The fluctuating dynamics of a network about its stable, noise-free steady state are theoretically investigated. Various causes of non-equilibrium dynamics are identified in terms of the properties and symmetry of the network connections and the noise covariance matrices. Several equivalent conditions are derived for the dynamics of the noisy network at equilibrium. In particular, non-equilibrium steady state (NESS) dynamics are analyzed in terms of the steady-state probability current and the drift velocity relative to the effective potential surface. Conventional physical Brownian dynamics for overdamped fluctuating dynamics is analyzed from the perspective of the linearized fluctuating noisy network dynamics. Connection with the network reconstruction from time-series data is discussed. It is demonstrated that the overdamped Brownian dynamics in the physical system is a special case of the general noisy directed network in a NESS. Furthermore, a general fluctuation-dissipation relation is derived for the general non-equilibrium noisy network dynamics. These theoretical results are verified by numerical simulations.

Systems of interacting trajectories were recently studied in~\cite{HGSTW24}. Such a system of $[0,1]$-valued piecewise linear trajectories arises as a scaling limit of the system of logarithmic subpopulation sizes in a population-genetic model (more precisely, a Moran model) with mutation and selection. By definition, the resident fitness is initially 0 and afterwards it increases by the ultimate slope of each trajectory that reaches height 1. We show that although the interaction of $n$ trajectories may yield $Ω(n^2)$ slope changes in total, the resident fitness function can be computed algorithmically in $O(n)$ time. Our algorithm uses the so-called continued lines representation of the system of interacting trajectories. In the special case of Poissonian interacting trajectories where the birth times of the trajectories form a Poisson process and the initial slopes are random and i.i.d., we provide a linear bound on the expected total number of slope changes.

This work investigates how grain boundaries (GBs) modify magnetic exchange interactions in bcc iron, with particular focus on the effect of phosphorus segregation. Using density-functional theory combined with the Liechtenstein-Katsnelson-Antropov-Gubanov Green's-function approach, we calculate Heisenberg exchange parameters for three symmetric tilt GBs, $\Sigma5(310)$, $\Sigma13(510)$, and $\Sigma13(320)$, and use these parameters in Monte Carlo simulations to evaluate finite-temperature magnetic behavior. All clean GBs exhibit strong local deviations from bulk exchange interactions, including antiferromagnetic coupling across the boundary plane. These negative exchange interactions are not governed by interatomic distance alone, but arise primarily from the altered local coordination and symmetry breaking at the GB. Phosphorus segregation, modeled in both substitutional and interstitial configurations at the $\Sigma5(310)$ GB, suppresses the antiferromagnetic couplings and significantly redistributes the local exchange landscape through chemical and electronic effects. Monte Carlo results show that, despite pronounced local perturbations, realistic GB densities cause only a small reduction in the Curie temperature because bulk-like regions dominate the global magnetic transition. A substantial decrease in Curie temperature appears only when the GB volume fraction is artificially increased. The results demonstrate that GBs strongly influence local magnetic interactions while having a limited effect on global magnetic ordering, and they establish a general framework for linking atomistic interfacial structure and chemistry to mesoscale magnetic behavior in Fe-based materials.

In this paper, we investigate the asymptotic behavior, as $β\to 0$, of positive solutions to the semilinear elliptic Robin problem \begin{equation*} \begin{cases} -Δu = u^p, & \text{in } Ω,\\ u > 0, & \text{in } Ω,\\ \frac{\partial u}{\partial ν} + βu = 0, & \text{on } \partial Ω, \end{cases} \end{equation*} where $p \ge 0$, $β> 0$, and $Ω$ is a bounded smooth domain. We will prove that, for all $p\ge0$, the solution $u_β$ behaves like a constant as $β\to0$. However, the value of this constant is strongly influenced by the value of $p$. Indeed, \begin{itemize} \item if $0 \le p < 1$, $u_β$ blows up uniformly in $Ω$ as $β\to 0$. \item if $p=1$ (eigenvalue problem), $u_β$ converge to a constant. \item if $p>1$ $u_β$ converge uniformly to zero. \end{itemize} In the critical and supercritical regime $p \ge \frac{N+2}{N-2}$, the existence of solutions is no longer guaranteed a priori. In this case, when $Ω$ is a ball and $0<β<\frac{2}{p-1}$ we prove the existence of a radial positive solution.

