Next-generation reservoir computing (NG-RC) has attracted much attention due to its excellent performance in spatiotemporal forecasting of complex systems and its ease of implementation. This paper shows that NG-RC can be encoded as a kernel ridge regression that makes training efficient and feasible even when the space of chosen polynomial features is very large. Additionally, an extension to an infinite number of covariates is possible, which makes the methodology agnostic with respect to the lags into the past that are considered as explanatory factors, as well as with respect to the number of polynomial covariates, an important hyperparameter in traditional NG-RC. We show that this approach has solid theoretical backing and good behavior based on kernel universality properties previously established in the literature. Various numerical illustrations show that these generalizations of NG-RC outperform the traditional approach in several forecasting applications.

We study the influence of thermal fluctuations on the two-time correlation functions of bosonic baths within a superstatistics framework by assuming that fluctuations follow the gamma distribution. We further establish a connection between superstatistics and Tsallis nonadditive thermodynamics by introducing a temperature-renormalizing parameter. Our results show that, for an Ohmic model, the system's correlation functions exhibit diverse time-dependent behaviors, with the real and imaginary parts displaying enhancement or suppression depending on temperature and fluctuation strength. Additionally, we analyze the impact of these fluctuations on the quantum master equation of a damped two-level atom coupled to an out-of-equilibrium radiation bath. We demonstrate that while the equation's algebraic structure remains intact, the coupling constants are modified by the fluctuation parameters and cavity volume. Specifically, we observe that the ac Stark effect undergoes significant modifications, with fluctuations influencing the transition between repulsive and attractive energy levels.

We theoretically investigate the quantum percolation problem on Lieb lattices in two and three dimensions. We study the statistics of the energy levels through random matrix theory and determine the level spacing distributions, which, with the aid of finite-size scaling theory, allows us to obtain accurate estimates for site- and bond-percolation thresholds and critical exponents. Our numerical investigation supports a localized-delocalized transition at finite threshold, which decreases as the average coordination number increases. The precise determination of the localization length exponent enables us to claim that quantum site- and bond-percolation problems on Lieb lattices belong to the same universality class, with $\nu$ decreasing with lattice dimensionality $d$, similarly to the classical percolation problem. In addition, we verify that, in three dimensions, quantum percolation on Lieb lattices belongs to the same universality class as the Anderson impurity model.

The inference of rankings plays a central role in the theory of social choice, which seeks to establish preferences from collectively generated data, such as pairwise comparisons. Examples include political elections, ranking athletes based on competition results, ordering web pages in search engines using hyperlink networks, and generating recommendations in online stores based on user behavior. Various methods have been developed to infer rankings from incomplete or conflicting data. One such method, HodgeRank, introduced by Jiang et al. [Math. Program. 127, 203 (2011) ], utilizes Hodge decomposition of cochains in Higher-Order Networks to disentangle gradient and cyclical components contributing to rating scores, enabling a parsimonious inference of ratings and rankings for lists of items. This paper presents a systematic study of HodgeRank's performance under the influence of quenched disorder and across networks with complex topologies generated by four different network models. The results reveal a transition from a regime of perfect retrieval of true rankings to one of imperfect retrieval as the strength of the quenched disorder increases. A range of observables is analyzed, and their scaling behavior with respect to the network model parameters is characterized. This work advances the understanding of social choice theory and the inference of ratings and rankings within complex network structures.

The existence and stability criteria of one-dimensional ion-acoustic solitons in a quantum cold, over-dense plasma are investigated through theoretical and numerical analyses. Within the quantum magnetohydrodynamic dominant regime, distinct governing equations are employed for spin-up and spin-down electrons, with the Coulomb exchange interaction specifically considered between spin-down electrons. The Bohm potential affects both spin-up and spin-down electrons. The dispersion relations, derived up to third-order approximations, are obtained using the reductive perturbation method. Explicit expressions for instability are determined at the first-order correction, revealing extensive instability regions. The spin polarization ratio, Bohm potential coupling, soliton velocity, and electron number density influence these instability regions. By incorporating higher-order corrections, including second and third orders, a nonlinear Schrödinger-type equation for the electrostatic potential is derived. Based on this nonlinear equation, numerical instability analysis refines the first-order instability regions and reveals new instability regions that are not apparent in the first-order approximation. The analysis underscores the significant effects of quantum interactions, particularly the spin exchange effect and Bohm potential, on the instability region.

