how these phenomena intertwine with the nature of such transitions. Numerical simulations corroborate the analytical findings.

West Nile virus is mainly transmitted by mosquitoes, posing a threat to the health of birds and humans. We propose an epidemic model incorporating higher-order temporal networks to capture key features of West Nile virus transmission. We analyze the conditions for the existence of the disease equilibrium point of the system and discuss the necessary conditions for the Turing instability of the system on natural coupling and different topological structures. Subsequently, the validity of the theory is verified by a series of numerical simulations. The results show that higher-order interactions can better explain the complex interactions of diseases among individuals. In addition, the model fitting based on actual data shows the correctness of the higher-order temporal model. Finally, based on the theoretical method of searching the key 2-simplex, the control process of West Nile virus is simulated, and the results show the effectiveness of the control method.

Magnetotactic bacteria are microorganisms with magnetite organelles that have been shown to be responsive to external magnetic fields. Despite their study for several decades, a complete theoretical understanding that connects the magnetic structure of these bacteria to their external magnetic field response has not been conclusively resolved. Combining nanomagnetic simulations with optical and transmission electron microscopy, it is shown that the response of magnetotactic bacteria to a strong external magnetic field is dependent on the internal arrangement of the magnetite organelles and can be understood at a fundamental level. With this information, nonpolar and polar velocity vector fields can be observed and defined in the bacteria's movement. By directly manipulating the bacteria with external magnetic fields, we are able to control large in-phase groups of bacteria, have precise control of individual bacterium trajectories, and generate structures with a topological charge in both their polar and nonpolar velocity vector fields. Being able to directly control these bacteria with external magnetic fields opens up the possibility of using them as self-propelled microrobots with biomedical applications, such as targeted magnetic hyperthermia and drug delivery.

Nanoporous capsules have been the subject of intense investigation in the field of drug delivery. One of the essential properties of such particles, which requires characterization, is their structure. Many experimental techniques have been used for this purpose, such as wide-angle neutron or x-ray scattering, or light scattering. Herein, we report theoretical data on the relationship between the size, porosity, and drag force of porous particles. Data were obtained from a numerical procedure based on the lattice Boltzmann method for the calculation of the creeping flow over porous spherical objects. Previous analytical solutions to the hydrodynamic equations yielded different predictions for the drag force under conditions of high permeability. In the light of our findings, we compared our data to previous divergent analytical solutions and analyzed experimental results for dynamic and static light scattering of porous membrane vesicles. Our findings strongly indicate a potential source of error that has led to inconsistencies in DLS measurements when compared to other techniques.

Classical density functional theory (cDFT) and dynamical density functional theory (DDFT) are modern statistical mechanical theories for modeling many-body colloidal systems at the one-body density level. The theories hinge on knowing the excess free-energy accurately, which is, however, not feasible for most practical applications. Dijkman et al. [Phys. Rev. Lett. 134, 056103 (2025)] recently showed how a neural excess free-energy functional for cDFT can be learned from bulk simulations via pair-correlation matching. In this article, we demonstrate how this same functional can be applied to DDFT, without any retraining, to simulate nonequilibrium overdamped dynamics of inhomogeneous densities. We evaluate this on a three-dimensional Lennard-Jones system with planar geometry under various complex external potentials, and we observe good agreement of the dynamical densities with those from expensive Brownian dynamic simulations, up to the limit of the adiabatic approximation. We further develop and apply an extension of DDFT based on gradient flows to a grand-canonical system modeled after breakthrough gas adsorption studies, finding similarly good agreement. Our results demonstrate a practical route for leveraging learned free-energy functionals in DDFT, paving the way for accurate and efficient modeling of many-body nonequilibrium systems.