We consider the problem of testing whether a multivariate distribution is axially symmetric about some unknown direction. Under a simple-spectrum assumption on the covariance matrix, any symmetry axis must coincide with an eigenvector of the covariance matrix, so the problem reduces to testing a finite set of candidate directions. For each candidate direction, we construct a Kolmogorov--Smirnov-type statistic based on projected data and sample splitting. We derive its asymptotic distribution in a triangular-array framework and establish bootstrap validity under suitable regularity conditions. This leads to a feasible testing procedure for axial symmetry when the symmetry direction is unspecified.

We present an extended optical monitoring of the quadruply-imaged gravitationally lensed quasar QSO 2237+0305, the Einstein Cross, including observations from different observatories in both hemispheres and using a new photometric technique. This technique uses a region far enough from the lens system to determine accurately the sky background level, and minimises contamination from the lensing galaxy by combining analytical and numerical modeling of its structure. The resulting light curves of the four quasar images describe variations across practically the entire optical spectrum and span about 9000 days in the $VRI$ bands. The multi-band microlensing variability is captured with an unprecedented level of detail, and a preliminary microlensing analysis reveals an almost linear scaling of source radius with wavelength, providing direct evidence for the wavelength-dependent structure of the region contributing to optical passband fluxes. Specifically, assuming a mean microlens mass $\langle M \rangle$ = 0.3 $\rm{M_{\odot}}$ and concentric Gaussian sources that move according to the velocity distribution peaks (speed and direction) reported in a previous microlensing analysis, we find that the half-light radius of the $g$-band source is 9.6 $\pm$ 2.7 lt-day and the size of the sources grows with wavelength with a power-law index of $α$ = 0.94 $\pm$ 0.05. We conclude that these long-term light curves set stringent empirical constraints on models of quasar emission and microlensing physics.

While textiles have existed throughout much of human history as complex mechanical metamaterials, textile science has largely been overlooked by the physics community until recently. In this review, we consider the symmetry, topology, and mechanics of woven and knitted materials, showing that they represent a unique, if under-explored, corner of condensed matter. We start with the basic construction and elementary mechanical model of spun yarn, reviewing recent developments twisted bundle structures. We then introduce woven and knitted fabrics as materials with layer symmetries that can be topologically characterized as knots and links in the thickened torus. We finally discuss fabric mechanics and geometry, invoking recent results surrounding yarn-level and stitch-level geometry, deformations, and defect structures.

Accurate vehicular localization remains a key challenge for cooperative intelligent transport systems (C-ITS), especially in areas without global navigation satellite system (GNSS) coverage, such as road tunnels. This paper proposes a novel vehicle positioning method with a single anchor equipped with multiple antennas, exploiting near-field (NF) propagation and passive radio-reflective structures deployed along the GNSS-denied tunnel. The method assumes a wideband vehicle-to-everything (V2X) communication between the vehicle and the anchor, in line with the undergoing standardization of cellular V2X beyond 5G. We first derive the validity condition that allows us to approximate the multipath channel with a single reflector point, defining a geometry validity bound on the number of antennas that can be employed. Building on this result, we propose JAVELIN, a 6G-compatible single-anchor localization framework that leverages tensor-based NF parameter estimation, adaptive NF/far-field (FF) processing, and recursive Bayesian tracking to enable sub-meter positioning without multi-anchor synchronization. The method integrates angle, delay difference, and curvature measurements into a variable-dimension extended Kalman filter with gated nearest-neighbor association, enabling operation without prior environmental knowledge. Radio-reflective road markings are further introduced to enhance geometric diversity. Simulation results in realistic tunnel scenarios demonstrate accurate and robust localization under different conditions, outperforming state-of-the-art single-anchor approaches and benefiting from passive reflector deployment