Alternating (temporally period-2) stripes and labyrinths have been observed in media of chemical and biochemical reactions; however, the mechanisms underlying the formation of these spatiotemporal patterns remain unclear. Here, we conduct computer simulation using a modified model of Belousov−Zhabotinsky reaction that incorporates a global feedback loop with a spatial strength profile of Gaussian distribution. The simulation results demonstrate that the transition from alternating stripes to alternating labyrinths occurs when the feedback is negative with a certain width of the Gaussian function. We add the same Gaussian-weighted feedback loop to an amplitude equation to describe the amplitude dynamics of the period-2 oscillation and show that the pattern dynamics of the Belousov−Zhabotinsky reaction can be well captured by this amplitude equation. Analyses of the amplitude equation demonstrate that the transition from stripes to labyrinths arises from the transverse instabilities of bistable fronts caused by the Gaussian-weighted negative global feedback.

Stochastic interactions generically enhance self-diffusivity in living and biological systems, e.g., optimizing navigation strategies and controlling material properties of cellular tissues and bacterial aggregates. Despite this, the physical mechanisms underlying this nonequilibrium behavior are poorly understood. Here, we introduce a model of interactions between an agent and its environment in the form of a local stochastic resetting mechanism, in which the agent's position is set to the nearest of a predetermined array of sites with a fixed rate. We derive analytic results for the self-diffusion coefficient, showing explicitly that this mechanism enhances diffusivity. Strikingly, we show analytically that this enhancement is optimized by regular arrays of resetting sites. Altogether, our results ultimately provide the conditions for the optimization of the macroscopic transport properties of diffusive systems with local random binding interactions.

Non-Maxwellian distributions are commonly observed across a wide range of systems and scales. While direct observations provide the strongest evidence for these distributions, they also manifest indirectly through their influence on processes and quantities that strongly depend on the energy distribution, such as reaction rates. In this paper, we investigate reaction rates in the general context of quasiequilibrium systems, which exhibit only local equilibrium. The hierarchical structure of these systems allows their statistical properties to be represented as a superposition of statistics, i.e., superstatistics. Focusing on the three universality classes of superstatistics—${\chi }^2$, inverse-${\chi }^2$, and log-normal—we examine how these nonequilibrium distributions influence reaction rates. We analyze, both analytically and numerically, reaction rates for processes involving tunneling phenomena, such as fusion, and identify conditions under which quasiequilibrium distributions outperform Maxwellian distributions in enhancing fusion reactivities. To provide a more detailed quantitative analysis, we further employ semiempirical cross sections to evaluate the effect of these nonequilibrium distributions on ionization and recombination rates in a plasma.

Temperature gradients represent energy sources that can be harvested to generate steady reaction or transport fluxes. Technological developments could lead to the transfer of free energy from heat sources and sinks to chemical systems for the purpose of extraction, thermal batteries, or nonequilibrium synthesis. We present a theoretical study of one-dimensional chemical systems subjected to temperature gradients, for sustaining nonequilibrium chemical fluxes. A complete theoretical framework describes the behavior of the system induced by various temperature profiles. An exact mathematical derivation was established for a simple two-compartment model and was generalized to arbitrary reaction-diffusion systems based on numerical models. An experimental system was eventually scaled and tuned to optimize either nonequilibrium chemical transport or reaction. The relevant parameters for this description were identified; they focused on the system symmetry for chemical reaction and transport. Nonequilibrium thermodynamic approaches lead to a description analogous to electric circuits. Temperature gradients lead to the onset of a steady chemical force, which maintains steady reaction-diffusion fluxes moderated by chemical resistance. The system activity was then assessed using the entropy production rate as a measure of its dissipated power. The chemical characteristics of the system can be tuned for general optimization of the nonequilibrium state or for the specific optimization of either transport or reaction processes. The shape of the temperature gradient can be tailored to precisely control the spatial localization of active processes, targeting either precise spatial localization or propagation over large areas. The resulting temperature-driven chemical system can in turn be used to drive secondary processes into either nonequilibrium reaction fluxes or concentration gradients.

Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multimodal foundation model for scientific problems, named PROSE-PDE. Our model, designed for bimodality to bimodality learning, is a multioperator learning approach which can predict future states of spatiotemporal systems while concurrently learning the underlying governing equations of the physical system. Specifically, we focus on multioperator learning by training distinct one-dimensional time-dependent nonlinear constant coefficient partial differential equations, with potential applications to many physical applications including physics, geology, and biology. More importantly, we provide three extrapolation studies to demonstrate that PROSE-PDE can generalize physical features through the robust training of multiple operators and that the proposed model can extrapolate to predict PDE solutions whose models or data were unseen during the training. Furthermore, we show through systematic numerical experiments that the utilization of the symbolic modality in our model effectively resolves the well-posedness problems with training multiple operators and thus enhances our model's predictive capabilities.

