We analyze the recovery of different roles in a network modeled by a directed graph, based on the so-called Neighborhood Pattern Similarity approach. Our analysis uses results from random matrix theory to show that, when assuming that the graph is generated as a particular stochastic block model with Bernoulli probability distributions for the different blocks, then the recovery is asymptotically correct when the graph has a sufficiently large dimension. Under these assumptions there is a sufficient gap between the dominant and dominated eigenvalues of the similarity matrix, which guarantees the asymptotic correct identification of the number of different roles. We also comment on the connections with the literature on stochastic block models, including the case of probabilities of order $log\left(n\right)/n$ where $n$ is the graph size. We provide numerical experiments to assess the effectiveness of the method when applied to practical networks of finite size.

Evolutionary transitions among ecological interactions are widely known, although their detailed dynamics remain absent for most population models. Adaptive dynamics has been used to illustrate how the parameters of population models might shift through evolution, but within an ecological regime. Here we use adaptive dynamics combined with a generalized logistic model of population dynamics to show that transitions of ecological interactions might appear as a consequence of evolution. To this purpose, we introduce a two-microbial toy model in which population parameters are determined by a bookkeeping of resources taken from (and excreted to) the environment, as well as from the byproducts of the other species. Despite its simplicity, this model exhibits all kinds of potential ecological transitions, some of which resemble those found in nature. Overall, the model shows a clear trend toward the emergence of mutualism.

Since the last century, deterministic compartmental models have emerged as powerful tools to predict and control epidemic outbreaks, in many cases helping to mitigate their impacts. A key quantity for these models is the so-called basic reproduction number, $R_0$, that measures the number of secondary infections produced by an initial infected individual in a fully susceptible population. Some methods have been developed to allow the direct computation of this quantity provided that some conditions are fulfilled, such that the model has a prepandemic disease-free equilibrium state. This condition is fulfilled only when the populations are stationary. In the case of vector-borne diseases, this implies that the vector birth and death rates need to be balanced. This is not fulfilled in many realistic cases in which the vector population grows or decreases. Here we develop a vector-borne epidemic model with growing and decaying vector populations that in the long term converge to an asymptotic stationary state, and study the conditions under which the standard methods to compute $R_0$ work and discuss an alternative when they fail. We also show that growing vector populations produce a delay in the epidemic dynamics when compared to the case of the stationary vector population. Finally, we discuss the conditions under which the model can be reduced to the Susceptible, Infectious, and/or Recovered (SIR) model with fewer compartments and parameters, which helps in solving the problem of parameter unidentifiability of many vector-borne epidemic models.

The conformational and dynamical properties of a tethered semiflexible polymer chain under tangential active force ($f_a$) are studied by using the Langevin dynamics simulation method. The head of the polymer is fixed near an infinite flat surface at $z=0$. The polymer is equilibrated first at $f_a=0$ and then subjected to the active force. Under the influence of the active force, the polymer is gradually compressed. Specially, for large $f_a$ and large bending rigidity ($k_b$), the polymer is buckled into a quasihelical structure rotating around the $z$ axis at the steady state. It is found that both the radius of the quasihelical structure ($R$) and the angular velocity of the rotation (ω) are nearly independent of the polymer length ($N$), but show scaling relations with $f_a$ and $k_b$, i.e., $R\propto f_a^{-1/3}{k}_b^{1/3}$ and $\omega \propto f_a^{4/3}{k}_b^{-1/3}$, which are explained by simple dynamical models. Before reaching the steady state, it is further found that the buckling velocity of the polymer is proportional to $f_a$ but roughly independent of $k_b$ and $N$, then the buckling time ($t_b$) can be described by a scaling relation $t_b\propto N{f}_a^{-1}$. The underlying mechanism of the buckling process is revealed.

