Let $M$ be a Fraïssé structure (a countably infinite ultrahomogeneous structure). We refer to the class of structures embeddable in $M$ as the $ω$-age of $M$. We consider the following two properties of $M$: we say that $M$ has a universal automorphism group if, for each $A$ in the $ω$-age of $M$, there is an embedding $\textrm{Aut}(A) \to \textrm{Aut}(M)$, and we say that $M$ has group-extensible $ω$-age if, for each $A$ in the $ω$-age of $M$, there is an embedding $A \to M$ such that each automorphism of the image extends to an automorphism of $M$ and the extension map preserves group composition. It is immediate that if $M$ has group-extensible $ω$-age, then $M$ has a universal automorphism group. We give an example of a Fraïssé structure with a universal automorphism group whose $ω$-age is not group-extensible, showing that the above two properties are not equivalent.

When a radio jet is partially optically thick in the launching region, its apparent compact core may display frequency-dependent positional shifts. High-precision astrometric measurements of core shifts enable astronomers to pinpoint the jet's origin and place tight constraints on the magnetic field. BL Lacertae, the archetypal BL Lac object, hosts a highly variable and well-collimated jet. To independently constrain its innermost core shifts, we conducted very long baseline interferometric (VLBI) observations at 8.4, 12.4, 15.2, 23.6, and 43.2 GHz. By exploiting a nearby (13.3 arcmin) steep-spectrum calibrator (NVSS J220340+420839) through inverse phase-referencing VLBI astrometry, we detect nearly unbiased two-dimensional core shift measurements with state-of-the-art precisions of 5-30 $μ$as, which are significant at $>3σ$ confidence. The core shift between 8.4 and 43.2 GHz reaches 250 $μ$as. The apparent core shifts scale with frequency as $ν^{-1/k_r}$, implying the existence of an optically thick region in the upstream of jet. The derived core-shift index, $k_r\!=\!1.18^{+0.59}_{-0.34}$, is consistent, within uncertainties, with the canonical $k_r\!=\!1$ expected under energy equipartition between the jet particle and magnetic field energy densities, while allowing for modest deviations given that BL Lacertae was captured in a flaring state.

This paper aims to provide a proof of concept of the accuracy of simulations for advanced networking study. The particular target technology is the Differentiated Services (DiffServ) architecture. The method has been to apply experimental activities conducted in a real network to a simulation environment, to gather the same performance parameters and to compare results. A worthy re-engineering of the DiffServ module of the deployed software program has been carried out and significant contribution have been made to overcome the encountered limitations and to enrich its modeling capabilities. Final results give useful suggestions for a more critical approach to simulations targeted for advanced networking study.

We compute a presentation for the integral Chow rings of the moduli stacks of degree $2$ maps from smooth rational curves to projective space $\mathbb{P}^r$, as a quotient of a three-variable polynomial ring. The relations as $r$ varies have rich combinatorial structure: all non-trivial relations are encoded by two generating functions which are rational functions.

We introduce a family of proximal discontinuous Galerkin methods for variational inequalities, focusing on the obstacle problem as a didactic example. Each member of this family is born from applying a different well-known nonconforming finite element discretization to the Bregman proximal point method. We explicitly treat four examples: the symmetric interior penalty discontinuous Galerkin, the enriched Galerkin, the hybridizable interior penalty and the hybrid high-order methods. We formulate a unified analysis framework for this family of methods and prove the existence and uniqueness of solutions, energy dissipation, and error estimates for both the primal and dual variables. Remarkably, the proximal hybrid high-order method with piecewise constant cell unknowns and piecewise affine facet unknowns leads to the first higher-order convergence result for any proximal Galerkin method.

Third-order pseudo-transitions in finite systems reflect reorganization beyond conventional criticality, yet their identification usually relies on microcanonical entropy, which is often inaccessible in practice. Here we introduce a spectral generalized response within the eigen-microstate framework. From the distribution of normalized spectral weights, we construct the third-order ratio $R_3=K_3/(K_2)^3$, which probes asymmetric redistribution among fluctuation modes beyond leading-mode condensation. Across Ising and Potts models on regular lattices and random regular networks, extrema of $R_3$ consistently track higher-order anomalies. Combined with spectral projection, the method further distinguishes dependent and independent branches: the former remain tied to the dominant ordering channel, whereas the latter arise from redistribution within the subleading fluctuation subspace. The effective spectral dimension $R_{\mathrm{eff}}$ provides the participation background in which these anomalies develop. These results establish a geometric characterization of third-order pseudo-transitions as reorganizations of statistical weight in configuration space and provide an order-parameter-free route to finite-size structural criticality.