A novel approach is proposed to establish a sharp upper bound on the expected supremum of a separable martingale random field, serving as an alternative to classical universal chaining-based methods. The proposed approach begins by deriving a new "stochastic maximal inequality" for a finite class of discrete-time martingales. This is achieved by using some variations of log-sum-exp and softmax functions, as well as martingale transforms, avoiding the simple use of the triangle inequalty. We apply this inequality to obtain a generalization of Lenglart's inequality for discrete-time martingales, extending it from the one-dimensional case to finite-dimensional settings, and further to certain infinite-dimensional cases through a "finite approximation device." The primary applications include several weak convergence theorems for sequences of separable martingale random fields under the uniform topology. In particular, new results are established for i.i.d. sequences, including a necessary and sufficient condition for classes of functions to possess the Donsker property. Additionally, we provide new moment bounds for the supremum of empirical processes indexed by classes of sets or functions. The results and methods presented in this paper are also expected to be highly useful for high-dimensional statistics, including LASSO and Dantzig selectors, as it is illustrated in the last part of this paper.

High-gain spontaneous parametric down-conversion (SPDC) produces bright squeezed vacuum with rich high-dimensional entanglement, but its output is inherently multimodal and non-perturbative, making the full modal characterization a major computational bottleneck. We propose a physics-guided deep neural network that reconstructs the source's modal fingerprint: the high-dimensional correlation signature across radial and azimuthal indices. We designed a FiLM-modulated convolutional architecture that predicts the joint (m,l) distribution, and training is driven by a hybrid loss that couples data-driven metrics (JSD, KL, MSE, Wasserstein) with a soft orbital-angular-momentum (OAM) conservation term, providing an essential inductive bias toward physically consistent solutions. Across gain regimes, our method achieves high-fidelity reconstruction with average JSD of 1.96e-3, WEMD of 1.54e-3, and KL divergence of 7.85e-3, delivering an approximate 128-fold speedup over full numerical simulation and more than 30% accuracy gains over U-Net baselines. These results demonstrate that physics-guided learning, via a soft OAM-conservation regularizer and physically generated training targets, enables rapid and data-efficient modal characterization. Compared with traditional numerical simulation, our mesh-free method has demonstrated good generalization with limited or contaminated training data and has enabled fast "online" prediction of the quantum dynamics of a high-dimensional entanglement system for real-world experimental implementation.

We propose a two-stage concatenated coding scheme for reliable and secure communication over intersymbol interference wiretap channels. We first establish the secrecy capacity. Then, motivated by the theoretical codes that achieve the secrecy capacity, our scheme integrates low-density parity-check (LDPC) codes in the outer stage, forming a nested structure of wiretap codes, with trellis codes in the inner stage to improve achievable secure rates. The trellis code is specifically designed to transform the uniformly distributed codewords produced by the LDPC code stage into a Markov process, achieving tight lower bounds on the secrecy capacity. We further estimate the information leakage rate of the proposed scheme using an upper bound. To meet the weak secrecy criterion, we optimize degree distributions of the irregular LDPC codes at the outer stage, essentially driving the estimated upper bound on the information leakage rate to zero.

Quantum gates executed on physical hardware are inevitably degraded by environmental noise. While state purification effectively distills static quantum resources, the dynamic execution of quantum algorithms requires a higher-order approach to mitigate errors on the operations themselves. In this work, we investigate universal unitary purification: the task of utilizing a quantum higher-order operation to partially restore the ideal action of an unknown unitary corrupted by a known noise model. Focusing on canonical depolarizing noise, we first reveal a fundamental operational obstruction. We prove that within the indefinite causal order framework, no nontrivial 2-slot higher-order operation can universally purify the set of single-qubit unitaries. Overcoming this strict limitation, we establish that a 3-slot parallel architecture provides the minimal realization for non-trivial purification. We analytically derive the optimal average fidelity within the parallel 3-slot class, demonstrating that it strictly surpasses trivial strategies by systematically utilizing ancillary qubits as a quantum memory to absorb errors. Furthermore, we provide a concrete quantum circuit construction attaining this parallel optimum. Our results establish the strict theoretical boundaries of distilling clean operations from noisy gates, offering immediate architectural insights for robust gate design.

