Papers

Multiresolution hash encodings have recently enabled fast and high-fidelity implicit neural representations by storing multi-scale features in fixed-size hash tables along a geometric resolution schedule. However, the standard design is data-agnostic: different resolution levels receive identical hash-table capacity despite large differences in image frequency content. As a result, some levels experience severe hash collisions while others underutilize parameters, leading to inefficient capacity allocation. To address this issue, we propose Collision-Aware Resolution Adaptation (CARA), a method that assigns per-level resolutions by balancing the effective information load across hash levels. This adaptive allocation reduces capacity bottlenecks and improves parameter efficiency. In addition, we introduce an invertible pixel-shuffle transform that reduces hash load factors by redistributing spatial information, thereby mitigating collision-induced information loss without enlarging the hash tables. To support evaluation on extremely high-resolution data, we also curate, to the best of our knowledge, the first uncompressed whole-slide image dataset for academic research. Experiments on Kodak images, gigapixel natural images, and raw whole-slide images demonstrate that CARA consistently improves the fidelity-parameter trade-off. Our method matches state-of-the-art performance while using only $27.76%$ of the parameters, and achieves up to $6.11$ dB PSNR improvement at comparable parameter counts. Code is provided in the supplementary.

We introduce centro-sectional measures with parameters q,m for log-concave functions on Rn, defined in terms of the q-th moments of their Radon transforms with respect to the Haar measure on m-dimensional subspaces, where m=1,...,n-1, and establish the corresponding variational formulas. Our measures generalize the notion of dual curvature measure if q=1, and are related to the Sine transform if q=2. In line with the coarea formula for log-concave functions as BV functions, the variational formulas give rise to the Euclidean centro-sectional measures and the spherical centro-sectional measures. In the symmetric setting, we solve the associated even functional centro-sectional Minkowski problem, which asks which pairs of measures can arise as the centro-sectional measures of an even log-concave function.

We use controlled N-body simulations to investigate whether dark matter subhaloes leave detectable signatures in the internal kinematics of dwarf spheroidal galaxies. At each snapshot, we fit a velocity distribution function to stellar line-of-sight velocities and proper motions, construct normalised residual fields for the projected velocity components, and analyse their power-spectra. We show that subhalo encounters generate a plethora of kinematic features. Amongst the most prominent are rotation-like signals, which arise in our models even though the stellar component is initialised without intrinsic rotation. In line-of-sight velocity alone, several snapshots resemble the classical blueshift–redshift pattern associated with stationary rotation. The plane-of-sky components, however, bring complexity, with alternating regions of expansion and contraction, as well as clockwise and anticlockwise streaming. Although we observe coherent streaming globally, these structures depart from typical equilibrium configurations, while their residual power-spectra quantify the characteristic spatial scales involved. This signal strengthens in models containing more massive subhaloes and becomes difficult to recover for small stellar samples: robust power-spectrum recovery of the full velocity-space signature usually requires O(10^{4}) tracers, although a rotation signal alone can be recovered with considerably smaller samples. These results suggest that dwarf spheroidal velocity fields can retain signatures of subhalo heating. Future spectroscopy, improved Gaia astrometry, and chemo-dynamical information should turn these diagnostics into population-level probes of dark matter substructure.

The AMOC and the Subpolar Gyre are key components of the Earth's climate system, both potentially prone to destabilization and abrupt shifts under anthropogenic forcing.Given the strong influence of the AMOC and the SPG on global climate, detecting changes in their stability is of high importance, yet is hindered by the limited length of observational records.In the absence of long-term direct AMOC observations, several observation-based fingerprints of the AMOC have been proposed.However, existing fingerprints do not clearly distinguish between SPG and AMOC variability, instead reflecting an opaque mixture of dynamics from both systems.Here, we assess the performance of widely used AMOC fingerprints across CMIP6 models and compare them with statistically optimal fingerprints that we derive from sea surface temperature and salinity.We show that traditional AMOC fingerprints exhibit weak correlations with both AMOC and SPG strength.In contrast, our statistically optimal fingerprints, trained on pre-industrial control simulations, consistently outperform existing approaches across independent segments of piControl simulations and historical experiments.These fingerprints accurately reconstruct AMOC and SPG variability while minimizing overlap, enabling a clear separation between the two systems.Our results provide the first tailored observational fingerprints that robustly distinguish AMOC and SPG, demonstrating the potential of statistically optimized approaches to improve detection and attribution of changes in Atlantic circulation, including precursor signals of potential tipping behavior.Applying our approach to sea surface temperature observations, we find that our optimized fingerprints do not confirm the substantial AMOC weakening in the recent decades as suggested by traditional fingerprints, but also do not rule out a loss of stability.