Liquid film coating inside a tube becomes unstable to surface-tension-driven Rayleigh-Plateau (RP) instability. The presence of interfacial surfactant reduces the growth rate of RP instability but is unable to completely eliminate it. Further, it is known that the surfactant mode, an eigenmode emerging because of the presence of surfactant, remains stable for such liquid films. However, the above two observations hold true only when the liquid film remains stationary (i.e., in the absence of base flow). Here, we investigate the linear stability of surfactant-laden liquid film inside of the tube with base flow included in the analysis. We observed a complete suppression of Rayleigh-Plateau instability because of the presence of surfactant when the basic flow is included in the analysis. However, the surfactant mode, which otherwise remains stable in the absence of base flow, is found to be unstable when the basic flow is taken into account in the stability analysis. More importantly, depending on the base flow strength, the wave number corresponding to maximum growth rate and cutoff wave number for surfactant mode are greater than unity for a wide variety of parameters. This is unlike the (RP) instability observed for surfactant-covered stationary films where the cutoff wave number is always less than unity. Further, we show that the growth rate observed for this surfactant-mode instability in the presence of sufficiently strong basic flow is significantly higher than the growth rate of RP instability observed for a stationary liquid film. These observations imply that depending on the strength of basic flow, the effect of presence of surfactant is destabilizing for such film flows as opposed to a stabilizing effect observed for stationary liquid films in earlier studies.

Precise 3D representation of complex materials, here the lithium-ion batteries, is a critical step toward designing optimized energy storage systems. One requires obtaining several such samples for a more accurate evaluation of uncertainty and variability, which in turn can be costly and time demanding. Using 3D models is crucial when it comes to evaluating the transport and heat capacity of batteries. Further, such models represent the microstructures more precisely where connectivity and heterogeneity can be detected. However, 3D images are hard to access, and the available images are often collected in two dimensions (2D). Such 2D images, on the other hand, are more accessible and often have higher resolution. In this paper, a deep learning method has been applied to take advantage of 2D images and build 3D models of heterogeneous materials through which more accurate characterization and physical evaluations can be achieved. While being trained using only 2D images, the proposed framework can be utilized to generate 3D images. The proposed method is applied to a few realistic 3D images of lithium-ion battery electrodes. The results indicate that the implemented method can reproduce important structural properties while the flow and heat properties are within an acceptable range.

We present simulation results from a comprehensive molecular dynamics (MD) study of surface-directed spinodal decomposition (SDSD) in unstable symmetric binary mixtures at wetting surfaces. We consider long-ranged and short-ranged surface fields to investigate the early stage wetting kinetics. The attractive part of the long-ranged potential is of the form $V\left(z\right)\sim z^{-n}$, where $z$ is the distance from the surface and $n$ is the power-law exponent. We find that the wetting-layer thickness $R_1\left(t\right)$ at very early times exhibits a power-law growth with an exponent $\alpha =1/(n+2)$. It then crosses over to a universal fast-mode regime with $\alpha =3/2$. In contrast, for the short-ranged surface potential, a logarithmic behavior in $R_1\left(t\right)$ is observed at initial times. Remarkably, similar rapid growth is seen in this case too. We provide phenomenological arguments to understand these growth laws. Our MD results firmly establish the existence of universal fast-mode kinetics and settle the related controversy.

We study discrete-time random walks on networks subject to a time-dependent stochastic resetting, where the walker either hops randomly between neighboring nodes with a probability $1-\varphi \left(a\right)$ or is reset to a given node with a complementary probability $\varphi \left(a\right)$. The resetting probability $\varphi \left(a\right)$ depends on the time $a$ since the last reset event (also called $a$, the age of the walker). Using the renewal approach and spectral decomposition of the transition matrix, we formulate the stationary occupation probability of the walker at each node and the mean first passage time between two arbitrary nodes. Concretely, we consider two different time-dependent resetting protocols that are both exactly solvable. One is that $\varphi \left(a\right)$ is a step-shaped function of $a$ and the other one is that $\varphi \left(a\right)$ is a rational function of $a$. We demonstrate the theoretical results on several different networks, also validated by numerical simulations, and find that the time-modulated resetting protocols can be more advantageous than the constant-probability resetting in accelerating the completion of a target search process.

Interconnected dynamical systems often transition between states of incoherence and synchronization due to changes in system parameters. These transitions could be continuous (gradual) or explosive (sudden) and may result in failures, which makes determining their nature important. In this study, we abstract dynamical networks as an ensemble of globally coupled Kuramoto-like phase oscillators with frequency-dependent coupling and investigate the mechanisms for transition between incoherent and synchronized dynamics. The characteristics that dictate a continuous or explosive route to synchronization are the distribution of the natural frequencies of the oscillators, quantified by a probability density function $g\left(\omega \right)$, and the relation between the coupling strength and natural frequency of an oscillator, defined by a frequency-coupling strength correlation function $f\left(\omega \right)$. Our main results are conditions on $f\left(\omega \right)$ and $g\left(\omega \right)$ that result in continuous or explosive routes to synchronization and explain the underlying physics. The analytical developments are validated through numerical examples.

