Entanglement asymmetry provides a quantitative measure of symmetry breaking in many-body quantum states. Focusing on inhomogeneous $U(1)$ charges, such as dipole and multipole moments, we show that the typical asymmetry is bounded by a universal fraction of its maximal value. Multipole charges naturally arise in systems with Hilbert-space fragmentation, where the dynamics splits into exponentially many disconnected sectors. Using the commutant algebra formalism, we generalize entanglement asymmetry to account for fragmentation. While the asymmetry grows logarithmically for conventional symmetries, it can scale extensively in fragmented systems and distinguish classical from quantum fragmentation. We derive general upper bounds for the asymmetry and identify states that saturate them. To study the typical behavior of the asymmetry, we consider the ensemble of random matrix product states. By identifying the bond dimension with an effective time parameter, we qualitatively reproduce recent results on asymmetry dynamics in random quantum circuits, suggesting a universal behavior for the asymmetry of $U(1)$ charges in local ergodic systems.

We develop a quark-diquark effective mass formalism for heavy-flavor baryon spectroscopy and apply it to the $J^P = \tfrac{1}{2}^+$ and $J^P = \tfrac{3}{2}^+$ spectra across the singly, doubly, and triply heavy sectors. The analysis is carried out in two complementary scenarios: Scenario I treats all quark-quark diquark channels dynamically, while Scenario II restricts the dynamics to scalar and axial-vector diquarks, providing a more selective and physically transparent description. Constituent quark masses, effective diquark masses, and chromomagnetic couplings are extracted from known heavy-baryon masses, with the couplings determined solely by the quark content of each state and no sector-dependent adjustment introduced. A mass-dependent binding term is implemented to account for spin-independent chromoelectric effects and to describe the transition from chromomagnetic to color-Coulomb dominance across the light-to-heavy quark regime, ensuring consistency with heavy-quark spin symmetry in the heavy-quark limit. The resulting predictions are in good agreement with available experimental measurements and lattice QCD results across both charm and bottom sectors. The extracted diquark parameters remain stable across all heavy-flavor sectors, establishing the present framework as a symmetry-constrained spectroscopic baseline for heavy-baryon structure.

Multi-scalar multiplication (MSM), MSM(vec{P},vec{x}) = sum_{i=1}^n x_i P_i, is a dominant computational kernel in discrete-logarithm-based cryptography and often becomes a bottleneck for verifiers and other resource-constrained clients. We present 2G2T, a simple protocol for verifiably outsourcing MSM to an untrusted server. 2G2T is efficient for both parties: the server performs only two MSM computations and returns only two group elements to the client, namely the claimed result A = MSM(vec{P},vec{x}) and an auxiliary group element B. Client-side verification consists of a single length-n field inner product and only three group operations (two scalar multiplications and one group addition). In our Ristretto255 implementation, verification is up to about 300x faster than computing the MSM locally using a highly optimized MSM routine (for n up to 2^18). Moreover, 2G2T enables latency-hiding verification: nearly all verifier work can be performed while waiting for the server's response, so once (A,B) arrives the verifier completes the check with only one scalar multiplication and one group addition (both independent of n). Finally, despite its simplicity and efficiency, we prove that 2G2T achieves statistical soundness: for any (even unbounded) adversarial server, the probability of accepting an incorrect result is at most 1/q per query, and at most e/q over e adaptive executions, in a prime-order group of size q.

We propose a reaction--diffusion model of predator--prey interaction in which the predators occupy only a subset of the prey's territory, leaving a predator-free exclusion zone. Ecological examples include marine protected areas where it is illegal to fish, or buffer zones left between the territories of rival predators. The prey are subject to a strong Allee effect, so excessive predation may lead to the extinction of both species. The exclusion zone mitigates this problem by providing the prey with a refuge in which to proliferate without predation. Thus, paradoxically, a smaller predator territory may be able to support a more substantial population than a larger one. Using a topological degree argument, we show in any dimensions that, provided the exclusion zone is large enough, the system possesses spatially heterogeneous coexistence equilibria with positive populations of both species. This result is global in the sense that it does not rely on local bifurcations from semi-trivial stationary states. We also show that as the predator domain becomes asymptotically small, the total predator population does not vanish, and in some cases may actually be maximized in this limit of shrinking predation area. Conversely, we show that as the predator domain becomes large, it may exhibit thresholding behavior, passing suddenly from a regime with coexistence solutions to one in which extinction becomes unavoidable, highlighting the need for careful analysis in the management of predator--prey systems.

