An obstacle to artificial general intelligence is set by continual learning of multiple tasks of a different nature. Recently, various heuristic tricks, both from machine learning and from neuroscience angles, were proposed, but they lack a unified theory foundation. Here, we focus on continual learning in single-layered and multilayered neural networks of binary weights. A variational Bayesian learning setting is thus proposed in which the neural networks are trained in a field-space, rather than a gradient-ill-defined discrete-weight space, and furthermore, weight uncertainty is naturally incorporated, and it modulates synaptic resources among tasks. From a physics perspective, we translate variational continual learning into a Franz-Parisi thermodynamic potential framework, where previous task knowledge serves as a prior probability and a reference as well. We thus interpret the continual learning of the binary perceptron in a teacher-student setting as a Franz-Parisi potential computation. The learning performance can then be analytically studied with mean-field order parameters, whose predictions coincide with numerical experiments using stochastic gradient descent methods. Based on the variational principle and Gaussian field approximation of internal preactivations in hidden layers, we also derive the learning algorithm considering weight uncertainty, which solves the continual learning with binary weights using multilayered neural networks, and performs better than the currently available metaplasticity algorithm in which binary synapses bear hidden continuous states and the synaptic plasticity is modulated by a heuristic regularization function. Our proposed principled frameworks also connect to elastic weight consolidation, weight-uncertainty modulated learning, and neuroscience-inspired metaplasticity, providing a theoretically grounded method for real-world multitask learning with deep networks.

A comparison of the movement characteristics between bacteria with and without wall accumulation could potentially elucidate the mechanisms of biofilm formation. However, authors of previous studies have mostly focused on the motion of bacteria that exhibit wall accumulation. Here, we applied digital holographic microscopy to compare the three-dimensional (3D) motions of two bacterial strains (Shewanella japonica UMDC19 and Shewanella sp. UMDC1): one exhibiting higher concentrations near the solid surfaces, and the other showing similar concentrations in near-wall and bulk regions. We found that the movement characteristics of the two strains are similar in the near-wall region but are distinct in the bulk region. Near the wall, both strains have small velocities and mostly perform subdiffusive motions. In the bulk, however, the bacteria exhibiting wall accumulation have significantly higher motility (including faster swimming speeds and longer movement trajectories) than the one showing no wall accumulation. Furthermore, we found that bacteria exhibiting wall accumulation slowly migrate from the bulk region to the near-wall region, and the hydrodynamic effect alone is insufficient to generate this migration speed. Future studies are required to test if the current findings apply to other bacterial species and strains.

Nucleation and subsequent expansion of gas bubbles in porous media is relevant to many applications, including oil recovery, carbon storage, and boiling. We have built an experimental setup using microfluidic chips to study the dynamics of bubble growth in porous media. Visualization experiments of the growth of carbon dioxide bubbles in a supersaturated dodecane solution were conducted. We show that bubbles grow as dissolved gas molecules inside the oversaturated liquid diffuse to the gas-liquid interface. Bubbles expanding inside a porous medium displace the liquid phase until the cluster of the gas-filled pores becomes connected to the outlet at the critical gas saturation, which is used as a measure for the total liquid displacement. Our experiments uniquely focus on the growth of a single bubble and show that larger pressure drops lead to faster bubble growth while resulting in lower critical gas saturations. A nonlinear pore-network model is implemented to simulate bubble growth. We compare model predictions for bubble growth dynamics to our experimental results and present the need for further theoretical development to capture deviations from invasion-percolation when a large pressure drop is applied.

We develop a perturbative technique for solving Markovian quantum dissipative dynamics, with the perturbation parameter being a small gap in the eigenspectrum. As an example, we apply the technique and straightforwardly obtain analytically the dynamics of a three-level system with quasidegenerate excited states, where quantum coherences persist for very long times, proportional to the inverse of the energy splitting squared. We then show how to bypass this long-lived coherent dynamics and accelerate the relaxation to thermal equilibration in a hyper-exponential manner, a Markovian quantum-assisted Mpemba-like effect. This hyperacceleration of the equilibration process manifests if the initial state is carefully prepared, such that its coherences precisely store the amount of population relaxing from the initial condition to the equilibrium state. Our analytical method for solving quantum dissipative dynamics readily provides equilibration timescales, and as such it reveals how coherent and incoherent effects interlace in the dynamics. It further advises on how to accelerate relaxation processes, which is desirable when long-lived quantum coherences stagnate dynamics.