We present a theoretical framework to investigate the microscopic structure of concentrated hard-sphere colloidal suspensions under strong shear flows by fully taking into account the boundary-layer structure of convective diffusion. We solve the pair Smoluchowski equation with shear separately in the compressing and extensional sectors of the solid angle, by means of matched asymptotics. A proper, albeit approximate, treatment of the hydrodynamic interactions in the different sectors allows us to construct a potential of mean force containing the effect of the flow field on pair correlations. We insert the obtained pair potential in the Percus-Yevick relation and use the latter as a closure to solve the Ornstein-Zernike integral equation. For a wide range of either the packing fraction $\eta$ and the Péclet ($\text{Pe}$) number, we compute the pair correlation function and extract scaling laws for its value at contact. For all the considered values of $\text{Pe},$ we observe a very good agreement between theoretical findings and numerical results from the literature, up to rather large values of $\eta .$ The theory predicts a consistent enhancement of the structure factor $S\left(k\right)$ at $k\to 0,$ upon increasing the $\text{Pe}$ number. We argue this behavior may signal the onset of a phase transition from the isotropic phase to a nonuniform one, induced by the external shear flow.

Inspired by groups of animals and robots, we study the collective dynamics of large numbers of active particles, each one trying to get to its own randomly placed target, while avoiding collisions with each other. The particles we study are repulsive homing active Brownian particles, self-propelled particles whose orientation relaxes at a finite rate towards an absorbing target in two-dimensional continuous space. For a wide range of parameters, these particles form synchronized system-wide chiral flocks, in spite of the absence of explicit alignment interactions. We show that this dramatic behavior obtains for different system sizes and density, that it is robust against the addition of noise, polydispersity, and bounding walls, and that it can exhibit dynamical topological defects. We develop an analogy to an off-lattice, ferromagnetic XY model, which allows us to interpret the different phases, as well as the topological defects.

A strong quasistationary magnetic field is generated in hollow targets with curved internal surface under the action of a relativistically intense picosecond laser pulse. Experimental data evidence the formation of quasistationary strongly magnetized plasma structures decaying on a hundred picoseconds timescale, with the magnetic field strength of the kilotesla scale. Numerical simulations unravel the importance of transient processes during the magnetic field generation and suggest the existence of fast and slow regimes of plasmoid evolution depending on the interaction parameters. The proposed setup is suited for perspective highly magnetized plasma application and fundamental studies.

Quantum computation builds on the use of correlations. Correlations could also play a central role for artificial intelligence, neuromorphic computing or “biological computing.” As a step toward a systematic exploration of “correlated computing” we demonstrate that neuromorphic computing can perform quantum operations. Spiking neurons in the active or silent states are connected to the two states of Ising spins. A quantum density matrix is constructed from the expectation values and correlations of the Ising spins. We show for a two qubit system that quantum gates can be learned as a change of parameters for neural network dynamics. These changes respect restrictions which ensure the quantum correlations. Our proposal for probabilistic computing goes beyond Markov chains and is not based on transition probabilities. Constraints on classical probability distributions relate changes made in one part of the system to other parts, similar to entangled quantum systems.

Optimizing embedded systems, where the optimization of one depends on the state of another, is a formidable computational and algorithmic challenge, that is ubiquitous in real world systems. We study flow networks, where bilevel optimization is relevant to traffic planning, network control, and design, and where flows are governed by an optimization requirement subject to the network parameters. We employ message passing algorithms in flow networks with sparsely coupled structures to adapt network parameters that govern the network flows, in order to optimize a global objective. We demonstrate the effectiveness and efficiency of the approach on randomly generated graphs.

Anomalous diffusion of an antibiotic (colistin) in a system consisting of packed gel (alginate) beads immersed in water is studied experimentally and theoretically. The experimental studies are performed using the interferometric method of measuring concentration profiles of a diffusing substance. We use the $g$-subdiffusion equation with the fractional Caputo time derivative with respect to another function $g$ to describe the process. The function $g$ and relevant parameters define anomalous diffusion. We show that experimentally measured time evolution of the amount of antibiotic released from the system determines the function $g$. The process can be interpreted as subdiffusion in which the subdiffusion parameter (exponent) $\alpha$ decreases over time. The $g$-subdiffusion equation, which is more general than the “ordinary” fractional subdiffusion equation, can be widely used in various fields of science to model diffusion in a system in which parameters, and even a type of diffusion, evolve over time. We postulate that diffusion in a system composed of channels and a matrix can be described by the $g$-subdiffusion equation, just like diffusion in a system of packed gel beads placed in water.