Progressing toward a new generation of mobile networks, a clear focus on integrating distributed intelligence across the system is observed to drive performance, autonomy, and real-time adaptability. Federated learning (FL) stands out as a key emerging technique, enabling on-device model training while preserving data locality. However, its operation introduces substantial energy and resource demands. Energy needs are mostly met by grid power sources, while FL resource orchestration strategies remain limited. This work introduces GreenFLag, an agentic resource orchestration framework designed to minimize the energy consumption from the grid power to complete FL workflows, guarantee FL model performance, and reduce grid power reliance by incorporating renewable sources into the system. GreenFLag leverages a Soft-Actor Critic reinforcement learning approach to jointly optimize computational and communication resources, while accounting for communication contention and the dynamic availability of renewable energy. Evaluations using a real-world open dataset from Copernicus, demonstrate that GreenFLag significantly reduces grid energy consumption by 94.8% on average, compared to three state-of-the-art baselines, while primarily relying on green power.

As in real microlocal analysis, we prove a Schwartz kernel theorem for $p$-adic distributions. We extend this result for motivic distributions using Cluckers-Loeser's motivic integration. In both settings, we give also a relation between the wave front sets of the distribution and its kernel.

In mathematical physics the Galois top, introduced by S. Adlaj, possesses a fixed point on one of two Galois axes through its center of mass. This heavy top has two algebraic motion invariants and an additional transcendental motion-invariant. This third invariant depends on an antiderivative of a variable in the canonical phase space. In this article an abelian semigroup and an abelian group are defined that are related to the application of the Huygens-Steiner theorem to points on the Galois axis of a rigid body. This yields non-linear representations of the one-dimensional, affine, linear (semi)group.

We propose and analyse an energy-stable and asymptotic-preserving finite volume scheme for the compressible Euler system. Using the relative energy framework, we establish rigorous error estimates that yield convergence of the numerical solutions in two distinct regimes. For a fixed Mach number $\varepsilon>0$, we derive error estimates between the numerical solutions and a strong solution of the compressible Euler system that are uniform with respect to the discretisation parameters, ensuring convergence as the underlying mesh is refined. In the low Mach number regime, we analyse the error between the numerical solutions and a strong solution of the incompressible Euler system and obtain asymptotic error estimates that are uniform in $\varepsilon$ and the discretisation parameters. These results imply convergence of the numerical solutions toward a strong solution of the incompressible Euler system as $\varepsilon$, and the discretisation parameters simultaneously tend to zero. Numerical experiments are presented to validate the theoretical analysis.

An X-ray background in the early Universe enhances molecular hydrogen formation, the main coolant of primordial gas, thereby lowering the threshold for Pop III star formation. Continuing our series on X-ray impacts on Pop III star formation, we investigate how a soft X-ray background promotes Pop III star formation using cosmological zoom-in simulations of ten cosmic volumes spanning a range of halo number densities. Each volume is irradiated by the Lyman-Warner (LW) H$_{2}$ dissociating background and a weak (J$_{21} \sim 10^{-5}$), soft ($E \sim 0.2-2.0$ keV) X-ray background produced by pair-instability SNe (PISNe) from Pop III stars and calculated self-consistently as described in a companion paper. We also compare the same simulations with and without X-rays to isolate the X-ray effect. The background promotes Pop III star formation in two ways: (1) by reducing the mean host halo mass by a factor of $\sim 2-3$, and (2) by enabling Pop III star formation in haloes that would otherwise remain sterile, thereby increasing the halo occupation fraction. The resulting gain in Pop III number density is largest in underdense regions (a factor of $\approx 3$ on average, reaching up to 7). In the most extreme case, Pop II stars form only in the presence of X-rays and the gas-phase metallicity rises by an order of magnitude, suggesting that dwarf galaxies in underdense regions may be significantly influenced by an early X-ray background. We also provide fitting functions for the halo occupation probability of Pop III stars as a function of redshift for both X-ray and LW-only simulations, which can serve as inputs for semi-analytic models.

