Quantum reservoir computing is an emergent field in which quantum dynamical systems are exploited for temporal information processing. Previous work found a feature that makes a quantum reservoir valuable: contractive dynamics of the quantum reservoir channel toward input-dependent fixed points. These results are enhanced in this paper by finding conditions that guarantee a crucial aspect of the reservoir's design: distinguishing between different input sequences to ensure a faithful representation of temporal input data. This is implemented by finding a condition that guarantees injectivity in reservoir computing filters, with a special emphasis on the quantum case. We provide several examples and focus on a family of quantum reservoirs that is much used in the literature; it consists of an input-encoding quantum channel followed by a strictly contractive channel that enforces the echo state and the fading memory properties. This work contributes to analyzing valuable quantum reservoirs in terms of their input-dependence.

Pruning the parameters and structure of neural networks reduces computational complexity, energy consumption, and latency during inference. Recently, an underlying mechanism for successful deep learning (DL) was presented based on a method that quantitatively measures the single-filter performance in each layer of a DL architecture, and a unique comprehensive mechanism of how deep learning works was presented. This statistical mechanics inspired viewpoint enables one to reveal the macroscopic behavior of the entire network from the microscopic performance of each filter and its cooperative behavior. Herein we demonstrate how this understanding paves the path to high quenched dilution of the convolutional layers of deep architectures without affecting their overall accuracy using the applied filter's cluster connections (AFCC). AFCC is exemplified on VGG-11 and EfficientNet-B0 architectures trained on CIFAR-100, and its high pruning outperforms other techniques using the same pruning magnitude. Additionally, this technique is broadened to single-nodal performance and high pruning of fully connected layers, suggesting a possible implementation to considerably reduce the complexity of overparametrized AI tasks.

Using the framework of classical nucleation theory in open systems with pumping and power-law size dependence of the attachment rates for large enough islands, the analytic island-size distribution (ISD) was previously obtained in the double-exponential form. The double-exponential shape of the distribution over invariant size (for which the regular growth rate of islands is independent of their size) is maintained in time. This result applies to large supercritical islands in systems with attachment-detachment kinetics. On the other hand, irreversible growth of surface islands with zero detachment rates or a small prescribed critical size is often described by the Family-Vicsek scaling functions versus the scaled natural size $x=s/\langle s\rangle$, with $\langle s\rangle$ as the average size. Here, we combine the two approaches by showing that the island-size distributions in classical nucleation theory, converted to the scaled natural size, often satisfy the Family-Vicsek scaling hypothesis in the large time limit. For size-linear capture coefficients $\sigma \left(s\right)=s$, the analytic scaling functions are monomodal and tend to zero at $x\to 0$. For power-law capture coefficients $\sigma \left(s\right)=s^{\alpha }$ with $\alpha <1$, the ISD transforms to the delta function $\delta \left(x-1\right)$ for large enough islands. These results reveal a nontrivial relationship between the ISDs in different variables, confirm the Family-Vicsek scaling in classical nucleation theory, and should be useful for understanding and modeling the growth kinetics and statistical properties within the ensembles of different nano-objects.

In traditional voter models, opinion dynamics are driven by interactions between individuals, where an individual adopts the opinion of a randomly chosen neighbor. However, these models often fail to capture the emergence of entirely new opinions, which can arise spontaneously in real-world scenarios. Our study introduces an element to the classic voter model: the concept of innovation, where individuals have a certain probability of generating new opinions independently of their neighbors' states. This innovation process allows for a more realistic representation of social dynamics, where new opinions can emerge and old ones may fade over time. Through analytical and numerical analysis, we find that the balance between innovation and extinction shapes the number of opinions in the steady state. Specifically, for low innovation rates, the system tends toward near-consensus, while higher innovation rates lead to greater opinion diversity. We also show that network structure influences opinion dynamics, with greater degree heterogeneity reducing the number of opinions in the system.

