Accurate beam prediction is essential for mitigating signalling overhead and latency in integrated sensing and communication-enabled massive multi-input multi-output systems. With the aid of multimodal learning, the prediction accuracy can be enhanced by leveraging the complementary information from other existing sensors, but the practical deployment is often constrained by the high cost of acquiring semantically aligned multimodal datasets. This paper proposes a variational-inference-based multimodal framework that decouples the optimization problem into modular feature extraction and cross-modal semantic alignment. Specifically, we develop a two-stage training strategy where the model utilises abundant unimodal data for representation learning before performing refined alignment on limited multimodal samples. This design enhances data efficiency and ensures robust feature fusion under sensing uncertainties. Experimental results on the DeepSense6G dataset demonstrate that the proposed framework achieves competitive beam prediction accuracy and maintains high reliability, while only requiring 20% of the multimodal training data compared to conventional end-to-end benchmarks.

We propose a framework designed to tackle a multi-objective optimization challenge related to the placement of applications in fog computing, employing a deep reinforcement learning (DRL) approach. Unlike other optimization techniques, such as integer linear programming or genetic algorithms, DRL models are applied in real time to solve similar problem situations after training. Our model comprises a learning process featuring a graph neural network and two actor-critics, providing a holistic perspective on the priorities concerning interconnected services that constitute an application. The learning model incorporates the relationships between services as a crucial factor in placement decisions: Services with higher dependencies take precedence in location selection. Our experimental investigation involves illustrative cases where we compare our results with baseline strategies and genetic algorithms. We observed a comparable Pareto set with negligible execution times, measured in the order of milliseconds, in contrast to the hours required by alternative approaches.

Many complex organic molecules (COMs) in star-forming regions are believed to form on dust grains. We thus expect both the reduced metallicity and dust-to-gas ratio in the outer Galaxy to have an impact on the chemical composition of these regions. We investigate if certain COMs are more sensitive than others to metallicity by measuring the chemical composition of hot cores in the outer Galaxy. We used NOEMA to perform an imaging spectral line survey of G135.27+2.79, located at a galactocentric distance of 13.1 kpc. We derived the rotational temperatures and column densities of the detected molecules while assuming local thermodynamic equilibrium and compared the chemical composition of G135.27+2.79 to other sources and to the predictions of the three-phase astrochemical code MAGICKAL. G135.27+2.79 hosts three continuum cores, labeled MM1, MM2, and MM3. Most species in MM1 trace a hot, compact region, confirming MM1 as a hot core. The chemical composition of MM1 correlates rather well with that of the inner and outer Galaxy hot cores G31.41+0.31 and WB89-789 SMM1, but its molecular abundances relative to methanol lie in between, which may reflect the influence of metallicity on COM formation. The model results agree reasonably well, though with a few notable exceptions, with the COM abundances of MM1 relative to methanol and with the abundance ratios between MM1 and G31.41+0.31. Sensitivity to the reduced metallicity and dust-to-gas ratio varies between molecules, with carbon chains and nitriles most negatively affected. The lower dust-to-gas ratio leads to slower adsorption under low-metallicity conditions so that more carbon is locked up into CO in the gas. Slow adsorption means that CO is hydrogenated more efficiently on grains, enhancing CO-related COM abundances above expectations. These results demonstrate that metallicity has a significant impact on the formation of COMs.

The statistical analysis of marked point processes requires disentangling complex spatial arrangements from attribute-dependent interactions. While classical summary statistics are effective for second-order dependencies, they frequently fail to capture higher-order topological structures and non-linear interactions between marks and space. In this work, we propose a novel multiscale topological inference framework for marked point processes by integrating mark-weighted filtrations with Euler Characteristic envelopes. We redefine the underlying metric space using an exponential mark-weighted distance, which modulates connectivity based on attribute similarity, effectively accelerating the merger of connected components among homophilic neighbors. To ensure rigorous statistical inference, we apply non-parametric global envelope tests to the resulting Euler Characteristic Curves, allowing for formal hypothesis testing against the null model of random labeling. Furthermore, we introduce a local decomposition of the topological signal via Z-scores at the critical filtration scale to identify and localize structural hubs and topological barriers. Systematic simulations across various scenarios demonstrate the framework's high specificity and sensitivity to attribute-space dependencies while remaining robust against purely geometric effects. This methodology provides a comprehensive and interpretable toolkit for identifying, quantifying, and localizing complex structural dependencies in marked spatial data, bridging the gap between topological data analysis and classical point process statistics.