One of the biggest challenges of value-based decision-making is dealing with the subjective nature of values. The relative importance of a value for a particular decision varies between individuals, and people may also have different interpretations of what aligning with a value means in a given situation. While members of a society are likely to share a set of principles or values, their value systems--that is, how they interpret these values and the relative importance they give to them--have been found to differ significantly. This work proposes a novel method for aggregating value systems, generating distinct value agreements that accommodate the inherent differences within these systems. Unlike existing work, which focuses on finding a single value agreement, the proposed approach may be more suitable for a realistic and heterogeneous society. In our solution, the agents indicate their value systems and the extent to which they are willing to concede. Then, a set of agreements is found, taking a decentralized optimization approach. Our work has been applied to identify value agreements in two real-world scenarios using data from a Participatory Value Evaluation process and a European Value Survey. These case studies illustrate the different aggregations that can be obtained with our method and compare them with those obtained using existing value system aggregation techniques. In both cases, the results showed a substantial improvement in individual utilities compared to existing alternatives.

We introduce and study modular truncations of the Ackermann function, formalized as discrete dynamical trajectories on the set of least non-negative residues. These maps form a hierarchy of rapidly increasing compositional complexity indexed by recursion depth. We investigate their structural properties, sensitivity to depth variation, and the induced distributions modulo powers of two. While such hierarchical constructions are superficially motivated by hash-type mixing functions, we analyze how powers of two interact with the recursive structure modulo $2^k$, leading to strong saturation effects in the depth $m=3$ case. Instead of the expected asymptotic equidistribution, an absorption phenomenon occurs where the uniform measure concentrates onto a localized subset of residues, driving the total variation distance from the uniform distribution to 1.

It is known that every nilpotent group contains solution of every finite unimodular system of equatiuons over itself. This statement, however, is not true for infinite systems. Moreover, there are abelian groups which disprove the infinite system analogue of the statement. It has already been researched which periodic abelian groups contain solutions of all infinite unimodular systems of equations over themselves. The present article covers the same question for periodic nilpotent groups and for torsion-free nilpotent groups.

Hierarchical crack patterns that arise during the drying of thin films of colloidal dispersions or polymer solutions on a solid substrate are of interest both from a fundamental standpoint and in the context of the creation of transparent electrodes for optoelectronics. This paper analyzes the morphology of such patterns based on image processing of real-world samples. Graph theory is used to extract chains of edges and analyze the network topology. A method based on the hierarchy of connections is applied to classify cracks by generation. The limitations of existing classification approaches related to the discreteness of the time scale and the use of only a part of the entire pattern are discussed. Three approaches are used to generate artificial hierarchical networks: random uniform partitioning, recursive Voronoi partitioning, and a crack growth simulation model, each modified to reproduce the hierarchical structure. A comparison was made of the geometric characteristics (distribution of crack angles, edge lengths, cell areas, and circularity coefficient) and topological properties (distribution of the number of cell sides) of real and simulated networks. It was shown that the simulation model best reproduces the key features of real cracks, including the characteristic right angles of their connections.

This note provides an intrinsic construction of the Carrollian superplane $Π\mathbb{S}\simeq \mathbb{R}^{2|4}$ as a supermanifold generalisation of the Carrollian plane. Moving away from the $c\rightarrow 0$ limit of relativistic spinors, we define Carroll spinors as sections of a degenerate Clifford module. We show that the Carrollian superplane is a principal $\mathbb{R}^{1|2}$-bundle. Once clock forms and a complementary basic one-form are specified, there is a pair of odd vector fields that generate novel $N =2$ Carrollian supersymmetry transformations, not all of which come from an Inönü--Wigner contraction of a Poincaré superalgebra