In this note we review and compare mathematical procedures aimed at rigorously deriving fluid-dynamic descriptions of classical particle systems in the large-scale limit of Hamiltonian dynamics. Despite the longstanding nature of this program, its fundamental problems remain open, with only a few notable exceptions that we briefly highlight.

Robots that leave structured, static environments must plan motions that are kinodynamically feasible and safe among moving obstacles. However, there are no dedicated benchmark frameworks that combine both aspects. To overcome this, we present DynoFluxBench, a framework to compare kinodynamic planners in known, dynamic environments with unbounded arrival time. To demonstrate its utility and establish strong baselines, we develop three dedicated planners, named ST-Db-RRT, ST-GBRRT, and KIST, that fuse kinodynamic and space-time methods, covering different kinodynamic search paradigms: ST-Db-RRT expands with randomly selected discontinuity-bounded motion primitives using trajectory optimization, whereas KIST and ST-GBRRT maintain a kinodynamically feasible tree with different heuristic guidance. We analyze the probabilistic completeness guarantees of those new planners in dynamic environments. Finally, we evaluate ST-Db-RRT, ST-GBRRT, and KIST using DynoFluxBench, showing that ST-Db-RRT reaches a first solution up to 32 times faster, while KIST and ST-GBRRT remain valuable where trajectory optimization is fragile. Videos and further analysis can be found at https://dynofluxbench.github.io/dynofluxbench/.

Egocentric motion forecasting has primarily focused on hands and manipulated objects, leaving future human head motion comparatively underexplored. During manipulation, the head both redirects perception toward the target to acquire task-relevant evidence and coordinates with body and hand motion. We therefore formulate future six Degree of Freedom (6-DoF) head-motion prediction conditioned on observed hand motion and inferred target context, and propose HAP, a Hand-Driven Active Perception framework. HAP infers confidence for each target object from observed hand motion and object geometry. Then constructs a dynamic Predictive Target-Centric Amodal Occlusion Graph (P-TAOG) representing current and potential occlusion among candidate objects. Directed graph and causal temporal reasoning encode the evolving target conditioned perceptual state, which is fused with hand and head motion history. A horizon-wise gate then blends the learned trajectory with a constant velocity prior. We further introduce Bottle, an egocentric RGB-D dataset of object manipulation toward specified targets, with coordinated head and hand motion under changing target visibility. Experiments on the public dataset and Bottle show that HAP achieves lower head motion prediction errors than representative baselines, supporting the value of hand driven intention and dynamic occlusion reasoning for anticipating human head motion. Code will be released at https://HAP-ego.github.io/HAP.

Photon blockade is a phenomenon where the presence of system nonlinearity causes the output to consist of single photons, which has been extensively studied in point atom systems, but it is barely explored in giant atom ones. In this paper, we propose giant atom-mediated photon blockade scheme based on two cavities and three cavities systems with driving field applied to the first cavity. We show that simultaneous unconventional photon blockades (UPBs) can not occur in the point atom system (the atom coupling only to the leftmost cavity) due to there always existing a cavity to have a single path. In contrast, the spatially extended nature of giant atom enables coupling to multiple cavities and allows for the introduction of a phase and coupling strength. Consequently, simultaneous UPBs in multiple cavities can be obtained due to the multipath destructive interference. Moreover, by manipulating the detuning, we observe simultaneous conventional photon blockades (CPBs) in multiple cavities. Finally, we study simultaneous two-photon blockades (2PBs) in point atom multiple cavities system.

