A weighted isotropic forest fire model (WFFM) is introduced with an external parameter $\beta$, representing environmental factors such as inverse temperature and humidity. The spatial configuration of trees is modeled either by uncorrelated percolation with occupation probability $p$ or by correlated percolation using the Ising model with an artificial temperature $T$, which controls correlations. The burning clusters are shown to exhibit a depinning transition at a $p$-dependent critical ${\beta }_c$ (or $T$-dependent in the correlated case), with critically pinned states indicating that $\beta$ acts as a driving force. For uncorrelated percolation, the critical exponents for nonfractal observables place the transition in the percolation universality class, while the hull fractal dimension varies from $1.34\left(1\right)$ at $p=1$ to $1.73\left(2\right)$ at $p=p_c$, showing that introducing correlation in the spatial structure changes the OP universality class to a new universality class for the driven interfaces. This challenges recent predictions and opens up new frontiers in our understanding concerning the effect of spatial correlations on the properties of driven interfaces.

Neural networks have become a widely adopted tool for tackling a variety of problems in machine learning and artificial intelligence. In this contribution, we use the mathematical framework of local stability analysis to gain a deeper understanding of the learning dynamics of feedforward neural networks. We derive equations for the tangent operator of the learning dynamics of three-layer networks learning regression tasks. The results are valid for an arbitrary number of nodes and arbitrary choices of activation functions. Applying the results to a network learning a regression task, we investigate numerically how stability indicators relate to the final training loss. Although the specific results vary with different choices of initial conditions and activation functions, we demonstrate that it is possible to predict the final training loss by monitoring finite-time Lyapunov exponents during the training process.

Dark-bright solitons of the integrable Manakov model with repulsive interactions were widely believed to possess negative mass due to the total densities admit dips. We report the dark-bright soliton can also admit positive effective mass for the Manakov case, by finding two branches of the phases and widths underlying the vector soliton solutions. The positive-mass soliton can evolve stably against noise and weak deviations from the Manakov conditions, and even a line-dark-bright soliton can exist stably in two-dimensional cases with suppressed snake instability, allowing further experimental investigations. When the soliton is driven by a constant force, it diffuses (for negative-mass ones) or splits (for positive-mass ones) as its velocity approaches the maximum moving speed, in contrast to the oscillating ones in nonintegrable cases. The diffusion can be understood by the excitation probabilities of the ground state (bright soliton) to the first excited state in the effective potential well. These results provide important supplements for the vector solitons in integrable cases, and would motivate more discussions on the dispersion relations of soliton in nonlinear coupled systems.

The fragility of financial systems was starkly demonstrated in early 2023 through a cascade of major bank failures in the United States, including the second, third, and fourth largest collapses in U.S. history. The highly interdependent financial networks and the associated high systemic risk have been deemed the cause of the crashes. The goal of this paper is to enhance existing systemic risk analysis frameworks by incorporating essential debt valuation factors. Our results demonstrate that these additional elements substantially influence the outcomes of risk assessment. Notably, by modeling the dynamic relationship between interest rates and banks' credibility, our framework can detect potential cascading failures that standard approaches might miss. The proposed risk assessment methodology can help regulatory bodies prevent future failures, while also allowing companies to more accurately predict turmoil periods and strengthen their survivability during such events.

Networks are ubiquitous in various fields, representing systems where nodes and their interconnections constitute their intricate structures. We introduce a network decomposition scheme to reveal multiscale core-periphery structures lurking inside, using the concept of locally defined nodal hub centrality and edge-pruning techniques built upon it. We demonstrate that the hub-centrality-based edge pruning reveals a series of breaking points in network decomposition, which effectively separates a network into its backbone and shell structures. Our local-edge decomposition method iteratively identifies and removes locally least connected nodes, and uncovers an onionlike hierarchical structure as a result. Compared with the conventional $k$-core decomposition method, our method based on relative information residing in local structures exhibits a clear advantage in terms of discovering locally crucial substructures. As an application of the method, we present a scheme to detect multiple core-periphery structures and the decomposition of coarse-grained supernode networks, by combining the method with the network community detection.

This paper introduces a class of random walks on graphs in which the probability of moving from a vertex $u$ to one of its neighbors $v$ is proportional to $d_v^{\alpha }$, where $d_v$ is the degree of $v$ and $\alpha$ a parameter that characterizes the walk. We derive the stationary distribution of the walks and study their expected behavior in the class of Barabasi-Albert random graphs. We find that the fastest exploration of the graph is for $\alpha <0$, that is, when there is a bias towards neighbors of low degree. This bias balances the bias of the degree distribution, leading to a uniform probability of being on a given vertex at a given time, thus leading to a faster exploration.