How does the arrow of time (dissipative, irreversible behavior) emerge from time-reversible Hamiltonian mechanics? Two ingredients are needed: the underlying system must be ergodic or phase-mixing, and our knowledge of the system must be incomplete. When the detailed dynamics explores its phase space and stays close to a submanifold parametrized by a reduced set of state variables, the lack-of-fit reduction method reveals that the effective equations for those reduced variables are necessarily irreversible. To make this precise, we present a path-integral formulation of the lack-of-fit reduction in non-equilibrium thermodynamics, which shows how the GENERIC framework (reversible Hamiltonian part plus irreversible gradient flow) emerges from purely Hamiltonian mechanics without any fitting parameters. The formulation is based on the Onsager-Machlup variational principle, and it yields reduced dynamical equations by minimizing the information discrepancy between the detailed and reduced evolutions. Subsequently, the reduction method is illustrated on the Kac--Zwanzig model, confirming that dissipation emerges from ignoring degrees of freedom, and on diffusion, where diffusion equation for the hydrodynamic mass density emerges from Vlasov equation. We also show how to generalize the Fisher information matrix and Kullback--Leibler divergence to arbitrary concave entropies via the principle of maximum entropy, including non-Boltzmann-Gibbs cases such as the Tsallis--Havrda--Charvát entropy.

This paper is devoted to the analysis of periodic solutions of nonlinear control-affine systems with bang-bang controls. Such problems naturally arise in periodic optimal control with constrained inputs, which have, in particular, important applications in the performance optimization of chemical reactions. We reduce the problem of constructing a periodic solution to that of finding a fixed point of a composition of exponential maps. The latter problem is then addressed using the Baker-Campbell-Hausdorff-Dynkin (BCHD) formula. We establish the equivalence between periodic solutions of the original control system and those of an associated autonomous system involving iterated Lie brackets. Applying incremental stability arguments allows us to further simplify the problem to finding the equilibria of this autonomous system. The developed theory is then applied to nonlinear chemical reaction models with constrained controls.

Algorithmic systems mediate sexual and reproductive health (SRH) information seeking. Standard HCI and AI evaluation centers usability, accuracy, and interaction quality, measures designed to assess task performance and interaction quality at the system level. We introduce CARE, the Capability Approach for Reproductive Equity, a measurement framework for human-AI interaction that adds capability outcomes as a unit of evaluation above task performance. CARE functions in two parts. The Normative Design Lens identifies the resources, conversion factors, capabilities, and functionings a system should support. The Evaluation lens assesses how design features, interaction patterns, and social conditions shape capability outcomes, tradeoffs, and lived experiences in use. We apply CARE to SRH-specific chatbots, general-purpose LLMs, and search engine features in a study with 12 participants, demonstrating that it surfaces capability outcomes standard metrics aggregate away. The same design features expanded capabilities for some users while constraining them for others: source-level organization, response format, tone, and SRH-specific features all shaped which capabilities expanded for which users and in which direction. Participants' professional backgrounds, gender identities, and prior AI familiarity further shaped these effects, producing capability outcomes that usability and accuracy metrics, aggregated across users, would not surface. These findings demonstrate capability outcomes as a measurable unit for human-AI interaction evaluation, extending existing metrics with a capability layer above task performance.

The inverse-temperature four-vector $β^μ= u^μ/(k_B T_0)$ has been the theoretically accepted description of relativistic equilibrium since van Kampen and Israel, yet no experiment has ever reconstructed $β^μ$ as a single observable. All existing methods -- Thomson scattering, spectral fitting, blast-wave models -- infer rest-frame temperature and flow velocity from separate measurements. We propose the first protocol that extracts both components of $β^μ$ from the same passive observable: electromagnetic fluctuation correlations emitted by a drifting medium. A dimensionless $E$-$B$ cross-spectral ratio yields the drift velocity from Lorentz mixing of the field-strength tensor, while angle-resolved noise power governed by the covariant fluctuation-dissipation theorem provides the rest-frame temperature via a ratio method that cancels absolute amplitude. Together, these reconstruct $β^μ$ without external probes, spectral lines, or absolute radiometric calibration. The protocol enables the first direct experimental test of whether the thermal state of a relativistic medium transforms as a four-vector -- a question unresolved since the Planck--Ott-Landsberg controversy of 1907. Monte Carlo simulations parameterized to the HIGGINS dual 100\,TW laser-plasma facility demonstrate sub-percent temperature recovery for $γ= 1.05$-$10$, with robustness to additive noise at SNR~$\gtrsim 10$.

