This note studies the quantized corner structure of four-dimensional $BF$ theory, classifies the associated free and physical corner algebras and constructs possible representations. In the abelian case, for arbitrary closed oriented surfaces and in the presence or absence of a cosmological term, explicit presentations of the corner algebras are obtained in terms of generators and relations, identifying them as infinite-dimensional oscillator-type Lie algebras with an abelian summand. A construction of infinite families of simple modules via bosonic Fock space representations is provided. In the non-abelian case on the torus, the corner algebras are described as quotients constructed from the central extensions of double-loop algebras over certain non-semisimple Lie algebras. A construction of infinite families of simple Fock-type modules of the free corner algebra via an induced module procedure is also provided. The resulting modules descend only trivially to the physical quotient, revealing an obstruction in the present construction in the non-abelian setting.

Large-scale quantum networks will enable entirely new applications of quantum information science in fields such as quantum communication, distributed quantum computing, sensing, and metrology. To build nodes of such networks, diamond color defects are one of the promising candidates. Their excellent optical properties, fast spin-qubit control, and long spin coherence times make them well-suited for quantum information processing and quantum memory applications. Additionally, recent advances in the heterogeneous integration of diamond nanophotonic structures with photonic integrated circuits have made these systems more efficient and well-suited for scalable quantum processor architectures. In this comprehensive review, we discuss the optical and spin properties of these systems, recent progress in the building blocks of quantum networks, and demonstrations of metropolitan-scale quantum networks, as well as the challenges associated with these systems at both the fundamental and experimental levels, along with potential solutions.

Developing high-order numerical schemes for two-phase flow in porous media that preserve key physical properties remains a significant challenge in numerical analysis. In this article, we propose a general framework to construct fully discrete first- and second-order numerical schemes for thermodynamically consistent model of incompressible and immiscible two-phase flow in porous media. The proposed schemes are rigorously proved to ensure five fundamental properties: (i) unique solvability; (ii) full decoupling; (iii) bound preservation for both phases; (iv) original energy dissipation; (v) local mass conservation for both phases. The key to ensure the unique solvability lies in guaranteeing the strict convexity of the discrete energy functionals associated with the constructed schemes. Departing from the coupled solution approach for the pressure and saturation variables, the proposed approach breaks traditional paradigm by subtracting the two-phase mass conservation equations to derive a fully decoupled system. In addition, the bound-preserving property for both phases is established by leveraging the singular nature of the logarithmic term around the limit values of $0$ and $1$. A rigorous error estimate for the first-order scheme, in the $\ell^{\infty}(0,T; H_h^{-1} (Ω)) \cap \ell^{2}(0,T; \ell^2(Ω))$ norm for the saturations of two phases, is established. Finally, various numerical examples are presented to verify the theoretical results and demonstrate the efficiency of the proposed schemes.

The transition toward Software-Defined Vehicles (SDVs) represents a major paradigm shift in vehicle design, transforming traditional hardware-centric systems into software-centric platforms capable of dynamic adaptation and continuous functional evolution. SDVs enable advanced capabilities such as Over-the-Air (OTA) updates, intelligent automation, and connected services driven by AI. This paper presents a comprehensive survey of the architectures, enabling technologies, and operational frameworks that define modern SDVs. It examines the evolution of vehicle architectures from distributed electronic control unit (ECU) systems to domain-based, zonal, and centralized computing platforms. Key enabling technologies are reviewed, including service-oriented software architectures, middleware, automation pipelines, artificial intelligence mechanisms, and cloud-based infrastructures. A structured taxonomy is introduced to organize SDV technologies into functional hardware, E/E architectures, software frameworks, automation mechanisms, and distributed infrastructure domains. The study also investigates the Software-Defined Internet of Vehicles (SDIoV) paradigm, integrating Software-Defined Networking (SDN) with edge and fog computing to support scalable vehicular communication and data processing. Furthermore, key technical challenges related to cybersecurity, interoperability, data management, and system scalability are discussed, along with emerging research directions and future development trends.