We develop a continuum theory to describe the collective dynamics of deformable epithelial cells, distinguishing the force-generating active filaments in the cells from their shape. The theory demonstrates how active flows driven by active filaments can create nematic domains and topological defects in the cell shape field. We highlight the role of the filament flow-aligning parameter, ${\lambda }_{\mathit{Q}}$, a rheological quantity that determines the response of the filaments to velocity gradients in the active flows, and plays a significant, to date unappreciated, role in determining the pattern of extensional and compressional active flows. In a contractile cell layer, local flows are expected to align elongated cells perpendicular to the active filaments. However, with increasing ${\lambda }_{\mathit{Q}}$, long-range correlations in the active turbulent flow field lead to extended regions where this alignment is parallel, consistent with recent experiments on confluent Madin-Darby canine kidney (MDCK) cell layers. Further, we distinguish defects in the filament director field, which contribute to the active driving, and those in the shape director field, measured in experiments, which are advected by the active flows. By considering the shape-filament orientation, we explain the unexpected motion of $+1/2$ defects towards their head in contractile cell layers, consistent with recent experiments on epithelial layers examining stress around shape defects.

Shape-anisotropy-induced transitions of densest-packed structures have been discovered for binary mixtures of circles and ellipses in parallel-slit confinement. A continuous increase in the aspect ratio of ellipses results in a crossover of densest-packed configurations, from structures composed of circles surrounded by ellipses, through an intermediate regime of phase-separated structures, to structures composed of ellipses surrounded by circles. Our findings conclude that the densest-packed structures of such systems are all ordered arrangements of particles with minimal excess-volume effects from grain-boundary-like pairs of dissimilar particles.

We consider a slow elastic string with Klein-Gordon dynamics coupled to a bath of run-and-tumble particles. We derive and solve the induced Langevin-Klein-Gordon string dynamics with explicit expressions for the streaming term, friction coefficient, and noise variance. These parameters are computed exactly in a weak-coupling expansion. The induced friction is a sum of two terms: one entropic, proportional to the noise variance as in the Einstein relation for a thermal equilibrium bath, and a frenetic contribution that can take both signs. The frenetic part wins for higher bath persistence, making the total friction negative, and hence creating a wave instability akin to inverse Landau damping. However, this acceleration decreases and eventually disappears when the propulsion speed of the active particles becomes much higher. Detailed simulations confirm the initial growth driven by this antidamping.

The intrinsic dimension (ID) is a powerful tool to detect and quantify correlations from data. Recently, it has been successfully applied to study statistical and many-body systems in equilibrium, yet its application to systems away from equilibrium remains largely unexplored. Here we study the ID of nonequilibrium growth dynamics data, and show that even after reducing these data to binary form, their binary intrinsic dimension (BID) retains essential physical information. Specifically, we find that, akin to the surface width, it exhibits Family-Vicsek dynamical scaling—a fundamental feature to describe universality in surface roughness phenomena. These findings highlight the ability of the BID to correctly discern key properties and correlations in nonequilibrium data, and open an avenue for alternative characterizations of out-of-equilibrium dynamics.

In a graph, we say that two nodes are topologically equivalent if their sets of first neighbors, excluding the two nodes, coincide. We prove that nonlinearly coupled heterogeneous oscillators located on a group of topologically equivalent nodes can get easily synchronized when the group forms a fully connected subgraph (or combinations thereof), regardless of the status of all the other oscillators. More generally, any change occurring in the remainder of the graph will not alter the synchronization status of the group. Typically, the group can synchronize when $k^{\left(\mathrm{OUT}\right)}\le k^{\left(\mathrm{IN}\right)}, k^{\left(\mathrm{IN}\right)}$, and $k^{\left(\mathrm{OUT}\right)}$ being the common internal and outgoing degree of each node in the group, respectively. Simulations confirm our rigorous analysis and suggest that groups of topologically equivalent nodes act as independent pacemakers.

Nonlinear local and global gyrokinetic simulations of tokamak plasmas demonstrate that turbulence-generated currents flatten the safety factor profile near low-order rational surfaces when magnetic shear is low, even when the plasma $\beta$ is small. A large set of flux tube simulations with different safety factor profiles (e.g., linear and nonlinear safety factor profiles) and global simulations with reversed magnetic shear profiles show that such stepped safety factor profiles dramatically reduce the heat transport and are a robust phenomenon. This mechanism may play a key role in the triggering of internal transport barriers and more generally reveal novel strategies for improving confinement in devices with low magnetic shear.