In this paper, we introduce the concept of anchor nodes in hypergraphs, providing a natural framework to unify and transition between the two primary classes of hypergraph percolation processes explored in the literature. The removal of anchor nodes deletes the hyperedges they belong to, whereas removing nonanchor nodes only reduces the size of the hyperedges without affecting their existence. Using a bipartite factor graph representation, we establish a versatile analytical framework based on message-passing theory to determine percolation thresholds, the critical probability of anchor nodes, the percolation critical exponent, and the size of giant clusters and finite clusters. Our analysis reveals that hypergraphs with heterogeneous cardinality distributions exhibit heightened sensitivity to the presence of anchor nodes, compared to those with homogeneous distributions. Intriguing crossover phenomena emerge, governed by the fraction of anchor nodes, underscoring the complex interplay between reinforcing and fragmenting effects of large hyperedges. Extending this framework to multiplex random hypergraphs, we uncover additional crossover behaviors and demonstrate how anchor nodes mediate the robustness of hypergraphs across varying structural properties. In both hypergraph models, we find strikingly that the absence of anchor nodes leads to a second-order phase transition, while any nonzero fraction results in a higher-order phase transition. These findings deepen our understanding of hypergraph percolation, providing a basis for future investigation into their application in real-world scenarios.

A dendritic neuron model subject to spatiotemporal fluctuating synaptic drive and a pointlike oscillating current stimulation is considered. Unlike for dendritic models that are statistically homogeneous in space, this experimentally plausible scenario allows for the electrotonic length constant to feature in quantities like the modulated firing rate as a function of the distance to current stimulation. The cable equation for the voltage is solved to find the modulated first- and second-order moments featuring the voltage and its rate of change. These are then used to calculate the frequency dependence of the firing-rate response in the upcrossing approximation as a function of the distance between a nominal soma and current stimulation. With an isopotential model as a reference, this minimal dendritic model exhibits some surprising features such as modulated first-order moments that grow with frequency. In addition, despite the model's passive membrane, the voltage moments and upcrossing rate exhibit frequency preferences in the form of resonances and troughs. These features are in the same class of morphological resonance phenomena previously seen in Purkinje cells and in models of cells driven by external electrical fields.

Molecular dynamics was used to evaluate the channel size dependence of force acting near a liquid-vapor-solid contact line. The shear stress distribution acting on the solid wall surface was calculated using the spatial distribution of the stress tensor to obtain the force acting near the contact line. The force, nondimensionalized by that acting at a region away from the contact line, is proportional to the ratio of the slip length to the channel size. The obtained equation also showed good agreement with the force obtained from the shape of the liquid-vapor interface. Moreover, the obtained equation was dependent on the channel size but independent on the channel size when the channel size was sufficiently large compared with the slip length. This result differs from the channel size dependence of the shear stress at the region distant from the liquid-vapor interface, indicating that the shear stress at the region away from the liquid-vapor interface is more important than the force owing to the surface tension in a nano-order channel.

The Mpemba and Kovacs effects are two notable memory phenomena observed in nonequilibrium relaxation processes. In a recent study [Phys. Rev. E 109, 044149 (2024)], these effects were analyzed within the framework of the time-delayed Newton's law of cooling under the assumption of instantaneous temperature quenches. Here, the analysis is extended to incorporate finite-rate quenches, characterized by a nonzero quench duration $\sigma$. The results indicate that a genuine Mpemba effect is absent under finite-rate quenches if both samples experience the same thermal environment during the quenching process. However, if $\sigma$ remains sufficiently small, the deviations in the thermal environment stay within an acceptable range, allowing the Mpemba effect to persist with a slightly enhanced magnitude. In contrast, the Kovacs effect is significantly amplified, with the transient hump in the temperature evolution becoming more pronounced as both the waiting time and $\sigma$ increase. These findings underscore the importance of incorporating finite-time effects in nonequilibrium thermal relaxation models and offer a more realistic perspective for experimental studies.

We report on an exact theory for ensembles of globally coupled, heterogeneous complex Riccati equations. A drastic dimensionality reduction to a few ordinary differential equations is achieved for Lorentzian heterogeneity. By applying this technique, we obtain low-dimensional firing-rate equations for populations of spiking neurons with a clustered substructure.

We study a model of diffusive oscillators whose internal states are subject to a periodic drive. These models are inspired by the dynamics of deformable particles with pulsating sizes, where repulsion leads to arrest the internal pulsation at high density. We reveal that, despite the absence of any repulsion between the diffusive oscillators, our model still captures the emergence of dynamical arrest. We demonstrate that arrest here stems from the discrete nature of internal states, which enforces an effective energy landscape analogous to that of deformable particles. Moreover, we show that the competition between arrest and synchronization promotes spiral waves reminiscent of the pulsating states of deformable particles. Using analytical coarse graining, we derive and compare the collective dynamics of diffusive oscillators with that of deformable particles. This comparison leads to rationalizing the emergence of spirals in terms of a rotational invariance at the coarse-grained level, and to elucidating the role of hydrodynamic fluctuations.

