Multimode cavity-QED systems can be leveraged to explore a wide range of physical phenomena; however, a complex multimode environment makes systematic characterization of light-matter interactions challenging. Here we present a general measurement protocol, applicable to both atomic and synthetic cavity-QED systems, that enables the determination of coupling to individual photonic modes. The method leverages measurements of the AC-Stark and Kerr effects, along with known detuning dependencies, to eliminate the need for single-photon resolution, independent photon-number calibration, or insertion-loss calibration. We demonstrate the method using a superconducting transmon qubit coupled to a one-dimensional microwave resonator lattice. We validate the consistency of the extracted light-matter couplings $g$ determined at multiple qubit detunings, and from the self-Kerr and cross-Kerr shifts for three photon modes, which provide separate measurements of $g$ for each of the three modes.

The Weierstrass function is a classic example of a continuous nowhere differentiable function, defined as a sum of high-frequency complex exponentials. In this paper, we follow a suggestion of M.V. Berry and study the convergence properties of Berry's superoscillating approximation to the truncated Weierstrass function. We provide sharp, explicit error estimates for this approximation and we analyze the subtle convergence properties of the associated double limits.

Magnetohydrodynamic (MHD) seismology uses naturally occurring MHD waves to infer plasma properties that are otherwise hard to measure, especially magnetic field strength and topology, electric currents, fine structuring, transport coefficients, and energy release. Across the solar atmosphere, heliosphere, and planetary magnetospheres, multi-wavelength remote sensing and in-situ observations of waves provide powerful diagnostics that can address major open problems including chromospheric and coronal heating, flare and eruption physics, solar wind acceleration, and space weather impacts. This White Paper sets out the case for a coordinated UK programme that couples high precision observations with advanced theory and numerical modelling, modern time-frequency methods for non-stationary signals, and machine learning approaches for detection, classification, and parameter inference from rapidly growing multi-instrument datasets. It outlines priority needs such as robust mode identification, reliable density and temperature constraints, multi line-of-sight capability, and models that include partial ionisation and non-adiabatic/collisionless effects, alongside enabling instrumentation such as next-generation spectropolarimetry, integral field units, and radio facilities including the Square Kilometre Array. The paper highlights the UK's strong track record and infrastructure, and argues that sustained investment will amplify UK scientific return through international partnerships and mission involvement, delivering transformative plasma diagnostics and downstream benefits for space weather forecasting and related applications.

We present the first application of spectral nudging in a probabilistic ensemble forecasting framework, combining the physics-based ECMWF Integrated Forecasting System ensemble (IFS-ENS) with forecasts from the probabilistic machine-learned AIFS-ENS ensemble. Large scales of virtual temperature and vorticity are relaxed toward the machine-learned forecasts, while mesoscale structures remain governed by the physics-based model. This hybrid ensemble shows substantial improvements in large-scale forecast skill, with gains in predictive skill extended by up to two days in the tropics and by approximately half a day in the extra-tropics relative to IFS-ENS. Despite nudging being applied only to upper-air fields, improvements are also found in several near-surface parameters. Tropical cyclone track forecasts improve significantly, consistent with improved representation of the large-scale steering flow, without degrading storm intensity or ensemble spread. These results demonstrate that spectral nudging can be successfully extended to ensemble prediction and provide an attractive pathway for combining machine-learned and physics-based weather prediction systems.