The accelerating growth of global data generation demands data storage platforms that offer high capacity, long lifespan, and low energy consumption beyond the limits of electronic memory technologies. Optical storage provides an attractive alternative. However, its density is fundamentally constrained by the optical diffraction limit and the limited scalability from the point-by-point laser writing, as well as thermal accumulation during high-speed writing. Here, we introduce a large-scale optical data storage scheme that is compatible with the progress in chip fabrication by combining electron-beam lithography (EBL) and ion implantation to deterministically encode high-density data. The approach achieves precise control of ion number and spatial distribution, enabling multi-bit grayscale encoding and wavelength division multiplexing with chip-scale patterning over millimeter areas. Wavelength-selective readout is performed using downconversion and upconversion fluorescence detection, allowing crosstalk-free retrieval of multiplexed data channels. We further develop a neural network-based super-resolution algorithm that reconstructs data beyond the diffraction limit, further increasing the effective storage density. Using this integrated framework, we achieve an optical data density of 10 Gbit/cm$^2$ with high fidelity. Our results establish a micro/nano-fabrication-compatible route to large-scale, high-density optical memory and provide a foundation for next-generation cold data optical storage technologies.

We present results on the Mellin moments of the unpolarized parton distribution function (PDF) of the pion and kaon up to the fourth order. The computation is done using one $N_f=2+1+1$ gauge ensemble of twisted mass fermions with quark masses tuned to approximately their physical values. We reconstruct the valence pion and kaon PDFs using the connected contributions to the three Mellin moments. We compare our results on the Mellin moments and the reconstructed PDFs with other lattice QCD and phenomenological determinations.

Superimposed pilot (SIP) transmission improves spectral efficiency by eliminating the dedicated pilot overhead required in orthogonal pilot (OP)-based schemes. However, SIP suffers from severe pilot-data coupling, which leads to a critical performance-complexity bottleneck at the receiver. To address this issue, this paper proposes a low-overhead transmission framework that revitalizes data-dependent superimposed training (DDST) with enhanced interference mitigation strategies. First, for quasi-static block-fading channels, an enhanced DDST receiver is developed to achieve non-iterative pilot-data decoupling by exploiting data-dependent algebraic structures. Second, to overcome the sensitivity of conventional DDST to channel variations and symbol misidentification in fast time-varying environments, a mix transmission scheme is developed. By strategically applying DDST to a subset of resource elements, the proposed scheme combines the interference-free transmission property of OP with the zero-pilot-overhead advantage of SIP, thereby improving demapping reliability and interference suppression. Furthermore, under the proposed mix scheme, a Vision Transformer-based neural receiver is designed to capture the orthogonal structure between pilots and perturbation-bearing data, as well as the underlying channel correlations, thereby relaxing the stringent quasi-static assumption required for interference disentanglement. Simulation results demonstrate that the proposed framework achieves significant performance gains in the low-to-medium SNR regime under time-varying channels while providing superior computational efficiency compared with state-of-the-art SIP receivers.

We study positive solutions of the Dirichlet problem $-Δu = u^p$ in a uniformly convex domain $Ω\subset \mathbb S^2$, $u= 0$ on $\partialΩ.$ For $p=1$, we assume that the right-hand side is replaced by $λ_1 u$, where $λ_1$ is the first eigenvalue of $-Δ$ on $Ω$ with zero Dirichlet boundary condition. We prove that for $0 \leq p < 1$ the unique positive solution $u$ is such that $u^{\frac{1-p}{2}}$ is strictly concave in $Ω$, while for $1 < p \leq 3$ every positive solution $u$ is such that $u^{\frac{1-p}{2}}$ is strictly convex in $Ω.$ For $p=0,$ our result gives the strict $1/2-$concavity of the torsion function in $Ω.$ For $p=1,$ a result due to Lee and Wang gives the strict log-concavity of the first eigenfunction in $Ω.$ As a consequence, for each $0 \leq p \leq 3,$ any positive solution has strictly convex superlevel sets and a unique nondegenerate maximum.