We show how to construct a compact quantum metric space from a proper continuous length function on an étale groupoid with compact unit space, where the unit space additionally has the structure of a compact metric space. Using compactly supported Fourier multipliers on the reduced groupoid $C^*$-algebra we provide a sufficient condition for verifying when we obtain a compact quantum metric space in this manner. The condition is sometimes also necessary, and is new even in the case of length functions on discrete groups. Lastly, we show that any AF groupoid with compact unit space can be equipped with a length function from which we obtain a compact quantum metric space, thereby providing a groupoid approach to understanding the quantum metric geometry of unital AF algebras.

Existing home energy management systems conceptualize occupants as passive recipients of energy information and control, which limits their ability to effectively support informed decision-making and sustained engagement. This paper presents Home Energy Management Assistant (HEMA), the first open-source, multi-agent system enabling sustained human-AI collaboration - multi-turn conversational interactions with preserved context - across diverse home energy management (HEM) tasks - from energy analysis and educational support to smart device control. HEMA combines large language model (LLM) reasoning capabilities with 36 purpose-built domain-specific tools through a three-layer architecture: a web-based conversational interface, a backend API server, and a multi-agent system. The system features three specialized agents - Analysis (energy consumption patterns and cost optimization), Knowledge (educational queries and rebate information), and Control (smart device management and scheduling) - coordinated through a self-consistency classifier that routes user queries using chain-of-thought reasoning. This architecture enables various energy analyses, adaptive explanations, and streamlined device control. HEMA also includes a comprehensive evaluation framework using an LLM-as-simulated-user methodology with 23 objective metrics across task performance, factual accuracy, interaction quality, and system efficiency, allowing systematic testing across diverse scenarios and user personas without requiring extensive human subject testing. Through demonstrations using real-world household energy consumption data, we show how HEMA supports informed decision-making and active engagement in HEM, highlighting its potential as a user-friendly, adaptable tool for residential deployment and as a research platform for HEM innovation.

In [CKM17], Chodosh, Ketover, and Maximo proved finite diffeomorphism theorems for complete embedded minimal hypersurfaces of dimension $\leqslant$ 6 with finite index and bounded volume growth ratio. In this paper, we adapt their method to study finite diffeomorphism types for complete immersed minimal submanifolds of arbitrary codimension in Euclidean space with finite total curvature and Euclidean volume growth.

Neutrino self-interactions (NSI) offer a potential pathway to address anomalies in standard cosmology and explain existing cosmological tensions. In this work, we present a novel framework to obtain the neutrino--neutrino collision term within the Boltzmann hierarchy, incorporating both neutrino and mediator masses as free parameters. Our calculations encompass both Dirac-like and Majorana neutrinos and distinguish between two neutrino mass eigenstates. This work provides a valuable tool for future analyses, should a NSI signal be detected. Remarkably, our results show a smooth transition from the light to the heavy mediator approximation as the Universe cools down for non-resonant cases. Thus, for the widely studied heavy mediator, our new scheme eliminates the need to approximate at high redshifts when the temperature increases above the mediator mass, and it provides the tools to test the threshold of validity of the heavy mediator paradigm. While this work focuses on NSI mediated by a scalar particle, the presented framework could be adapted to a broader range of neutrino NSI and possibly to warm dark matter self-interacting scenarios.

Hecke operators acting on modular functions arise naturally in the context of 2d conformal field theory, but in seemingly disparate areas, including permutation orbifold theories, ensembles of code CFTs, and more recently in the context of the AdS$_3$/RMT$_2$ program. We use an equidistribution theorem for Hecke operators to show that in each of these large $N$ limits, an entire heavy sector of the partition function gets integrated out, leaving only contributions from Poincaré series of light states. This gives an immediate holographic interpretation as a sum over semiclassical handlebody geometries. We speculate on further physical interpretations for equidistribution, including a potential ergodicity statement.