This paper reports the first multi-channel joint analysis to identify the properties of the exotic charmonium-like state $T_{c\bar{c}}(4020)$ via the electron-positron annihilation process $e^{+}e^{-}\toπ^{+}T_{c\bar{c}}(4020)^{-}+c.c$. A partial wave analysis is performed simultaneously in three decay channels $T_{c\bar{c}}(4020)^{-}\to {D}^{*0}D^{*-}$, $π^{-}J/ψ$, and $π^{-}h_{c}$, based on data samples taken at $\sqrt{s}=4.395$ and $4.416\,\mathrm{GeV}$ with an integrated luminosity of $1598.9\,\mathrm{pb}^{-1}$ collected with the BESIII detector operating on the BEPCII collider. For the first time, the spin-parity of the $T_{c\bar{c}}(4020)^{-}$ is determined to be $J^{P}=1^{+}$ with a significance $11.7σ$. Pole positions are extracted on the Riemann sheets with three branch points in the complex energy plane. Furthermore, the relative branching fractions are obtained as $\mathcal{B}[T_{c\bar{c}}(4020)^{-}\toπ^{-}J/ψ]/\mathcal{B}[T_{c\bar{c}}(4020)^{-}\to{D}^{*0}D^{*-}]=(3.6\pm0.6\pm1.6)\times10^{-3}$ and $\mathcal{B}[T_{c\bar{c}}(4020)^{-}\toπ^{-}h_{c}]/\mathcal{B}[T_{c\bar{c}}(4020)^{-}\to{D}^{*0}D^{*-}]=(8.9\pm1.3\pm2.3)\times10^{-2}$, where the first uncertainties are statistical, and the second are systematic.

This paper develops a nonlinear theoretical framework to analyze the dynamics of public expenditure reallocation in Uruguay. Motivated by recent debates on fiscal reform and expenditure efficiency, the paper models fiscal adjustment as a dynamic process in which expenditure categories exhibit heterogeneous institutional rigidity and convex adjustment costs. Using the national budget for the 2026-2030 fiscal period as an institutional reference, the paper presents a calibrated illustration of the theoretical framework that captures key features of the structure of public spending, including transfers, the public wage bill, operating expenditures, and public investment. The calibration translates institutional characteristics of the budget into quantitative transition dynamics rather than estimating structural parameters econometrically. The framework allows the evaluation of short-, medium-, and long-run fiscal implications of alternative reform strategies, including administrative restructuring, pension reform, and the gradual reallocation of resources toward human capital and productivity-enhancing investment. In contrast to descriptive expenditure reviews based on static budget comparisons, the model explicitly incorporates nonlinear transition dynamics and institutional frictions. Simulations show that structural expenditure reforms generate significant transitional fiscal costs arising from overlapping institutional systems, labor adjustment frictions, and pension transition liabilities. As a result, fiscal reform produces a J-shaped expenditure trajectory in which total spending initially increases before gradually converging toward a more efficient long-run allocation. These findings highlight the importance of accounting for adjustment costs and transition dynamics when evaluating the feasibility and timing of structural fiscal reforms.

Adaptive sample size re-estimation, early stopping, and trial re-design at interim analyses can reduce expected sample sizes in randomised trials. Cluster randomised trials, in which groups of participants are randomly allocated to treatment status, may particularly benefit as they can be costly and their required sample sizes depend on one or more auxiliary parameters governing correlations within and between clusters, which are often estimated with high uncertainty. We adapt a combination test approach to the cluster trial setting allowing for early stopping for futility or efficacy and accounting for correlations between trial stages and other nuisance parameters. We consider design decisions for multi-dimensional sample sizes involving clusters, participants, and time and allowing for modifications to intervention roll-out patterns. We use a Pareto optimality approach to balance objectives relating to different components of the sample size and costs. We also examine the interim estimation of auxiliary parameters and trial re-design for efficiency. We illustrate the methods including examples of stepped-wedge trial re-design and a re-analysis of the large cluster randomised trial E-MOTIVE.

We review the Analogue Gravity description of a unidirectional water wave system, assuming no prior knowledge of General Relativity or differential geometry. In so doing, we generalize established results concerning an effective curved spacetime for surface waves on irrotational 2D flows, by including flows with constant shear. We show that such flows remain perfectly compatible with the existence of an effective curved spacetime and, in particular, of a metric description.