Needle-tip localization in ultrasound remains challenging because the needle may appear weak, discontinuous, or partially invisible, while imaging artifacts and anatomical structures can produce similar responses. To address this problem, we propose STUNet-Fusion, a spatiotemporal framework for needle-tip localization in ultrasound videos. The proposed method formulates the input as a tri-channel spatio-temporal fusion tensor, comprising grayscale appearance, grid-based motion feature, and raw frame difference. A shared ResNet-34 encoder extracts spatial features, ConvLSTM integrates temporal dependencies, and a U-Net decoder reconstructs a dense probability heatmap. The final coordinates are extracted via a soft-argmax operation to achieve sub-pixel localization accuracy. Experimental results demonstrate that this spatiotemporal fusion strategy significantly improves localization robustness compared to conventional baselines.

In this paper, we study the detection of an echo chamber in a social network, i.e., the identification of a set of nodes that agree on a topic, while disagreeing with the rest of nodes. We argue that this problem is different from other social network analysis problems such as community detection, and from other graph problems such as maximum graph cut and maximum clique. To the best of our knowledge, we are the first to formalize the objective function of echo chamber detection, by using the theory of Fourier transforms of set functions (Stobbe and Krause, 2012). We propose scalable semidefinite relaxation, solved via an interior point method and sparse linear algebra. Experimentally, our algorithm recovers the ground truth echo chamber better than competing methods on small synthetic experiments. Our algorithm produces echo chambers with better network properties than competing methods on large real-world datasets. To independently validate our proposed objective function, we show that our algorithm finds echo chambers with more agreements with suspended users than competing methods on a small real-world dataset.

Endovascular implants prevent intracranial aneurysm rupture by altering the mechanical and hemodynamic environment at the aneurysm neck. Yet many in silico workflows prescribe or reconstruct the post-deployment geometry before computing flow, leaving unresolved the mechanics that create the clinically relevant interface. Here we review braided intraluminal flow diverters, intrasaccular devices, and emerging flow-disruption concepts across deployment mechanics, inter-wire and wire-wall contact, superelasticity, wall apposition, pore geometry, computational fluid dynamics, and fluid-structure interaction. We connect these modeling choices to neck coverage, malapposition, migration, deformation, and durability, and distinguish established evidence from mechanistic inference and prospective hypotheses. We argue that model fidelity should match the clinical question: prescribed or fast placement may support screening, whereas questions of coverage, apposition, compaction, and migration benefit from mechanically plausible deployment states. An interface-resolved mechanics-to-flow framework, supported by measurable validation targets and standardized reporting, could improve device design and enable more reliable patient-specific treatment planning.

We present results on new optical Gran Telescopio CANARIAS OSIRIS+ spectroscopy and radio Very Large Array (VLA) observations at 360 MHz of the optical object behind the radio emission 20 arcseconds east of the archetypal restarted compact symmetric object (CSO) J0111+3906. The optical counterpart is a post-starburst galaxy at redshift $z$ = 1.042, ruling out any physical relation between this object and the CSO radio galaxy J0111+3906 at redshift $z$ = 0.668. The radio emission is therefore not the remnant of a past activity of the CSO J0111+3906 that took place around 10$^7$ years ago. When observed with the high angular resolution of VLA and the International LOw Frequency ARray telescope the East radio source is resolved in a compact component with spectral index 0.7, centred on the optical galaxy, surrounded by diffuse emission with a slightly steeper spectrum. The upper limit to the radiative age of the East radio source is a few million years. If the trigger of the radio emission and the recent burst of star formation observed in the East radio source are causally connected, there must be a long time gap between the two phenomena. The multi-frequency analysis of the CSO radio galaxy J0111+3906 pointed out excess flux density at 150 MHz, which may indicate the presence of fossil plasma confined within the host galaxy. In this scenario, the past activity of the CSO J0111+3906 switched off not long after its trigger, suggesting a duty cycle of about 10$^4$ yr.