Hydrogen (H2) is a promising carbon-neutral energy carrier. However, its deployment is limited by the lack of lightweight, reversible storage media that operate under practical conditions. Here, we establish nitrogen-doped graphdiyne (N-GDY) as a programmable two-dimensional platform for stabilizing dispersed light-metal dopants and enabling high-capacity physisorption of molecular H2. The computational package involves density functional theory (DFT) combined with ab initio molecular dynamics (AIMD) and Langmuir-based statistical thermodynamic modeling. The results revealed that N-sites of N-GDY bind up to five Li, Na, K, and Ca atoms per primitive cell with binding energies of -2.27, -1.57, -1.80, and -2.13 eV, respectively, exceeding their respective bulk cohesive energies. AIMD simulations at 400 K further confirm the structural robustness of the decorated frameworks and the absence of metal aggregation. The polarised metal centres activate reversible H2 adsorption through electrostatic and dispersion interactions, with average adsorption energies falling within the optimal window (-0.15 to -0.35 eV per H2). Sequential adsorption analysis reveals uptake of up to 25 H2 molecules per primitive cell, achieving intrinsic gravimetric capacities of 13.08, 10.82, 9.23, and 9.15 wt% for Li-, Na-, K-, and Ca-functionalized systems, respectively. Thermodynamic analysis indicates favorable adsorption-desorption behavior under near-ambient conditions, with Li- and Ca-functionalized systems exceeding the 6.5 wt% U.S. Department of Energy's ultimate system-level target when considering intrinsic material capacity. These results identify N-GDY as a chemically tunable scaffold for dispersing lightweight metals and provide a mechanistic design strategy for achieving high-capacity, reversible hydrogen storage in porous two-dimensional materials.

Positive maps that are not decomposable are a key resource in entanglement theory because they can detect bound entangled states, yet systematic methods for constructing them remain limited. We introduce an optimization framework based on differentiable semidefinite programming (SDP) for generating positive non-decomposable maps under flexible structural constraints on their Choi matrices. The method combines SDP-based certificates of non-decomposability and positivity with gradient-based optimization, enabling a systematic search over maps with different input and output dimensions. Within this framework, we generate previously unknown numerical examples, identify a parametrized family of maps arising from masked Choi matrices, and construct real non-decomposable maps. We further show that the same approach can be adapted to explore open questions in quantum information theory, including the PPT square conjecture and recently proposed eigenvalue bounds for 2-positive trace-preserving maps.

This paper presents a distributionally robust model predictive control (DRMPC) framework for the optimal Virtual Power Plant (VPP) operation under electricity price uncertainty. A unified VPP model is formulated that captures the interaction between buildings, battery storage, and renewable generation, all influenced by exogenous weather and market signals. The proposed approach integrates data-driven forecasting with quantile-based uncertainty quantification to construct time-varying Wasserstein ambiguity sets that adapt to forecast dispersion and distributional shifts. This yields a tractable DR-MPC formulation that incorporates predictive distribution information directly into real-time decision making. The method is evaluated using real weather and market data from a Nordic case study across two seasonal scenarios. The results show that DR-MPC improves economic performance relative to standard forecast-based MPC when the ambiguity radius is chosen appropriately, with consistent gains of up to 0.8% for small radii across both seasonal scenarios. Larger radii become overly conservative and reduce revenue, underscoring the importance of proper radius selection. These findings demonstrate the practical value of distributionally robust optimization for uncertainty-aware VPP operation.

We study scattering for continuous-time quantum walks on finite graphs with two attached leads. We derive explicit formulae for the two-terminal scattering matrix in terms of characteristic polynomials of the finite graph and its vertex-deleted subgraphs. For real-weighted two-terminal graphs, we then introduce three real quantities, $μ_1$, $μ_2$, and $ν$, which are each additive under parallel composition of graphs. In these variables, perfect transmission at fixed momentum is characterized by the condition $μ_1=μ_2$ together with a hyperbola in the corresponding $(μ,ν)$-plane, whose points determine the transmission phase. This turns the search for graphs with prescribed transmission properties into a geometric vector-sum problem for smaller building blocks.