We develop a perturbative, diagrammatic framework for constructing Nicolai maps and apply it to four-dimensional $\mathcal{N}=1$ Poincaré supergravity expanded around flat Minkowski space. It provides an alternative to the coupling-flow-operator construction, which faces several obstructions when extended to local supersymmetry. Expanding the bosonic effective action and the Nicolai map jointly in the gravitational coupling $κ$ and the loop-counting parameter $\hbar$, we derive the Nicolai-map defining conditions, i.e. the free-action and determinant-matching conditions, order by order. The diagrammatics enumerates all admissible local terms in the Nicolai-map ansatz from the effective-action diagrams and reduces the construction to a finite system of nonlinear polynomial equations. Carried through order $κ^{2}$, the resulting constraints are found to be independent of the detailed bosonic input and hierarchical, order-$κ^{2}$ consistency further restricting the order-$κ$ data. A consistent Nicolai-map construction for the Einstein--Hilbert graviton sector is found to require the Rarita--Schwinger gravitino already at this order: Einstein gravity admits a Nicolai map only through its $\mathcal{N}=1$ supersymmetric completion, Poincaré supergravity, supporting Nicolai's characterization of supersymmetry.

We present a theoretical investigation of the magnetic and thermodynamic properties of the triangular spin-1/2 cluster with Dzyaloshinskii-Moriya (DM) interaction, described by a spin-1/2 Heisenberg Hamiltonian with antisymmetric exchange interactions. The energy spectrum and ground-state phase diagram reveal the presence of ferromagnetic (FM), ferrimagnetic (FI), and frustrated (FR) phases, strongly influenced by the total spin and the DM interaction. We analyze magnetization and susceptibility, showing that at low temperatures the system exhibits a characteristic 1/3 magnetization plateau, while thermal fluctuations suppress magnetic order at higher temperatures. The entropy and specific heat display residual entropies due to ground-state degeneracies, Schottky-type anomalies at intermediate temperatures, and additional low-temperature features related to phase transitions. Particular attention is given to the magnetocaloric effect (MCE), characterized by both direct and inverse regimes depending on the magnetic field variation. We find that the DM interaction enhances the complexity of the MCE, leading to nontrivial entropy variations as a function of the magnetic field. These results provide insights into the role of frustration and anisotropy in tuning the MCE of properties triangular spin clusters, with relevance to \mathrm{Cu}_{3}-based molecular magnets.

Safety applications in vehicle-to-everything communications and Cooperative Intelligent Transport Systems rely on reliable and timely message exchange, which in turn depends on accurate modeling of wireless signal propagation. Simulation frameworks such as VEINS are widely adopted to design and evaluate such systems before deployment; however, their realism strongly depends on the validity of the underlying channel and antenna models. This work presents an empirical validation of the VEINS simulator against real-world data collected from the MASA living laboratory. Using the default configuration, we compare Received Signal Strength Indicator (RSSI), number of messages, and attenuation of the signal. The results show that VEINS systematically overestimates the RSSI value, while losing approximately 18% of the total number of messages received compared to the MASA, revealing inconsistencies between simulation and reality. The contribution of this study is a direct comparison between simulated and real world data, establishing a quantitative basis for future calibration of VEINS parameters to improve the fidelity of VANET simulations in C-ITS safety research.

In this work, we analyze the feasibility of room-temperature superconductivity in the lanthanum-scandium hydride $\textit{P6/mmm}$-LaSc$_2$H$_{24}$. We demonstrate that the electron-phonon coupling calculations performed using the $σ$-broadening of the double $δ$-function at the Fermi surface lead to a very strong dependence of $\textit{T$_c$}(σ)$ on the arbitrary $σ$, whereas the tetrahedral method for the electron-phonon interaction is free from this drawback and leads to $\textit{T$_c$}$ > 300 K at 300 GPa in agreement with previous predictions. By analyzing the stability of the metallic state of LaSc$_2$H$_{24}$ at 250-300 GPa, we show that this compound is at the edge of the stability region ($ξ$ = 0.54), similar to $\textit{fcc}$ LaH$_{10}$ at 140-150 GPa. Experimental attempts to synthesize LaSc$_2$H$_{24}$ at 250-280 GPa starting from the (La,Sc$_2$) alloy are unsuccessful and indicate the absence of even traces of superconductivity at 245-300 K in all the resulting La-Sc-H hydrides. The method for preparing the precursor by simultaneous deposition of La and Sc metals may be a key factor for the successful synthesis of LaSc$_2$H$_{24}$.