4D radar has emerged as a promising next-generation sensor for improving the robustness of autonomous driving perception systems because of its stable sensing capability under adverse weather conditions. However, deploying 4D radar in embedded environments with limited hardware resources requires radar-representation preprocessing that jointly considers perception accuracy, real-time performance, and computational complexity. This paper proposes a preprocessing framework for 4D-radar-based 3D object detection. First, Percentile-based 3D Shape Preservation (P3DP) extracts point clouds from radar tensors while preserving object-shape information and suppressing noise and false alarms. Second, Multi-frame-based Noise Point Discrimination using Kernel Density Estimation (MF-KDE) improves the density and reliability of sparse radar point clouds. Finally, Embedded & NetScore (ENS) evaluates suitability for embedded deployment by jointly considering accuracy, real-time performance, adverse-weather robustness, and model complexity.

This paper aims to develop efficient numerical approximations for a class of stochastic differential equations with state-dependent fast switching processes. The direct Euler–Maruyama (EM) scheme fails when the scaling parameter is small. Based on the heterogeneous multiscale method of \cite{e2005analysis}, we propose three algorithms and prove their strong $L^p$-convergence with explicit rates for any $p\geq 2$. In the first algorithm, we combine the averaging principle with an EM scheme for the averaged equation, where the invariant measure of the Markov chain can be explicitly obtained by solving a linear system. However, computing this invariant measure incurs cubic cost as the number of switching states increases. To avoid solving large linear systems, we approximate the invariant measure instead. Thus the second and third algorithms both combine a macroscopic EM scheme for a modified averaged equation with micro-solvers that estimate the averaged drift. More precisely, in the second algorithm, a discrete-time Markov chain is simulated with a micro time step, and the averaged drift is obtained by averaging over finitely many micro transitions. However, both the first and second algorithms only work when the switching process has finite states. Therefore, we introduce a third algorithm that allows for switching processes with countably infinite states, in which exact continuous-time Markov chain is generated via the Gillespie algorithm, and the averaged drift is computed by exact time averaging over a specified interval. Numerical experiments verify the theoretical results and demonstrate the computational advantages of these three algorithms.

Most keyframe selection studies focus on offline settings, assuming access to the full video and query in advance. In contrast, real-world streaming scenarios require online frame selection under unknown video duration, without access to either the query or future frames during selection. To address this, we introduce Streaming Video Memory (SVMem), a compact and representative memory of previously observed content, updated continuously as the video stream unfolds. Building on this setting, we propose the Streaming Video Memory Agent (SVMemAgent), which dynamically maintains a memory by deciding at each timestep whether to replace an existing memory frame with the incoming frame or discard it. SVMemAgent is trained using Group Relative Policy Optimization (GRPO) with task-driven rewards derived from diverse question-answer pairs, implicitly exposing the policy to a distribution of queries during training so that SVMem retains generally informative frames at inference, when queries are unavailable. Experiments on both online and offline video benchmarks show that SVMemAgent consistently outperforms online frame selection baselines and achieves competitive performance with offline methods that assume access to the full video and query. Through task-driven rewards, SVMemAgent learns an emergent keyframe selection policy that prefers frames containing textual information, which may benefit downstream VideoQA tasks.

Problem L of Fröberg–Lundqvist–Oneto–Shapiro asks for the difference between the Hilbert series of ordinary and symbolic powers of the ideal of general points in projective space. We solve this completely for \(n\) general points of \(\PP^{n-1}\). Besides a closed formula for \[ \HS(S/I^m)-\HS(S/I^{(m)}), \] we determine all minimal monomial generators of \(I^{(m)}\), and describe the symbolic Rees algebra. We also show that containment \(I^{(m)}\subseteq I^r\) is detected solely by initial degrees. This gives the exact containment threshold, the Waldschmidt constant \(\walpha\), the resurgence \(\Res\), and the asymptotic resurgence \(\aRes\): \[ \walpha(I)=\frac{n}{n-1}, \qquad \Res(I)=\aRes(I)=\frac{2(n-1)}{n}. \] We also take the first step beyond \(n\) points: for \(n+1\) general points of \(\PP^{n-1}\) — again a rigid, non-monomial configuration — we identify the defining quadrics, resolve the case \(n=3\) completely (a complete intersection, with \(J^{(m)}=J^m\) for all \(m\) and resurgence \(1\)), and propose an exact Waldschmidt-constant formula \(\walpha=\frac{n+1}{n-1}\) for all \(n\), verified computationally in every case we could check.