We investigate localization and spectral topology in a non Hermitian quasiperiodic Su Schrieffer Heeger lattice with Rashba spin orbit coupling and spin-dependent hopping. By analyzing the inverse participation ratio, complex energy spectrum, and spectral winding numbers, we demonstrate the emergence of a re-entrant transition from extended to localized and back to extended phases as the non-Hermitian parameter increases. The localization transition is accompanied by a simultaneous real-complex-real spectral transition in the complex-energy plane. In the absence of spin dependent hopping, the spectrum forms two nearly spin-degenerate loops characterized by winding numbers w = 2. Upon introducing finite spin-dependent hopping, each loop splits into two independent spin-resolved spectral branches, resulting in four disconnected spectral contours carrying distinct winding sectors. Our results reveal a direct correspondence between localization, spectral topology, and spin-resolved spectral splitting in non-Hermitian quasiperiodic systems.

The electronic structure of Samarium (Sm) was calculated using the density functional theory combined with the single-site dynamical mean-field theory. In this work, we investigated the electronic properties of α, \b{eta} and γ phases at ambient pressure, including the band structures, density of states, self-energy functions and valence state histograms. Our results agree with the experimental data.The calculation shows that the 4f electrons in all these phases are well localized, the Kondo peaks are suppressed and the hybridization between the 4f electrons and conduction electrons are quite weak. Our results also show the strong correlation effect is significant in Sm metal.

Real-time decoding plays a crucial role in practical fault-tolerant quantum computing. Window decoding, in which the decoding problem is divided into windows, is a promising approach. While reducing the window size is desirable for faster decoding, each window contains a buffer region whose size must typically be at least the code distance to avoid degrading the logical error rate, which limits how much the window can shrink. In this paper, we propose an adaptive decoding scheme in which window decoding is first performed with a small buffer size and a decoding confidence (soft information) is computed; if the confidence is low, the buffer size is enlarged and decoding is redone. This approach reduces the average decoding time, since most shots are decoded with a small buffer. A central challenge in realizing this scheme is that existing forms of soft information are not directly applicable to window decoding, especially with a small buffer. We address this challenge by introducing a new form of soft information, the spatiotemporal complementary gap, specifically designed for this setting. Numerical simulations demonstrate that the proposed scheme reduces the average buffer size by approximately 40% while maintaining the logical error rate.

Capacitive touchscreens in modern smartphones introduce severe side-channel vulnerabilities. However, existing attacks often require restrictive conditions or invasive measurements. This paper presents TESLA, a novel, contactless electromagnetic (EM) side-channel attack that exploits inherent EM emanations during touchscreen scanning. We demonstrate that these emanations encode the spatiotemporal evolution of touch interactions, forming a unified leakage basis. By secretly placing an EM probe near the victim's device, TESLA enables attackers to extract highly sensitive information, including screen-unlocking PIN codes, keyboard inputs, interacting application categories, and continuous handwriting trajectories. Compared to existing attacks, TESLA offers a broader range of attack targets, more efficient sample acquisition, and operations in practical attack scenarios. Extensive evaluations on popular commercial smartphones, specifically the iPhone X, Xiaomi 10 Pro, Samsung S10, and Huawei Mate 30 Pro, validate the effectiveness of TESLA. It achieves remarkable inference accuracy in diverse settings such as private meeting rooms and public libraries, with success rates of 99.3% for PIN code recognition, 97.6% for keyboard input reconstruction, and 95.0% for application inference, respectively. Simultaneously, it attains a 76.8% character recognition accuracy and a high geometric similarity (Jaccard index of 0.74) for 2D handwriting trajectory reconstruction.