Three-dimensional experiments are presented on a school of three pitching hydrofoils. Two side-by-side leader foils maintain the same relative positions while the location of a third follower foil is varied. Force and flow measurements detail the mechanisms that drive the school to achieve collective thrust and efficiency that are 58% and 24% higher than isolated foils, respectively. Traditional drafting involves positioning yourself in the wake of an upstream object. In wakes with a net momentum deficit, drafting reduces drag by lowering oncoming flow speed. By contrast, wakes from oscillatory swimmers feature strong momentum surplus regions, which increases drag by increasing the oncoming flow. Despite that, our results show that the best performance benefits occur for compact schools where the follower is directly in the vortex wake of a leader, whereas regions of reduced mean flow do not improve performance. The thrust and efficiency benefits are shown to be driven by vortex-body interactions that increase the thrust and efficiency of the follower and by body-to-body upstream interactions that reduce the power of the leaders. There is an optimal spatial phase to maximize the thrust and efficiency of the follower that depends upon the actual wake wavelength rather than the estimated wavelength used in previous literature. Moreover, wake breakdown, and its associated elimination of vortex-body performance benefits, is not observed within at least three chord lengths downstream of the leaders. Lastly, measurements of the cross-stream stability of the downstream foil indicate that compact, high-performance formations may require active control strategies in order to maintain their organization and maximise the hydrodynamic benefits of schooling.

For an operator T from X to Y denote m(T) the infimum of $||Tx||$ on the unit sphere $S_X$ of X. A sequence $(x_n)$ in $S_X$ is said to be minimizing for T if $||Tx_n||$ tends to m(T). In 2020 U. S. Chakraborty introduced and studied the following weak minimizing property (WmP): a pair (X,Y) of Banach spaces is said to have the WmP if, for every bounded linear operator $T: X \to Y$ that admits a non-weakly null minimizing sequence, the function $x \mapsto \|Tx\|$ attains its minimum on the unit sphere. We present the following new results about the WmP for pairs of infinite-dimensional separable Banach spaces: (i) If (X,Y) has the WmP, then X is reflexive. (ii) If X is reflexive and Y does not contain isomorphic copies of X, then (X,Y) has the WmP. (iii) If X is reflexive and Y contains an isomorphic copy of X, then there is an equivalent norm on Y such that, for this equivalent norm, (X,Y) does not have the WmP. The first result extends to non-separable X if and only if X possesses a countable total set of functionals.

We study the set $S(q)$ of residue classes $r$ modulo the Pisano period $π(q)$ for which $q \mid φ(F_m)$ for every $m \equiv r \pmod{π(q)}$. We prove that if $q$ is a Sophie Germain prime and $z(2q+1) \mid π(q)$, then $S(q)$ is a nonempty arithmetic progression, and for $q > 5$ its cardinality is odd and $q \equiv 8 \pmod{15}$. Conversely, we show that if a prime $p \equiv 1 \pmod{q}$ has $z(p) \mid π(q)$, then necessarily $p = 2q+1$, so $q$ is Sophie Germain. We conjecture that $S(q) \neq \emptyset$ forces the existence of such a prime $p$; this is verified for all $q \leq 50000$. Assuming that $z(2q+1) \mid π(q)$ holds for infinitely many Sophie Germain primes (verified computationally for approximately 23.9% of them), the Sophie Germain conjecture implies the existence of infinitely many primes $q \equiv 8 \pmod{15}$ with $(2q+1) \mid F_{π(q)}$ -- a purely Fibonacci-theoretic condition. These results generalize to arbitrary Lucas sequences $U_n(P,Q)$ with non-square discriminant.