The two-leg magnetic ladder is the simplest and ideal model to reflect the coupling effects of lattice and magnetic field. It is of great significance to study some novel phases, topological characteristics, and chiral characteristics in condensed matter physics. In particular, the left-right leg degree of freedom can be regarded as a pseudospin, and the two-leg magnetic ladder also provides an ideal platform for the study of spin dynamics. Here the ground state, Bloch oscillations (BOs), and spin dynamics of the interacting two-leg magnetic ladder subject to an external linear force are studied by using variational approach and numerical simulation. In the absence of the external linear force, the critical condition of transition between the zero-momentum state and plane-wave state is obtained analytically, and the physical mechanism of the ground-state transition is revealed. When the external linear force presents, the occurrence of BOs excites the spin dynamics, and we reveal the chiral BOs and the accompanied spin dynamics of the system in different ground states. In particular, we further study the influence of periodically modulated linear force on BOs and spin dynamics. The frequencies of the linear force corresponding to the resonances and pseudoresonances are obtained analytically, which result in rich nonlinear dynamics. In resonances, stable and strong BOs (with larger amplitude) are observed. In pseudoresonances, because the pseudoresonance frequencies are related to the initial momentum and phase of the wave packet, a dispersion effect takes place and strong diffusion of wave packet occurs. When the frequency is nonresonant, drift and weak dispersion of wave packet occur simultaneously with the wave-packet oscillation. In all cases, the wave-packet dynamics is accompanied with periodic but anharmonic pseudospin oscillation. The BOs and spin dynamics are effectively controlled by periodically modulating the linear force.

With the use of microscopic traffic simulations, physical features of microscopic traffic prediction for automated driving that should improve traffic harmonization and safety have been found: During a short-time prediction horizon (about 10 s), online prediction of the locations and speeds of all vehicles in some limited area around the automated-driving vehicle is possible; this enables the automated vehicle control in complex traffic situations in which the automated-driving vehicle is not able to make a decision based on current traffic information without the use of the microscopic traffic prediction. Through a more detailed analysis of an unsignalized city intersection, when the automated vehicle wants to turn right from a secondary road onto the priority road, the statistical physics of the effect of a data uncertainty caused by errors in data measurements on the prediction reliability has been studied: (i) probability of the prediction reliability has been found; (ii) there is a critical uncertainty, i.e., a maximum amplitude of errors in data measurements: when the uncertainty does not exceed the critical uncertainty, the prediction reliability probability is equal to 1, otherwise, the prediction is not applicable for a reliable automated vehicle control; (iii) physical characteristics of the microscopic traffic prediction, at which the critical uncertainty can be increased considerably, have been found; and (iv) there is an optimal automated vehicle control at which the critical uncertainty reaches a maximum value.

When data are available for all nodes of a Gaussian graphical model, then, it is possible to use sample correlations and partial correlations to test to what extent the conditional independencies that encode the structure of the model are indeed verified by the data. In this paper, we give a heuristic rule useful in such a validation process: When the correlation subgraph involved in a conditional independence is balanced (i.e., all its cycles have an even number of negative edges), then a partial correlation is usually a contraction of the corresponding correlation, which often leads to conditional independence. In particular, the contraction rule can be made rigorous if we look at concentration subgraphs rather than correlation subgraphs. The rule is applied to real data for elementary gene regulatory motifs.

We model the behavior of a single colloid embedded in a cross-linked polymer gel, immersed in a viscous background fluid. External fields actuate the particle into a periodic motion, which deforms the embedding matrix and creates a local microcavity, containing the particle and any free volume created by its motion. This cavity exists only as long as the particle is actuated and, when present, reduces the local density of the material, leading to swelling. We show that the model exhibits rich resonance features, but is overall characterized by clear scaling laws at low and high driving frequencies, and a pronounced resonance at intermediate frequencies. Our model predictions suggest that both the magnitude and position of the resonance can be varied by varying the material's elastic modulus or cross-linking density, whereas the local viscosity primarily has a dampening effect. Our work implies appreciable free-volume generation is possible by dispersing a collection of colloids in the medium, even at the level of a simple superposition approximation.