Metal nanoparticle-drug binding, along with the controlled release of these drugs, plays a crucial role in the progress of personalized medicine. Understanding the intricate microscopic mechanisms that drive these processes holds the key to improving therapeutic results, especially since the efficiency of binding and unbinding can vary significantly depending on the specific drug payload and the perturbing agent used to trigger the release. We investigated the microscopic machinery that governs the controlled release of a specific cargo, vitamin B1 (VB1), conjugated with citrate-capped gold nanoparticles (cAuNPs), in response to externally added calcium ions (${\mathrm{Ca}}^{2+}$) in a sol of physiological pH. We employed optical spectroscopic techniques for our studies. Furthermore, to understand the drug-specific molecular interactions involved in the release of VB1 over hours/days, we designed a model based on classical molecular dynamics simulation. The results obtained from simulations and experiments reveal that the release of VB1 from the cAuNP-VB1 conjugate could be due to the stripping off and rearrangement of negatively charged citrate ions, which are a mediator of AuNP-VB1 binding, induced by ${\mathrm{Ca}}^{2+}$. The investigation has been carried out on the benchtop and in silico for varying concentrations of ${\mathrm{Ca}}^{2+}$ ions. Essentially, this study offers a framework for understanding ion-induced drug release mechanisms, bridging experimental and theoretical approaches.

We investigate the frequency response of the graphene-based electrochemical systems containing room-temperature ionic liquids using the method of matched asymptotic expansion in the limit of thin double-layers to study the diffuse-charge dynamics of graphene electrodes interfaced with the ionic liquids. The theory in the framework of the asymptotic matching is mainly supported by (1) the length scale $\sqrt{{\lambda }_D{L}_c}$ that suitably characterizes the structure of the double layer in ionic liquids, with ${\lambda }_D$ referring to the Debye length and $L_c$ referring to the electrostatic correlation length, and (2) the charging time, ${\tau }_c={\lambda }_D^{3/2}L/\left(D{L}_c^{1/2}\right)$, where $D$ is the diffusion coefficient and $L$ is the thickness of the electrolyte. With this response time, the diffuse-charge dynamics is deduced at the leading order to obtain an analytic expression for low-frequency impedance. As a result of the new length scaling $\sqrt{{\lambda }_D{L}_c}$, we additionally study the behavior of double-layer in graphene-metal electrochemical systems involving ionic liquids, where electrostatic correlation length $L_c$ is found to play a prominent role in the linear regime. The results are then compared with the conventional electrochemical cells containing a metal-metal electrode pair.

Maggi and Orozco [Phys. Rev. E 109, 034402 (2024)] address the question of the origin of the subdiffusional dynamics observed in molecular dynamics (MD) simulations of proteins. Confirming the conclusions of previous publications that used closely similar methods [Neusius et al. Phys. Rev. Lett. 100, 188103 (2008); Phys. Rev. E 83, 021902 (2011)], Maggi and Orozco conclude that a random walk on a fractal surface is an appropriate model. However, the logic used in their paper to make that conclusion is erroneous.

We present here the response to the criticisms raised by Neusius et al. This paper contains new results and analyses which, we believe, clarify and strengthen the findings of Maggi et al. [Phys. Rev. E 109, 034402 (2024)] and make them even more general.

Liquid-liquid phase separation (LLPS) in a confining environment is believed to play an important role in cell biology. At least in some cases, this form of LLPS involves free energy consumption, which could lead to breakdown of the fundamental Principle of Detailed Balance (PDB). Recently, it was shown that when active noise at the microscopic level is included in the classical theory of nucleation and growth this does not cause the breakdown of detailed balance at the macroscopic level provided that the droplet radius is the only collective coordinate. Here we present a simple model for active LLPS in a confining environment with the droplet location in a confining potential functioning as a second collective coordinate. Using the Fluctuation-Dissipation Theorem as a diagnostic, we show that the PDB now is broken at the macroscopic level but in an unusual fashion: the active noise suppresses both the linear susceptibility and the quasicritical thermal noise spectrum in an asymmetric manner.

Parity represents the spatial inversion symmetry of a physical phenomenon under mirror reflection. Commonly, the parity of interatomic interaction is broken in crystalline solids due to asymmetric repulsion between atoms. Symmetry breaking often involves a phase transition; however, it is still unclear if there are any comparable behaviors in crystalline solids as the result of asymmetric interatomic interaction. In this paper, we show that a crossover behavior of thermal conduction occurs in a Fermi-Pasta-Ulam-Tsingou $\alpha \text{−}\beta$ superlattice, consisting of periodic cells of arithmetically increased cubic nonlinearity, due to strengthened interaction asymmetry. Before a critical point of interaction asymmetry, thermal conductance is a cell-length-independent constant, and it becomes cell length dependent after crossing the critical point. The reflection symmetry and configuration entropy of the atomic displacement are calculated as functions of interaction asymmetry, where a discontinuity appears at the critical point in their second derivatives and thus this crossover behavior is third-order-like. We also find that the sound speed and scaling exponents of energy carriers exhibit a similar crossover owing to the strengthened interaction asymmetry. Our numerical result reveals a peculiar microscopic mechanism for adjusting thermal conduction behavior in phononic superlattice systems.

We propose the concept of mutual information for particle pair (MIPP) in curved spacetime, and show that MIPP has potential to be a proper chaos indicator. We tested this method in the Schwarzschild and Kerr spacetime and compared it with the fast Lyapunov indicator. The results show that the MIPP effectively identify orbital states and demonstrate prominent performance in recognizing transitions between orbital states. Our result show that information theory is helpful to deepen our understanding of dynamics of few-body system significantly.