The classical Projected Hessian Lemma, originating from Finsler's theorem, characterizes definiteness over a constraint null space through quadratic penalties. However, it does not quantify the corresponding constrained eigenvalues or the associated eigenvalue penalty path. This work develops a quantitative penalty theory for constrained symmetric eigenvalue problems and establishes exact characterizations of the extremal eigenvalues of the reduced Hessian via full-space penalized eigenvalue problems. Three proofs are provided based on orthogonal decomposition, Schur complement analysis, and semidefinite programming duality. We characterize finite exact recovery along the extremal-eigenvalue penalty paths and, in the absence of finite recovery, establish asymptotic convergence with a first-order error expansion and an explicit leading coefficient. The associated Hellmann–Feynman sensitivity relation leads to a strategy for predicting penalty parameters. Based on these results, we develop a matrix-free Penalty–Split–Merge method for successive constrained extremal eigenpairs using penalty continuation, Split–Merge iterations, deflation, and projected certification. Numerical experiments illustrate the predicted penalty regimes, evaluate projected certification, and assess computational performance on moderate-scale benchmarks and large-scale matrix-free test instances.

The classical Babuška paradox shows that solutions of simply supported plate problems on polygonal approximations of a curved domain may converge to an unintended limit. We develop a boundary-corrected $H({\rm divdiv};\mathbb S)$-$L^2$ mixed finite element method for the simply supported Kirchhoff-Love plate problem. The correction uses only the discrete boundary geometry. Introducing the bending moment as an independent unknown allows the condition $M_{nn}=0$ to be imposed directly, while an edgewise mean constraint on the effective shear suppresses the leading geometric inconsistency. This constraint improves the boundary consistency error from $\mathcal O(h^{1/2})$ to $\mathcal O(h^{3/2})$. The associated boundary corrections act in the kernel of $\rm{divdiv}$, leaving the discrete equilibrium equation unchanged and yielding a uniformly stable scheme. Under suitable regularity assumptions, we prove $L^2$-error estimates of order $h^{3/2}$ for the bending moment and the broken Hessian of the postprocessed displacement, and of order $h^2$ for the displacement. The analysis covers multiply connected domains and polygonal approximations whose boundaries may cross the physical boundary. Numerical experiments confirm these rates and the improvement over the uncorrected method.

In 2009, Yano, Yano and Yor asked whether the $\alpha$-Cauchy distributions are self-decomposable or at least infinitely divisible in their study of hitting times for symmetric stable processes. Recently, the first named author proved that $\alpha$-Cauchy distribution is infinitely divisible if and only if $1 < \alpha \leq 2$. In this paper, we prove that $\alpha$-Cauchy distribution is self-decomposable if and only if $\alpha = 2$. The proof is based on a new criterion for self-decomposability in the symmetric case. As an application, we show that the first hitting time of a nonzero point by a symmetric stable process of index $1<\alpha<2$ starting from zero is not self-decomposable.

Causal discovery aims to recover causal relationships from observed data. In various fields, exploring causal relationships among variables remains an important topic, but this task becomes challenging due to the existence of latent confounders. Ignoring such confounders can lead to false associations and incorrect edge directions. In this paper, we study the linear structural equation model with latent confounders. We propose an algorithm that iteratively identifies terminal (observed) nodes and reconstructs the directed acyclic graph of the observed variables. To do this, we recover the precision matrix of the observed variables as a sparse plus low-rank matrix: a sparse matrix captures the conditional dependencies among observed variables, while a low-rank matrix captures the combined influence of a few latent confounders. We establish that for $p$ observed variables, $r$ latent confounders and $s$ edges, our procedure correctly identifies the directed causal relationship among observed variables, for $n \gtrsim \max\{s\log p,\ r p\}$ samples. Experimental results validate our theoretical contributions.