We present SmartWalkCoach, a mobile AI companion that supports the full walking journey: from pre-walk planning to in-walk guidance through to post-walk reflection. Addressing a gap between map navigation and motivational coaching, SmartWalkCoach orchestrates three lightweight agents: (1) GeographyAgent for conversational route curation from nearby points of interest and user preferences while delegating pathfinding to map APIs; (2) AccompanyAgent for context-aware, just-in-time prompts that blend informational cues with relational encouragement; and (3) SummaryAgent for concise reflection and next-step planning. This end-to-end, tool-using design aims to lower cognitive load in planning and sustain engagement and motivation during walking through delivering dynamic, cadence-aware interventions. We conducted an in-the-wild, two-period AB/BA crossover study (N=12), where each participant completed two comparable walks with counterbalanced conditions: Information-only versus Information+Motivation. Linear mixed models show that adding motivational, companion-like dialogue significantly improved outcomes: participants reported higher positive feelings and better user experience, with no evidence of carryover. Thematic analysis surfaced two design imperatives for mobile companions: supportive, relational expression and context-aware timing (e.g., avoiding high-load moments, intervening at fatigue/milestones). Our contributions are: (i) an end-to-end, tool-using agent architecture for everyday walking that reduces cognitive load during planning and accompaniment; (ii) a controlled field evaluation linking context-aware motivation to affect and UX gains; and (iii) actionable design guidance on expression, timing, and frequency for mHealth companions.We outline limitations and paths toward multimodal, voice-first companions, with adaptive personalization mechanisms.

A graph is called $F$-free if it does not contain a copy of $F$. Let $G(r,s)$ denote a $K_{r+1}$-free graph of order $n$ with chromatic number at least $s$ that maximizes the spectral radius. Nikiforov [Linear Algebra Appl., 2007] proved the spectral Turán theorem, which implies that $G(r,s)$ is the $r$-partite Turán graph $T_{n,r}$ for $s\leq r$. Lin, Ning, and Wu [Combin. Probab. Comput., 2021] characterized the unique spectral extremal graph $G(2,3)$. This result was later extended by Li and Peng [SIAM J. Discrete Math., 2023] to all $s=r+1\geq 3$. In this paper, we push the characterization further by determining the unique extremal graph $G(2,4)$ for all sufficiently large $n$. Specifically, we show that $G(2,4)$ is precisely a blow-up of the Grötzsch graph. Interestingly, under the same conditions, $G(2,4)$ also coincides with the unique edge-extremal graph identified by Ren, Wang, Wang, and Yang [arXiv:2404.07486v2].

Efficient digital twin (DT) synchronization relies on maintaining high-fidelity virtual representations with minimal age of information (AoI). However, the synergistic potential of cooperative sensing and autonomous mobility of the sensing agent remains underexplored in existing DT synchronization frameworks. In this paper, we propose an agentic AI-empowered mobile embodied AI network (MEAN) framework for DT synchronization. In the proposed hybrid architecture, the base station (BS) conducts global orchestration, while the agents autonomously execute a five-stage closed-loop workflow: move-to-sense, cooperative sensing, onboard semantic processing, channel-aware mobility, and uplink transmission. To optimize synchronization performance, we formulate a joint topology dispatching and multidimensional resource allocation problem aimed at minimizing the maximum twin deviation across regions, subject to heterogeneous sensing fidelity and energy budget constraints. To tackle this, we develop a hierarchical two-layer optimization algorithm, where the outer-layer refines multi-agent assignment via a dynamic matching game, and the inner-layer iteratively optimizes the continuous resources. Extensive simulation results verify the convergence of the proposed algorithm and demonstrate its substantial superiority over multiple baseline schemes in reducing synchronization deviation. Furthermore, the results reveal that semantic compression serves as a vital substitute for channel resources in latency reduction under constrained bandwidth, while autonomous velocity adaptation provides an essential degree of freedom for the system to navigate the fundamental energy-time trade-off.

We present an analysis of 17 years of Fermi-LAT observations of the microquasar SS~433. We detect four GeV sources in the region: a newly identified source, PS J1910+0550, located outside W50; the previously reported source J1913+0512; and two features, denoted as the East and West excesses, apparently associated with the X-ray lobes. We focus on the three sources located within W50. We do not confirm the previously reported periodic modulation from J1913+0512, as no significant periodicity is found in the full 17-year dataset. The East and West excesses exhibit distinct morphological and spectral properties, suggesting different physical origins. The East excess shows a hard spectrum with photon index $\sim1.7$, consistent with inverse Compton emission from relativistic electrons accelerated together with the particles responsible for the X-ray and TeV emission. In contrast, the West excess has a much softer spectrum with photon index $\sim2.6$ and is spatially offset from the known X-ray and TeV emission regions in the western lobe. The spectral shape and offset position of the West excess make it strikingly similar to J1913+0512. The emission from these two regions can be explained by GeV particles accelerated in SS~433, distributed throughout the source volume, and interacting with localized dense gas targets. Under reasonable assumptions regarding particle transport and energetics, both proton-proton and bremsstrahlung scenarios are viable, although the hadronic scenario is more naturally accommodated. These findings may therefore represent the first observational evidence for the acceleration of cosmic-ray protons in large-scale outflows from Galactic microquasars.