The widely accepted definition of grid-forming (GFM) inverter states that it should behave as a (nearly) constant voltage source behind an impedance by maintaining a (nearly) constant internal voltage phasor in the sub-transient to transient time frame. Some system operators further mandate permissible ranges for this effective impedance. However, these specifications do not clearly define the location of the internal voltage source, and no systematic method exists to quantify its effective impedance for a black-box GFM model. To address this, we first compare the transient responses of an ideal voltage source and a GFM to show that an idealistic GFM maintains a (nearly) constant voltage across the filter capacitor, rather than at the inverter switches. Then we propose a systematic method to quantify the effective impedance of a GFM from its black-box model using frequency-domain admittance plots. Using standard PSCAD GFM models developed by NLR (formerly NREL), we demonstrate that the GFM's equivalent impedance model captures the sub-transient response and static voltage stability limit accurately. Further, replacing the GFM with the proposed equivalent circuit model in the modified IEEE-39 bus system is shown to reproduce the small-signal stability characteristics with reasonable accuracy.

Visual language model (VLM) agents show great promise in automating end-to-end (E2E) web testing against requirements in natural language. However, the probabilistic nature of language models can have inherent hallucinations. Therefore, given a detected inconsistency between the requirement and the web application, it is hard to distinguish whether it stems from the hallucination or a real application bug. Addressing this issue presents two core technical challenges: the implicit oracle inference challenge, where the agent must act as its own oracle to implicitly decide if the application's behavior is correct without guidance, and the probabilistic inference challenge, where an LLM's inconsistent reasoning undermines its trustworthiness as an oracle. Existing LLM-based approaches fail to capture such implicit oracles, either by treating any page navigation that doesn't crash as a success, or by checking each state in isolation, thus missing bugs dependent on context from prior steps. We introduce WebTestPilot, an LLM-based agent designed to address these challenges. WebTestPilot uses (1) a symbolization layer which detects and symbolizes critical GUI elements on the web application into symbols (i.e., variables) and (2) translates natural language specification into a sequence of steps, each of which is equipped with inferred pre- and post-conditions over the symbols as an oracle. This oracle captures data, temporal, and causal dependencies, enabling the validation of implicit requirements. To advance research in this area, we build a benchmark of bug-injected web apps for evaluating NL-to-E2E testing. The results show that WebTestPilot achieves a task completion rate of 99%, with 96% precision and 96% recall in bug detection, outperforming the best baseline (+70 precision, +27 recall). The agent generalizes across diverse natural language inputs and model scales.

In this paper, we investigate a class of port-Hamiltonian systems with singular vector fields. We show that, under suitable conditions, their interconnection with passive systems ensures convergence to a prescribed non-equilibrium steady state. At first glance, this behavior appears to contradict the seemingly passive structure of port-Hamiltonian systems, since sustaining a non-equilibrium steady state requires continuous power injection. We resolve this apparent paradox by showing that the singularity in the vector field induces a sliding mode that contributes effective energy, enabling maintenance of the steady state and demonstrating that the system is not passive. Furthermore, we consider regularizations of the singular dynamics and show that the resulting systems are cyclo-passive, while still capable of supplying the required steady-state power. These results clarify the role of singularities in port-Hamiltonian systems and provide new insight into their energetic properties.

It is well known that the ground-state correlation energy from the particle-hole channel of the random phase approximation (RPA) is formally equivalent to that from a simplified coupled cluster doubles (CCD) model that includes only ring diagram contraction contributions in the residual equations [{\em J. Chem. Phys.} {\bf 129}, 231101 (2008)]. We generalize this analytic result to the cavity quantum electrodynamics (QED) case and demonstrate the numerical equivalence of QED-RPA and a QED ring-CCD model that accounts for double electron excitations, coupled single electron excitations / single photon creation, and double photon creation.