In this paper, we investigate the evolution of cooperation in a haploid population subdivided into $d$ demes, each composed of $N\ge 2$ individuals interacting according to a Prisoner's Dilemma. Using a discrete-time Moran process with migration of offspring, we analyze the fixation probability ${\rho }_C$ of a single cooperative mutant. Our model incorporates a baseline migration probability $m$, with cooperators exhibiting an additional migration tendency proportional to the local frequency of defectors. Using a two-time-scale approach, we derive a diffusion approximation valid for a large number of demes $d$ to analytically determine ${\rho }_C$. We show that, in the absence of differential migration and for a single-round Prisoner's Dilemma, the fixation of cooperation remains generally disfavored by selection in the sense that ${\rho }_C<1/\left(Nd\right)$ even as the baseline migration probability increases. In contrast, in a repeated Prisoner's Dilemma, selection favors the fixation of cooperation when the number of repetitions $n$ exceeds a critical threshold $n^{*}$, which is inversely related to $m$ and $N$. The probability of fixation ${\rho }_C$ increases as the level of differential migration increases, setting a threshold beyond which the fixation of cooperation is favored even in a single-round game. This threshold is modulated by the size of the deme, the probability of baseline migration and the cost of cooperation, with larger demes and a higher probability of baseline migration requiring a higher differential migration level. Numerical simulations validate the accuracy of our diffusion approximation, showing strong agreement with the simulated fixation probabilities for large $d$. These findings highlight the pivotal role of repeated interactions, migration strategies, and population structure in promoting the evolution of cooperation.

Biological molecular machines convert free energy between different forms in cells, often at high efficiency. Optimal control theory provides a framework to elucidate design principles governing energetically efficient driving. Here, we use linear-response theory to design efficient protocols exercising dynamic control of trap center and stiffness in a model of driven ${\mathrm{F}}_1$-ATPase. We find that the key design principles of an efficient protocol can be satisfied either by dynamic control of both parameters or by dynamic control of a single parameter and a good static choice for the second. These results illustrate that accessing a new degree of dynamic control provides varying performance improvements in different systems.

The binding of the C2AB domain of the calcium sensor synaptotagmin-1 (Syt1) to lipid bilayers is a critical step in triggering neurotransmitter release at nerve terminals. However, effective regulation of this binding remains a significant challenge. In this study, we used all-atom molecular dynamics (MD) simulations to explore the underlying mechanisms of the $\mathrm{C}2\mathrm{AB}/\mathrm{C}{\mathrm{a}}^{2+}\_\mathrm{C}2\mathrm{AB}$ interaction with lipid bilayers and examined how external terahertz (THz) waves influence this binding. We first identified the key residues and interactions involved in $\mathrm{C}2\mathrm{AB}/\mathrm{C}{\mathrm{a}}^{2+}\_\mathrm{C}2\mathrm{AB}$ binding to phospholipids in the absence of THz waves. Then, we analyzed the effects of 42.55 THz waves on the binding dynamics. Importantly, the predominant vibration mode at 42.55 THz waves induces rotational movements of negatively charged phospholipid heads by affecting the vibrations of $-\mathrm{CO}{\mathrm{O}}^{-}$ and $-\mathrm{CH}$ bonds. This shift alters charge distributions within the lipid bilayers, increasing the distance between certain residues and phospholipids, and consequently reducing the binding energy. Overall, our findings suggest that THz radiation can act as a novel modulator of neurotransmitter release by disrupting the Syt1–phospholipid interaction, offering potential insights into the regulation of synaptic activity.

Synchronized locomotion of undulatory swimmers occurs ubiquitously in nature, ranging from microorganisms such as sperms to larger aquatic animals such as eels and knifefish. To develop a unified understanding of this phenomenon, we use Taylor's two-dimensional infinitely long undulatory sheet model to study the side-by-side locomotion of two swimmers at nonzero Reynolds numbers. Our quasi-steady-state analysis of the far-field hydrodynamics demonstrates that fluid inertia causes the swimmers to reach a stable antiphase synchronized state. Numerical simulations confirm this result for two swimmers separated by a relatively large gap distance. However, when the distance falls below a critical value, the two swimmers settle into a stable in-phase state. The antiphase configuration increases the coswimming speed, the power expenditure, as well as the energy efficiency of both swimmers.