We establish sharp weighted smoothing estimates for limit solutions to the Cauchy-Dirichlet problem for the fast diffusion equation on smooth bounded domains. We demonstrate that the critical exponent governing these estimates coincides with the classical Brezis--Turner exponent known in the theory of semilinear elliptic equations. As a primary application, we derive improved global Harnack inequalities and describe asymptotic behavior of positive ancient solutions.

UAV multi-site inspection often reduces to choosing a high-quality visiting order after target sites have been extracted from a map. This paper develops LA-BHH, a landscape-aware bandit hyper-heuristic that learns an operator-selection policy online for this routing layer. LA-BHH treats 2-opt, swap, relocate, and Or-opt moves as low-level arms, builds context from static landscape descriptors and online search-state features, and updates a LinUCB controller from improvement rewards during the same run. Experimental results on 45 generated Euclidean TSP instances show that LA-BHH achieves the best mean final gap and convergence AUC, with 0.0223 and 0.0389 respectively. It reduces final gap by 17.6\% over UCB-HH, 22.6\% over Random-HH, and 68.2\% over nearest-neighbor construction. Ablation results further show that contextual credit assignment, 2-opt repair, and stagnation-aware state use are the main contributors.

Electrodynamic balances (EDBs) have been widely used to investigate reactions between levitated particles and background gases. In this paper, we report the development of an EDB that exposes trapped particles to alkali-metal vapor. The apparatus was developed principally to investigate the interactions between such vapor and the paraffin used as a spin anti-relaxation coating for alkali-metal vapor cells by atomic physicists. The trap electrodes of the EDB were installed in a vacuum glass cell. Particles were loaded via laser launching, without venting or contaminating the cell. Alkali-metal vapor was released from a dedicated dispenser. We found changes in the charge-to-mass ratios of trapped particles irradiated with ultraviolet light after exposure to alkali-metal vapor. These results demonstrate the utility of the apparatus.

Full-dimensional reactive potential energy surfaces (PESs) for the OCS$^+$ cation are constructed to describe S$^+$ loss in the electronic ground state and seven low-lying electronically excited states. High-level \textit{ab initio} reference energies were computed at the MRCI+Q/aug-cc-pVTZ level and were used to generate PESs employing reproducing kernel Hilbert space representations (RKHS). The PESs accurately reproduce the measured dissociation limits to CO(X$^1Σ^+$)+S$^+$ in different electronic states. The topology of the PESs reveals multiple linear and T-shaped minima, pronounced angular anisotropy, and state-crossing manifolds. Exploratory quasi-classical trajectory simulations on selected PESs confirm numerical stability and energy conservation, illustrating the suitability of the surfaces for dynamical applications. The present work represents the most comprehensive characterization to date of the lowest PESs of OCS$^+$ and provides a reliable foundation for future studies of the photodissociation of OCS$^+$ and the chem-ionization dynamics of OCS.