We characterize all lattices $Λ\subset \mathbb{R}^2$ and all compactly supported functions $g \in L^2(\mathbb{R})$ for which the Gabor system $\left \{ e^{2πi s x} g(x-t) : (t,s) \in Λ\right \}$ forms an orthonormal basis for $L^2(\mathbb{R})$. The characterization is given in geometric terms through translation tilings and discreteness properties of lattice projections. In particular, this resolves a conjecture of Han and Wang on the non-existence of Gabor bases along specific irrational lattices. Finally, we construct Gabor bases that cannot be realized by any product set, answering a problem of Iosevich and Mayeli.

Full-disk observations of the Sun in the Ca II K line have been carried out since the late 19th century at various observatories worldwide. These long-term records of solar activity are crucial for reducing discrepancies among solar irradiance reconstructions and for advancing our understanding of the solar dynamo. To construct a consistent composite record, data from different observatories must be cross-calibrated to account for variations in spectral passband and spatial resolution, which are the primary sources of discrepancies between archives. In this study, we use high spectral and spatial resolution observations in the Ca II K line from the state-of-the-art Sunrise III mission to emulate different passbands and derive empirical contrast-contrast relationships between them. We find that these relationships are well described by a power law and provide coefficients for different combinations of passband widths in the range 0.1--9 Angstroms and spatial resolutions between 1 arcsec and 6 arcsec. Applying such a relationship to observations from two major Ca II K archives demonstrates its potential to improve their cross-calibration. The results provide a foundation for the construction of a consistent, century-long time series of solar activity from historical and modern Ca II K observations.

The streaming instability is the leading model for planetesimal formation in protoplanetary disks, but it typically operates within the first ~Myr. In the Solar System, however, some planetesimals (the chondrite parent bodies) formed 2-4 Myr after disk formation, implying that dust must have been retained for extended periods. Pressure bumps efficiently trap dust, but trapping alone does not guarantee planetesimal formation: even modest gas turbulence can inhibit vertical settling and radial concentration, preventing dust density from reaching Hill density. This motivates the study of alternative dust-gas instabilities, such as the Dusty Rossby Wave Instability (DRWI). We investigate the viability of such instabilities in global disk simulations using the multi-fluid code fargOCA. We first reproduce previous 2D shearing-box results in a global 2D viscous disk and characterize the dust clumping produced by the DRWI. We find that the instability is suppressed in fully 3D viscous disks by unperturbed high-z gas layers caused by dust settling near the midplane. We then explore the inviscid limit and find that multiple dust sub-rings form, concentrating solids into thin ring structures. These would appear observationally as a single radially broad, vertically thin ring, explaining observed protoplanetary disk rings without invoking anisotropic turbulence. Dust concentrations in the sub-rings may remain below the threshold for gravitational collapse, but gas photoevaporation enhances dust settling and radial concentration, eventually forming dense dust clumps in both viscous and inviscid cases. We conclude that planetesimal formation within dust-trapping pressure bumps is favored in very low-viscosity disks at late evolutionary stages, after sufficient gas removal by photoevaporation. This is consistent with the inferred late formation of chondrite parent bodies in the Solar System.

Four-wave mixing (FWM) is an efficient source of light waves emitted at various frequencies, usually associated with third-order optical nonlinearities. Whereas attention has mostly been paid in the past to the generation of Stokes (e.g., visible) modes by mixing two nonharmonic frequencies in degenerate FWM, the present work aims to analyze the weaker components, i.e., the anti-Stokes (resp. mid-IR) radiation and cascaded satellites, and characterize their conversion efficiency and tunability. Here we report the production of tunable mid-infrared radiation around 3.3 $μ$m delivered by two-color femtosecond filaments in air combining $\sim 800$ nm fundamental and $\sim 1.3$ $μ$m seed waves. Although the Kerr response of air plays a key role in creating both visible and mid-IR radiations, we show that plasma nonlinearities also contribute by broadening and mixing the pump frequencies. Two experimental setups are exploited to focus, separately, on the production of FWM modes and cascaded satellites - called secondary radiations. A first filamentation setup employing different focal lengths for the two colors displays an ionization-induced broadening of the mid-IR radiation during the plasma stage. A second setup focusing the two pump components over equal propagation distances allows us to unveil the secondary radiations emerging at lower intensity levels when plasma occurs. We examine which player, among the plasma- or Kerr-induced FWM, is the most active in the conversion process. Numerical simulations based on a local-current model and a unidirectional solver highlight the role of the Kerr stage in amplifying the FWM radiations prior to the development of the weaker satellites in plasma regime. Their results, agreeing well with the experimental data, demonstrate that a broad visible emission is needed to trigger secondary radiations.