We study the sensitivity of the proposed DarkSHINE experiment to displaced dark photon decays, $A'\to e^+e^-$, using an 8~GeV electron beam incident on a tungsten target. We consider $2m_e<m_{A'}<2m_\mu$ and assume a unit branching fraction to electron–positron pairs. Signal events generated at tree level with CalcHEP are propagated through a detailed Geant4 detector simulation. A close tracker, graph-neural-network-based track reconstruction, and displaced vertex selections suppress prompt pair-production and photon-conversion backgrounds, while calorimeter and invariant-mass requirements render hadronic backgrounds negligible. Extrapolation of the residual prompt-background distribution yields 0.3 expected events for $9\times10^{14}$ electrons on target. The median expected 90% confidence-level exclusion covers masses of approximately 30–70~MeV and kinetic mixing parameters from approximately $5\times10^{-5}$ to $2\times10^{-4}$. This visible decay search complements DarkSHINE searches for invisible dark photon decays.

Automatic speech recognition (ASR) systems exhibit unequal error rates across speaker groups, motivating interventions on their internal representations. We ask whether speaker-linked attributes that are linearly readable from pretrained ASR encoders yield useful directions for reducing group word-error-rate (WER) gaps. Across Whisper-medium, HuBERT-large, and Wav2Vec2-large on Common Voice and the Speech Accent Archive, we probe every encoder layer for metadata-derived sex/gender, age, and native/accent labels; construct centroid and probe-derived directions; inject them at selected layers; and compare downstream probe trajectories with matched WER changes. Sex labels are highly decodable (best macro-F1 0.924–0.941), native/accent labels are also above chance (0.544–0.696), and age is weaker (0.354–0.397). Of 22 post-selected reruns, nine have 95% paired-bootstrap intervals entirely below zero, yet every absolute source-group WER reduction is below 0.7 percentage points. Conversely, a local target-class probe rate can rise from 8.09% to 99.87% while WER worsens. Linear readability is therefore neither evidence of causal use nor a reliable mitigation method. Our results motivate evaluating speech-bias interventions jointly at representation, propagation, and task levels.

Mask-based speech enhancement is widely used for suppressing noise and interference, but its performance in spatial audio algorithms with multichannel output has not been studied extensively. In such settings, speech enhancement must improve speech quality while preserving spatial cues that are essential for localization, spatial awareness, and spatial release from masking. In this work, we systematically compare time frequency masking applied to three signal representations: microphone signals, beamformer outputs, and Ambisonics signals. Performance is evaluated in terms of speech quality, intelligibility, binaural cue preservation, and reverberation preservation. Results reveal a clear trade-off between enhancement and spatial fidelity: beamformer-domain masking achieves the highest speech enhancement scores, while Ambisonics-domain masking better preserves the spatial attributes of the residual interference. All methods preserve the target's localization cues.

Satellite ocean color algorithms translate water-leaving radiance into ecological information at spatial and temporal scales that cannot be achieved by field sampling alone. One important variable derived from water-leaving radiance is chlorophyll-a concentration ($\mathrm{CHL\text{-}a}$), a widely used indicator of phytoplankton biomass and physiology. Empirical retrieval algorithms are commonly used for $\mathrm{CHL\text{-}a}$ estimation, but their performance can vary across sensors and optically diverse waters. The Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission provides unprecedented spectral resolution, expanding the visible spectral information available for ocean color retrievals and raising a practical algorithm design question: how can this fine resolution spectrum be used to derive the next generation of interpretable $\mathrm{CHL\text{-}a}$ retrieval algorithms? We use symbolic regression to identify sparse equations that estimate $\log_{10}(\mathrm{CHL\text{-}a})$ from multi- and hyperspectral remote sensing reflectances. The analysis first tests the standard multispectral ocean color algorithm (OC3–OC6) inputs to ask whether symbolic regression recovers standard band ratio structure, then extends the search to hyperspectral PACE-like reflectances. The best expression discovered achieved a held out root mean square deviation of 0.253 in log$_{10}$ $\mathrm{CHL\text{-}a}$, compared with 0.307 for a fitted OC6 polynomial on the same split. Ablations showed that the predictive skill of hyperspectral models is almost 12% better than the best standard ocean color retrieval models in root mean squared deviation against held out data. When evaluated by environmental regime, differences were larger for high-chlorophyll samples, which often represent turbid water conditions.