Fluctuations of nonequilibrium localized waves are shaped not only by direct stochastic forcing but also by deterministic transfer among coupled collective degrees of freedom. We develop a pathway-resolved stochastic collective-coordinate theory that makes this transfer explicit for stationary driven-dissipative solitons of the generalized Lugiato--Lefever equation with Raman response. The reduction yields a refined stationary phase-locking relation, providing a fixed point for the subsequent stochastic theory. Projecting field-level fluctuations onto four soliton coordinates: amplitude, frequency shift, temporal position, and global phase, yields a reduced Langevin model and, after linearization about a stable stationary state, an analytic power-spectral-density matrix. This framework separates direct stochastic injection from deterministic inter-coordinate conversion and thereby resolves how each observable spectrum is assembled from distinct internal fluctuation pathways. It shows that timing jitter is governed primarily by Gordon--Haus-type frequency-to-timing conversion, while phase noise is often dominated by amplitude-to-phase transfer rather than by direct phase diffusion. Raman response opens additional cascaded pathways, and the low-detuning hump in the intensity and phase spectra is traced to the driven response of an underdamped amplitude--phase subsystem preceding the breathing instability. Comparisons with stochastic simulations of both the reduced model and the full generalized Lugiato--Lefever equation show good agreement throughout most of the stable stationary single-soliton regime, with systematic deviations mainly near the Hopf boundary. The theory provides a general route for connecting internal fluctuation-transfer mechanisms of dissipative solitons to measurable noise observables.

The Fibonacci cube $Γ_n$ is the subgraph of the hypercube $Q_n$ induced by vertices with no consecutive $1$s. Munarini introduced Pell graphs, a variation of Fibonacci cubes defined on ternary strings. A generalization of Pell graphs to $(k+1)$-ary strings has recently been proposed. In this paper we introduce Munarini graphs, which constitute an alternative generalization of Fibonacci cubes and Pell graphs. One of the main advantages of Munarini graphs is that, unlike previously proposed generalization, they are daisy cubes, as are Fibonacci cubes and Pell graphs. In this first article, we study some of their fundamental properties including the size, the recursive structure, the cube and maximal cube polynomials.

We present a flexible, automated, and basis-set insensitive domain-based charge-transfer (CT) decomposition framework that can be combined with any CI-type excited-state wavefunction. Our approach is not based on excited-state densities and allows the excited-state character to be dissected into local and domain-based CT excitations and measures the individual contributions to each excited state. To guarantee a broad applicability, we introduce two domain-accumulation strategies to translate hole-particle substitutions to domain-domain excitations: a strict domain partitioning and a weighted approach suitable for small molecules and a large number of domains. The performance of both schemes is assessed for inter- and intramolecular CT excitations and various basis sets using EOM-CCSD and its simplified counterpart EOM-pCCD+S. Most importantly, the CT character is, to a large extent, basis-set independent, and both domain-accumulation schemes give consistent results. Overall, our framework provides a robust CT analysis and a domain resolution of the excitation character for a variety of computational setups and excited-state models.

In this paper, we study the effective rank of the canonical polyadic decomposition applied to the electron repulsion integrals, ubiquitous in quantum chemistry. We demonstrate, both mathematically and numerically, that in general the effective rank of this decomposition cannot grow linearly as a function of the system size. Moreover, we derive a lower bound for the effective rank in the form $\propto N_{\mathrm{AO}}^2/\log_2^7 N_{\mathrm{AO}}$, where $N_{\mathrm{AO}}$ is the number of atomic orbitals in the molecule, under mild conditions imposed on the decomposition threshold $ε$. As a result, while a subquadratic growth of the CPD rank is not excluded, a linear relationship between the rank and $N_{\mathrm{AO}}$ cannot hold universally. The implications of these findings for the use of the canonical polyadic format to represent electron repulsion integrals in quantum chemistry are analyzed.

In this article, we construct infinite families of quaternary (that is, over the ring $\mathbb{Z}_4$) $\mathcal{C}_{D}$-codes, where the defining set $D$ is derived utilizing a two-generator simplicial complex, and determine their Lee weight distributions. As a result, we find at least 32 new or improved quaternary linear codes as per the database \cite{aydin2022updated} of best-known quaternary codes, including codes from a Plotkin-optimal family. We also report 6 projective quaternary linear codes with best-known parameters that might outperform the currently reported best-known codes due to their projectivity. Further, we establish necessary and sufficient conditions for their Gray image to be linear, which in turn gives an infinite family of Griesmer codes and several infinite families of minimal binary linear codes.