How many canonical degrees of freedom does a quantum field theory actually use during its Hamiltonian evolution? For a UV/IR-regularised classical scalar field, we address this question directly at the level of phase-space dynamics by identifying the minimal symplectic dimension required to reproduce a single trajectory by an autonomous Hamiltonian system. Using symplectic model order reduction as a structure-preserving diagnostic, we show that for the free scalar field this minimal dimension is controlled not by the volume-extensive number of discretised field variables, but by the much smaller number of distinct normal-mode frequencies below the ultraviolet cutoff. In flat space, this leads to an area-type scaling with the size of the region, up to slowly varying corrections. On geodesic balls in maximally symmetric curved spaces, positive curvature induces mild super-area growth, while negative curvature suppresses the scaling, with the flat result recovered smoothly in the small-curvature limit. Numerical experiments further indicate that this behaviour persists in weakly interacting $λϕ^4$ theory over quasi-integrable time scales. Beyond counting, the reduced dynamics exhibits a distinctive internal structure: it decomposes into independent oscillator blocks, while linear combinations of these blocks generate a larger family of apparent field modes whose Poisson brackets are governed by a projector rather than the identity. This reveals a purely classical and dynamical mechanism by which overlapping degrees of freedom arise, without modifying canonical structures by hand. Our results provide a controlled field-theoretic setting in which area-type scaling and overlap phenomena can be studied prior to quantisation, helping to identify which aspects of such structures--often discussed in holographic contexts--can already arise from classical Hamiltonian dynamics.

High-order perturbative $\textit{ab initio}$ calculations are challenging due to the rapidly growing configuration space and the difficulty of assessing convergence. In this work, we introduce perturbation theory quantum Monte Carlo (PTQMC), a stochastic approach designed to compute high-order many-body perturbative corrections. By representing the perturbative wave function with random walkers in configuration space, PTQMC avoids the exponential scaling inherent to conventional constructions of high-rank excitation operators. Benchmark calculations for the Richardson pairing model demonstrate that PTQMC accurately reproduces exact many-body perturbation theory (MBPT) coefficients up to 16th order, even in strongly divergent regimes. We further show that combining PTQMC with series resummation techniques yields stable and precise energy estimates in cases where the straightforward perturbative series fails. Finally, we propose the effective number of configurations, $e^{S}$, as a global measure of perturbative wave-function complexity that can be directly extracted within PTQMC. We demonstrate that the saturation behavior of $e^{S}$ provides a more reliable indicator of the validity of perturbative expansions than energy convergence alone.

We provide a link between response theory, pullback measures, and optimal fingerprinting method that paves the way for a) predicting the impact of acting forcings on time-dependent systems and b) attributing observed anomalies to acting forcings when the reference state is not time-independent. We derive formulas for linear response theory for time-dependent Markov chains and diffusion processes. We discuss existence, uniqueness, and differentiability of the equivariant measure under general (not necessarily slow or periodic) perturbations of the transition kernels. Our results allow for extending the theory of optimal fingerprinting for detection and attribution of climate change (or change in any complex system) when the background state is time-dependent amd when the optimal solution is sought for multiple time slices at the same time. We provide numerical support for the findings by applying our theory to a modified version of the Ghil-Sellers energy balance model. We verify the precision of response theory - even in a coarse-grained setting - in predicting the impact of increasing CO$_2$ concentration on the temperature field. Additionally, we show that the optimal fingerprinting method developed here is capable to attribute the climate change signal to multiple acting forcings across a vast time horizon.

Over the past three decades, extreme climate events have caused losses of worth USD 4.5 trillion. Using collective bargaining model, I find that the gendered labour supply response to adverse shocks is not straightforward since it depends on relative strength of income and substitution effects of men's and women's participation. Using a panel of 151 countries (1995-2019), I examine how extreme climate conditions shape gender gap in labour force participation. This study finds that the gender gap in paid labour exhibits a U-shaped relationship with droughts and an inverted U-shaped relationship with extreme wet conditions. The drought pattern is primarily driven by gender gap in employment while wetness affects gender gap in participation through unemployment. These relationships vary with country characteristics. Countries with high disaster-displacement risk exhibit declining gender gaps in participation during excess wetness while moderate-risk economies experience expanded gaps during droughts. Furthermore, the drought U-shape is most pronounced in countries with low to moderate empowerment while the nonlinear wet responses is concentrated only in moderately empowered countries. Lastly, both droughts and excess wetness expands gender gap in countries with weak net resilience to climate shocks.