The paper deals with the second order regularity properties of the weak solutions $u\in W^{1,ϕ}(Ω, \real^n)$ } of systems of the form \begin{equation*}\label{equareg} -\dive A(x,\E u)=f, \end{equation*} in a bounded domain $Ω\subset\R^n$, $n>2$, where the operator $ A(x,P)$ is Lipschitz continuous with respect to the $x$-variable and satisfies growth conditions with respect to the second variable expressed through a Young function $Φ$. We prove the Sobolev regularity of a function of the symmetric gradient $\E u$ that takes into account the nonlinear growth of the operator $A(x,P)$, {assuming that the force term $f$ belongs to a suitable Orlicz-Sobolev space. {The main result is achieved through some uniform higher differentiability estimates for solutions to a class of approximating problems, constructed adding singular higher order perturbations to the system.

Parahoric group schemes are certain possibly non-reductive, smooth, affine integral models of reductive group schemes defined over a henselian discretely valued field $K$ whose residue field is perfect. We show that any such group scheme $\mathscr{P}$ becomes reductive, in a particular regard, after a (possibly wildly ramified) finite Galois extension $L/K$. More precisely, we prove that there exists a reductive integral model $\mathscr{G}$ of the base change $\mathscr{P}_L$ such that $\mathscr{P}$ can be recovered as the smoothening of the subgroup of Galois invariants of the Weil restriction of $\mathscr{G}$. Our work extends results of Balaji--Seshadri and Pappas--Rapoport from the tamely ramified and simply-connected semisimple setting. As an application, we establish a parahoric analogue of the Grothendieck--Serre conjecture in sufficiently good residue characteristics. Specifically, we confirm that generically trivial parahoric torsors are trivial whenever the generic reductive group is simply-connected. The proof proceeds by reducing the problem to a statement about a stacky reductive group over a stacky discrete valuation ring.

We prove that every sufficiently large odd integer can be expressed as a sum of one square and fourteen fifth powers, all of primes. In addition, we establish that every sufficiently large even integer can be written as a sum of one square, one biquadrate, and twelve fifth powers of primes.

Tissue fluidity regulates many critical biological processes, including embryonic development, wound healing, and cancer metastasis. In confluent epithelia, where cell packing fraction is effectively fixed, the prevailing paradigm postulates that transitions between solid-like jammed and fluid-like unjammed states are governed by a geometric cell shape index determined by the balance of cortical tension and intercellular adhesion. Here, we challenge this geometric framework by reporting a mode of fluidization in epithelial monolayers that is entirely shape-independent. We observe that reducing cell-cell adhesion triggers a substantial increase in fluidity, yet this occurs without any corresponding change in cell shape, cell density, substrate traction, or junctional line tension. This decoupling of shape and fluidity reveals that current vertex models, which treat adhesion solely as a contribution to interfacial tension, are incomplete. To reconcile these findings, we extend the theoretical framework to account for the dual nature of adhesion -- its thermodynamic role in setting interfacial adhesion energy at the cell-cell junctions and its kinetic role in generating viscous drag as cells slide past their neighbors. This generalized model quantitatively captures the experimental data, demonstrating that the interplay between adhesive energetics and dissipative friction is essential for a complete understanding of epithelial fluidity.

The acoustic signature of thermal spray processes is known to vary with changes in operating conditions, which also influence particle in-flight velocity and distribution. Building on this idea, the present work first develops an analytical model that links chamber and nozzle parameters to far-field acoustic levels using gas-dynamics relations and simplified acoustic power propagation. The model is then calibrated to reduce systematic error associated with neglected turbulence effects and to improve agreement across operating conditions. In addition, a numerical framework is implemented to complement the analytical model and to resolve supersonic jet flow and in-flight particle transport. The second part of the study uses unsteady compressible simulations with hybrid turbulence modeling such as Unsteady Reynolds-Averaged Navier-Stokes (URANS) and Delayed Detached Eddy Simulation (DDES) to capture the development of the shock-containing jet and the associated near-field pressure fluctuations. Far-field sound is predicted using the Ffowcs Williams-Hawkings acoustic analogy, while a Lagrangian approach tracks particles injected at the nozzle exit to quantify velocity evolution, radial spreading, and downstream flux distributions. The influence of operating conditions (e.g., chamber pressure and temperature) is assessed, and predictions are evaluated against published microphone spectra and particle flux measurements. Overall, the combined analytical and numerical approach captures how changes in nozzle operating conditions affect jet unsteadiness and mixing, leading to measurable shifts in acoustic level and spectral content. These results suggest that aeroacoustic signatures could be used as a non-intrusive pathway to monitor and potentially control thermal spray operating conditions.