This paper introduces two methods for analyzing periodic leaky-wave antennas (LWAs) within a new framework denoted as multi-modal network theory (MNT) with open periodic boundaries (OPBs). The approach is hybrid, combining analytical techniques with a commercial full-wave solver. The first method computes the dispersion diagram of periodic LWAs. It is iterative and relies on the full-wave simulation of a single unit-cell of a LWA, coupled with the analytical solution of an eigenvalue problem. This method effectively captures both the phase and attenuation constants of periodic LWAs while using fewer modes than previous methods with commercial frequency-domain solvers. The method is validated by computing the dispersion of classic LWA unit-cells and comparing them to those obtained through full-wave simulations of the full-length antenna and other state-of-the-art methods. The second, also based on OPB-MNT, focuses on LWA analysis in reception. Specifically, it determines the response of a unit-cell to an incident plane wave. To validate this method, we compute the response of LWA with different unit-cell designs. By comparing these results with the corresponding dispersion analysis, we show that the receiving case and the eigenvalue problem are related but not simply time-reversed versions of each other.

We report experimental results on Rydberg facilitation, whereby Rydberg levels can be excited off-resonantly in the presence of a nearby Rydberg atom because of Rydberg-Rydberg interactions, for high-lying $S$, $P$ and $D$ levels in rubidium. Facilitation is detected both through an enhancement of the number of excited atoms for off-resonant excitation (either blue or red detuning) and a positive Mandel $Q$ parameter indicating correlated excitation events (super-Poissonian counting statistics). We also calculate the pair-state potentials for the Rydberg states involved and find that our experimental results agree with the expected facilitation conditions for repulsive potentials (blue detuning) and attractive potentials (red detuning), with $P$ and $D$ states exhibiting facilitation on both sides of the resonance. Finally, we investigate inter-state facilitation between two different Rydberg levels (70 $S$ and 70 $P$).

Altermagnetism, known for its non-relativistic spin-split band structures with yet compensated moments, is being intensively investigated. Discovering new altermagnetic materials with characteristics suitable for practical use remains an important ongoing task. Recently a metallic room-temperature altermagnet candidate Rb1-xV2Te2O with a layered structure and d-wave spin symmetry has been reported based on experimental results from the spin-resolved photoemission spectroscopy and scanning tunnelling microscopy/spectroscopy (STM/STS) measurements. Here we report neutron powder diffraction (NPD) investigations on the magnetic structure of Rb1-xV2Te2O, which shows a G-type antiferromagnetic structure below the transition temperature of 337 K. The result is different from the original theoretical expectation, which might lead to new insights on the physics of this altermagnet candidate.

Background: Clinical documentation and information retrieval consume over half of physicians working hours, contributing to cognitive overload and burnout. While artificial intelligence offers a potential solution, concerns over hallucinations and source reliability have limited adoption at the point of care. This study aimed to evaluate physician-perceived time efficiency, decision-making support, and satisfaction with DR. INFO, an agentic AI clinical assistant, in routine clinical practice. Methodology: In this prospective, single-arm, pilot feasibility study, 29 physicians and medical students across multiple specialties in Portuguese healthcare institutions used DR. INFO v1.0 over five working days within a two-week period. Outcomes were assessed via daily Likert-scale evaluations (time saving and decision support) and a final Net Promoter Score (NPS). Non-parametric methods were used throughout, with bootstrap confidence intervals (CIs) and sensitivity analysis to address non-response. Results: Physicians reported high perceived time saving (mean = 4.27/5; 95% CI = 3.97-4.57) and decision support (mean = 4.16/5; 95% CI = 3.86-4.45), with ratings stable across the five-day study window. Among the 16 (55%) participants who completed the final evaluation, the NPS was 81.2, with no detractors; sensitivity analysis indicated an NPS of 44.8 under conservative non-response assumptions. Conclusions: Physicians across specialties and career stages reported positive perceptions of DR. INFO for both time efficiency and clinical decision support within the study window. These findings are preliminary and should be confirmed in larger, controlled studies that include objective performance measures and independent accuracy verification.

We establish versions of Matsuki duality for loop groups. The main result is a bijection between symmetric loop group orbits and real polynomial loop group orbits on the affine Grassmannians or affine flag varieties. Along the way we obtain orbit parametrizations and make connections with vector bundles on real and twistor-$\mathbb P^1$ and Kottwitz sets .