Externally stressed brittle rocks fail once the stress is sufficiently high. This failure is typically preceded by a pronounced increase in the total energy of acoustic emission (AE) events, the so-called accelerated seismic release. Yet, other characteristics of approaching the failure point such as the presence or absence of variations in the AE size distribution and, similarly, whether the failure point can be interpreted as a critical point in a statistical physics sense differs across experiments. Here, we show that large-scale stress heterogeneities induced by a notch fundamentally change the characteristics of the failure point in triaxial compression experiments under a constant displacement rate on Westerly granite samples. Specifically, we observe accelerated seismic release without a critical point and no change in power-law exponent $\epsilon$ of the AE size distribution. This is in contrast to intact samples, which exhibit a significant decrease in $\epsilon$ before failure. Our findings imply that the presence or absence of large-scale heterogeneities play a significant role in our ability to predict compressive failure in rock.

The FitzHugh-Nagumo equation is a simple model equation that exhibits spiking. The output signal of a neuron is represented in the spiking frequency or firing rate. We consider a few control methods for spiking from the viewpoint of nonlinear dynamics. The repetitive spiking can be suppressed in the FitzHugh-Nagumo model by the periodic sinusoidal force with high frequency. We study the transition to the suppressed state numerically and perform a linear stability analysis to understand the suppression of the spiking. Next, we study coupled FitzHugh-Nagumo equations. We find that the periodic forcing makes the system chaotic, and the desynchronization induced by chaos weakens the total output of spiking in a certain parameter range. Finally, we propose a method of feedback control for the spiking frequency. We can get the desired spiking and bursting frequency using this feedback control. The feedback control method is analyzed using a mapping for the input.

Noise is ubiquitous in natural and artificial systems. In a noisy environment, the interactions among nodes may fluctuate randomly, leading to more complicated interactions. In this paper we focus on the effects of noise and network topology on the Turing pattern of ecological networks with activator-inhibitor structure, which may be interpreted as prey-predator interactions. Based on the stability theory of stochastic differential equations, a sufficient condition for the uniform state is derived. The analytical results indicate that noise is beneficial for the uniform state. When the ratio between the diffusion coefficients of the predator and prey increases, the ecosystems can exhibit a transition from a uniform stable state to a Turing pattern, while when the ratio decreases, the ecosystems transit from a Turing pattern to a uniform stable state. There are two crucial critical points in Turing patterns, forward and backward. We find that both forward and backward critical points increase as the noise intensity increases. This means that noise favors a stable homogeneous state compared to a state with a heterogeneous pattern, which is consistent with the analytical results. In addition, noise can weaken the hysteresis phenomenon and even eliminate it in some cases. Furthermore, we report that network topology plays an important role in modulating the uniform state of ecosystems, such as the size of prey-predator systems, the network connectivity, and the strength of interaction.

A resistive pulse sensor measures the electrical impedance of an electrolyte-filled channel as particles flow through it. Ordinarily, the presence of a nonconductive particle increases the impedance of the channel. Here we report a surprising experimental result in which a microfluidic resistive pulse sensor experiences the opposite effect: The presence of a nonconductive particle decreases the channel impedance. We explain the counterintuitive phenomenon by relating to the Braess paradox from traffic network theory, and we call it the complex-valued Braess paradox (CVBP). We develop theoretical models to study the CVBP and corroborate the experimental data using finite element simulations and lumped-element circuit modeling. We then discuss implications and potential applications of the CVBP in resistive pulse sensing and beyond.

We demonstrate a framework of interpreting data from x-ray photon correlation spectroscopy experiments with the aid of numerical simulations to describe nanoscale dynamics in soft matter. This is exemplified with the transport of passive tracer gold nanoparticles in networks of charge-stabilized cellulose nanofibers. The main structure of dynamic modes in reciprocal space could be replicated with a simulated system of confined Brownian motion, a digital twin, allowing for a direct measurement of important effective material properties describing the local environment of the tracers.

We characterize the steady states of a suspension of two-dimensional active Brownian particles (ABPs). By approximating the first-order correction to the steady-state probability distribution to lowest order in Peclet number, we show that macroscopic quantities can be calculated in analogous way to equilibrium systems using this probability distribution. We then derive expressions for the macroscopic pressure and position-orientation correlation functions. We check our results by direct comparison with extensive numerical simulations. A key finding is the importance of many-body effective interactions even at very low densities.