We present VarP-GP, a new cost-efficient Bayesian emulator for expensive computational models with variable statistical precision. We focus on the interpretation of measurements of the quark-gluon plasma (QGP) generated in high-energy nuclear collisions, through comparison to numerical models using Bayesian Inference. Such inference calculations are computationally expensive and require surrogate model emulation, which is commonly implemented using Machine Learning (ML)--based Gaussian processes (GPs). Emulator training data are generated by Monte Carlo simulations whose numerical precision depends on the computational resources utilized; improved precision entails greater computational cost. This study utilizes JETSCAPE simulations of inclusive hadron and jet measurements in nuclear collisions at RHIC and the LHC. The VarP-GP emulator combines information from multiple simulation runs with varying precision across the model parameter space, taking advantage of the smoothness in that space of QCD-driven processes. Comparison to a traditional emulator approach shows a marked reduction in emulator uncertainty at fixed computational cost, indicating that knowledge of the overall contours of the parameter design space is more important for precise emulation than detailed information at a more limited number of design points. As an initial application of VarP-GP, a computationally-expensive model parameter sensitivity study of jet quenching data is reported. The VarP-GP emulator enables new multi-model and many-observable calibrations of QGP data and modeling, which would otherwise not be possible with achievable computing resources.

Motivated by quantum gravity effects suggested by string theory, we investigate gravitational configurations sourced by an effective energy density inspired by T-duality. This density naturally introduces a minimal length scale $l_0$ that acts as an ultraviolet regulator, allowing the description of nonsingular geometries within a classical framework. By employing it as the matter source in the Einstein equations, we construct static and spherically symmetric spacetimes that interpolate smoothly between regular black holes and traversable wormholes, providing a geometric realization of the black bounce scenario. We examine the curvature invariants and confirm the absence of curvature singularities throughout the spacetime. The conditions for the existence of event horizons are analyzed in detail, which allows us to determine the causal structure of the solution. A comprehensive study of the geodesic motion is performed for both massive and massless particles, revealing the presence of photon circular orbits and an innermost stable circular orbit for massive particles. Using observational data from the Event Horizon Telescope, we constrain the minimal length parameter through the black hole shadow radius, finding that for $l_0 \lesssim 1.15\, M_{\text{ADM}}$ our solution remains consistent with observations within the $2σ$ confidence level. The optical appearance of spacetime is further investigated by considering a thin accretion disk surrounding the black bounce. From the heat capacity, we analyze the thermodynamic stability of the solution and identify the presence of a phase transition. Finally, we examine the energy conditions and discuss which of them are violated by the effective fluid supporting this geometry.