Transient plasma events, such as plasma disruptions, are anticipated in the future magnetic-confinement nuclear fusion reactors. The events are accompanied by a rapid change in the magnetic field generated by the plasma current and, accordingly, induction of strong eddy currents and Lorentz forces within the reactor structure. This work targets processes within liquid-metal components of the reactor's breeding blankets. Order-of-magnitude analysis and exploratory numerical simulations are performed to understand the response of liquid metal to a rapidly changing magnetic field and to evaluate the accuracy of commonly used simplifying model assumptions. The response is found to consist of two stages: an initial brief stage ($\sim 1$ ms) characterized by a rapid increase in the induced currents, forces, and fluid velocity; and a subsequent stage, which is triggered by the growing velocity of the metal and marked by reversals of Lorentz force, and oscillations and decreases in the amplitude of the induced fields. The transition to the second stage sets the upper limit of the velocity ($\sim 0.5$ m/s in our tests), to which an initially quiescent metal can be accelerated during the event. The simulations indicate that many widely used model assumptions, such as the negligible role of Joule dissipation in the heat balance and the constancy of physical property coefficients, remain valid during the response. However, the assumption of liquid metal incompressibility is found to be questionable due to the potential significant effects of pressure waves.

One great challenge of modeling granular systems lies in capturing the rheologic dependencies on scale. For example, there are marked differences between quasistatic, intermediate, and rapid flow regimes. In this study, we demonstrate that assumptions for infinite stiffness of rigid particles, an assumption upon which the state-of-the-art $\left[\mu \right(I)$-rheology] modeling approaches are constructed, must be relaxed in order to recover the physical mechanisms behind many scale-dependent and nonlocal rheological effects. Any relaxation of the infinite stiffness assumption allows for particles to compress in series, whereby the number of simultaneously compressed particles controls the extent to which end-member particles experience a modified coefficient of effective friction, analogous to reduced stiffness for springs in series. To demonstrate the importance of such a mechanism in setting the dynamics for dense rigid granular systems, we show that modifying simple models to include the kinematics introduced by compression in series captures the emergence of thin layer stability, a widely observed yet incompletely explained nonlocal granular phenomenon. We also discuss, in general, how knowledge of the contact network and softness provides a potential physical basis for the diffusion of granular temperature.

The $1/r$ long-range interaction, induced by laser illumination, offers a mechanism for the implementation of stable self-trapping in Bose-Einstein condensates (BECs) in the three-dimensional free space. Using the variational approximation and numerical solutions, we find that self-trapped states in this setting, with attractive nonlocal and repulsive local interactions, resemble tightly bound compactons. However, these are not true compactons but rather tightly self-trapped modes (TSTMs), with small-amplitude nonvanishing tails. The structure of the self-trapped states is explained by an analytical solution for their tails. Further, we demonstrate that stable TSTMs with embedded vorticity exist in the same setting, with winding numbers up to $S=6$ (at least). Addressing two-TSTM interactions, we find that pairs of ground states (GSs, with $S=0$), as well as vortex-vortex and vortex-antivortex pairs (with $S_1=S_2$ and $S_1=-S_2$, respectively), form stably rotating bound states. Head-on collisions between vortex TSTMs, set in slow motion by kicks, are inelastic, resulting in their merger into a GS soliton, that may either remain at the collision position or move aside, shedding the angular momentum with emitted radiation, or, alternatively, lead to the formation of a vortex that also moves aside.