We present a non-perturbative approach to correlation functions and polyspectra of locally non-Gaussian fields and develop a semi-perturbative framework that does not rely on a local expansion. This enables the computation of $N$-point functions of non-Gaussian fields even when the mapping between the auxiliary Gaussian field $ζ_{\rm G}$ and the non-Gaussian field $ζ({\bf x}) = F(ζ_{\rm G}({\bf x}))$ is non-analytic. As an example, we consider non-Gaussian fields with exponentially tailed distributions, which can arise, for instance, in ultra-slow-roll models of inflation, and derive some exact analytic results in the strongly non-Gaussian regime.

The computational acceleration of orbital-invariant local correlation methods on graphics processing units (GPUs) has remained largely unexplored due to substantial algorithmic complexities. The runtime efficiency of GPU-implemented local correlation theories can be significantly constrained by the parallelizable degree of the orbital localization procedure, the iterative solution of the local wave function, and the adaptation of CUDA kernels to inherently local or sparse operations. Using the second-order Møller-Plesset perturbation (MP2) theory, we present a multi-GPU implementation for large-scale third-order many-body expansion orbital-specific virtual MP2 (MBE(3)-OSV-MP2) energy calculations. Accordingly, our algorithms and implementation address the GPU parallelization ability for peak utilization and parallelism of local MP2 computation in several aspects, including Jacobi-Pipek-Mezey localization, randomized OSV generation, direct MP2 integral regeneration, as well as CUDA kernel adaptation to local operations. The GPU-based MBE(3)-OSV-MP2 energy computation achieves $O(N^{1.9})$ scaling and 84\% parallel efficiency up to 24 GPUs distributed on multiple nodes. The present implementation delivers 40-fold wall-time speedup of the canonical RI-MP2 and 10-fold speedup of the CPU-based MBE(3)-OSV-MP2 for (H$_2$O)$_{128}$/cc-pVDZ and (H$_2$O)$_{190}$/cc-pVDZ, respectively. A large scale computation of 784-atom insulin peptide yields the full MBE(3)-OSV-MP2 energies in 24 minutes with cc-pVDZ (7571 basis functions) and 6.4 hours with cc-pVTZ (17448 basis functions) on 8 NVIDIA A800 GPUs. Our work opens up new possibilities for performing fast GPU-based local correlation calculations on real-life macromolecules.

Recent theoretical and experimental advances have demonstrated spatiotemporal photonic and acoustic vortex beams in free space. Such spatiotemporal vortex beams possess orbital angular momentum oriented perpendicular to the wave propagation direction. Herein, we report the discovery of spatiotemporal magnonic vortex beams in a confined ferromagnetic nanostrip geometry. The spatiotemporal magnonic vortex beam features stationary phase dislocations and exhibits wave propagation along a zigzag-like trajectory. Notably, the transverse orbital angular momentum carried by these phase dislocations displays spatial alternation. Our results differ distinctly from their photonic and acoustic counterparts, offering new insights into the fundamental research of spatiotemporal vortex beams.

This paper proposes a two-stage distributionally robust model predictive control (TSDR-MPC) scheme for stochastic disturbances with unknown time-varying means and covariances. By defining a Wasserstein ambiguity set on the disturbance-to-constraint space, constraint violation penalties are formulated as a second-stage problem, enabling adaptive tightening. A finitely convergent cutting-plane algorithm is developed for real-time implementation. The framework naturally degrades to deterministic MPC as uncertainty vanishes, without pre-specified tightening parameters. Theoretical guarantees include feasibility, finite-time termination, and an asymptotic average cost bound. Numerical simulations validate its adaptability and robustness.