Collaborative training across multiple institutions is becoming essential for building reliable medical image segmentation models. However, privacy regulations, data silos, and uneven data availability prevent hospitals from sharing raw scans or annotations, limiting the ability to train generalizable models. Latent-space collaboration frameworks such as privacy-segmentation framework (SF) offer a promising alternative, but such methods still face challenges in segmentation accuracy and vulnerability to latent inversion and membership-inference attacks. This work introduces a privacy-preserving collaborative medical image segmentation framework (PPCMI-SF) designed for heterogeneous medical datasets. The approach combines skip-connected autoencoders for images and masks with a keyed latent transform that applies client-specific orthogonal mixing and permutation to protect latent features before they are shared. A unified mapping network on the server-side performs multi-scale latent-to-latent translation, enabling segmentation inference without exposing raw data. Experiments on four datasets: PSFH ultrasound, ultrasound nerve segmentation, FUMPE CTA, and cardiac MRI show that the proposed PPCMI-SF consistently achieves high Dice scores and improved boundary accuracy, as reflected by lower 95th percentile Hausdorff distance (HD95) and average symmetric surface distance (ASD) compared to the current state-of-the-art and performs competitively with privacy-agnostic baselines. Privacy tests confirm strong resistance to inversion and membership attacks, and the overall system achieves real-time inference with low communication overhead. These results demonstrate that accurate and efficient medical image segmentation can be achieved without compromising data privacy in multi-institution settings.

Intracellular delivery of biomolecules remains a critical challenge in both basic cell biology and translational therapeutics. We introduce Programmable Acoustic Standing-wave Transfection (PAST), a microfluidic tool that leverages dynamically programmable ultrasonic fields to transiently permeabilize cell membranes and enhance biomolecular transport within cell clusters. By generating programmable acoustic potential landscapes, PAST drives cells through cycles of hydrodynamic and acoustic stresses that induce reversible pore formation, enabling diffusion-based delivery without chemical carriers or contrast agents. Experimental studies demonstrate controlled influx and efflux dynamics across multiple biomolecular species, with transport rates tunable via acoustic power, frequency modulation, and duty cycles. Theoretical scaling and numerical simulations reveal that membrane tension, pore energetics, and acoustic field distributions collectively govern transmembrane transport of biomolecules. Post-treatment assays confirm high cellular viability and sustained proliferation, underscoring the biocompatibility of the method. Remarkably, effective diffusivity estimates derived from model predictions closely match experimental transport timescales. Together, these findings establish PAST as a programmable, high-throughput, and non-invasive intracellular delivery platform, offering new opportunities for precision drug screening, gene editing, and mechanistic exploration of cellular membrane biophysics.

Confounding pathology with normal anatomical variation remains a significant challenge in unsupervised medical-image anomaly detection, resulting in numerous false positives. To enhance integration of healthy variation, we augment the latent representation of a CNN autoencoder with contextual similarities within a normal cohort through batch-wise hypergraph estimation and a shared-weights graph convolution layer, producing a population-aware embedding. On a heterogeneous brain-tumor dataset of 2D MRI scans, the method improves separability between healthy and pathological samples, achieving an AUC-ROC of 0.90 (95% CI 0.84-0.95, 5.7% absolute gain), and a 16% absolute improvement in average precision (0.78 AP, 95% CI 0.66-0.89), thereby lowering false-positive rates. Moreover, both anomaly detection and downstream tumor versus no-tumor classification performance improve with the size of the mini-batch context captured in the augmented representation, suggesting a tunable lever for integrating healthy variation.

Sampling molecular conformations from the Boltzmann distribution is essential for computational chemistry, but iterative diffusion methods are prohibitively slow. Drifting Models offer one-step generation, yet their equilibrium matches the \emph{training} distribution, which may deviate from the true Boltzmann distribution due to sampling bias. We introduce Drifting Models to molecular conformation generation for the first time, establishing a theoretical bridge via the \emph{Drifting Score Identity}: for Gaussian kernels, the drifting field's attraction equals a kernel-weighted average of \emph{any} distribution's score function. Substituting molecular force labels -- which directly encode the Boltzmann score -- yields the \emph{Drifting Force Identity} and decomposes the field into standard drift plus a Boltzmann correction. We further discover a striking phenomenon unique to molecular systems: force incorporation's effectiveness \emph{reverses across representations}. In coordinate space, Force-Interpolated Drifting (FI) dominates by blending physical force directions with data displacements. In distance feature space, Force-Aligned Kernel (FK) achieves superior accuracy by modifying only kernel weights, thereby preserving the manifold of geometrically valid molecules. On MD17 Ethanol, both approaches achieve one-step generation with over 1000x speedup relative to recent score-matching methods with Boltzmann guiding, providing more than million-fold acceleration over traditional molecular dynamics, while ensuring perfect structural validity and distributional accuracy rivaling multi-step methods.