We investigate the geodesic structure and optical appearance of compact objects with primary scalar hair in shift- and parity-symmetric beyond Horndeski gravity. The analytic solution considered here depends on a theory parameter and a dimensionless mass parameter \cite{Bakopoulos:2023sdm}. For a fixed theory parameter, varying the mass traces a family of static spacetimes that can interpolate between timelike naked singularities, regular solitons, regular black holes, Reissner-Nordström-like black holes, multi-horizon black holes, and Schwarzschild-like black holes. We classify these branches by their horizon structure and analyze null and timelike geodesics, focusing on light rings, innermost stable circular orbits, and static spheres. We then compute thin-disk optical images by ray tracing. We find that the number of horizons is not directly encoded in the image: horizonless objects can show shadow-like central depressions, while multi-horizon black holes can closely resemble single-horizon black holes when their exterior light ring and disk structures are similar. Thus, the optical appearance is governed mainly by the photon potential and the disk inner edge, with the deeper horizon structure leaving only an indirect imprint. Quantitative radial-profile diagnostics confirm that the degeneracy is mainly morphological: the profiles differ at fixed impact parameter, but become much closer after rescaling by the critical impact parameter. These results provide a concrete example of how distinct compact object branches in beyond Horndeski gravity can share similar observational signatures.

We present and show how to implement a non-trivial all-to-all communication algorithm for arbitrary $d$-dimensional tori effectively in MPI. Given a factorization of the number of processes $p$ into $d$ factors that can be mapped onto a $d$-dimensional torus, we first utilize a Cartesian communicator to split a given $p$-process MPI communicator into, for each MPI process, $d$ smaller communicators spanning each of the dimensions of the torus to which the process belongs, and cache these communicators in order to avoid expensive splitting at each all-to-all operation. The all-to-all operation itself is decomposed into a sequence of $d$ MPI_Alltoall operations on the dimension-wise communicators. The non-trivial data rearrangement before and after each MPI_Alltoall call is implicit only and effected by MPI derived datatypes. This makes the implementation of the algorithm formally \emph{zero-copy}, meaning that no explicit process-local reordering of data blocks ever has to be performed. In order to achieve this, the algorithm employs a double-buffering scheme with modest temporary buffer requirements. By choosing the factorization of $p$ and selecting appropriate implementations for the component MPI_Alltoall operations, the presented implementation gives ample opportunities for algorithm tuning and adaptation to the particular high-performance system. A few, select experimental results show competitive performance with native MPI_Alltoall implementations and illustrate problems that common MPI_Alltoall implementations may have.

Machine learning interatomic potentials (MLIPs) have transformed materials discovery by leveraging graph neural networks (GNNs) to predict material properties with near density functional theory (DFT) accuracy. While large-scale pretrained foundation models offer transferable baseline representations, they frequently struggle to generalise to out-of-distribution (OOD) target systems -- a common challenge in modelling complex or chemically diverse materials. Fine-tuning is the standard remedy, but the high cost of generating DFT-labelled configurations confines adaptation to data-scarce regimes, where over-parameterised GNNs amplify overfitting and degrade target-domain performance. To address this, we propose a prototype-based alignment approach for data-efficient fine-tuning of MLIPs. Our method identifies local structural similarities between the source and target domains by grouping atoms with analogous chemical environments based on their latent representations. Each target-domain atom's energy contribution is aligned to its source-domain prototype, introducing an inductive bias that anchors fine-tuned representations to the pretrained structure, encouraging effective reuse of learned interactions and improving generalisation without restrictive assumptions on the target chemistry. We evaluate our method on the rMD17 benchmark using equivariant MACE and invariant SchNet across varying data budgets, and extend evaluation to the MACE-OFF foundation models on the SPICE dataset. Our approach consistently improves predictive accuracy in the low-data regime, reducing energy MAE by up to 18% over standard fine-tuning baselines.