The inability of the Navier-Stokes-Fourier equations to capture rarefaction effects motivates us to adopt the extended hydrodynamic equations. In the present work, a hydrodynamic model, which consists of the conservation laws closed with the recently propounded coupled constitutive relations (CCR), is utilized. This model is referred to as the CCR model and is adequate for describing moderately rarefied gas flows. A numerical framework based on the method of fundamental solutions is developed to solve the CCR model for rarefied gas flow problems in quasi two dimensions. To this end, the fundamental solutions of the linearized CCR model are derived in two dimensions. The significance of deriving the two-dimensional fundamental solutions is that they cannot be deduced from their three-dimensional counterparts that do exist in literature. As applications, the developed numerical framework based on the derived fundamental solutions is used to simulate (i) a rarefied gas flow between two coaxial cylinders with evaporating walls and (ii) a temperature-driven rarefied gas flow between two noncoaxial cylinders. The results for both problems have been validated against those obtained with the other classical approaches. Through this, it is shown that the method of fundamental solutions is an efficient tool for addressing quasi-two-dimensional multiphase microscale gas flow problems at a low computational cost. Moreover, the findings also show that the CCR model solved with the method of fundamental solutions is able to describe rarefaction effects, like transpiration flows and thermal stress, generally well.

Using a minimal continuum model, we investigate the interplay between circular confinement and substrate friction in active nematics. Upon increasing the friction from low to high, we observe a dynamical phase transition from a circulating flow phase to an anisotropic flow phase in which the flow tends to align perpendicular to the nematic director at the boundary. We demonstrate that both the flow structure and dynamic correlations in the latter phase differ from those of an unconfined, active turbulent system and may be controlled by the prescribed nematic boundary conditions. Our results show that substrate friction and geometric confinement act as valuable control parameters in active nematics.

A study of the effect of thermal dissipation on quantum reinforcement learning is performed. For this purpose, a nondissipative quantum reinforcement learning protocol is adapted to the presence of thermal dissipation. Analytical calculations as well as numerical simulations are carried out, obtaining evidence that dissipation does not significantly degrade the performance of the quantum reinforcement learning protocol for sufficiently low temperatures, in some cases even being beneficial. Quantum reinforcement learning under realistic experimental conditions of thermal dissipation opens an avenue for the realization of quantum agents to be able to interact with a changing environment, as well as adapt to it, with many plausible applications inside quantum technologies and machine learning.

Irreversible behavior in open stochastic dynamical systems is quantified by stochastic entropy production, a property that measures the difference in likelihoods of forward and subsequent backward system evolution. But for a closed system, governed by deterministic dynamics, such an approach is not appropriate. Instead, we can consider the difference in likelihoods of forward and “obverse” behavior: the latter being a backward trajectory initiated at the same time as the forward trajectory. Such a comparison allows us to define “dissipation production,” an analog of stochastic entropy production. It quantifies the breakage of a property of the evolution termed “obversibility” just as stochastic entropy production quantifies a breakage of reversibility. Both are manifestations of irreversibility. In this study we discuss dissipation production in a quantum system. We consider a simple, deterministic, two-level quantum system characterized by a statistical ensemble of state vectors, and we provide numerical results to illustrate the ideas. We consider cases that both do and do not satisfy an Evans-Searles Fluctuation Theorem for the dissipation production, and hence identify conditions under which the system displays time-asymmetric average behavior: an arrow of time.

We discuss the majority vote model coupled with scale-free networks and investigate its critical behavior. Previous studies point to a nonuniversal behavior of the majority vote model, where the critical exponents depend on the connectivity. At the same time, the effective dimension $D_{\mathrm{eff}}$ is unity for a degree distribution exponent $5/2<\gamma <7/2$. We introduce a finite-size theory of the majority vote model for uncorrelated networks and present generalized scaling relations with good agreement with Monte Carlo simulation results. Our finite-size approach has two sources of size dependence: an external field representing the influence of the mass media on consensus formation and the scale-free network cutoff. The critical exponents are nonuniversal, dependent on the degree distribution exponent, precisely when $5/2<\gamma <7/2$. For $\gamma \ge 7/2$, the model is in the same universality class as the majority vote model on Erdős-Rényi random graphs. However, for $\gamma =7/2$, the critical behavior includes additional logarithmic corrections.