Chemical reaction engineering is key to industrial might and sustainable chemistry. This will be enabled using smart, efficient catalysts or catalysis ecosystems. This is possible with advanced artificial intelligence and machine learning (AI/ML) workflows that need to be employed as agentic AI projects. The fundamentals of catalysis need to be emphasized. A strong focus on catalyst design, mechanistic studies, reaction engineering, and scale-up must use ML-driven workflows, along with high-throughput experimentation (HTE) and an autonomous, self-driving laboratory (SDL). Laboratory experience and data-driven approaches are valuable when working together to accelerate this development. Parametrize and create a virtuous circle for data-driven discovery across heterogeneous, homogeneous, and biocatalysts to enable utility in many chemical process industries as agentic AI tasks. This article builds the case for discovery science in catalysis and continuous improvement in chemical reaction engineering with this new ecosystem.

We introduce a data-driven framework for approximating the convex set of $N$-representable two-electron reduced density matrices (2-RDMs). Traditional approaches characterize this set through linear matrix inequalities that define its supporting hyperplanes. Here, we instead learn a vertex-based approximation to its boundary from molecular data and use this information to improve the set defined by low-order positivity constraints, without explicitly constructing higher-order conditions. The resulting semidefinite machine learning approach -- combining an input convex neural network with semidefinite programming -- drives a direct variational calculation of the 2-RDM with enhanced accuracy at computational cost comparable to two-positivity calculations. Applications to the potential energy curves of ${\rm C}_2^{2-}$, ${\rm N}_2$, and ${\rm O}_2^{2+}$ demonstrate these systematic improvements as well as close agreement with complete active space configuration interaction results. Overall, semidefinite machine learning interweaves data-driven boundary information with semidefinite positivity constraints to yield more accurate energies and 2-RDMs without explicit higher-order positivity conditions.

Predicting the occurrence of transitions in the qualitative dynamics of many natural systems is crucial, yet it remains a challenging task. Generic early warning signals like variance and lag-1 autocorrelation identify critical slowing down near tipping points but lack practical thresholds for predicting imminent transitions. More recent studies found that the dynamical eigenvalue is rooted in the framework of empirical dynamical modeling and then estimates the dominant eigenvalue of a system from time series, providing a threshold ($|$DEV$|$ = 1) to predict bifurcations and classify their types. However, its application requires careful calibration of the hyperparameters and focuses on reconstructing system dynamics directly from data. Here, we employ Ornstein-Uhlenbeck process to derive analytic approximations for the lag-$τ$ autocorrelation function prior to period-doubling bifurcation thereby estimating the dominant eigenvalue of dynamical systems, named dominant eigenvalue extracted from autocorrelation (DE-AC), and revealing its dynamic behaviour when approaching a period-doubling bifurcation. Theoretically, dominant eigenvalue tends to $-1$ when the system approaches a period-doubling bifurcation. In particular, we evaluated DE-AC on simulation data from cardiac alternans model and on experimental data from chick heart aggregates undergoing a period-doubling bifurcation. DE-AC reliably detected the beginning of the cardiac arrhythmia (period-doubling bifurcation) in most cases. Moreover, it demonstrated superior sensitivity and specificity as an early warning signal compared to the three widely used indicators -- variance, lag-1 autocorrelation, and dynamical eigenvalue. Our theoretical and empirical results suggest that DE-AC represents a quantitative measure for predicting the onset of potentially dangerous alternating rhythms in the heart.