We investigate the dynamics of active paths during a two-phase flow of immiscible fluids under an external pressure drop $\mathrm{\Delta }P$. We demonstrate that this dynamics of new path opening plays a crucial role in understanding the nonlinear rheology for the one-dimensional capillary fiber bundle model in the limit where the capillary forces are comparable with the viscous forces. The contribution of gradual path-opening dynamics is controlled by tuning maximum value of the capillary thresholds ($P_M$) around which one observes the following situation: flow through existing paths plus new path opening for $\mathrm{\Delta }P<P_M$ and flow through existing paths only beyond $P_M$. The nonlinear rheology is expressed in terms of the $Q-\mathrm{\Delta }P$, with continuously varying $P_M$, showing two different nonlinear behavior around $P_M$ where one can be explained from the information of the other. $P_M$ is also the point around which the kinetic energy of the system is rearranged and expressed through a variation in participation number ($\pi$). $\pi$ in the Fourier space shows a signature of red noise through inverse square decay of power spectrum indicating toward equipartition of energy as well as the underlying self organized criticality.

A spherical-implosion platform diagnosed with the “beamlets” scattered-light detector provides high sensitivity to the impact of plasma screening on inverse bremsstrahlung absorption. Contrary to the more restrictive screening length suggested previously [D. Turnbull et al., Phys. Rev. Lett. 130, 145103 (2023); D. Turnbull et al., Phys. Plasmas 31, 063304 (2024)], the beamlets data indicate that the electron-only Debye length is the relevant screening length for high-density inverse bremsstrahlung absorption. Using the updated absorption model, we simulate the OMEGA direct-drive inertial confinement fusion implosion database and show that bang times are well reproduced without any ad hoc multipliers.

Nanomechanical sensors have gained significant attention as powerful tools for detecting target analytes; however, their signals are often influenced by environmental humidity. In static mode operation, the sensing signals of nanomechanical sensors are obtained by a concentration-dependent sorption-induced mechanical strain/stress. In this study, we derive an analytical model to describe the response of viscoelastic material-coated nanomechanical sensors by incorporating humidity effects based on sorption kinetics and viscoelastic stress relaxation of receptor materials. This model is capable of reproducing the dynamic responses observed in the experiments under varying humidity conditions. Moreover, it allows for the subtraction of humidity effects, facilitating the precise isolation of analyte-specific signals. These results provide a theoretical framework for decoupling environmental background factors, such as humidity effects, in nanomechanical sensors.

In this study, we present an oscillatory anisotropic sandpile model as an extension of the Bak, Tang, and Wiesenfeld (BTW) model. We focus on exploring the statistical properties of both local and global measures. The model introduces oscillations controlled by a time period, $T$, applied in the parallel direction, while the perpendicular direction follows the standard BTW model. Our results provide strong evidence of a directionality crossover at $T=T^{*}$: for $T$ above (below) this value, avalanches predominantly extend along the spatial parallel direction. Notably, the spanning avalanche probability (SAP) in both directions reaches zero within an interval around $T^{*}$, indicating a localization of avalanches at the crossover point. SAP shows distinct behaviors on either side of this interval. Our scaling analysis reveals an additional crossover between small and large spatial scales, each characterized by unique scaling exponents. The distribution functions for avalanche mass $m$, size $s$, and duration $D$ exhibit power-law behavior within this regime, with notable peaks at positions aligning with the crossover points; these peaks scale with $T$, introducing new scaling exponents. The scaling relations between mass, size, and linear perpendicular avalanche extent $l_{\perp }$ allow us to identify and estimate the scaling exponents ${\gamma }_{m{l}_{\perp }}=2.0\pm 0.05$ and ${\gamma }_{ms}=0.95\pm 0.03$ in the small-scale regime and ${\gamma }_{m{l}_{\perp }}=2.66\pm 0.05$ and ${\gamma }_{ms}=0.68\pm 0.03$ in the large-scale regime for all $T$ values. The mass-duration scaling exponent, ${\gamma }_{mD}=1.57\pm 0.05$, remains robust against changes in $T$.