We present a solvable same-sector effective theory for anomaly-inspired axion inflation, in which a heavy trace-anomaly mode dynamically backreacts on the axion potential. The tree-level elimination of the radial field resums the backreaction into a closed-form Lambert-$W$ potential, naturally flattening the hilltop potential without external plateau operators. By deriving the exact trough metric, we evaluate all the observables on the fully reduced one-field action, bypassing uncontrolled kinetic approximations. Calibrated at $N_\star=56$, reheating-compatible branches yield $r\simeq0.033$--$0.036$ and $α_s\simeq-(4.6$--$4.7)\times10^{-4}$, comfortably satisfying the current ACT/SPT/BICEP constraints. The evolution remains strictly adiabatic ($m_\perp^2/H^2\gtrsim6.1$, $Ω/H\lesssim7.6\times10^{-4}$) with negligible sound-speed and metric corrections. We provide analytic control over the constant-$w_{\rm eff}$ reheating map, the $N_{\rm re}=0$ boundary, and robustness against vacuum-offset deformations. This Lambert-$W$ backbone establishes a precise, deformable benchmark for confining axion inflation, with microscopic matching and reheating microphysics accessible as systematic EFT refinements.

We compute the quasinormal mode spectrum of scalar perturbations on Kaigorodov pp-wave spacetimes, the horizonless gravity duals of zero temperature null fluids. The pp-wave deformation promotes the Poincaré horizon at $r=0$ to an irregular singular point of rank $(d+2)/2$, which acts as a geometric absorber for ingoing waves: rank~$0$ corresponds to thermal dissipation, rank~$1$ to quantum-critical (extremal black hole), and rank~$\geq 2$ to gapped, horizonless dissipation. For $d=2$ (extremal BTZ) the radial equation reduces to the Whittaker equation with exact non-dissipative spectrum $\mathrm{Im}(ω)=0$; for $d \geq 3$ all modes satisfy $\mathrm{Im}(ω_n) < 0$, establishing zero temperature dissipation without horizon or entropy. At zeroth order the radial equation becomes Bessel's equation of order $μ=d/(d+2)$, proving all scalar QNMs are gapped. Numerical spectra for $d=3,4,5$ yield a discrete dissipative tower and confirm linear stability.

The population of natural objects in a 1:1 mean motion resonance with Earth are known as Earth's co-orbitals. Main belt objects can dynamically evolve into Earth co-orbitals but taxonomic studies of some of them have suggested that they are more likely to be lunar material. While it has long been known that lunar ejecta can achieve Earth co-orbital status, in this work we calculate their expected steady-state size-frequency distribution from the impact rate of asteroids and comets on the Moon's surface, the ejecta's size-frequency and speed distribution, and dynamical integration of the particles for millions of years, among other factors. We also classify known and synthetic co-orbitals by their regime (quasi-satellite, horseshoe, tadpole, or compound) and compute the probability of transitions between them. Our nominal solution predicts that there are $\gtrsim 70$ Earth co-orbitals in the steady-state population larger than $10$ m in diameter with a lunar provenance but there are orders-of-magnitude systematic uncertainty on the value. We used NEOMOD3 to calculate that about 1600 are expected in the co-orbital population with a main belt provenance and they have higher eccentricity and inclination than those from the Moon. New taxonomic classifications for more Earth co-orbitals will reduce the uncertainties on e.g. crater scaling relations that will, in turn, reduce the uncertainties in the calculation of the steady-state population of Earth's co-orbitals with a lunar origin. The mineralogy and abundance of Earth's co-orbitals is also of interest to commercial asteroid mining ventures because they are the lowest $Δv$ targets in the asteroid population.

The heart of the a priori and a posteriori error control in convex minimization problems is the sharp control of the differences of discrete and exact minimal energy. Conforming finite element discretizations for p-Laplace type minimization problems provide upper bounds of the energy difference with optimal convergence rates. Even for smooth solutions, known convergence rates for higher-order non-conforming finite element discretizations for the same problem class with $2 < p < \infty$, however, are exclusively suboptimal. Thus the popular a posteriori error control within the two-energy principle, that generalize hyper-circle identities, appears unbalanced. The innovative point of departure in a refined analysis of two discontinuous Galerkin (dG) schemes exploits duality relations between a discrete primal and a semi-discrete dual problem. The infinite-dimensional dual problem leads to a tiny duality gap that even vanishes for polynomial low-order terms. For a class of degenerated convex minimization problems with two-sided $p$ growth, the novel duality provides improved a priori convergence rates for the error in the minimal energies. This closes the misfit of convergence rates for the conforming and nonconforming schemes at least for the local discontinuous Galerkin schemes at hand. The motivating two-energy principle and some post-processing for a Raviart-Thomas dual variable provides an a posteriori error control, that also may drive adaptive mesh-refining. Computational benchmarks provide striking numerical evidence for improved convergence rates of the adaptive beyond uniform mesh-refining.