Understanding pedestrian dynamics is critical for mitigating crowd-related risks and improving public safety. In this work, we propose a data-driven mesoscopic modeling framework that combines the kinetic theory of active particles with data assimilation techniques. The framework uses an ensemble Kalman filter to sequentially estimate the time-dependent spatial distribution of pedestrians and model parameters by fusing observations with the mesoscopic forward model state. Through a series of twin experiments, we show that the panic factor -- a key behavioral parameter -- is identifiable within this framework. We also evaluate the robustness of the approach by assimilating synthetic observations generated by an agent-based model (ABM). This setup introduces structural model error because the ABM is governed by microscopic rules that differ fundamentally from the mesoscopic kinetic equations. Despite this discrepancy, the ensemble Kalman filter, through the observation-based innovation term, successfully drives the kinetic model to track the observed pedestrian density while simultaneously recovering the panic factor. In this framework, observations act as a physical constraint on the evolution of the kinetic model. Crowd-dynamics models, including ABMs and kinetic models, often rely on phenomenological terms to describe social interactions, with parameters that are highly uncertain. Our findings indicate that in such systems, free-running simulations inevitably may diverge from the true state, whereas an online data-driven approach effectively constrains the system's trajectory to its underlying dynamical manifold.

Tailoring microscopic details to tune bulk rheology is a key paradigm in soft matter physics, yet the vast parameter space associated with constituent interactions precludes a fully systematic approach. To address this, we have designed a synergistic strategy to explore the parameter space that comprises simulations, experimental rheology, and machine learning. As a case study, we choose DNA-based self-assembled fluids whose viscoelastic response can be fine-tuned by manipulating the base sequencing of the constituent nucleic acid nanostars. We use coarse-grained simulations, benchmarked against experimental data, to obtain the rheology of the DNA fluids, which feeds forward to a framework of Gaussian Process Regression and active learning. The latter is then used to explore the rheological design space with high predictive precision. The pipeline is designed to be deployed iteratively for the rational design and accelerated discovery of generic soft matter suspensions.

Compiling arbitrary-connectivity NISQ circuits onto monolithic single-zone neutral-atom devices is constrained by a finite interaction range and a minimum separation between simultaneously addressable sites. Under the minimum-separation constraint, the SWAP-only configuration of our pipeline does not return a schedule within a practical time budget on a range of circuits, including circuits as small as nine qubits. We address this with hub traps, a small number of dynamically placed empty traps that serve as transit waypoints, together with a per-gate rule that chooses between SWAP-based routing and hub-mediated shuttling. We evaluate the compiler on seventeen benchmarks using analytic estimates of execution time and a per-layer fidelity proxy, comparing against a placement-matched baseline and against ablations of our own pipeline. Hub traps make these otherwise-unsolved circuits compile in seconds to minutes and remove SWAP gates entirely on every completed circuit, so their role is to enable routing rather than only to optimize fidelity. The benefit is concentrated on routing-dominated circuits and is absent on routing-free ones, which we separate by the structure of the interaction graph. On the most routing-dominated circuit the fidelity proxy improves by up to three orders of magnitude over the placement-matched baseline. The gain comes primarily from eliminating SWAP overhead, as the absolute fidelities there remain low.

We consider $N\times N$ matrices $X$ with independent, identically distributed entries, and prove that the sequence of measures $\frac{ | \det (X-z)|^γ}{\mathbb{E}[ | \det (X-z)|^γ]}$ converge to the Gaussian Multiplicative Chaos in the full subcritical regime $γ\in (0, 2 \sqrt{2})$ as $N \to \infty$. Our result holds for both symmetry classes and in particular is new even for real Ginibre matrices, and is the first such convergence for any non-invariant ensemble of random matrices. We also establish the asymptotics for the $K$-point function of $| \det (X-z)|$ at any collection of mesoscopically separated points $z_i$. Our methods are analytic and probabilistic in nature, relying in part on the dynamical approach based on Dyson Brownian motion.