The uncountability of the reals was first established by Cantor in what was later heralded as the first paper on set theory. Since the latter constitutes the official foundations of mathematics, the logical study of the uncountability of the reals is a worthy endeavour for historical, foundational, and conceptual reasons. In this paper, we shall study the following principle: $\textsf{NIN}_{[0,1]}$: there is no injection from the unit interval to the natural numbers. We show that relatively strong logical systems cannot prove $\textsf{NIN}_{[0,1]}$. In particular, the former system implies second-order arithmetic and fragments of the Axiom of Choice, including dependent choice. We also study the latter choice fragments in Kohlenbach's higher-order Reverse Mathematics.

Nonlinear spectroscopic techniques using entangled photon pairs can provide an opportunity to exploit non-classical correlations encoded in two-photon wavefunctions to manipulate two-exciton wavefunctions. We propose an entangled photon pair-enhanced multidimensional spectroscopic technique that is sensitive to exciton-exciton interactions and correlations at the femtosecond timescale. Simulations for a dissipative system, namely, the photosynthetic aggregate reveal the superior ability of entangled photon pairs, compared to both transform-limited and frequency-chirped laser pulses, to manipulate excited-state absorption pathways. The corresponding spectral features in the two-dimensional spectrogram are interpreted in terms of one- and two-exciton resonances. The signal scales linearly with the incoming intensity of the photon sources. We show that classifying these resonances using entangled photon source in the perturbative limit allow for probing exciton correlations at the natural energy scale. These insights can be used to explore multi-exciton dynamics in molecular systems using multiphoton entanglement.

The surface-brightness-color (SBC) relationship for Red Clump stars provides a critical foundation for precision distance ladder measurements, including the 1\% distance determination to the Large Magellanic Cloud. Current SBC calibrations rely on angular diameter measurements of nearby Red Clump stars obtained through long-baseline optical interferometry using the Very Large Telescope Interferometer. We explore the application of intensity interferometry to measure limb-darkened angular diameters of Red Clump stars, offering a complementary approach to traditional amplitude interferometry. We describe the framework for extracting angular diameters from squared visibility measurements in intensity interferometry, accounting for limb darkening through the stellar atmosphere models. For the Red Clump star HD~17652, we show that intensity interferometry in the $H$ band at baselines matching PIONIER ($\sim$100~m) could achieve $<1$\% angular size uncertainties in 2-hour exposures by measuring the primary peak of the visibility function, enabling direct comparison with existing measurements. Critically, observations at shorter wavelengths probe the secondary visibility maximum, providing independent checks of both measurement and systematic errors that are largely insensitive to limb-darkening assumptions. Exploiting the multiplex advantage of simultaneous multi-bandpass observations and the large number of baselines available with telescope arrays such as the Cherenkov Telescope Array Observatory can reduce observing times to practical levels, making intensity interferometry a viable tool for validating the angular sizes for a subset of the Red Clump star calibration sample.

Recent discussions at the intersection of journalism, HCI, and human-centered computing ask how technologies can help create reader-oriented news experiences. The current paper takes up this initiative by focusing on immigrant readers, a group who reports significant difficulties engaging with mainstream news yet has received limited attention in prior research. We report findings from our co-design research with eleven immigrant readers living in the United States and seven journalists working in the same region, aiming to enhance the news experience of the former. Data collected from all participants revealed an "unaddressed-or-unaccountable" paradox that challenges value alignment across immigrant readers and journalists. This paradox points to four metaphors regarding how conversational AI agents can be designed to assist news reading. Each metaphor requires conversational AI, journalists, and immigrant readers to coordinate their shared responsibilities in a distinct manner. These findings provide insights into reader-oriented news experiences with AI in the loop.

We investigate how the orbital evolution and mass distribution of infalling satellite galaxies shape the phase-space and radial distributions of intracluster light (ICL) relative to the underlying cluster dark matter (DM) halo. Using N-body simulations, we follow the tidal stripping and orbital evolution of satellite galaxies as they are accreted into a live cluster halo, systematically varying satellite-to-host mass ratio and orbital circularity. We measure the specific orbital energy and angular momentum of stripped stellar and DM material, finding that the stripped stars consistently occupy lower-energy and lower-angular momentum regions of phase-space than the stripped DM. The magnitude of this difference increases strongly towards more equal satellite--to--host mass ratios, while the dependence on orbital circularity is weak. We construct a predictive model for the phase-space properties of stripped stars and DM from a whole infalling satellite population and find that the resulting phase-space difference between the components are driven primarily by the characteristic mass of the infalling satellite stellar mass function. We find that the ICL is always more centrally concentrated than the DM. The magnitude of this offset depends on the characteristic mass and increases towards higher characteristic masses. Comparisons with four independent cosmological hydrodynamical simulations show that, once the infalling satellite stellar mass function is matched, the model reproduces the radial stellar-to-DM density profile offsets to better than the inter-simulation scatter. This demonstrates that the radial relationship between the ICL and the DM distribution is largely governed by satellite demographics. With adequate constraints on the infalling satellite population, ICL density profiles can therefore be used as informative tracers of the underlying radial DM distribution in clusters.