We study the topological structure of random geometric forests $G$ in the Euclidean plane under mild assumptions: non-crossing edges, stationarity, and finite edge intensity. The framework covers a broad range of constructions, including models based on stationary point processes as well as lattices, and encompasses many already well-studied examples among drainage networks, geodesic forests arising from first- and last-passage percolation, and minimal or uniform spanning trees. First, denoting by $N_k$ the number of $k$-ended connected components in $G$ for each $k\geq0$, we show that almost surely, all trees of $G$ have at most two topological ends, $N_0\in\{0,\infty\}$, $N_1\leq2$, and $N_1=2\implies N_2<\infty$. We then construct explicit examples realizing all possibilities compatible with these constraints, yielding a complete classification of the admissible topological structures for $G$. As a second result, we prove that under the additional assumptions that $G$ is non-empty, oriented, out-degree one, with all its directed paths going to infinity along a fixed deterministic direction, the situation reduces to a dichotomy: $G$ consists almost surely of either a unique one-ended tree, or infinitely many two-ended trees. The latter extends a theorem of Chaika and Krishnan (2019), who considered a lattice setting. Our proofs combine classical Burton-Keane type arguments with substantial new conceptual ideas using planar topology, resulting in a robust, unified approach.

First, we consider general Brylinski--Deligne covers of the $p$-adic general linear groups, and discuss the theory of Bernstein--Zelevinsky derivatives. We also recall the Zelevinsky-type classification of the irreducible genuine spectrum for the Kazhdan--Patterson and Savin covers. Following this, for these two special families of covers, we determine the wavefront sets of their irreducible genuine representations, expressed in terms of the iterated degrees of the highest Bernstein--Zelevinsky derivatives. Finally, for Kazhdan--Patterson covers, we reinterpret this result on the wavefront set using a version of the local Langlands correspondence and the covering Barbasch--Vogan duality.

Universal $T$-matrices, or Hopf algebra dual forms, for quantum groups are revisited, and their contraction theory is developed. As a first illustrative example, the (1+1) timelike $κ$-Poincaré $T$-matrix is explicitly worked out. Afterwards, motivated by recent results on the role of the Hopf algebra dual form of a quantum (1+1) centrally extended Galilei group as the algebraic object underlying non-relativistic quantum reference frame transformations, a new quantum deformation of the (1+1) centrally extended Poincaré Lie algebra is obtained, and its universal $T$-matrix is presented. Finally, the Hopf algebra dual form contraction is applied to this Poincaré $T$-matrix, showing that its corresponding non-relativistic counterpart is precisely the Galilei $T$-matrix associated with quantum reference frames. In this way, the Poincaré Hopf algebra dual form introduced here stands as a natural candidate for describing the symmetry structure of relativistic quantum reference frame transformations. In the appropriate basis, the associated quantum Poincaré group is recognized, remarkably, as a non-trivial central extension of the (1+1) spacelike $κ$-Poincaré dual Hopf algebra.

We establish that nonconvex definable parametric optimization problems with possibly nonsmooth objectives, inequality constraints, conic constraint systems, and non-unique primal and dual solutions admit an adjoint state formula under a mere qualification condition. The adjoint construction yields a selection of a conservative field for the value function, providing a computable first-order object without requiring differentiation of the solution mapping. Through examples, we show that even in smooth problems, the formal adjoint construction fails without conservativity or definability, illustrating the relevance of these concepts to grasp theoretical aspects of the method. This work provides a tool which can be directly combined with existing primal-dual solvers for a wide range of parametric optimization problems.