This paper considers how to classify the effects of interventions in causal models for outcomes and exposures observed over time. First, we demonstrate the limitations of the most common uses of potential outcomes and causal directed acyclic graphs for capturing all possible interventions in a time varying framework, particularly in problems where the key question concerns interventions to maintain or change equilibrium behaviour. Second, we adopt a system and state based approach rather than a measurement-based approach to identify the causal parameters. In particular, we discuss how assumptions about the system's equilibrium and the effects of interventions on that equilibrium can allow for more specific causal interpretations and clarify the goals of design and analysis. Third, we show how the ability to identify the the causal parameters of a time varying system depends on the selection of timepoints for measuring the system's states. We address this by proposing a novel version of the null effect, which is designed to distinguish between transient and lasting causal effects.

The $k$-local Hamiltonian problem is a central model for quantum many-body systems and Hamiltonian complexity. Semidefinite programming and noncommutative sum-of-squares hierarchies provide systematic certificates for ground-state energies, but existing finite-convergence results give no quantitative guarantee on the accuracy of the low hierarchy levels accessible in computation. We prove explicit finite-level convergence rates for these hierarchies in the Pauli setting. For $k$-local Hamiltonians whose Pauli expansion contains only even-weight terms, we show that both the NPA-type lower-bound hierarchy and the upper-bound hierarchy on the spectral minimum have error at most $C(k)ξ^{n,4}_{d+1}/n$, where $ξ^{n,4}_{d+1}$ is the smallest root of a Krawtchouk polynomial and $C(k)$ is independent of the number of qubits $n$ and the hierarchy level $d$. General $k$-local Hamiltonians reduce to this even-weight case by adding one ancilla qubit while preserving the spectrum. The proof constructs almost-reproducing kernels for the Pauli algebra and relates their spectra to Krawtchouk polynomials, giving a noncommutative analogue of recent kernel-based convergence analyses for commutative polynomial optimization. These results provide the first quantitative finite-level accuracy guarantees for noncommutative semidefinite relaxations of Pauli Hamiltonians.

We extend the ``Brownian bees'' model of Berestycki et al. (2021, 2022) to cooperative reproduction, $kA\to(k{+}1)A$, of a population of $N$ symmetric random walkers with removal, at each birth event, of the particle farthest from the origin. Working in the limit $N\to\infty$, we formulate a hydrodynamic free-boundary problem for this model. Using this formalism, we determine steady state population densities for all~$k$ and prove their linear stability for $k\le 2$ and instability for $k\ge 4$. In the marginal case $k=3$, there is a whole continuous family of steady states at a single, critical ratio of the reproduction and diffusion rates. Above criticality the population undergoes an asymptotically self-similar finite-time collapse to the origin. Below the criticality the population spreads diffusively, but the reproduction remains quantitatively relevant. For $k\ge 4$, the unstable steady state separates regimes of a finite-time collapse and a diffusive spreading. Here the collapse dynamics is asymptotically self-similar, and the population density exhibits a scale separation requiring a matched-asymptotic description. Our analytical predictions are confirmed by numerical solutions of the hydrodynamic free-boundary problem and by Monte Carlo simulations of the original microscopic model.

Biological, artificial, and physical systems dissipate energy to accurately transmit information. While tools of information theory have been used to characterize information-processing capabilities, how reliably this information is acquired along individual trajectories, and which aspects require a thermodynamic cost, is an open question. In this work, we focus on the stochastic predictability of an arbitrary Langevin dynamics, defined as the pointwise mutual information between the current and future states of a system. We show that the fluctuations of predictability obey a universal thermokinetic decomposition at short times, which reveals that information fluctuations are suppressed by energy dissipation and become stronger with increased dynamical activity. Remarkably, we find that the average predictability, i.e., the short-time mutual information, does not carry any dependence on the underlying thermodynamic and kinetic features. Thus, the role of dissipation at short times is not to enhance information, but to reduce its fluctuations. Such dissipative control is effective only when instantiated by nonlinear operations. Moreover, energy consumption governs short- and long-time precision in stochastic oscillators through structurally different mechanisms that can be independently tuned. Our decomposition offers a fundamental thermodynamic basis for understanding the reliability of information transmission in nonequilibrium systems, the constraints on precision in biological systems, and the design of energy-limited control strategies.