Considerable work has been dedicated to hyperspectral single image super-resolution to improve the spatial resolution of hyperspectral images and fully exploit their potential. However, most of these methods are supervised and require some data with ground truth for training, which is often non-available. To overcome this problem, we propose a new unsupervised training strategy for the super-resolution of hyperspectral remote sensing images, based on the use of synthetic abundance data. Its first step decomposes the hyperspectral image into abundances and endmembers by unmixing. Then, an abundance super-resolution neural network is trained using synthetic abundances, which are generated using the dead leaves model in such a way as to faithfully mimic real abundance statistics. Next, the spatial resolution of the considered hyperspectral image abundances is increased using this trained network, and the high resolution hyperspectral image is finally obtained by recombination with the endmembers. Experimental results show the training potential of the synthetic images, and demonstrate the method effectiveness.

There is a long-acknowledged deficiency of bright red giants relative to fainter old stars within a few arc seconds of Sgr A*. We explore whether this could be due to tidal stripping by the central black hole. This requires putting the stars onto highly eccentric orbits, for which we evaluate diffusion by both scalar resonant and non-resonant relaxation of the orbital angular momentum. We conclude that tidal stripping does not discriminate sufficiently between main-sequence and red giant stars. While the tidal loss cone increases with stellar radius, the rate of diffusion into the loss cone increases only logarithmically, whereas the lifetime on the red giant branch decreases more rapidly than $R_*^{-1}$. In agreement with previous studies, we find that stellar collisions are a more likely explanation for the deficiency of bright red giants relative to fainter ones.

We consider adaptive finite element methods (AFEMs) with inexact algebraic solvers for second-order symmetric linear elliptic diffusion problems. Optimal complexity of AFEM, i.e., optimal convergence rates with respect to the overall computational cost, hinges on two requirements on the solver. First, each solver step is of linear cost with respect to the number of degrees of freedom. Second, each solver step guarantees uniform contraction of the solver error with respect to the PDE-related energy norm. Both properties must be ensured robustly with respect to the local mesh size h (i.e., h-robustness). While existing literature on geometric multigrid methods (MG) or symmetric additive Schwarz preconditioners for the preconditioned conjugate gradient method (PCG) that are appropriately adapted to adaptive mesh-refinement satisfy these requirements, this paper aims to consider more general solvers. Our main focus is on preconditioners stemming from contractive solvers which need not be symmetrized to be used with Krylov methods and which are not only h-robust but also p-robust, i.e., the contraction constant is independent of the polynomial degree p. In particular, we show that generalized PCG (GPCG) with an h- and p-robust contractive MG as a preconditioner satisfies the requirements for optimal-complexity AFEM and that it numerically outperforms AFEM using MG as a solver. While this is certainly known for (quasi-)uniform meshes, the main contribution of the present work is the rigorous analysis of the interplay of the solver with adaptive mesh-refinement. Numerical experiments underline the theoretical findings.

In this analysis, we investigate the polarization radiation imaging of Kerr-Newman black holes, with a particular focus on the impact of black hole charge on photon propagation and polarization characteristics. By extending the traditional Walker-Penrose method, which is limited by its reliance on specific symmetric structures and Killing tensors, we overcome these limitations by constructing an ordinary differential equations (ODEs) numerical framework that combines the photon orbit equation with the polarization parallel transport equation. This allows for the self-consistent evolution of photon trajectories and polarization states in any spacetime backgrounds without relying on specific symmetries. Using this framework, we analyze the effects of black hole spin and charge on the polarization characteristics of radiation from both prograde and retrograde accretion disks. Our results show that black hole charge can significantly modify photon trajectories and polarization patterns: increasing charge compresses and distorts the EVPA structure on photon-ring scales, inducing localized rotations and asymmetries that may provide a potential diagnostic of a nonzero black hole charge.