Dark matter experiments are rare event search experiments that require zero background environment over very long exposures. To achieve this condition, a detailed simulation of detector geometry and experimental setup is required before the experiment is executed. Simulation plays a significant role in detector design and also provides a cost-effective and risk-free approach for predicting outcomes before real world experimentation. The present simulation work is focused on neutron background reduction for a dark matter direct detection experiment in India, the Indian Dark matter search Experiment (InDEx). The FLUKA and FLAIR simulation tools have been used throughout the simulation process. The experimental and simulation results available in the literature are being reproduced using FLUKA for validation purposes. The calibration and InDEx experiment are simulated, and the results are compared against the experimental results. For neutron background reduction in future experiments, the use of high density polyethylene (HDPE) is suggested and a shielding design using HDPE is presented. The results show that shielding reduces detector event rates by two orders of magnitude compared to the prior InDEx experiment without shielding.

The classical linear ordering problem seeks a single ranking representing a given preference matrix. While suitable for homogeneous populations, it fails when observed preferences arise from several latent groups with distinct ranking patterns. To address this limitation, we introduce an extension partitioning the population into latent groups, each characterized by its own linear order, relative size, and preference structure. The observed matrix is then explained as the aggregate outcome of these group-specific preferences. We develop mixed-integer programming formulations, including a compact reformulation yielding a geometric interpretation within the linear ordering polytope. Because exact solutions become computationally demanding for larger instances, we propose a multi-start alternating-direction matheuristic iteratively updating group rankings and weights. Computational experiments on synthetically generated instances, matching sizes typical in preference aggregation scenarios, demonstrate the effectiveness of the exact approach in successfully recovering the underlying groups. Furthermore, the proposed heuristic delivers high-quality solutions in substantially shorter times, occasionally improving upon the exact method's best incumbent in difficult instances within the imposed time limit.

Measurements of positional coordinates and dimensions - whether by human vision or optical instrumentation - are fundamental to safety, industrial productivity, manufacturing quality/accuracy, and scientific discovery. The ultimate precision of such measurements is governed by the Fisher information conveyed from an object to a detector through the optical field, and strategies for enhancing measurement performance often focus on reducing detector noise and/or refining estimation algorithms. Building on the emerging understanding of Fisher information as a physical quantity that propagates through space in a wave-like fashion, we demonstrate that substantial gains in precision can also be made by engineering the electromagnetic environment of a measurement target to optimise the generation and transmission of Fisher information. Using nanowire position metrology based on light scattering at a wavelength λ = 640 nm as an architype system, we achieve a multifold enhancement in localisation precision, reaching beyond λ/10,000. Our results establish target environment engineering as a powerful and broadly applicable strategy for advancing measurement and sensing performance across platforms ranging from optical characterisation of micro- and nano-objects to microwave radars and optical LiDAR navigation systems.

The fundamental quandle is an invariant for distinguishing surface knots, yet computable presentations have traditionally been limited to surfaces embedded in the $4$-sphere. Building on the framework of banded unlink diagrams introduced by Hughes, Kim, and Miller, we give a Wirtinger type presentation of the fundamental quandle of surface links in arbitrary $4$-manifolds. As applications, we extend the work of Sato and Tanaka to show that for any $b \geq 4$ and $m \geq 0$, there exist infinitely many pairwise non-local surface knots with bridge number $b$ in $\mathbb{C}P^2 \#m\overline{\mathbb{C}P^2}$, and we distinguish infinite families of surface knots with isomorphic knot groups, extending results of Tanaka and Taniguchi.

Privacy auditing provides empirical lower bounds on the differential privacy parameters of learning algorithms. Existing methods, however, require interventional access to the training pipeline, either to retrain multiple times or to randomize data inclusion. This is often infeasible for large deployed systems such as foundation models. We introduce Zero-Run privacy auditing, a post-hoc framework for auditing models using two fixed datasets: examples known to be training-set members and examples known to be non-members. In this observational regime, membership is no longer randomized; instead, member and non-member data often differ in distribution, so membership inference scores may reflect a distribution shift rather than algorithmic leakage. Drawing on ideas from causal inference, we formalize this confounding effect and propose two complementary corrections that yield valid privacy audits. Our first approach models the combined effect of distribution shift and algorithmic leakage as an adaptive composition, producing conservative global corrections. Our second approach conditions on observed data and adjusts pointwise membership guesses, yielding sharper instance-dependent bounds. Experiments on synthetic data and large-scale models show that Zero-Run auditing enables practical privacy evaluation when retraining or controlled data insertion is infeasible.