We report on a new method for incorporating interactions between dark matter (DM) and baryons in cosmological simulations, capable of handling the challenging regime in which the dark matter particle mass is comparable to or lighter than the baryon mass. The method hybridizes two distinct approaches: gas particles receive momentum and energy transfer according to a mean-field calculation while DM particles undergo Monte Carlo scatterings. These approaches are derived from the Boltzmann equation and shown to be statistically equivalent. We present an open-source implementation of this method in the simulation code GIZMO. As a first application, we investigate the effects of DM-baryon interactions on an isolated Milky Way-like disk galaxy for dark matter having twice the proton mass, which roughly maximizes the average energy transfer per collision. For cross sections of order 1 barn ($10^{-24}$ cm$^2$), these interactions cause strong changes to the mass distribution in the center of the galaxy in less than 1 Gyr, even when bar formation is suppressed by hand. For cross sections typical of hadronic interactions ($\lesssim 30$ mb), high-fidelity galaxy formation simulations will be needed to assess the effects on observable features of galaxies.

Let $K/\mathbb{Q}_p$ be a finite extension whose ramification index is coprime to $p^2-p$. We study height-one commuting pairs $(f, u)$ of noninvertible and invertible formal power series defined over the ring of integers $\mathcal{O}_K$ of $K$. We begin by extracting a crystalline character of weight $1$ from the $\mathrm{Gal}(\overline K/K)$-set $T_f$ of $f$-consistent sequences. This character is used in order to equip $T_f$ with a $\mathbb{Z}_p$-module structure for which $f$ is an endomorphism. We then apply explicit functors in integral $p$-adic Hodge theory to $T_f$ to recover a formal group defined over $\mathcal{O}_K$ for which $(f, u)$ is a pair of endomorphisms. This proves new cases of a conjecture of Lubin.

We construct the Extended Real Line with Reentry (ERI): identify $\{-\infty, 0, +\infty\}$ to a single point $\ast$ in $\overline{\mathbb{R}}$, and require every neighborhood of $\ast$ to have dense preimage. The resulting space is compact, path-connected, and sober; it is $T_1$ and US (uniquely sequential), but not weakly Hausdorff, not KC, and not Hausdorff. In the refined hierarchy of Clontz, ERI sits at the $k_2$-Hausdorff level. A search of pi-Base for compact US-not-KC spaces returns three entries -- $\mathbb{Q}^{\ast} \times \mathbb{Q}^{\ast}$, $ω_1+1$ with doubled endpoint (S37), and the one-point compactification of the Arens-Fort space (S165) -- all totally disconnected. ERI is the first compact path-connected example. The same density condition on a general compact Hausdorff base without isolated points defines a Filter-Modified Quotient (FMQ). We prove that the density modifier $\mathcal{D}_Y$ is the least restrictive admissible modifier preserving US, and that the hierarchy level $k_2\mathrm{H}$-not-$\mathrm{wH}$ is invariant under infinite closed nowhere-dense collapse sets, iteration of the construction, and arbitrary products. The only remaining direction toward a US-not-$k_2\mathrm{H}$ level runs through non-first-countable base spaces.

As quantum networking hardware remains costly and not yet widely accessible, simulation tools are essential for the design and evaluation of quantum network architectures and protocols. However, designing a scalable and computationally efficient quantum network simulator is intrinsically challenging: i) quantum dynamics must be emulated on classical computing platforms while capturing the stateful and non-local nature of entanglement, a quantum resource without any classical networking analog; ii) quantum networking is inherently hybrid, as protocol execution also fundamentally depends on classical signaling. This makes a tight and faithful co-simulation of quantum operations and classical message exchanges a core requirement. In this light, we present Q2NS, a modular and extensible quantum network simulator, built on top of ns-3, designed to seamlessly integrate quantum-network primitives with ns-3's established classical protocol stack. Q2NS adopts a modular architecture that decouples protocol control logic from node- and channel-level operations, enabling rapid prototyping and adaptation across heterogeneous and evolving Quantum Internet scenarios. Q2NS natively supports multiple quantum state representations through a unified interface, allowing interchangeable state-vector, density-matrix, and stabilizer backends. We validate Q2NS through realistic use-case studies and comprehensive benchmarks, demonstrating superior computational efficiency over representative state-of-the-art alternatives, while preserving modeling flexibility. Finally, we provide a dedicated visualization tool that jointly captures physical and entanglement-enabled connectivity and supports entangled-state manipulations, facilitating an intuitive interpretation of entanglement dynamics and protocol behavior. Q2NS offers a flexible, open, and scalable simulation platform for advancing Quantum Internet research.