The Hong–Ou–Mandel (HOM) effect is a hallmark of two-photon quantum interference, in which two indistinguishable photons impinging on a balanced beam splitter bunch into the same output port. Here, we show that a giant atom (GA), coupled to two waveguides through two coupling points each, can function as a programmable HOM interferometer, enabling continuous control over single-photon beam splitting and two-photon interference. This programmability arises from coupling-phase differences in the GA, which tune its self-interference and directionality, and thereby its scattering response. To characterize the two-photon interference, we analyze the scattering of two Gaussian single-photon wave packets injected through different waveguides and evaluate the bunching and antibunching (coincidence) probabilities of the resulting four output ports. At the operating point where the GA acts as an effective 50:50 beam splitter for single photons, we observe a pronounced HOM dip as the relative input delay between the two wave packets is varied. Away from this point, adjusting the coupling phases continuously tunes the two-photon output statistics between bunching into the same output port and antibunching across distinct output ports. In addition, we explore an application to quantum parameter estimation, showing that small deviations of coupling phases can be estimated from the two-photon output statistics, with the achievable sensitivity quantified by the classical Fisher information associated with a binary coincidence measurement. Our giant-atom beam splitter thus provides a programmable platform for two-photon interference in waveguide quantum electrodynamics, with potential applications in quantum information processing, quantum communication, and quantum sensing.

UNESCO considers the Assyrian (Syriac) language an endangered language. Although Assyrians speak the language worldwide, the speaking population is uncertain (ranging from 500,000 to 1,500,000). Syriac is also one of the least studied languages in Natural Language Processing (NLP). Despite advances in Machine Translation (MT) over the past decade, the lack of publicly available corpora and the orthographic complexity of the Syriac script, specifically the Madnkhaya script, have left this language entirely ignored in the computational linguistics literature. This study develops the first phrase-based Statistical MT (SMT) model for English-to-Assyrian MT using the Moses framework. We created a dataset of 38,847 sentence pairs from the complete English and Syriac Bible, merging a pre-existing New Testament dataset with an Old Testament built from scratch through PDF extraction, using custom segmentation scripts and manual alignment review by three bilingual annotators. The Syriac side of the corpus undergoes diacritic removal and Byte-Pair Encoding tokenization to reduce orthographic sparsity before training. We trained and evaluated six models using different configurations and splitting-scheme ratios, language model order, distortion limits, and the inclusion of an Operation Sequence Model. The best-performing configuration achieves a word-level BLEU score of 23.54. Human evaluation by 11 native Assyrian speakers resulted in mean adequacy and fluency scores of 3.42 and 3.34 out of 5, respectively. These results are consistent with comparable low-resource SMT models trained on Biblical corpora for morphologically rich Semitic languages. The corpora, scripts, and trained model are publicly available, providing the research community with the first systematically curated English-Syriac dataset and a reproducible baseline for future MT and broader NLP work on this endangered language.