We present calculations of electrical resistivity for expanded boron, aluminum, titanium, and copper plasmas using the Ziman formulation in the framework of the average-atom model. Our results are compared to experimental data, as well as to other theoretical calculations, relying on the Ziman and Kubo-Greenwood formulations, and based on average-atom models or quantum-molecular-dynamics simulations. The impact of the definition of ionization, paying particular attention to the consistency between the definition and the perfect free electron gas assumption made in the formalism, is discussed. We propose a definition of the mean ionization generalizing to expanded plasmas the idea initially put forward for dense plasmas, consisting in dropping the contribution of quasibound states from the ionization due to continuum ones. It is shown that our recommendation for the calculation of the quasibound density of states provides the best agreement with measurements.

We study the thermalization process in a one-dimensional lattice with two-dimensional motions. The phonon modes in such a lattice consist of two branches. Unlike in general nonlinear Hamiltonian systems, for which the only conserved quantity is the total energy, the total angular momentum $J$ is also conserved in this system. Consequently, the intra- and interbranch energy transports behave significantly differently. For the intrabranch transport, all the existing rules for the one-dimensional systems including the Chirikov overlap criterion apply. As for the interbranch transport, some trivial processes in one-dimensional lattices become nontrivial. During these processes, all the conservation laws can be satisfied exactly; thus the Chirikov criterion does not apply. These processes provide some fast channels for the interbranch transport, although the thermalization cannot be reached through them alone. A system with nonzero-$J$ initial state, however, can never be thermalized to an equipartition state having zero $J$. Quite counterintuitively, the corresponding asymptotic mode energy distribution greatly concentrates to a few lowest-frequency modes in one branch.

The $q$-neighbor Ising model for the opinion formation on multiplex networks with two layers in the form of random graphs (duplex networks), the partial overlap of nodes, and LOCAL&AND spin update rule was investigated by means of the pair approximation and approximate master equations as well as Monte Carlo simulations. Both analytic and numerical results show that for different fixed sizes of the $q$-neighborhood and finite mean degrees of nodes within the layers the model exhibits qualitatively similar critical behavior as the analogous model on multiplex networks with layers in the form of complete graphs. However, as the mean degree of nodes is decreased the discontinuous ferromagnetic transition, the tricritical point separating it from the continuous transition, and the possible coexistence of the paramagnetic and ferromagnetic phases at zero temperature occur for smaller relative sizes of the overlap. Predictions of the simple homogeneous pair approximation concerning the critical behavior of the model under study show good qualitative agreement with numerical results; predictions based on the approximate master equations are usually quantitatively more accurate but yet not exact. Two versions of the heterogeneous pair approximation are also derived for the model under study, which, surprisingly, yield predictions only marginally different or even identical to those of the simple homogeneous pair approximation. In general, predictions of all approximations show better agreement with the results of Monte Carlo simulations in the case of continuous than discontinuous ferromagnetic transition.

We consider a disk-like Janus particle self-driven by a force of constant magnitude $f$, but an arbitrary direction depending on the stochastic rotation of the disk. The particle diffuses in a two-dimensional channel of varying width $2h\left(x\right)$. We applied the procedure mapping the $2+1$-dimensional Fokker-Planck equation onto the longitudinal coordinate $x$; the result is the Fick-Jacobs equation extended by the spatially dependent effective diffusion constant $D\left(x\right)$ and an additional effective potential $-\gamma \left(x\right)$, derived recursively within the mapping procedure. Unlike the entropic potential $\sim lnh\left(x\right)$, $\gamma \left(x\right)$ becomes an increasing or decreasing function also in periodic channels, depending on the asymmetry of $h\left(x\right)$ and thus it visualizes the net force driving the ratchet current. We demonstrate the appearance of the ratchet effect on a trial asymmetric channel; our theory is verified by a numerical solution of the corresponding Fokker-Planck equation. Isotropic driving force $f$ results in the monotonic decrease of the ratchet current with a growing ratio $\alpha =D_R/D_T$ of the rotation and the translation diffusion constants; asymptotically going $\sim 1/{\alpha }^2$. If we allow anisotropy of the force, we can observe the current reversal depending on $\alpha$.