Lattice QCD simulations are computationally expensive, with the solution of the Dirac equation being the major computational bottleneck of many calculations. We introduce a novel gauge-equivariant neural-network architecture for preconditioning the Dirac equation in the regime where critical slowing down occurs. We study the behavior of this preconditioner as a function of topological charge and lattice volume and show that it mitigates critical slowing down. We also show that this preconditioner transfers to unseen gauge configurations without any retraining, therefore enabling applications not possible with competing methods.

Ultrasonic imaging methods often assume linear direct models, while in reality, many nonlinear phenomena are present, e.g. multiple reflections. A family of imaging methods called Full Waveform Inversion (FWI), which has been developed in the field of seismic imaging, uses full acoustic wave simulations as direct models, taking into account virtually all nonlinearities, which can ultimately enhance the accuracy of ultrasonic imaging. However, the problem of cycle skipping -- the existence of many local minima of the Least Squares (L2) misfit function due to the oscillatory nature of the signals -- is worsened when FWI is applied to ultrasound data because of a lack of low-frequency components. In this paper, we explore the use of the squared Wasserstein (W2) Optimal Transport Distance as the metric for the misfit between the acquired and the synthetic data, applying the method to Nondestructive Evaluation with ultrasonic phased arrays. An analytical continuous time-domain derivation of the adjoint acoustic field related to the W2 misfit is presented and used for the computation of the gradients. To cope with the computational burden of FWI, we apply a low-memory strategy that allows for the computation of the gradients without the storage of the full simulated fields. The GPU implementation of the method (in CUDA language) is detailed, and the source code is made available. Six prototypical cases are presented, and the corresponding sound speed maps are reconstructed with FWI using both the L2 and the W2 misfit functionals. In five of the six cases, the pixel-wise sum of squared errors obtained with W2 was at least one order of magnitude lower than that obtained with W2, with an increase in the gradient computation time not exceeding 2\%. The results highlight both the adequacy of the W2 misfit for ultrasonic FWI with phased arrays and its computational feasibility.

Many quantum phases, from topological orders to superfluids, are destabilized at finite temperature by the proliferation and motion of topological defects such as anyons or vortices. Conventional protection mechanisms rely on energetic gaps and fail once thermal fluctuations exceed the gap scale. Here we examine a complementary mechanism of entropic protection, in which defect nucleation is suppressed by coupling to mesoscopic auxiliary reservoirs of dimension $M$, generating an effective free-energy barrier that increases with temperature. In the Ising chain, this produces a characteristic three-regime evolution of the correlation length as a function of temperature - linear growth, entropy-controlled plateau, and eventual breakdown - indicating a general modification of defect behavior. Focusing on two spatial dimensions, where true finite-temperature topological order is forbidden in the thermodynamic limit, we show that entropic protection can nevertheless strongly enhance stabilization at finite system size, the regime directly relevant for quantum memory and experiments. Owing to the topological character of the defects, creation and transport are independently suppressed, yielding a double parametric reduction of logical errors in the entropic toric code and enhanced coherence when the framework is extended to Berezinskii-Kosterlitz-Thouless transitions. Entropic barriers thus provide a passive and scalable route to stabilizing quantum phases in experimentally relevant regimes. We propose an experimental setup for entropic toric code using dual species Rydberg arrays with dressing.

Modern scientific instruments operate under increasingly extreme constraints on bandwidth, latency, and power. Inference at the sensor edge determines experimental data collection efficiency by deciding which information to save for further analysis. Particle tracking detectors at the Large Hadron Collider exemplify this challenge: pixelated silicon sensors generate rich spatiotemporal ionization patterns, yet most of this information is discarded due to data-rate limitations. Concurrently, advancements in co-design tools provide rapid turn-around for incorporating machine learning into application-specific integrated circuits, motivating designs for particle detectors with new integrated technologies. We demonstrate that neural networks embedded in the front-end electronics can infer charged-particle kinematic parameters from a single silicon layer. We regress hit positions and incident angles with calibrated uncertainties, while satisfying stringent constraints on numerical precision, latency, and silicon area. Our results establish a path toward probabilistic inference directly at the edge, opening new opportunities for intelligent sensing in high-rate scientific instruments.