We conducted a scoping review to map the rapidly evolving landscape of wearable and ambient sensing technologies for monitoring people with dementia across home and institutional settings. We analyzed empirical sensing studies (2015-2025) to identify and inform future technical and human-centered design requirements. Five key implementation principles emerge: (1) human-centered design involving all stakeholders to augment rather than replace caregivers; (2) personalized, adaptable solutions that support autonomy across settings and severity levels instead of standardized approaches; (3) integration with existing workflows with adequate training and support; (4) proactive privacy and consent considerations, especially for ambient monitoring of residents and caregivers; and (5) cost-effective, ethical, equitable, scalable solutions with quantifiable outcomes. This paper identifies gaps, trends and opportunities for developing sensing systems that address the complex challenges, while enhancing automation and autonomy, in dementia care.

Tool calling allows large language models (LLMs) to interact with external systems like APIs, enabling applications in customer support, data analysis, and dynamic content generation. While recent benchmarks have advanced tool-use research, they suffer from key limitations, including reliance on simulated or restricted APIs, limited reproducibility, and a lack of cultural and geographic diversity. To address these gaps, we introduce International Tool Calling (ITC), a large-scale, multilingual benchmark designed for realistic, globally distributed tool-calling scenarios. ITC includes 3,571 real APIs and 17,540 tool calling tasks across 20 categories and 40 countries. Experiments reveal substantial performance gaps between open- and closed-source LLMs, while fine-tuning on ITC yields significant improvements, particularly for non-English queries, enhancing cross-lingual generalization, reasoning consistency, and robustness to out-of-domain tools. ITC provides a valuable benchmark for advancing LLM robustness and performance in complex, multi-tool, and international scenarios. Dataset: https://anonymous.4open.science/r/International-Tool-Calling-ITC-dataset-FAF4/.

This study focuses on the roadmapping of biometric technologies onto personalized Augmentative and Alternative Communication (AAC), a branch of assistive technologies for people with communication disabilities. This technology roadmapping revolves around the proposed notions of an AAC biometric register and biometric-enabled reconfigurable AAC channels. The biometric register is referred to as a tool for acquiring and processing physiological and behavioural traits that are essential for augmentative and alternative communication. It links biometric traits, such as gestures, to intermediate traits, such as synthesized speech, for customizable communication channels. The proposed methodology is used to assess the gaps between the social and practical demands, such as assisting people with communication disabilities in the contemporary semi-automated border control, and the emerging advances in AI, such as advanced video and speech processing. We provide two case studies of the AAC that rely on hand gesture recognition and sign language word recognition, and conclude that the current accuracy of those AI technologies does not meet the practical requirements. The proposed roadmapping provides recommendations for further improvement to close these gaps.

The growing complexity and information content of data, together with the need to understand both the complex structures, relationships, and phenomena present in these data spaces, compounded with the emerging need to understand the results produced by AI tools used to analyze the data, requires development of novel, effective data visualization tools. Much of the growing complexity is reflected in the increasing dimensionality of data spaces, where extended reality (XR) naturally emerges as a candidate to help extend our capability for higher dimensional understanding. However, humans often understand lower dimensionality representations more effectively. Still, XR offers an opportunity for a seamless integration of simulated traditional data displays within the 3-dimensional virtual data spaces, leading to more intuitive and more effective data analytics. In this paper we present an overview of the benefits of seamlessly integrated 2-dimensional and 3-dimensional interactive visual representations embedded in XR spaces, and present three case studies that leverage these approaches for more efficient data analytics.

In this paper we develop a data-driven approach for marking nonblocking supervisory control of discrete-event systems (DES). We consider a setup in which models of DES to be controlled are unknown, but a set of data concerning the behaviors of DES is available. We ask the question: Under what conditions of the available data set can a valid marking noblocking supervisor be designed for the unknown DES to satisfy a given specification? Answering this question, we identify and formalize a novel concept called marking data-informativity. Moreover, we design an algorithm for the verification of this concept. Next, if the data set fails to be marking informative, we propose two related new concepts of restricted marking data-informativity and marking informatizability. Finally, we develop an algorithm to compute the largest subset of control specification for which the data set is least restricted marking informative.