Retrieval Augmented Generation (RAG) improves the question answering capabilities of Large Language Models (LLMs) by incorporating external knowledge and has recently been extended to multimodal settings through Vision-Language Models (VLMs) that integrate visual and textual information. Despite these advances, generated answers can still be incorrect or misleading. Uncertainty Quantification (UQ) methods aim to estimate the reliability of model outputs, but most existing approaches are designed for text-only models and perform poorly in multimodal RAG scenarios. A key challenge is capturing uncertainty arising from multiple stages of the pipeline, including retrieval, visual understanding, and generation. In this work, we show that modeling uncertainty using multimodal and retrieval-aware probability signals improves estimation in multimodal RAG systems. We introduce LeMUQ, a Learnable Multimodal UQ method that analyzes token probabilities under input modifications, such as removing modalities or retrieved context. By encoding these signals as probability tokens and processing them with a finetuned model, our approach captures interactions between modalities and retrieval. Experiments across datasets, retrievers, and VLMs show consistent improvements over baseline and finetuned UQ methods. Our proposed LeMUQ increases the AUROC metric by 3.8% on average. Additionally, our method shows strong generalization performance across different retrieval setups and datasets with mixed results when transferring across different VLMs. Our findings highlight the importance of modeling multimodal uncertainty and provide a step toward more reliable and safer multimodal RAG systems. Code is available on GitHub.

Preload loss in bolted joints results in alterations of the stiffness, damping, and nonlinearity of the structure, but existing monitoring techniques for rail-vehicle systems are often not capable of combining controlled shaker tests and sensing of nonlinear features. This paper proposes a method for detecting bolt loosening using a vibro-acoustic technique, where the structure is subjected to controlled shaker tests to sense the nonlinear features. A triaxial accelerometer was attached to the demonstrator, a microphone was placed in close proximity, and one of the bolts was tested under 0%, 20%, 40%, and 80% preload conditions. Single-tone and frequency-modulated (FM) signals close to the main natural frequency of 130 Hz, which was identified using sine sweep and narrow-band excitation, were applied to the demonstrator. When the structure was subjected to 130 Hz single-tone excitation, the loose state of the bolt exhibited several additional high-frequency spectral peaks. FM excitation between 125 and 135 Hz further distinguished between the states. Harmonic band power ratios, normalized to the carrier, distinguished between the loose state and the 80% preload state, where the difference between the loose and 80% preload states was 17.5 dB for l = 2 and 36.5 dB for l = 6.

Hubble is still in prime observing condition for making transformative discoveries in UV astronomy. In this white paper we describe the science case for a deep (S/N>30) UV spectroscopic survey with HST/COS targeting approximately 20 QSOs at 0.5<z<1.5 at good resolution (20 km/s). This survey would capitalize on our current UV capability, produce a legacy dataset enabling community science in many areas of galactic and extragalactic research, and pioneer a path for future UV science with the Habitable Worlds Observatory. Such high-S/N spectra are largely missing from the MAST archives, and would be analogous to the deep Hubble imaging fields (HDF, UDF, Frontier Fields) that have been enormously successful and far-reaching in their science impact. This legacy dataset would enable frontier science programs in several areas, including (1) studies of the CGM and IGM at unparalleled sensitivity, covering a wide range of UV metal lines and reaching very low H I column densities of log N=12.6 and low metallicities near [Z/H]=-2, enabling precision studies of the chemical abundances, ionization, temperature, and baryon and metal budgets of the CGM and IGM; (2) diffuse gas in the Milky Way and Local Group, including high-velocity clouds and gas streams from satellite mergers; (3) AGN outflows, which would be probed in the rest-frame extreme ultraviolet (EUV), covering continuum-generation mechanisms and diagnostics of gas in accretion-disk outflows.