Faster diffusion of cations along grain boundaries is reported in the literature for a variety of acceptor-doped $AB\mathrm{O}_{3}$ perovskite-type oxides. The ratio $r$ of the activation enthalpy of grain-boundary diffusion ($ΔH^\mathrm{gb}$) to the activation enthalpy of bulk diffusion ($ΔH^\mathrm{b}$) is seen experimentally to lie in the range $0.7 < r = ΔH^\mathrm{gb} / ΔH^\mathrm{b} < 1.3$, albeit with substantial errors. In a previous publication [Parras and De Souza, Acta Mater. 195 (2020) 383] it was shown through a set of continuum simulations that cation-vacancy accumulation within negative space-charge layers at grain boundaries in acceptor-doped perovskites will give rise to faster grain-boundary diffusion of cations, with the associated values of $r$ approaching but not exceeding unity. In the present study, we demonstrate by means of continuum simulations that $r > 1$ is possible for faster cation diffusion along grain boundaries in an acceptor-doped perovskite. The specific case we consider is cation diffusion occurring by two related mechanisms, by slower (charged) isolated cation vacancies and by faster (neutral) defect associates of cation and anion vacancies. Within the negative space-charge layers, the isolated cation vacancies are strongly accumulated, whereas the neutral associates are unaffected. We calculate diffusion profiles for a two-dimensional bicrystal geometry by solving, first, Poisson's equation, and subsequently, the diffusion equation. We find that, if a small concentration of faster defect associates is responsible for bulk diffusion, and a hugely enhanced concentration of slower isolated vacancies yields faster diffusion along space-charge layers, $r>1$ is obtained. The conditions under which $r > 1$ may be observed are described, and issues with experimental confirmation are discussed.

Fluid antenna system (FAS) leverages dynamic reconfigurability to unlock spatial degrees of freedom and reshape wireless channels. Blind interference alignment (BIA) aligns interference through antenna switching. This paper proposes, for the first time, a robust fluid antenna-driven BIA framework for a K-user MISO downlink under imperfect channel state information (CSI). We formulate a robust sum-rate maximization problem through optimizing fluid antenna positions (switching positions). To solve this challenging non-convex problem, we employ group relative policy optimization (GRPO), a novel deep reinforcement learning algorithm that eliminates the critic network. This robust design reduces model size and floating point operations (FLOPs) by nearly half compared to proximal policy optimization (PPO) while significantly enhancing performance through group-based exploration that escapes bad local optima. Simulation results demonstrate that GRPO outperforms PPO by 4.17%, and a 100K-step pre-trained PPO by 30.29%. Due to error distribution learning, GRPO exceeds heuristic MaximumGain and RandomGain by 200.78% and 465.38%, respectively.

We study joint source-channel coding over Markov channels through the empirical coordination framework. More specifically, we aim at determining the empirical distributions of source and channel symbols that can be induced by a coding scheme. We consider strictly causal encoders that generate channel inputs, without access to the past channel states, henceforth driving the Markov state evolution. Our main result is the single-letter inner and outer bounds of the set of achievable joint distributions, coordinating all the symbols in the network. To establish the inner bound, we introduce a new notion of typicality, the input-driven Markov typicality, and develop its fundamental properties. Contrary to the classical block-Markov coding schemes that rely on the blockwise independence for discrete memoryless channels, our analysis directly exploits the Markov channel structure and improves beyond the independence-based arguments.

In this paper, we study the existence of solutions to sweeping processes in the presence of stochastic perturbations, where the moving set takes uniformly prox-regular values and varies continuously with respect to the Hausdorff distance, without smoothness assumptions. We propose a minimal geometric framework for such moving sets, make precise the logical implications between several standard hypotheses in the literature, and provide practical sufficient conditions that apply in particular to constraints defined as finite intersections of sublevel sets. Within this setting, we establish existence of weak and strong solutions and prove pathwise uniqueness for the associated stochastic differential equations reflected in time-dependent domains.