Correlated noise is a critical failure mode in quantum error correction (QEC), as temporal memory and spatial structure concentrate faults into error bursts that undermine standard threshold assumptions. Yet, a fundamental gap persists between the stochastic Pauli models ubiquitous in QEC and the microscopic, non-Markovian descriptions of physical device dynamics. We close this gap by introducing Spatiotemporal Pauli Processes (SPPs). By applying a multi-time Pauli twirl, operationally realised by Pauli-frame randomisation, to a general process tensor, we map arbitrary multi-time, non-Markovian dynamics to a multi-time Pauli process. This process is represented by a process-separable comb, or equivalently, a well-defined joint probability distribution over Pauli trajectories in spacetime. We show that SPPs inherit efficient tensor network representations whose bond dimensions are bounded by the environment's Liouville-space dimension. To interpret these structures, we develop transfer operator diagnostics linking spectra to correlation decay, and exact hidden Markov representations for suitable classes of SPPs. We demonstrate the framework via surface code memory and stability simulations of up to distance $19$ for (i) a temporally correlated "storm'' model that tunes correlation length at fixed marginal error rates, and (ii) a genuinely spatiotemporal 2D quantum cellular automaton bath that maps exactly to a nonlinear probabilistic cellular automaton under twirling. Tuning coherent bath interactions drives the system into a pseudo-critical regime, exhibiting critical slowing down and macroscopic error avalanches that cause a complete breakdown of surface code distance scaling. Together, these results justify SPPs as an operationally grounded, scalable toolkit for modelling, diagnosing, and benchmarking correlated noise in QEC.

We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in the long-time limit, by a non-normalizable infinite invariant density. Extreme events in such systems emerge in a joint limit where the observation time $t$ is long and the number of variables $N$ is large. We show that the resulting extreme value statistics are controlled by the return exponent $α$ and the infinite invariant measure, and therefore depart from the classical Fréchet, Gumbel, and Weibull universality classes. We illustrate the theory for weakly chaotic intermittent maps, overdamped diffusion in an asymptotically flat potential, and a stochastic model of sub-recoil laser cooling, and show how measurements of extremes can be used to infer the infinite-density structure.

We investigate the fate and robustness of topological strong zero modes (SZMs) in random Ising-Majorana chains using the SZM fidelity, ${\cal F}_{\rm SZM}$, as a many-body diagnostic that quantifies how accurately SZM operators map the {\it entire} spectrum between opposite parity sectors. In clean systems, ${\cal F}_{\rm SZM}=1$ in the topological phase, vanishes in the trivial regime, and takes the universal value $\sqrt{8}/π$ at the $(1+1)$D Ising critical point. Here we study how quenched disorder modifies this picture across the infinite-randomness fixed point (IRFP) governing the criticality of the random chain. In both microcanonical and canonical ensembles, SZMs persist throughout the topological phase, including the gapless Griffiths regime, with fidelities converging exponentially to unity. At the IRFP, however, the fidelity distributions become ensemble dependent: the microcanonical ensemble displays bimodal peaks at $\{0.5,1\}$, while the canonical ensemble develops a triple-peak structure at $\{0,0.5,1\}$ with power-law singularities. Our results establish ${\cal F}_{\rm SZM}$ as a robust probe of localization-protected topological order and uncover distinctive topological features of infinite-randomness criticality. Unlike the clean Ising CFT, where the finite critical value arises from a cancellation of power laws, the IRFP seems to exhibit an intrinsically stronger topological character. The edge-selective structure of the critical distributions may suggest a boundary manifestation of the average Kramers-Wannier duality symmetry at the IRFP.