Building on recent advances in describing redundancy and synergy in multivariate interactions among random variables, we propose an approach to quantify cooperative effects in feature importance, a key technique in explainable artificial intelligence. Specifically, we introduce an adaptive version of the widely used metric Leave One Covariate Out (LOCO), designed to disentangle high-order effects involving a particular input feature in regression problems. LOCO measures the reduction in prediction error when the feature of interest is added to the set of features used in regression. Unlike the standard approach that computes LOCO using all available features, our method identifies the subsets of features that maximize and minimize LOCO. This results in a decomposition of LOCO into a two-body component and higher-order components (redundant and synergistic), while also identifying the features that contribute to these high-order effects in conjunction with the driving feature. We demonstrate the effectiveness of the proposed method in a benchmark dataset related to wine quality and to proton versus pion discrimination using simulated detector measurements generated by GEANT.

Geometrical methods are extensively applied to thermodynamics, including stochastic thermodynamics. In the case of a slow-driving linear response regime, a geometrical framework, known as thermodynamic geometry, is established. The key to this framework is the thermodynamic length characterized by a metric tensor defined in the space of controlling variables. As the metric tensor is given in terms of the equilibrium time-correlation functions of the thermodynamic forces, it contains the information on timescales, which may be useful for analyzing the performance of heat engines. In this paper, we show that the metric tensor for underdamped Langevin dynamics can be decomposed in terms of the relaxation times of a system itself, which govern the timescales of the equilibrium time-correlation functions of the thermodynamic forces. As an application of the decomposition of the metric tensor, we demonstrate that it is possible to achieve Carnot efficiency at finite power by taking the vanishing limit of relaxation times without breaking trade-off relations between efficiency and power of heat engines in terms of thermodynamic geometry.

Chaotic dynamics are ubiquitous in nature and useful in engineering, but their geometric design can be challenging. Here we propose a method using reservoir computing to generate chaos with a desired shape by providing a periodic orbit as a template, called a skeleton. We exploit a bifurcation of the reservoir to intentionally induce unsuccessful training of the skeleton, revealing inherent chaos. The emergence of this untrained attractor, resulting from the interaction between the skeleton and the reservoir's intrinsic dynamics, offers a semisupervised framework for designing chaos.

We introduce a methodology for investigating vortex solitons (VSs) within quasi-phase-matched (QPM) photonic crystals, featuring competing quadratic and cubic nonlinearities. The photonic crystal is introduced with a checkerboard structure, which is feasible through contemporary technological advancements. The VS family is constructed as quadrupole and 8-pole configurations, with the quadrupole solitons displaying rhombus and square modes depending on different phase-matching conditions. Notably, an intriguing transformation from the quadrupole to the 8-pole configuration can be achieved by modulating the cubic nonlinear coefficient. Additionally, the square-shaped VSs would transfer to rhombus patterns by adjusting the power and size of the checkerboard cell in the framework of cubic nonlinearity. This work presents a versatile and powerful tool for exploring and manipulating vortex solitons in QPM photonic structures, with potential applications in optical signal processing, optical communications, and nonlinear optics research.

An analytical model to study the perturbation flow that evolves between a rippled piston and a shock is presented, based on previous published work. Only the rigid piston boundary condition is considered at the piston surface driving the shock. Any time a corrugated shock is launched inside a fluid, pressure, velocity, density, and vorticity perturbations are generated downstream. As the shock separates, the pressure field decays in time and a quiescent velocity field emerges in the space in front of the piston. Depending on the boundary conditions imposed at the driving piston, either tangential or normal velocity perturbations evolve asymptotically on its surface. The goal of this work is to present explicit finite and closed form analytical formulas to calculate the different perturbed quantities in the compressed fluid, namely, shock pressure perturbations and compressed fluid velocity perturbations for very large times, in contrast to previous work in which only an iterated solution was presented. Comparison to published experiments is shown.

Using a thermodynamically consistent, mesoscopic model for modern complementary metal-oxide-semiconductor transistors, we study an array of logical circuits and explore how their function is constrained by recent thermodynamic uncertainty relations when operating near thermal energies. For a single NOT gate, we find operating direction-dependent dynamics and a trade-off between dissipated heat and operation time certainty. For a memory storage device, we find an exponential relationship between the memory retention time and energy required to sustain that memory state. For a clock, we find that the certainty in the cycle time is maximized at biasing voltages near thermal energy, as is the trade-off between this certainty and the heat dissipated per cycle. We identify a control mechanism that can increase the cycle time certainty without an offsetting increase in heat dissipation by working at a resonance condition for the clock. These results provide a framework for assessing the thermodynamic costs of realistic computing devices, allowing for circuits to be designed and controlled for thermodynamically optimal operation.