We study the near-horizon charged-scalar instability associated with Schwinger pair production in the charged regular black hole geometry of the zero-point-length T-duality prescription. Using the same effective geometry and regularized gauge potential, we construct the extremal branch, its ${\rm AdS}_2 \times S^2$ near-horizon throat, and the charged-scalar instability threshold for a general form factor. For the explicit T-duality form factor the extremal branch terminates at $r_\mathrm{ext} = \sqrt2 \, l_0$, where the extremal charge and the near-horizon electric field vanish while the ${\rm AdS}_2$ radius remains finite at $\sqrt3 \, l_0$. At this endpoint the exact near-horizon instability parameter is negative. In the semiclassical regime the corresponding charge-to-mass threshold diverges as the endpoint is approached. Thus, for each fixed massive species with finite $q/m$, a sufficiently near-endpoint portion of the extremal branch is free of the local charged-scalar instability. For comparison, the Ayón-Beato-García (ABG) Einstein-nonlinear-electrodynamics solution has a nonvanishing extremal near-horizon electric field. For an additional minimally coupled charged-scalar probe, the corresponding local Schwinger threshold remains finite. Thus the divergent near-endpoint Schwinger barrier found in the T-duality branch is not a generic consequence of regularity.

Structured prediction is the simultaneous prediction of multiple labels, and is widely used in various fields, such as natural language processing and computer vision. In this paper, we study binary node label recovery on signed graphs with edge-flip noise, a model introduced by (Globerson et al., 2015), via a simple spectral method that decodes node labels from the signs of the principal eigenvector of the noisy signed adjacency matrix. We develop graph structure-agnostic theoretical guarantees for approximate inference of node labels as well as guarantees for maximum angle deviation with respect to the ground truth node labels. By leveraging tools from matrix concentration theory and eigenvector perturbation analysis, we derive new concentration inequalities that explicitly quantify the effect of the spectral gap of the adjacency matrix, number of nodes, degree distribution, and noise level. As a corollary, we relate our general results to the Cheeger constant and provide results for different classes of graphs. We perform several synthetic experiments to validate our theory. To the best of our knowledge, we are the first to provide theoretical guarantees for the spectral-based approach. As a byproduct of our analysis, we derive technical results that might be of independent interest and useful for other machine learning problems.

Running large language models (LLMs) locally is often considered more private than cloud-hosted inference because user prompts remain on the device. We ask whether keeping inference local is, by itself, sufficient to keep those prompts confidential. Our results show that it is not: prompt confidentiality also depends on how the surrounding serving software handles prompt data before, during, and after inference. We examine four boundaries at which prompt confidentiality can fail in consumer local-LLM serving systems: model loading, runtime memory, wrapper-level persistence, and the serving interface. To study these boundaries, we develop LLAnalyzer, a measurement framework that tests each boundary separately and traces observed failures to the responsible software component. Applying LLAnalyzer to four open-weight model families and two consumer deployment platforms, we find markedly different behaviour across boundaries. In a 24-hour AFL++ campaign with more than 12 million executions, we observe no parser crashes or successful malformed GGUF loads within the explored state space. Runtime memory tells a different story: we recover prompts after inference because multiple plaintext representations survive in allocator-managed memory, and sanitisation reduces this residue without eliminating it. We also find that consumer wrappers can extend prompt lifetime through plaintext persistence. At the serving boundary, we uncover a previously undocumented authorization flaw in llama.cpp that allows one authenticated client to restore another tenant's saved conversation state; the attack succeeds in 200/200 controlled trials. Separately, shared prompt-prefix caching exposes a remote timing oracle that remains distinguishable under WAN conditions. We argue that local LLM systems need explicit guarantees for prompt lifetime, persistent storage, and tenant isolation.

Modern evaluation of learning pipelines often reduces to downstream accuracy, leaving open the question of why tasks succeed or fail. TriProbe addresses this gap with a multi-level probing framework for explainable diagnosis of task separability. Rather than treating models as black boxes, TriProbe traces how separability evolves across inputs, learned features, and final classifiers. It decomposes multi-task problems into binary subtasks and applies three complementary probes: a Foundational Probe on input spaces, a Latent Probe on feature representations, and a Final Probe on classifier outputs. Using Maximum Fisher's Discriminant Ratio as a principled separability metric, TriProbe identifies bottlenecks and affected task pairs. Experiments on the Roshambo sEMG benchmark show how TriProbe reveals hidden breakdowns, guiding data collection, validation, and architecture design.